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"Paris, April 1 958." "Dear family," "Memory is a strange muscle." "It moves on its own when we least expect it." "Today I went to the theatre where we are to perform." "While climbing the stairs I asked myself:" ""Have I locked the door?" "."" "as if I was home." "I remembered the stairs, the strange way that grandmother looked at them, as if it was a forbidden place." "Poor grandma." "Daughter!" "Lean on me, mother." "One, two..." "Celia!" "Don't be afraid." "Come on." "I'm not sure you remember, she was so afraid of falling backwards." "Nobody understood why, but we all walked behind her to help." "I remember, although I might be making it up, one Christmas Eve she drank a bit too much, and it was the only time she spoke about it." "If I ever fall down I'll never get up again." "But we're all here to help you." " lt's all the same." " Ernesto!" " Come on!" " Merry Christmas!" "The real discovery came later." "For one reason or another we never spoke about it again." "However the whole family continued their efforts to help grandmother." "Mom searched the whole city for shoes with nonskid soles and things of the kind." "Nora became a human cane." "Jorge and I could only play in the garden." "Dad had all the floor tiles changed and forbade carpets." "The house became a little strange but our life went on the same." "And it wasn't worse than others." "white lies" "What are you doing there:" "I couldn't sleep." "Why didn't you come:" "I had work to do." "It was my farewell, Jorge." "Well..." "Next time I'll go." " Here." " The last one." " Have it." " What do you want:" "Smoke." " Do you have everything ready:" " Yes, Auntie prepared everything." "Did you speak to Mom:" "I didn't want to worry her." "You're shameless." "What's better:" "To tell her the truth and sadden her:" "No..." "I don't know." "She'll find out anyway." "Why:" "Are you going to tell her, Jorge:" "No..." "Nora:" "No." "Then how will she find out:" "Eventually Mom always finds out about everything." "Put your hand like this." "What are you doing:" "Stop talking nonsense." "Here, put it out." " Listen to me." " Don't do noise." "Who is she:" "Patricia:" "Nice picture." " When did she give it to you:" " Just now." " Did you see her last night:" " Yes." " So:" " So..." "So what:" "In the end, yes." " Did you tell her:" " Yes." "And she thinks it's a great idea." "That I can be successful in Paris." "Like other musicians." "That's what they say." " Excuse me." " How will I do in Paris:" "Great!" "Where did you go dressed like that:" "To mass." " Where did he go:" " To mass, yes." " What about breakfast:" " What:" " You won't prepare it:" " Why me:" "Because you make it delicious, you're the best." "Ok, ok, I'm going." "Jorge..." "Why don't you check if the car's arrived:" "Slightly out of tune." "They'll send you back soon." " l hope." " Don't start, Mom." "How many students did the teacher invite:" "One." "But it's for so long, you're still so young." "Three months." "I'll be back before you know it." " Will you write to me:" " No, not even a single letter." "It's cold, stay in bed." "Pablo..." " Take care." " Take care." "And don't go around partying too much." "The car is here." "Are you ready:" "Yes." "Can you help me with this:" "It doesn't close." "Pablo!" "Excuse me." "Pablo, before you finish I want you to pack this." " What is it:" " Something for the trip." "Uncle!" "It's what your father would have wanted to do." "Yes, sure." "Go to Paris to play in a cabaret." " Dad would have loved it!" " Ok, let's go." "I'll tell Nora." "Don't listen to your brother." "He's so inexperienced." "Pablo." "I made something for the trip." "They serve meals on the ship." "You never know what they use to prepare them." "Take it!" "What is it:" " Sandwiches." " For the journey." "Can you take this for me:" " Pablo..." " What:" " l don't know how this works." " Simple." " There." " Okey." "It's late, come on, you'll miss your ship." "Mom." "What did I tell you:" "So we can all be in the photograph." "Let's go to the car." "Let's go." "Can you believe this woman:" "Give me your hand." "Here:" "Come on, it's my turn." "Come on." " What:" " Come on." "A picture:" "Mom should be in the middle." " Ahí." "Ahí, ma." " !" "Pará!" " Smile." " No, wait." "Come, Pablo." "I'll take it." "Get ready..." "One..." "Two..." "Three." " What's the matter:" " The engine won't start." " Maybe it ran out of fuel." " No, it's flooded." " What's the matter, Ernesto:" " lt's flooded!" " Can't you do something:" " What do you want me to do:" "Jorge..." "Take." "Take care of it." "Try again." " He'll miss the boat." " He won't!" " There it goes..." " That's it." "Bye!" "Be a good boy!" "Mom..." " Something else:" " What:" " Something else:" " No, it's fine." "Take a deep breath." "Again." "Again." "Jorge..." "Hello." "Hello." "It's been a while." "How are you:" " l'm fine, studying." " That's good!" "How are your Aunt and Uncle:" " Fine." " Say hello to them for me." "And Pablo:" "How is he:" "Fine." "He was to send us a postcard from a stop at a port, but it seems he didn't have the time..." " Didn't he write to you:" " No." "Well, you know how things are." "To arrive in a new place..." "Yes, it must be a mess." "Ok, I'm going..." "Regards." "I'll prescribe her some vitamins." " She's worried, that's all." " Yes, that's all..." "But it's all she talks about all day." "When did your nephew leave:" "About..." "Next Thursday it will be a month and a half." "Boys don't realize those things." "Yes, but he should send a letter to his mother, at least." "Maybe you could write it yourselves." "A short note, to calm her down." "Dear family:" "I'm sorry I couldn't write before, but rehearsals take very long." "Paris is a beautiful city." "I hope everyone is fine." "A big hug, and a kiss for mom, Pablo." "Very nice, isn't it:" " Rubbish." "He doesn't say anything." " What do you want him to say:" "Where's the stamp:" " l threw it away." " Why did you do that:" "It was on the envelope. I was so excited when I opened it that I tore it apart." "How are we going to answer to him:" "I copied the address on a piece of paper." "So, let's write to him now." "Fetch a pen and paper." "Dear, unruly Pablo, I was very glad." " We were very glad." " We were very glad... to receive your postcard... but we are also a little worried." "You didn't tell us about yourself." "We are glad everything is fine, but we want you to come back soon." "Look after yourself." "A big kiss." "Mom." "It's my fault." "I should have written something else." "We did it in a hurry." "What I'm worried about is Pablo." "What should we do:" "Keep waiting:" "I was thinking..." "Do you remember that employee we had:" "She married a Frenchman..." " Adela..." "Azucena..." " Almudena." "Almudena." "They moved to Paris." "Dad was so good to them in the past." "We can write her, and ask her to help us find Pablo." "Could she look for him:" "At least she can go to that place where he was to play." "Meanwhile she can send another letter to Pablo." "Another letter:" "I'll send it in an envelope and she only has to send it back." "We can give her some money." "What should we tell Mom now?" "." "We can tell her he is doing very well, playing with his teacher, that they asked him to play in more concerts." "Avery good offer, one he can't refuse." "In Paris... for a while." "For a little while, that's why he accepted it." "The offer is to play with an opera singer who is on a tour." " A famous singer." " An aristocratic woman..." " Called:" " Margarita!" " A French name..." " Veronique:" "Veronique..." " Mimi:" " Yes, Mimi Pinzon..." "Give me a break!" "Ludovica:" "And where is he:" "He's staying in a very elegant hotel in the center of Paris." "From the windows he can see the Eiffel Tower..." "With flags from every country..." "The hotel has a café" "The hotel has a café as big as our house... with glass chandeliers and brass doors." "Madam!" "Nora!" "It's Autumn here and the streets are covered with fallen leaves." "There are cafes everywhere, crowded until late at night." "Everyone is so elegant." "Last night the teacher and I had dinner with a very famous opera singer who came to congratulate us." "Her name is Marie Bergere." "She wants us to accompany her in some concerts that she is giving in cities all over France." "Can you imagine such a trip:" "It's an incredible opportunity for my career." "I hope you are as happy as I am." "I love you a lot." "A big hug, and a kiss for Mom." "Pablo." "Hey, good." "Our boy is doing well." "I'm so proud!" " Yes..." " Of course!" " What's the matter, Mom:" " l don't know." "I have something in my stomach." "Happiness!" "Yes." "But..." "I'm thinking of Patricia." "How will she react to the news:" " She'll be glad." " Sure." "We haven't heard from her for a while." "Why hasn't she come over anymore:" "Perhaps she doesn't want to bother us, with Pablo gone... I'm sure she doesn't know anything." "We should tell her." "Let's invite her for a meal." "We have to look after Patricia until Pablo returns." "It's the least we can do for him." " Come in!" " Thank you." "I brought this." "Mom loves chocolates." "You should give them to her." " Are you staying here:" "I'll bring her down." " Yes." "Patricia." " Hello." " Thank you for coming." "How could I not come:" " Have you had news:" " No, and you:" "We're trying to find out about him through a friend of the family in Paris." "She went to the place where he was going to play and it was shut down." "That's so strange." "That's Pablo... I don't know." "I'm scared." "Scared of what:" "Don't be silly." "I brought this." "You shouldn't have." "You're already one of the family." "Norita, put them on a plate, come on." "Excuse me." "See you later." "You're sad." "What's wrong:" "Nothing." "I was studying a lot." "Look me in the eyes." "You're lying!" "You don't need to feel that way." "Pablo loves you." "The thing is that he had an important offer for his future" "For the future of both of you." "Yes, I know... but it's difficult to think he is so far away." "I miss him too." "Between us, Pablo was always my favorite." "You're so lucky." "He is as well." "I believe that when he returns, he'll want to marry quickly." "Seriously, it's a premonition I have." "You may be right, but we have to wait." "We can't get our hopes up." " One can't live without hopes." " One can't live without hopes." " You'll be a beautiful bride." " Thank you." " But I think we should wait for a while." " No, on the contrary." "Let's begin preparing everything ourselves." "Dear Pablo, comma." "How could you start such an adventure without asking us:" "Are you forgetting about your family:" "You must finish your work and return." "You have commitments here as well." "What does your teacher say about all this?" "I don't want you to listen to everything he says." "You have to think about us." "Be careful." "France can be a dangerous country." "Return as soon as possible." "We need you, Mom." "Dear family, I know Mom is right, I was selfish." "But it was the only way to make a quick decision, lf you knew how difficult it was for me." "But, well, it's done." "Fortunately everything is working out very well." "Marie is a great singer, very thin, bony." "She always wears feathers on the stage;" "sometimes green, other times, black." "They always match her shoes." "She likes to wear eccentric hats, like Aunt Celia." "I told her we have a hat store, one of the most well-known shops in Argentina." "Well, I exaggerated a bit." "Last week we had our first concert." "It was in the Palace of Versailles." "You can't imagine how big it is." "There are almost 200 bathrooms." "I was so nervous that I got lost." "The concert was a success." "There were a lot of important guests, including ministers and film stars." "It's a pity I couldn't understand them." "I have to start learning French." "At least a few lessons..." "Excuse me." "You can't imagine how happy I am." "But don 't think this is easy for me, I miss you all, especially Patricia." "I sent several letters to her, but she hasn't replied yet." "You didn't write to him:" "I didn't receive any letters, yet." "Why don't you write to him now:" "Nora, fetch a sheet of paper for Patricia." "Not now." "I have to think of what to write." " But you'll write soon." " Yes." "It's a time of sacrifice for us all, I know that." "How lucky that Jorge is taking care of business, otherwise we'd be on the street." "I see French girls walking along the Seine and think of Nora." "Her commitment to her classes with those dull students who can't even learn the tables... I also think of auntie and uncle, always so supportive." "Uncle used to tell me:" ""You have to go far in life, very far." "So we can no longer hear you. " He was right finally." "Auntie would go mad in Champs Elysees." "There are trees shaped like animals." "A bear, a giant rabbit... ln Autumn the perfume of the trees fills the city." "I wish you were here with me." "Look what has arrived from Paris." "I love you all." "Pablo." "No." "Auntie, did the postman come:" "Yes." "He brought a package from Paris." "Your mother has it." " ls Patricia here:" " Yes, she's in the back." " Hi." " Look Jorge!" "A gift from Pablo." " What is it:" " l don't know..." " A kind of lamp." " lt's got a pattern inside." " What is it Nora:" " l don't know." "Does it revolve:" " l'll catch it." " No!" "Be careful!" "What a shame, your husband!" "And you:" "Help him go upstairs." "Don't let the children see him." " Let's cook it!" " lt's mine, leave it!" "Dad gave it to me." " Mom, where's Mr. Rabbit:" " lsn't he in the garden:" "We can't find him anywhere." " He must have gone into the forest." " The forest:" "Sure." "Rabbits live in the forest." "Dad brought him so that he could spend a holiday with us." "Perhaps he got tired of being so far away and returned..." " But, why:" " Perhaps he missed home." "Yes:" "Excuse me." "Mr. Millstein, come in." "I'm sorry to bother you in your own house, but I haven't seen you in the store lately." "I'm working a lot at home." "Yes, your uncle just told me that." "What can I do for you:" " l wanted to tell you the store is having some problems. -l know." "Then you'll agree that we should make some changes." " What kind of changes:" " First of all, to cut down expenses." "Perhaps we can do without one of the employees," "Or raise the prices." "Yes, that's reasonable." "Which of the options:" "I wouldn't dispense with one of the employees." "Perhaps reduce wages... I don't know." "You can figure this out better than me." "Do you know the wise saying:" ""The eye of the owner fattens the calf:" "My father used to say it." "Your father was a smart man." "If I were you, I would follow his advice." "I'll keep that in mind." "Now if you excuse me, I have to go back to work." "But we haven't decided what to do yet." "The lemons are so little." "They aren't ripe yet." " lf you want I can ripen some for you." " No, leave them." "Norita, cross lemons out." "Nora..." "Cross peppers out." "Do you have apples there:" "Apples, three kilos." "Stand up straight." "Do you know where they sat her:" "On the wicker chair." "She looks beautiful, it frames her." "What an idea to sit her on a wicker chair!" "That will blur the background." "Bring a green chair from the dining room." "That will emphasize her neck." "The neck..." "Nora!" "Don't use that chair." "Your mother says to bring one from the dining room." " Tell me, what's her hair like:" " Nora is tidying it." "She's leaving a fringe on her forehead." "That fringe, oh my god." "Clear her forehead, that tuft always covering her eye." "It's horrible, poor thing." "Nora!" "Don't leave that tuft covering her eye." " Like this:" " Yes." "I can't tell her it's horrible..." "What is she holding in her hands:" "Nothing, she has them crossed." "Make her hold a jasmine." "Nora!" "Your mother says that she should hold a jasmine!" "But the dress is pale." "In that case, a rose." "Nora!" "Not a jasmine;" "a rose would be better then." " Make up your minds!" " We're doing what we can!" "Celia!" "Don't shout at Norita." "They brought a rose for her." "Red..." "Red like blood." "A smile, please." "The garden is covered with flowers and you're still in France." "I hope that..." "No, we hope... that with these photos, you will remember your family." "Fa...mi..." "ly." "We love you madly." "Beautiful eyes..." "Raise your leg." "That's it." "Let's see." "Nice shoulder." "That's right." "Very well!" "Another one." "Your eyes glowing for uncle Ernesto, come on!" "The Naked Maja!" "What's the matter:" "Oil." " Did you ask Uncle:" " He's busy." "Can you use cooking oil:" "I'll check." "Hundreds, tens... and units." "How many there are:" " Uncle:" " Jorge?" "Can you open this for me?" "What are you doing:" " The key got stuck." " Which key, Uncle:" "The inventory:" "I'll keep it for you." "Dear family, I have great news to share with you." "Marie offered us to make a record with her." "Norita, the scissors!" "I'm sending you one, I hope it arrives in one piece." "It's on sale in all the shops in Paris." "I hope it didn't break." "There were very good critics in the papers." "I hope you like it." "Even better, we have many concerts to promote it already scheduled." "Not only in France, we'll tour Germany." "I have to prepare the luggage." "I love you all." "Take it, Norita." "Pablo." "Grands Opéras Françaises, Marie Berger." " This is wonderful!" " So important, isn't it:" " What are you doing, Mom:" " Let's listen to it!" "Leave it to us, you can listen to it from here." "No, I want to listen to it properly." "I'll come with you, wait." "Hold it for me." "And those musicians he brought:" "Does he think this is a cabaret:" "They're his friends, grandma." "Did you see the garden:" "No, you never see anything." "Only the naked dancers are missing!" "Mother, a party, once in a while..." "Once in a while your husband comes to visit." "Show a little respect, grandma." "My brother supplies for all our needs." "Respect:" "This is a family house, dear, and in my family..." "Please, stop fighting!" "The guests are arriving." "The guests, the guests." " Welcome." " Thank you." " Mr. Millstein." " Thank you for the invitation." " Please, step into the garden." " Yes, thank you." " The children room." " lt's really pretty." "Do you smoke:" "Thank you." "Norita!" "Come here." "Go upstairs to see where your father is." "Tell him I need to talk to him." "Mom, mom!" "This is the last time I hear you say something like that." "Mrs. Millstein felt bad and dad was helping her." "is that clear:" "Go and wash your face." "Doctor:" "Do you know an Opera Singer, called Marie Bergere:" "What:" "Marie Bergere:" " Yes." " The French singer:" "Yes." "Yes, I know her." "Let's see." "Take a deep breath." "Leave everything here." "I'll take care of that." "Excuse me." "Your uncle raised the prices again:" "Talk to him, I wouldn't charge you a thing." "Lito!" " Can you give me some water:" " Yes, sorry." "Why do you always treat me bad:" "Stop that." "My aunt is around." "Where:" "Under the table:" "No, she's with the doctor." "She took Mom's tests to him." " How is your Mom:" " Not very good." "She's worried about Pablo." "And your brother:" "He's doing very well." "He's touring with his band." " Really:" "What a surprise!" " Surprise:" "You know, the kind of friends he travelled with..." " l don't mean anything, but..." " Then don't say anything." "What's wrong:" "What have I done to you:" "You make me feel nervous, Lito." "Why so nervous:" "I have things to do." "You do too." "When are you going to have some time for me:" "When my brother comes back, we'll talk." "And what if he never does:" "Go away, Lito." " Ernesto, we are not making anything." " l know." "Today I went to the workshop and I talked to Caceres." "We're going to reduce the production." " Did you go to the Consulate:" " Yes, I did." " And:" " Nothing." "They only know he entered France." "What are we going to do:" "The only option is for somebody to go there." "And keep looking for him." " Yes, or claim him." " Claim him:" "At the mortuary, Celia." "The mortuary." "Such a pessimist." "We must be reasonable, Celia." "It's a possibility." " lt's Pablo's face, look." " And this..." "Maybe this is his room..." "It looks nice." "Such a good idea to send us these drawings." "He's more and more like Dad." "You haven't been to the club lately." "I don't go out much, actually." "You should go out, have fun..." "meet someone..." "That's what Pablo always says." "Pablo knows how to have fun." " l have to take care of Mom." " Sure." "Everyone has commitments." "Yes, of course." " Do you miss Pablo:" " Yes." "Like everyone else." "I'm sure he's fine." "And he'll come back soon." "I don't know what to think." "Well, we have to think about the wedding now." "Wedding:" "Patricia." "Hello, Jorge." "How are you:" "How did you do on your exam:" "Good." " That's good." " Yes." " Shall we go:" " Yes." " Patricia:" " Yes:" "Are you staying for dinner tonight:" " No, I can't." " Another day, then." "Another day, yes." "Let's go." "Mom is growing impatient." "Excuse me." "Did you see Patricia today:" "She's weaker every day." " Yes, poor thing." " Why poor:" "She should think more about Pablo." "Well, she's helping us a lot, isn't she:" "I think she's losing hope." "But I'm sure Pablo is fine." "Don't you think, Jorge:" "Sure!" "Besides, we can't think of him all day." "Pablo is a grown up and knows how to look after himself." "We have other things to take care of." " The store, for example." " Mom's health." "Despite what the doctor says, I see her improving every day." "Her spirit lifts every time she receives a present from Paris." "Yes, but we have to think about our finances." "How much is this comedy costing us:" "Mom's health is not a joke." "Of course." "But do you have any idea of how business is going:" " Not so well." " Like hell." "Ernesto!" "That's the way it is." "The numbers aren't good." "How to pay our debts:" "Production on the farm isn't good, either." "The foreman cannot handle it on his own." " Millstein says..." " Millstein will lead us to bankruptcy." "Since he took over things have worsened." "We must do something." "Like what:" "I don't know." "We must think about it." "I have an idea." "Dear family, I'm writing from the train that takes us on another tour." "From my window I can see beautiful houses under the snow." "It's a wonderful landscape, but I can't stop thinking about you." "One learns to value things when they are far away." "I miss my bed, Auntie's meals, Uncle's jokes... I was trying to find a place in town where they make pasta... I imagine Norita is still giving lessons and Jorge is taking care of the store." "It's hard to think that life continues the same, while I'm here in Paris... I saw a picture, and without a second thought I bought it." "It sometimes goes unnoticed but for me, here in Paris, the memory of the family is greater everyday." "I can't forget dad screaming:" ""Come back, you half-wit" when I broke the dinning room glass." "I think the glass was never replaced." "But I miss Patricia the most." "I think more of her everyday, I even write her name on steamy windows." "Please, convince her that this is the best for us." "Soon we'll finish the concerts, although the distance between cities is bigger." "Next week we are going to Berlin." "Then, Frankfurt, Viena, Milan, Rome... I hope we can soon be together." "Travels are more enjoyable when you share them with someone." "You can 't imagine how much I miss you all." "Pablo." "You look just like me the day I married." " lt should be... that way." " Yes." "It bothers me here." "Take it off and I... lt's the emotion." "Patricia." " What's the matter:" " l feel ridiculous." " Why:" " Jorge..." "Come in." "What's all this:" "Pablo's life in France." "I have something for you." "Pablo's favorite book." "He would want you to have it." "Pablo didn't read books." "Never mind, I accept it." "From you, not from Pablo." "Thank you." "Didn't you see Patricia:" " She left." " What did she do with the dress:" "She took it." "She liked it so much, she wanted to show it to her family." "That's so nice." "I'll tell your mom." "Attention!" " Very good!" " One more time, dad." "No, tomorrow." "Now Uncle and I have to leave." "What's that:" "Voilá!" "You should be the Finance Minister." "Don't play with the food." "Good morning." "Excuse me for a minute." "Keep eating, children." "Norita..." "Norita, are you ready:" "I'm almost done." "They're bringing her down." "Very good!" "You're going to kill me." "Be careful, Uncle." "Easy..." "Watch the door." "Be careful." "Be careful." " There you go." " A bit closer..." "Here Mom, I'll fetch the food." " Are you cold:" " l'm fine." "Just a bit out of breath." "Mom, we have a surprise for you." " Pablo will call tonight." " What do you mean:" "From Europe:" " ls that possible:" " lt's very expensive and difficult, but it's possible." " Excuse me." " That looks so good!" " Let's see." " What time is he going to call:" "I don't know, it depends on an international operator." "Who wants some salad:" "Mom, do you want salad:" "No, no, later." " Shall we make a toast:" " Yes, of course!" " Merry Christmas!" " Cheers." "Merry Christmas!" "Merry Christmas!" " To Pablito!" " To Pablo!" "Hello:" "Operator:" "Yes, I'll wait." "Pablo!" "Pablo!" "It's been a while!" "How are you:" "We're fine here." "We're all working hard." "What:" "Yes, I'll put her on the phone." "Hello:" "Hello:" "Pablo:" "Pablo, son!" "How are you:" "I don't understand!" "I know." "love you too so much!" "Hello:" "Hello!" "Pablo:" " Take me upstairs, please." " l'll take you." " Call the doctor, Ernesto." " Hello:" "Pablo:" "Pablo:" "Pablo:" "It was not a long distance call." "It was from Avellaneda." "What's the difference:" "You don't have to worry about money." "Who's talking about money:" "Nora and I have talked about this." " We decided that we're going to sell some furniture and clothes." "What:" "We both have clothes that we don't wear." "And Millstein always liked the chandelier in the living room." "Well, now he can buy it." "Don't you think we'd be better move to a smaller house:" "To take Mom out of this house:" "With what it means to her:" "To us:" " lt's the family house." " l think that..." "The house is the house." "We are not leaving it." "Period." "Doctor, how is she:" "The situation is complicated." " Be honest, please." " Four months." "Five." "I'm sorry." " This has gone up again." " The new government." "It's temporary until things settle down again." "That's what all governments say." "Dreams keep hope alive." "It's an antique, isn't it:" " Do you like it:" " Yes, very much." "It belonged to my father." "He won it in a brothel, playing cards." "If he won the bet, he'd keep the owner's woman," " a Polish woman with green eyes." " And if he lost:" "He'd have to give up his daughter." "What happened:" "The game was even, everyone in the brothel was there." "In the last hand dad was winning, but the police appeared." "There was a terrible stir." "Some ran away." "The polish girl was deported." "Her husband didn't even stop to protect her." "Dad grabbed the lamp and broke it on a policeman's head." "That's how he escaped." "I'll buy it." " l don't know..." "It's very valuable." " Tell me how much." "Mom, Mr. Millstein wants to say hello." "Excuse me." "Good evening." " How are you, Madam:" " Here I am." " How's the store doing:" " Much better." "It will be a great store, some day." " Like Gatt Chavez." " Something like that." "Why not:" "Your husband always had a good nose for business." "Yes." "Osvaldo was an intelligent man." "He also had a very good taste..." "in general." "What about your wife:" "Fine." "A beautiful woman." "You are a very lucky man." " Yes, that's true." " Well, I'll show you to the door." "Wait." "Celia, look in the wardrobe, on the upper shelf." " lt's late, Mom." " Just a second, Jorge." "The purple box." "Thank you." "Do you like it:" "It's very elegant." "Osvaldo loved it." "I kept it for a special occasion." " lt's unique." " Take it." " What:" " lt's a gift." "It will look better on your wife." " She would thank you, but..." " Try it on." "Precious..." "Take it." "Thank you so much." "No, thank you for all you do for us." "Well, I'd better leave now." "Good night." "I'll show you to the door." " What are you doing:" " Can't I give a gift:" "Don't you remember his wife left him:" "Besides, everybody knew he was cuckolded." "She took the shirt off his back." "Don't you remember:" "Terrible..." "I didn't remember." "How are the lessons:" "I'm not giving lessons anymore." "Too much housework." "Why don't you go out a bit:" "To distract yourself." "No." " Why not:" " Because. I can't." "They need me here." " Thank you." " Thank you." " Goodbye." " Goodbye." "Yes:" "It's Patricia." "Can I come in?" " Are you all right:" " Yes, why:" "I thought that..." "Mom's getting worse." "We had to bring oxygen." "I just wanted to see you." "And see if you are well." " l'm fine, yes." " Ok." "Wait." "No." "No." "Pablo." "What are we going to do when he returns:" "He won't return." "Why not:" "Pablo can't be alive." "Why can't he:" "Because we never got any news from him, Jorge." "Not even a postcard." "We don't know what happened to him." "He vanished." "Because if he were alive and he were doing this to us, he would be a bastard." " Pablo did send a letter." " What:" "Six months ago." "Nobody knew." "It arrived when I was by myself." "I didn't show it to anybody." " What:" " Pablo sent a letter." "He said he's all right, that things didn't turn out as expected, but he was looking for other opportunities." "When he has enough money for the ticket, he will return." " You're lying to me." " No, it's true." "I have the letter, I can show it to you." "I don't want to see it." "It's in the right drawer." "Look!" "Look!" "Don't you think Patricia is acting strange:" " Why strange:" " l don't know, she looks confused." "Perhaps she's overwhelmed with the wedding arrangements." "Yes, we shouldn't put pressure on her." "It's so much work... for all." "You shouldn't have fired the maid." "She was an unnecessary expense." "Maybe..." "But you all look so tired." " You don't look very good, Celia." " l'm better than ever." "Are you sure:" "It's the asthma." "It comes and goes." "My brother was the same." "He came and went." "Until one day he didn't come anymore." "And with Ernesto, how are you:" "Well." " Sure:" " Please... let's not start again." "If I say well, it means well." " See:" "You're out of breath again." " lt's the asthma, I told you." "You need fresh air." "Yes." "Sometimes I envy Pablo." "He must be well with his asthma." "You left it downstairs." "Aunt!" "We have to do some tests." "When:" "Tomorrow." "She'll have to stay at the hospital." " At the hospital:" " Yes, this is not a joke." "Will the tests be expensive:" "Don't worry." "I'll arrange that with your nephew." "What if I leave a note instead:" "You can't leave without saying goodbye." " Celia, Take care." " You too." "Say hello to the foreman, and to his wife." "I'll do it." "Dear Pablo:" "Change of the season has brought us some surprises." "Aunt Celia is not feeling very well, it's nothing too serious, don't worry." "The doctor said that all she needs is to spend some time in the countryside." "Uncle went with her, of course, two weeks ago." "They called from the village yesterday." "The farm seems to be improving." "This year the sheep had double breeding." "Patricia went on a trip with some classmates, too." "That's why she hasn't visited us for a couple of weeks." "Excuse me." "As you can see, you are not the only one who has been moving around." "I finished the letter." "Kisses to you." " Shall I read it:" " No, I'm tired." "Won't you sign it:" "Come on." "No, you sign it." "Hello." "Uncle!" "How's Aunt:" "Uh..." "What are you going to do:" "I understand." "The store:" "Fine as usual." "is it raining there:" "All the roads are blocked..." "No, if you're fine, stay as long as you want." "I'll tell them, don't worry." "Goodbye." "Kisses to Auntie." "We know it is hard, Uncle, but there's no other choice." "If Mom sees you she will ask about Auntie." "Yes, of course." "Besides, the people on the farm need a guide." "It'll be good for you to have other things to think about." "Yes, you're right." "This house holds too many memories." "I must insist, are you sure you won't take my offer:" "I believe my brother was clear." "The piano is not for sale." "Such a pity." " Here you are." " Thank you." "As soon as I have the money, I'll bring it." "Yes." "With this weather I'd prefer not to leave the house." "Thank you." " l'm leaving." " Aren't you staying for dinner:" "No." "All right." "See you." "Nora, I'm not coming back." "What:" "I've been thinking." "I can't go on. I'm sorry." " But Mom..." " Nora, she knows." " What:" " She realizes." "You're shameless." "I understand. I apologize." "I know that..." "You're making it up to justify yourself." "Did you forget about Pablo:" "Or did you find another man:" "I'm leaving." "Dear Mom, I hope that Aunt Celia gets better from her asthma." "The country will surely do her good, it did me good." "Living in the city is not healthy." "Last week here, a tiger escaped from the zoo." "Can you imagine?" "On the radio they asked people to stay in their houses." "People closed the doors and windows, fearing the tiger might enter." "Meanwhile, the tiger walked freely through the city, starving, scratching billboards and roaring." "In the end they caught it in a butcher shop." "They added poison to the meat." "The poor tiger crawled to the Seine and threw himself in." "From my window, I saw his body pass, floating on the river, swollen like a feather cushion, orange and black." "I received a letter from Patricia, telling me about her trip to the lakes in the South." "At least, there are no tigers there." "She says that the landscape was beautiful, but that the best thing about traveling is to return home." "I know we will meet soon, and I will give you a big hug." "I promise." "Pablo." "He writes better and better, doesn't he:" "Aren't you going to reply:" "No." "You write to him." "Tell him the news." " l'll leave it here." " Thank you, son." "Nora, what do you do with the stamps:" "What:" "What do you and Jorge do with the stamps:" "Jorge removes them with steam." "I stick them on a sheet and we cover them with tracing paper." "In the green album." "Don't you remember:" "Incredible..." "So much effort you put into this." "It's nothing, Mom, what are you saying:" "You're so good to me." "Uncle Ernesto called today." "He says that the fields won't be ready until next year." "With some luck." "Too bad." "Yes." "Lito came to the shop." "How is he:" "He's getting married." "Really:" "To whom:" "To the fisherman's daughter." "She's pregnant." "He doesn't want to be involved." "Her father is forcing him." "What a disaster, that boy..." "Did you hear that noise:" "No." "Jorge!" "ARGENTlN EAN TANGO musicians SUCCEED in paris" "Jorge!" "What is she doing here:" "Mom!" "Grab her legs, Nora." "Grab her legs!" "Sometimes the house seems too big." "Without the maid, and Aunt and Uncle on the farm, it seems to have too many rooms." "There are some places I don't enter anymore." "It will remain like this until we get used to it... or until you return." "You can 't imagine how much we wish to see you." "Patricia wants to organize a welcome party for you." "She asked me not to tell you, but I can't keep secrets from you." "If we can't trust our family, who can we trust?" "Nice earrings." "Do you like them:" "They are from Paris." "It seems this winter is colder than usual." "It hasn't stop snowing since New Year's Eve." "No." "Pablo told me there's so much snow that people can't get out of their houses." "He's lucky to live on the third floor." "Anyway, he always finds a way out of everything." "To go to work he skates on the Seine." " You must be lying..." " No, it's true!" | Low | [
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Posts filtered on Tag Tag: Houston Zoo March 24, 1986: On this day, Houston zookeeper William Neuser was attacked by the zoo’s largest mammal, an 18-year-old Asian elephant named Thai. According to horrified witnesses, the Thai picked the … | Mid | [
0.5973451327433621,
33.75,
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Opinion issued April 15, 2010. In The Court of
Appeals For The First District
of Texas ———————————— NO. 01-09-00822-CV ——————————— Texas Department of Public Safety, Appellant V. Kristina Ann
Potter, Appellee On Appeal from the County Court at Law Austin County, Texas Trial Court Case No. 09CV4474 MEMORANDUM OPINION After
Kristina Potter refused to perform field sobriety tests or provide a blood or
breath specimen following her involvement in a car accident, the Texas
Department of Public Safety (Department) suspended her driving-license privileges
for 180 days. See Tex. Transp. Code Ann.
§§ 724.035, 742.042 (Vernon Supp. 2009).
An administrative law judge (ALJ) upheld the suspension, and Potter
appealed the decision to county court.
The county court granted Potter’s appeal and reversed the
suspension. The Department now appeals
that ruling, contending that the county court failed to apply the proper
standard in reviewing the administrative decision. We reverse the county court’s judgment and reinstate the suspension. Background The accident In the early morning hours of
November 29, 2008, Texas State Trooper Vacek was dispatched to a one-vehicle
rollover accident on State Highway 159 in Bellville. When he arrived, Vacek first spoke with Michael
Blezinger, who told him that he had reported the accident. Potter stood near a drainage ditch beside the
road and an overturned gray Jeep Liberty.
Blezinger pointed at Potter and told Vacek that she was the driver of
the Jeep, and that he thought she had been drinking. Vacek walked over to Potter, noting
various items, apparently thrown from the car during the rollover, strewn all
over the ground. In particular, he noticed
an open can of beer that appeared to have condensation on it. When he approached, Potter identified herself
as the driver of the vehicle. Once Vacek
established that Potter did not need medical attention, he asked her to explain
what happened. Potter said that she lost
control while she was trying to send a text message. During her interaction with Vacek,
Potter was crying uncontrollably and had several emotional outbursts. Vacek also noticed that Potter’s eyes were
bloodshot and glassy and that her breath smelled strongly of alcohol. Vacek asked Potter if she had been drinking. Potter admitted to having two beers, but said
that she did not remember how long it had been since she drank them. When Vacek asked Potter if she was
willing to perform field sobriety tests, Potter replied that she was told to
wait for her attorney to arrive. Based
on his observations, Vacek concluded that Potter had lost the normal use of her
mental and physical faculties due to alcohol ingestion, placed Potter under
arrest, handcuffed her, and placed her in the patrol car of a local deputy at
the scene. When Potter’s attorney arrived,
Potter consulted with him. Then, the
deputy took Potter to the Austin County jail while Vacek continued his
investigation of the accident scene. When
he was finished, Vacek met Potter at the jail.
He requested that she give a breath specimen to analyze the
concentration of alcohol in her system and began to read her the statutory
warning informing her that her license would be suspended for 180 days if she refused
to do so. After Vacek finished the first
paragraph, Potter told him that she was going to refuse to give a specimen. Vacek finished reading the statutory warning
and gave Potter a copy of the form. Potter
next complained of wrist pain and was taken to a nearby hospital. Once there, she refused to submit to a blood
exam, but consented to an x-ray. Proceedings below At Potter’s request, a hearing on
the suspension took place before an ALJ.
The ALJ decided that the Department was authorized to suspend Potter’s
license for the prescribed period, based on findings that (1) Potter was
operating the Jeep at the time of the accident, (2) probable cause existed to
believe that Potter was operating a motor vehicle in a public place while
intoxicated, based on Vacek’s observations of her condition and her own admission
that she had consumed alcoholic beverages before operating the Jeep, and (3)
Potter refused to perform any field sobriety tests or provide any breath or
blood specimen. Potter appealed the suspension to
the county court at law. After reviewing
the hearing transcript and evidence presented to the ALJ, as well as arguments
of counsel, the county court signed an order granting Potter’s appeal. The Department timely filed its appeal of
this order. Discussion Standard of review “[C]ourts review administrative license suspension decisions
under the substantial evidence standard.” Mireles
v. Tex. Dep’t of Pub. Safety, 9 S.W.3d 128, 131 (Tex. 1999); see Tex.
Transp. Code Ann. § 724.047 (Vernon 1999) (“Chapter 524 governs an
appeal from an action of the department, following an administrative hearing
under this chapter, in suspending or denying the issuance of a license.”); id. § 524.043 (Vernon 2007)
(establishing rules for appeal but not defining the scope of review). In contested cases, if more than a scintilla
of evidence supports the administrative findings, we affirm those findings;
“[i]n fact, an administrative decision may be sustained even if the evidence
preponderates against it.” Mireles, 9 S.W.3d at 131. Courts may not substitute their judgment for the judgment of the state agency on the weight of the evidence on
questions committed to agency discretion but . . . (2) shall reverse
or remand the case for further proceedings if substantial rights of the
appellant have been prejudiced because the administrative findings, inferences,
conclusions, or decisions are: . . . (E) not reasonably supported by
substantial evidence considering the reliable and probative evidence in the
record as a whole. . . . Tex. Gov’t Code Ann. § 2001.174 (Vernon 2008). We review the county court’s substantial
evidence review of the administrative ruling de novo. See
Tex. Dep’t of Pub. Safety v. Alford, 209 S.W.3d 101, 103 (Tex. 2006)
(noting that ALJ’s findings are entitled to deference but that “whether there
is substantial evidence to support an administrative decision is a question of
law” and as such, neither county court nor ALJ’s determination of issue is
entitled to deference on appeal). License suspension Under the Transportation Code, if a peace officer arrests a person
and he has reasonable grounds to believe that the person is driving while
intoxicated, he may request specimens of the person’s breath or blood. Tex.
Transp. Code Ann. § 724.012(a)(1) (Vernon Supp. 2009). If the person refuses to submit to the taking
of a specimen, the Department must suspend the person’s license to operate a
motor vehicle on a public highway for 180 days.
Id. § 724.035(a)(1)
(Vernon Supp. 2009). If a person’s
license is suspended under this chapter, she may request a hearing on the
suspension. Id. § 724.041 (Vernon Supp. 2009). At the hearing, the issues, as applicable
here, are whether: (1) reasonable
suspicion or probable cause existed to stop or arrest the person; (2) probable cause existed to
believe that the person was: (A) operating a motor vehicle in a public place while
intoxicated; . . . . (3) the
person was placed under arrest by the officer and was requested to submit to
the taking of a specimen; and (4) the
person refused to submit to the taking of a specimen on request of the officer. Id. § 724.042 (Vernon Supp. 2009). Applying the applicable standard of review,
then, the reviewing court must uphold the administrative decision if the record
contains substantial evidence to support an affirmative finding on each of
these issues. Reasonable suspicion for stop or probable cause for arrest Officer Vacek’s offense report recites that Blezinger
identified Potter as the driver and stated that he thought that she had been
drinking. When Officer Vacek approached
Potter, he observed that Potter had glassy eyes, was crying, and was otherwise behaving
very emotionally, which are consistent with intoxication. Contrary to Potter’s assertion, a witness
does not have to be an expert to testify that a person he observes is
intoxicated by alcohol; a police officer’s lay opinion testimony that a person
is intoxicated is probative. Henderson v. State, 29 S.W.3d 616, 622
(Tex. App.—Houston [1st Dist.] 2002, pet. ref’d). Blezinger and Vacek’s observations provide
more than a scintilla of evidence in support of the ALJ’s finding that Vacek
had reasonable suspicion for the stop. Probable cause to believe that the licensee was driving a motor vehicle
in a public place while intoxicated A license suspension is a civil matter, requiring only
probable cause to believe the driver was driving while intoxicated. See Tex.
Transp. Code Ann. § 724.048(a) (Vernon 1999); Mireles, 9 S.W.3d at 131; Tex.
Dep’t of Pub. Safety v. Butler, 110 S.W.3d 673, 675 (Tex. App.—Houston
[14th Dist.] 2003, no pet). Probable
cause to arrest exists when the facts and circumstances that are apparent to
the arresting officer support a reasonable belief that an offense has been or
is being committed. Amores v. State, 816 S.W.2d 407, 413 (Tex. Crim. App. 1991). Probable cause requires more than a suspicion
but far less evidence than that needed to support a conviction or to support a
finding by a preponderance of the evidence. See
Guzman v. State, 955 S.W.2d 85, 87 (Tex. Crim. App. 1997). Potter’s statement to Vacek that she lost control of the
vehicle while texting constitutes an admission that she was driving the vehicle
when it crashed. As for the
administrative finding that Potter was intoxicated, evidence of her
uncontrollable crying, emotional outbursts, and glassy, red eyes—coupled with evidence that her breath
smelled strongly of alcohol and of a beer can with condensation on it found at
the scene—constitutes
substantial evidence in its support. See Tex. Dep’t of Pub. Safety v.
Perkins, No.
01-04-00093-CV, 2004 WL 2749141, at *6 (Tex. App.—Houston [1st Dist.] 2004, no
pet.) (finding probable cause based on officer’s report that Perkins’s eyes
were red and glassy, and his breath had very strong odor of alcohol); Tex. Dep’t of Pub. Safety v. Pruitt, 75
S.W.3d 634, 640–41 (Tex. App.—San Antonio 2002, no pet.) (finding probable
cause for arrest and to believe Pruitt was operating a motor vehicle on a
public roadway while intoxicated where Pruitt admitted to officer that he was
driving vehicle involved in accident, officer smelled mild odor of alcohol on
Pruitt’s breath, Pruitt’s speech was slurred, and Pruitt admitted to officer
that he had been drinking); see also Tex.
Dep’t of Pub. Safety v. Varme, 262 S.W.3d 34, 41 (Tex. App.—Houston [1st
Dist.] 2008, no pet.) (holding that officer had probable cause to arrest Varme;
officer observed Varme speeding and observed that Varme had strong odor of
alcohol and slurred speech; Varme admitted he had been drinking, his balance
was “poor,” and his eyes were “bloodshot”).
Potter contends that the fact that she was crying and emotional, and had
glassy, red eyes is no evidence that she was driving while intoxicated because
it equally supports a reasonable inference that she had a natural reaction to
the accident as it does the ALJ’s finding that there was probable cause that
she was driving while intoxicated.
Potter, however, does not account for the officer’s additional
observation that Potter’s breath smelled strongly of alcohol, which renders her
benign explanation less plausible. The
equal inference rule thus does not apply here.
See Lozano v. Lozano, 52
S.W.3d 141, 148 (Tex. 2001) (observing that equal inference rule precludes fact
finder from reasonably inferring ultimate fact from meager circumstantial
evidence which could give rise to any number of inferences, none more probable
than another). In her appeal of the ALJ’s decision to the county court,
Potter also contended that the Department failed to prove a temporal link
between her driving and intoxication. To
the extent the county court relied on that contention as grounds for granting
Potter’s appeal, it erred. When Officer
Vacek appeared at the scene within minutes of the accident report, he noticed
condensation on the open can of beer near the vehicle, signs of intoxication, and
a strong smell of alcohol on Potter, and Potter herself admitted to Officer Vacek
that she had drunk beer earlier that night.
These facts and circumstances are sufficient to warrant the belief of a
person of reasonable caution that Potter had consumed alcohol close enough in
time to the accident to have been impaired by it at the time. We thus hold that substantial evidence
supports the ALJ’s finding that probable cause existed to arrest Potter and to
believe that Potter was operating a motor vehicle on a public roadway while
intoxicated. The licensee refused to perform field sobriety tests or provide a blood
or breath specimen for testing Potter does not dispute that she refused to perform a field
sobriety test or provide a blood or breath specimen, but she specifically
points to the absence of testing results as supporting her contention that
substantial evidence does not support the ALJ’s decision. But the fact that Potter refused the testing supports,
rather than undermines, an inference that Potter was intoxicated at the time of
her arrest. Refusal to submit to testing
is a factor that weighs in favor of finding probable cause of DWI. See Partee v. Tex. Dep’t of Pub. Safety,
249 S.W.3d 495, 501–02 (Tex. App.—Amarillo 2007, no pet.); Tex. Dep’t of Pub. Safety v. Nielsen,
102 S.W.3d 313, 317 (Tex. App.—Beaumont 2003, no pet). Conclusion Substantial evidence supports the ALJ’s decision to suspend
Potter’s driver’s license for 180 days under sections 724.042 and 724.035 of
the Texas Transportation Code. We
therefore reverse the judgment of the county court and render judgment
reinstating the suspension of Potter’s driving-license privileges. See Tex. Transp. Code Ann. § 2001.174(1). Jane
Bland Justice
Panel
consists of Justices Jennings, Hanks, and Bland. | Mid | [
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pragma solidity >=0.4.24 <0.6.0; contract LoopNestedFor { uint[2][2] a; function testNestedForLoop() public { for (uint i = 0; i < 2; i += 1) { for (uint j = 0; j < 2; j += 1) { a[i][j] = 2 * i + j; } } assert (a[0][0] == 0); assert (a[0][1] == 1); assert (a[1][0] == 2); assert (a[1][1] == 3); } } | Mid | [
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#include <unittest/unittest.h> #include <thrust/set_operations.h> #include <thrust/execution_policy.h> template<typename ExecutionPolicy, typename Iterator1, typename Iterator2, typename Iterator3, typename Iterator4, typename Iterator5, typename Iterator6, typename Iterator7> __global__ void set_symmetric_difference_by_key_kernel(ExecutionPolicy exec, Iterator1 keys_first1, Iterator1 keys_last1, Iterator2 keys_first2, Iterator2 keys_last2, Iterator3 values_first1, Iterator4 values_first2, Iterator5 keys_result, Iterator6 values_result, Iterator7 result) { *result = thrust::set_symmetric_difference_by_key(exec, keys_first1, keys_last1, keys_first2, keys_last2, values_first1, values_first2, keys_result, values_result); } template<typename ExecutionPolicy> void TestSetSymmetricDifferenceByKeyDevice(ExecutionPolicy exec) { typedef thrust::device_vector<int> Vector; typedef typename Vector::iterator Iterator; Vector a_key(4), b_key(5); Vector a_val(4), b_val(5); a_key[0] = 0; a_key[1] = 2; a_key[2] = 4; a_key[3] = 6; a_val[0] = 0; a_val[1] = 0; a_val[2] = 0; a_val[3] = 0; b_key[0] = 0; b_key[1] = 3; b_key[2] = 3; b_key[3] = 4; b_key[4] = 7; b_val[0] = 1; b_val[1] = 1; b_val[2] = 1; b_val[3] = 1; b_val[4] = 1; Vector ref_key(5), ref_val(5); ref_key[0] = 2; ref_key[1] = 3; ref_key[2] = 3; ref_key[3] = 6; ref_key[4] = 7; ref_val[0] = 0; ref_val[1] = 1; ref_val[2] = 1; ref_val[3] = 0; ref_val[4] = 1; Vector result_key(5), result_val(5); typedef thrust::pair<Iterator,Iterator> iter_pair; thrust::device_vector<iter_pair> end_vec(1); set_symmetric_difference_by_key_kernel<<<1,1>>>(exec, a_key.begin(), a_key.end(), b_key.begin(), b_key.end(), a_val.begin(), b_val.begin(), result_key.begin(), result_val.begin(), end_vec.begin()); cudaError_t const err = cudaDeviceSynchronize(); ASSERT_EQUAL(cudaSuccess, err); iter_pair end = end_vec[0]; ASSERT_EQUAL_QUIET(result_key.end(), end.first); ASSERT_EQUAL_QUIET(result_val.end(), end.second); ASSERT_EQUAL(ref_key, result_key); ASSERT_EQUAL(ref_val, result_val); } void TestSetSymmetricDifferenceByKeyDeviceSeq() { TestSetSymmetricDifferenceByKeyDevice(thrust::seq); } DECLARE_UNITTEST(TestSetSymmetricDifferenceByKeyDeviceSeq); void TestSetSymmetricDifferenceByKeyDeviceDevice() { TestSetSymmetricDifferenceByKeyDevice(thrust::device); } DECLARE_UNITTEST(TestSetSymmetricDifferenceByKeyDeviceDevice); void TestSetSymmetricDifferenceByKeyCudaStreams() { typedef thrust::device_vector<int> Vector; typedef Vector::iterator Iterator; Vector a_key(4), b_key(5); Vector a_val(4), b_val(5); a_key[0] = 0; a_key[1] = 2; a_key[2] = 4; a_key[3] = 6; a_val[0] = 0; a_val[1] = 0; a_val[2] = 0; a_val[3] = 0; b_key[0] = 0; b_key[1] = 3; b_key[2] = 3; b_key[3] = 4; b_key[4] = 7; b_val[0] = 1; b_val[1] = 1; b_val[2] = 1; b_val[3] = 1; b_val[4] = 1; Vector ref_key(5), ref_val(5); ref_key[0] = 2; ref_key[1] = 3; ref_key[2] = 3; ref_key[3] = 6; ref_key[4] = 7; ref_val[0] = 0; ref_val[1] = 1; ref_val[2] = 1; ref_val[3] = 0; ref_val[4] = 1; Vector result_key(5), result_val(5); cudaStream_t s; cudaStreamCreate(&s); thrust::pair<Iterator,Iterator> end = thrust::set_symmetric_difference_by_key(thrust::cuda::par.on(s), a_key.begin(), a_key.end(), b_key.begin(), b_key.end(), a_val.begin(), b_val.begin(), result_key.begin(), result_val.begin()); cudaStreamSynchronize(s); ASSERT_EQUAL_QUIET(result_key.end(), end.first); ASSERT_EQUAL_QUIET(result_val.end(), end.second); ASSERT_EQUAL(ref_key, result_key); ASSERT_EQUAL(ref_val, result_val); cudaStreamDestroy(s); } DECLARE_UNITTEST(TestSetSymmetricDifferenceByKeyCudaStreams); | Mid | [
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BATTLESTAR GALACTICA December 3, 2005 The new BATTLESTAR GALACTICA on the Sci-Fi Channel has been a pleasant surprise. While I would not put it in a class with ROME or DEADWOOD, the episodes I’ve seen to date have pretty damn good… and certainly much better than godawful original series, the one with Lorne Greene that fans used to mock as BATTLESTAR PONDEROSA. It is easily the best thing on the Sci-Fi Channel (it puzzles me how the Sci-Fi Channel can start with a classic like EARTHSEA and turn it into drek, and then start with drek like BATTLESTAR PONDEROSA and turn it into something quite watchable, but there you are) and the best space show in many a year. I am intrigued to note that the humans on the new GALACTICA call the Cylons “toasters” as a pejorative. As best I can recall, this was never used on the original show. My guess is that they picked up the usage from “Measure of a Man,” one of the few good episodes of STAR TREK: THE NEXT GENERATION, written by Melinda M. Snodgrass. This was the episode where Data is on trial to determine if he is man or a machine; during the trial, he is referred to as a toaster. Ron Moore, who created the new GALACTICA, worked on the NEXT GEN with Melinda, and was certainly familiar with her “toaster” usage. Melinda in turn borrowed that riff from Walter Jon Williams, who had Dr. Travnicek call Modular Man a “toaster” in his WILD CARDS stories way back in 1985-86… though Modular Man appeared in our SuperWorld games long before WILD CARDS, and it may be that “toaster” (as applied to a mechanical man rather than a device for burning bread) made its first world appearance some late night in one of our games. It bemuses me to think that a witticism first tossed out in a RPG has now entered the common parlance of SF, via WILD CARDS, STAR TREK, and the new BATTLESTAR GALACTICA. Toasters of the galaxy, unite. | High | [
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676 F.Supp. 140 (1987) KLEIER ADVERTISING, INC., Plaintiff, v. NAEGELE OUTDOOR ADVERTISING, INC., Defendant. Civ. A. No. C 85-1067-L(A). United States District Court, W.D. Kentucky, Louisville Division. December 18, 1987. *141 Jack A. Wheat, Robert, Miller & Thomas, Louiseville, Ky., for plaintiff. M. Stephen Pitt, William Hollander, Wyatt, Tarrant & Combs, Louisiana, Ky., for defendant. MEMORANDUM AND ORDER ALLEN, Senior District Judge. This copyright infringement action is scheduled for jury trial on January 11, 1988. The matter is now before the Court on defendant's motion for summary judgment, and on plaintiff's motion for sanctions. Defendant Naegele contends that the damages, if any, recoverable by plaintiff Kleier must exclude actual and statutory damages. The basis for Naegele's argument is that it was an "innocent infringer" within the meaning of 17 U.S.C. Sec. 405(b). That statutory subsection provides, in part, as follows: Any person who innocently infringes a copyright, in reliance upon an authorized copy ... from which the copyright notice has been omitted, incurs no liability for actual or statutory damages ... for any infringing acts committed before receiving actual notice that registration for the work has been made ... if such person proves that he or she was misled by the omission of notice. Materials of record reflect Kleier's representation that it routinely placed copyright notification on its designs, but Kleier has not offered any testimony that the drawing provided to Naegele did bear copyright notice. Naegele contends that this circumstance means that Kleier has failed to create a dispute of fact regarding omission of notice. Kleier, on the other hand, points out that Naegele's witnesses have not testified that the drawing bore no copyright notice, but only that they do not recall seeing a notice. While it represents a very close question, we are inclined to believe that the present state of the record does reflect a dispute of fact concerning omission of copyright notice. Nonetheless, for purposes of this motion, we will assume that the drawing provided by Kleier to Naegele did not bear a copyright notice. In all other respects, we take all facts and inferences in favor of Kleier, the non-movant. Viewed from this standpoint, the following chronology appears. In March or April of 1983, Kleier provided Naegele with rough drawings of the design in question, and we assume those drawings did not bear a copyright notice. In August 1984, having learned of Naegele's unauthorized use of the design, Kleier notified Naegele that the design belonged to Kleier, and that its use constituted copyright infringement. Kleier obtained a copyright registration certificate bearing the date September 9, 1985. Naegele was not aware of the registration until November 19, 1985, when it was served with the present lawsuit. On approximately December 3, 1985, Naegele removed the last infringing work. Naegele's argument is that it has presented evidence that it was misled by the omission of the copyright notice, and that it did not have "notice that registration for the work [had] been made" until November 19, 1985. No infringing work was erected after that date, and a short time later the last of the previously erected infringing work was removed. Accordingly, argues Naegele, it is an "innocent infringer" entitled to the protection of 17 U.S.C. Sec. 405(b). Distilled to its essence, Naegele's view of the law is that once a defendant has presented some evidence of having been initially misled by omission of copyright notice, that defendant is necessarily an innocent infringer until receipt of actual notice of formal registration. *142 Kleier's view of the statutory provision is somewhat different. Kleier contends that Naegele could not claim the status of an "innocent" infringer after being notified of Kleier's copyright claim, despite the fact that such notification occurred a year prior to formal registration. In support of this argument, Kleier has cited the Court to cases that have construed 17 U.S.C. Sec. 405(b) in conjunction with Sec. 405(a). Sec. 405(a) sets forth the circumstances in which omission of copyright notice "does not invalidate the copyright in a work." There appears to be no dispute that the design in question here falls within those circumstances. Kleier appears to argue that if its copyright could statutorily survive omission of copyright notice, then notice of that copyright, regardless of registration, must destroy Naegele's status as an "innocent infringer." In M. Kramer Mfg. Co., Inc. v. Andrews, 783 F.2d 421 (4th Cir.1986), the court recognized that "innocence" of the defendants was a question of fact. Nonetheless, the court reversed the trial court's determination that defendants were innocent infringers, holding that such a conclusion was clearly erroneous in the presence of evidence that defendants knew plaintiff was claiming a copyright in the game. The appellate court noted, inter alia, that defendants had received a letter from plaintiff stating plaintiff's copyright claim. The court observed, at page 447: [W]e find it impossible to conclude that the defendants relied on the lack of notice to conclude that the work was in the public domain.... While it may be that the defendants believed that Kramer did not own a valid copyright ... the evidence is clear that they were not misled by the lack of proper copyright notice when they knew that various parties were claiming copyrights in the game. In Canfield v. Ponchatoula Times, 759 F.2d 493 (5th Cir.1985), the court was primarily concerned with interpretation of the requirements of 17 U.S.C. Sec. 405(a). In the course of its analysis, the court noted the importance of reading sections (a) and (b) together in order to effectuate Congressional intent to encourage notice. The court observed, at pages 498-499, "A publisher who reprints an unnoticed work which falls within one of the 405(a) exceptions has the burden, under section 405(b), of proving good faith." In Wales Indus. Inc. v. Hasbro Bradley, Inc., 612 F.Supp. 510 (S.D.N.Y.1985), the court suggested that the question of whether an infringer is "innocent" is coterminous with the question of whether he acted with a good faith belief that the work was in the public domain. The court concluded that the infringer's "innocence" was a question of fact to be resolved at trial, since the infringer had received notification of the copyright claim. It is significant that the copyright was not recorded until after the litigation had begun; thus, the notification of the claim necessarily predated recording. Similarly, in Williams v. Arndt, 626 F.Supp. 571 (D.Mass.1985), registration of copyright was obtained only ten days prior to the filing of the litigation. This was not a factor in the court's consideration of the "innocence" issue. The court noted that the infringer had received a letter from the copyright claimant's attorney advising him "to stop selling the program because it was [plaintiff's] property," and held that the defendant had failed to satisfy his burden of proof that he "acted in good faith or reasonably relied upon the absence of a copyright notice." The court showed no concern with the date of registration, but relied on the rationale behind the subsection, which is that one acting "in good faith and with no reason to think otherwise" should be able to assume that a work bearing no copyright notice is in the public domain. 1976 U.S.Code Cong. & Admin. News 5659, 5764. 17 U.S.C. Sec. 408 clearly provides that registration is not required in order for a copyright to have validity. It seems clear that the overall thrust of the legislative scheme is to encourage copyright notice, not to punish copyright holders who fail to register their ownership. We cannot agree with Kleier that such a purpose would be furthered by withholding "innocent *143 infringer" status from anyone who fails to investigate or inquire before copying a work that appears to be in the public domain. On the other hand, we cannot agree with Naegele that such a purpose would be furthered by allowing "innocent infringer" status to be terminated only by formal registration. As we read 17 U.S.C. Sec. 405(b), there are five elements to an "innocent infringer" defense. The party desiring this protection must show (1) innocent infringement (2) in reliance on (3) an authorized copy (4) which omitted the copyright notice, and (5) that the party was misled by the omission. We believe that Naegele's statutory analysis errs in rendering the first requirement a nullity, melding it seamlessly with elements (2) and (5). On the present state of the record, we believe there is a genuine issue of fact as to whether Naegele's infringement was innocent, which we equate with having a good faith belief that the work was in the public domain. This dispute arises from such factors as the original source of the design, notification of Kleier's copyright claim, and the conflicting evidence regarding custom in the industry. The motion for partial summary judgment must be overruled. Turning now to plaintiff's motion for sanctions, we note that Naegele contends vigorously that sanctions are inappropriate. The Court has already compared the information requested during the discovery process with both the information provided then and the information proposed for introduction at trial. In continuing the trial, we expressed our belief that Naegele had not properly complied with its duties as a litigant during discovery. We continue to believe that determination was correct. The most extreme sanction would presumably have been that originally proposed, i.e., proceeding with trial and prohibiting the introduction of the new evidence. Instead, we agreed to continue the trial to allow defendant to use the evidence without unfair prejudice to plaintiff. As we explained at the time of the continuance, it is entirely appropriate that Naegele, having necessitated the continuance, should pay any additional expenses resulting from that continuance. We will sustain the request for sanctions and will make an award after the conclusion of the trial. At that time we will expect Kleier to be in a position to present its itemization of additional fees and expenses attributable to the continuance of the trial. Accordingly, IT IS ORDERED that defendant's motion for partial summary judgment is overruled. IT IS FURTHER ORDERED that plaintiff's motion for sanctions is sustained. IT IS FURTHER ORDERED that within ten days of the conclusion of the trial, plaintiff shall tender to the Court its request for fees and expenses attributable to the continuance of the trial. | Low | [
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Q: How to bind Observable Collection and Save to Database I will be doing an MVVM Project soon and I'm working a couple tutorial/examples out. How do I take the following code and connect it to a database. If I were to have a datagrid, how can I change information in the datagrid and have it automatically update? I'll be using MS SQL. Thanks for any tips or advice. Class Person Property _name As Integer Property Name As Integer Get Return _name End Get Set(value As Integer) _name = value RaisePropertyChanged("Name") End Set End Property End class Then in another class: Class Collections Public namelist As New ObservableCollection(Of Person) namelist.Add(New Person With {.Name = Nothing}) --- Then in XAML <ObjectDataProvider x:Key="test" ObjectType="{x:Type local:Collections}" <DataGrid ItemsSource="{Binding Source= {StaticResource test}}"> <DataGridTextColumn Header="Name" Binding="{Binding Sample, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" /> ect...ect....ect... Now where or how do I connect my MS SQL table to all this? A: IF you're using MVVM, then your bindings (if wired properly) will propagate changes you make in the GridView to the properties their bound too if you wire the events when a cell edit is finished, etc. Here's a source on that: http://www.dotnetcurry.com/ShowArticle.aspx?ID=563 I'm coming from a C# only background but, for instance if you have a property of an observable collection: public ObservableCollection<string> Collection {get; set;} on the ViewModel, if you had bound your view (the .xaml) to the VM by setting the DataContext of the View, and you had bound this OC to a combobox changing the selectedValue on the combobox would update the SelectedValue you bound to in the .xaml. So if you had chosen for this combobox to be bound on SelectedValue to a property: public string SelectedValue {get; set;} when you selected one of the choices in the combobox would update that value on the view model and it would step into the set portion of the property. The same goes for whatever you have bound to the GridView. If you have an ObservableCollection that your gridview binds too, you'll need to wire up the events on the view for when you feel a change should update the ViewModel and use the ICommand to propagate the change to the VM. Another question would be are you required to use VB? I know the frameworks that make MVVM easier like Caliburn.Micro are in C#, there must be some frameworks out there to make MVVM easy with VB. Although with what you're trying, basic MVVM wouldn't be that hard to setup, these frameworks usually save you time from having to wire up the bindings manually. | Mid | [
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Heparin and protamine use in peripheral vascular surgery: a comparison between surgeons of the Society for Vascular Surgery and the European Society for Vascular Surgery. It was the intent of this study to document, in general, the patterns and complications of heparin and protamine usage during carotid endarterectomy, aortic and femoral-popliteal-tibial reconstructions for occlusive disease, elective and emergent abdominal aortic aneurysmectomy, thromboembolectomy, and dialysis arteriovenous (AV) fistula placement by surgeons from North America and Europe. All vascular surgeons from the Society for Vascular Surgery (SVS) and the European Society for Vascular Surgery (ESVS) were surveyed by a voluntary, self-reported questionnaire. Six hundred and forty-six completed questionnaires (284 from SVS and 362 from ESVS), representing a 62% response rate, were returned for evaluation. Systemic and regional administration of heparin was common during vascular procedures performed by both SVS and ESVS surgeons. Use of protamine to reverse heparin anticoagulation varied among SVS and ESVS surgeons, respectively, during: carotid endarterectomy (54% vs. 26%, p < 0.01), elective aortic reconstruction for occlusive disease (58% vs. 23%, p < 0.001), elective aortic reconstruction for abdominal aortic aneurysm (63% vs. 27%, p < 0.001), and femoral-popliteal-tibial reconstruction (44% vs. 15%, p < 0.001). Adverse reactions to protamine among the 25,219 and 12,902 cases reported from SVS and ESVS surgeons, respectively, included: hypotension (1209 and 495 cases), pulmonary artery hypertension (65 and eight cases), anaphylaxis (52 and 10 cases), and death (seven and two cases). These adverse responses accounted for 5.3% and 4.0% of the SVS and ESVS cases, respectively. Although this study is subject to the known limitations of a retrospective survey, it is clear that heparin use is common. Protamine reversal of heparin anticoagulation is more common in North America.(ABSTRACT TRUNCATED AT 250 WORDS) | Mid | [
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SAN FRANCISCO (Reuters) - The biggest California gay rights advocacy group on Wednesday said it needed three years to build a coalition to repeal a ban on same-sex marriage in the state, creating a rift in the movement with those who want to go back to the polls next year while anger is hot. Gay couple Ethan Collings (L), 32, and his spouse Stephen Abate, 36, hug as they celebrate their one-year wedding anniversary in West Hollywood, California, June 16, 2009. REUTERS/Lucy Nicholson California, the most populous state and often a standard-bearer for social liberalism, is the biggest prize in U.S. culture wars. Its next fight over gay marriage is sure to draw in national organizations, cost $100 million or more, and may affect the next U.S. presidential campaign if it takes place in 2012. California’s November 2008 vote to ban same-sex marriage, months after the state’s top court legalized it, bolstered the power of social conservatives and sparked nationwide protests among gays and their allies. It was followed by legalization of gay marriage in a handful of mostly Northeastern states and a court challenge aimed at the U.S. Supreme Court. “It takes time, commitment and lots of lots of volunteers to undo the untruths that our opponents have been telling,” said Marc Solomon, marriage director of Equality California, in a conference call. “We can have majority support by 2012.” His group raised the most money and led the 2008 campaign against Proposition 8, which defines marriage as between a man and a woman and was approved by California voters. Big donors are not ready to fund a new fight so soon after failure, and a door-to-door campaign will take time, he said. A bigger turnout in the 2012 presidential election year, as well as more younger voters, will add 4 percentage points to the margin of victory, the group estimated. GRASS-ROOTS WON’T WAIT But smaller groups have said waiting will sap momentum among gays and their allies still smarting from the unexpected ballot results. They vowed to mount a 2010 challenge, which would coincide with federal mid-term elections. “This is not some kitchen table group. If you stop that momentum now, those people won’t necessarily be there in 2012 when you decide to start your campaign back up,” John Henning, executive director of Love Honor Cherish, said ahead of Equality California’s expected announcement. Henning’s group has a plan to gather more than a million signatures with volunteers and says a $32 million war chest would be enough to win the fight. The California debate reflects a national question over how solid opposition is to same-sex marriage. Many advocates say that exposure to stable same-sex couples and assurances that churches will not be forced to marry gays will convince a silent majority that anyone should be able to marry. But most states explicitly ban such gay unions, and have often done so by popular vote. Activism among gay rights groups has intensified since the November defeat in California, but social conservatives with deep pockets and legendary organizational skills are preparing for the next fight, too. “California will continuously stay in play and it is a big prize,” said Tom McClusky, vice president of the legislative arm of the Family Research Council, a conservative Christian lobby. “Of course we would be willing to go toe to toe again.” ProtectMarriage.com, which helped coordinate passage of the ban, scoffed at the division among gay marriage advocates. “While the other side issues many press releases about their activity, we are quietly but effectively building on our majority in California,” it said in a statement. Proponents of the 2010 challenge say the decision will be made from the bottom up and that big groups will join as a campaign plan is laid out and early efforts show success. “We’re in a movement era,” said Rick Jacobs, who chairs the Courage Campaign, which trains grass-roots organizers. The day after the California ban passed -- and after President Barack Obama was elected -- was a wake-up call for gay advocates, he said. “On the one hand they put an African American man in the White House when it was impossible. On the other hand they had their rights taken away.” He said his group has raised more than $100,000 in a few days for a fight to repeal the ban. Equality California said it would take a lot more money and said gay marriage opponents were raising money faster in Maine, which is likely to vote on gay marriage in November. “We are very concerned that $100,000 is not $50 million,” said Equality California Executive Director Geoff Kors, adding that he saw only one shot to win in the next two California elections. (Additional reporting by Ed Stoddard in Dallas) | Low | [
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either way he's not necessary to install ... and I'd actually recommend against using him as he has custom contrails which won't play well with all my characters installed, in addition to him displaying the old textures which will look out of place when using character retexture. Re: Anniversary Edition Seven is here! guys did you by any chance change the way mods are downloaded through the installer ? I know you were trying to make them faster, before not sure if that has anything to do with it. but for some reason the download just gets stuck at a certain point ... I'd usually blame my own internet but it's stable now and downloading at 50KB\s (which is the best speed I ever get). Re: Anniversary Edition Seven is here! Re: Anniversary Edition Seven is here! Hi all,I was wondering, AEI's source isn't published, right? Is there any way to obtain it and maybe contribute? I've read wiki and forums, but found no information about this, there were only just a few words about localization contributions. Re: Anniversary Edition Seven is here! Hi split2. It seems that we've accidentally hidden the code from people pretty well ^_^ See http://websvn.chrilly.net/listing.php?r … &path=%2F&, under the "java" directory. The actual repo is at svn.oni2.net. Obviously you'd need an account to make commits yourself, though if you specifically just want to contribute a localization, that won't really require an account since a localization is just composed of a group of plain-text files which you could email to Alloc to be added to the AEI. Sorry for the lack of documentation on that. What are you interested in contributing? Re: Anniversary Edition Seven is here! Cool, thanks. I thought I might be able to help out with some coding in C or Java. For now, I will dive in the sources and see how the things are working. You guys have pretty nice project going on here Re: Anniversary Edition Seven is here! Yep, I think Alloc did a pretty nice job with the AEI 2. So far he's the only one who's written code for it (as opposed to AEI 1, which Gumby and I worked on in C/C++), but I've been wondering lately if I shouldn't be getting into the code for AEI 2 as well, since there are a number of open bugs, and I don't think Alloc has the time to work on them. Re: Anniversary Edition Seven is here! JustSmile12 wrote: I like it but i have been curious because im spanish so i want to ask you ¿you will release a spanish version? thanks for the work and bring us a excelent support There're various game versions with different languages such as Japanese and German. If you can find a Spanish version somewhere it might work with the mod. AFAIK, someone found a Japanese voice pack for the game some time ago and it was released as a mod as well. Re: Anniversary Edition Seven is here! I think he's asking about the AE Installer. So far, it's only in German and English. It would be nice to support Spanish. I was just waiting for a response from Alloc before I replied to JustSmile12's question because I wanted to have something more substantial to say. But all that's needed for supporting a new language is to have someone translate some text files and then to distribute those with the AEI. Re: Anniversary Edition Seven is here! Guys we all know I've had quite a lot of issues with Samer. But as a general tip for everyone in response to post #230:For Windows, reset network settings by typing 'netsh winsock reset' in Run or CMD.exe then use Optimal setting from a utility TCPOptimizer. Install FoxSpeed Ultimate and run using '/accel' command in DOS prompt. Then use Xtreme Download Manager with your browser and set 32 connections instead of 8.OPEN EACH PROGRAM AS ADMINISTRATOR TO ENSURE ALL SETTINGS APPLY THE WAY THEY ARE INTENDED TO.And just in case you guys thought I was going off-topic, you could default to 32 or 64 connections in the downloader in the AE to put pressure on server instead of client (the PC).I'm writing this down in the bed at 6 am. Going to elaborate more and give more tips for enhancing the downloaded part of AE. Each one should contribute their tricks they know to make AE the best customiser for Oni. Re: Anniversary Edition Seven is here! FYI, Mono framework does not work in Mac OS X 10.11, I upgraded to the 10.11 beta, installed the latest Mono framework and got the error in the terminal mono: command not found. Doing some research, I found mention that the next update with Mono should fix this issue. Otherwise Oni seems to be working fine in 10.11 Re: Anniversary Edition Seven is here! It really depends on what kind of modding you want to do. We tried to write an introduction to modding here: http://wiki.oni2.net/Modding_Oni. It's not done, but it mentions the sort of tools to use for each kind of task. If you have a specific question about a modding task, you can make a thread in the Modifications forum. Re: Anniversary Edition Seven is here! Just an update for Mac users -- Mono still doesn't play nicely with 10.11 El Capitan, which released today. The Mono site claims to be serving a hotfix for El Capitan, but it's not serving the correct file (4.0.4.1 instead of 4.0.4.4), and when I change the provided URL to actually point to 4.0.4.4 and download that, it still doesn't make Mono available to the AE Installer (and I can see that the Mono binaries were not installed on the hard drive, so it's not the AEI at fault). I'd be interested to know if this supposed hotfix works for anyone else. The worst part is that simply upgrading to 10.11 clears any existing Mono installation from your system, so it's not like this issue only affects users who never installed Mono before 10.11. | Low | [
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A hospital you never ever want to be admitted to. We all have that one wacko job for a relative or friend. Multiply that by like 300 and stick them all in a tiny room painted baby blue and make them talk about the issues they have and watch them go. It's like playing a game of stick the yellow shapes in the right spots and wait for the red box to explode and blow pieces everywhere. If you live near one I suggest you move because the crazy ass-holes break out the glass and run free. Then it is like playing a game of "Where's Weirdo". I worked at one and I will say that I could not wait to get to work. There was never a dull moment. If you love caos and mayhem you really should consider a career at the nut house. Working at a psychiatric hospital is like having a year longpassto the freak show. | Low | [
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Interfaith meeting shows support for Western Massachusetts Muslims WEST SPRINGFIELD — Before an overflow crowd at the Islamic Center of Western Massachusetts, speakers from different faiths and from law enforcement on Thursday night spoke in support of followers of the Islamic faith and against those who commit acts of terror in the name of Islam. More than 250 people packed the hall. Organizers continued to add seats throughout the program as more people entered the back of the hall. The interfaith meeting was intended to bring people of different faiths together in the spirit of unity, and to push back against the wave of what was called “anti-Islamic rhetoric” in the media and even on the presidential stump by those who equate the religion with acts of Islamic extremists committing acts of terror. West Springfield Mayor Will Reichelt spoke briefly, as did school superintendent Michael Richard. Each said the town of West Springfield is committed to acceptance of people of all faiths and backgrounds. Northwestern District Attorney David E. Sullivan also was present but did not speak. Zubair Kareem, president of the Islamic Society of Western Massachusetts, said the numbers of the crowd in attendance and the diversity of faiths and faces was spoke of the hope and acceptance that many Muslims are looking for in American culture today. For all the hateful rhetoric directed at the religion, Kareem said, “We have received many messages of kindness, support and hope.” Rev. Martin Pion of the Roman Catholic Diocese of Springfield, also head of the Interfaith Council of Western Mass., said the level of anti-Islamic rhetoric that fills the airwaves makes this “a very critical time.” “It is important for everyone to know of the many, many people, of many voices who support the Islamic community, across the United States and across the world,” he said. “As we observe what is happening, we recognize the need to do something.” He read a statement from Bishop Mitchell T. Rozanski of the Diocese of Springfield: “To compromise the right of any one religion is to compromise the rights of all religions.” “In the face of so much negativity, this outpouring of positivity is outstanding.” John Robbins of the Boston chapter of the Council of American Islamic Relations (CAIR), the country’s largest advocacy group for Muslims, said the organization has been pressed lately in its goal of pushing back against Islamic discrimination in the mass media. “We’ve been very busy lately. Very busy,” he said. “In the face of so much negativity, this outpouring of positivity is outstanding,” he said. Rabbi Mark Shapiro of Sinai Temple spoke briefly about how Jews, Muslims, and Christians are all different, but all three have common roots that go back to the creation of the world in the Book of Genesis. “Yes, we have differences, but differences are simply that,” he said. “Different is not meant to be frightening.” Kevin O’Regan, the head of the U.S. Attorney’s Office in Springfield, and Julia Cowley, of the FBI office in Boston, each told the crowd that the U.S. Justice Department is committed to protecting everyone equally, regardless of faith. O’Regan said he first came in contact with the Islamic Center of Western Massachusetts in the days after the 9/11 terrorist attacks. He said he knew little of the Islamic faith, but came to know the people at the center. The U.S. Attorney investigates and has prosecuted people “who act in the name of Islam,” he said. He said those acts have been horrific on many levels, but he said because of his relationships with the people at the center, he has come to see that regardless of what terrorists claim, their actions do not represent Islam. Cowley said the FBI is committed to investigating and prosecuting any civil rights violations, and that includes against Muslims. She said one of her reasons for attending was to let people see the face behind the phone number on her business card. “We will help you if you ask for it,” she said. | Mid | [
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When McDaniels stayed in New England, pulling out of the Colts job at the last minute, so did O’Shea. This year, O’Shea was reportedly a candidate for the Lions offensive coordinator opening, potentially joining former Patriots assistant Matt Patricia, but he never interviewed for the position that was filled by the hiring of Darrell Bevell last week. | Low | [
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/* This file was generated by SableCC's ObjectMacro. */ package org.sablecc.objectmacro.codegeneration.c.macro; public class MParamParam { private final String pName; private final MParamParam mParamParam = this; MParamParam( String pName) { if (pName == null) { throw new NullPointerException(); } this.pName = pName; } String pName() { return this.pName; } private String rName() { return this.mParamParam.pName(); } @Override public String toString() { StringBuilder sb = new StringBuilder(); sb.append("char* _p"); sb.append(rName()); sb.append("_"); return sb.toString(); } } | Low | [
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Q: Redirect after login? in my Grails app I have a couple of simple security filters (please note it's just a prototype, not a commercial app: securityCheckFilter(controller:'overview', invert:true) { before = { if(!session?.gaSession?.gaUser) { flash.message = "You are not authorised to see this page. Please login." redirect(controller:'overview',action:'login') return false } return true } } Which means that, apart from the controller 'overview' that handles the login/registration, all the other controllers require authentication. The problem is that I'd like to implement this typical flow: (1) user tries protected url (2) redirection to login (3) successful login (4) redirection to url In my code it works until point 3, but I'm missing 4. Any hints? A: It's actually quite easy. Just submit the target URI (from point 1 in your question) as a parameter to the login action/view make sure your login form forwards this parameter to the authentication action (eg. via a hidden field) in the authentication action, if the login was successful, just redirect to this URI To get the target URI (in your filter), just remove the context path from the forward URI: def targetURI = request.forwardURI - request.contextPath | Mid | [
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16
] |
Q: ng-repeat over a non-array/object / dealing with arrays and non-arrays the same way Often times I want to deal with both arrays and single objects in the same fashion. For example I have the property of an object that can either be an array or just a string (look at the scale property): [ { "name": "Experiment type14", "id": "00000000014", "scale": ["Whole Brain", "Cell"], }, { "name": "Experiment type15", "id": "00000000015", "scale": "Cell", } ] What I want is to show my scale like here: <span ng-repeat="scale in experimentType.scale"> <!--some decoration here--> {{scale}} </span> Of course this won't work for a single string values. Is there any elegant way not to worry whether I'm dealing with a string or with an array? A: You can create your custom filter, please see below var app = angular.module("app", []);
function MainCtrl() {
this.message = "Welcome";
this.data = [{
"id": "00000000014",
"name": "Experiment type14",
"scale": ["Whole Brain", "Cell"],
},{
"id": "00000000015",
"name": "Experiment type15",
"scale": "Cell",
}];
}
function toArray() {
return function(input) {
console.log(input);
if (angular.isArray(input)) {
return input;
} else {
return [input];
}
};
}
angular.module("app").controller("MainCtrl", MainCtrl);
angular.module("app").filter('toArray', toArray); <script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script>
<body ng-app="app">
<div ng-controller="MainCtrl as vm">
<div class="container">
<h3>{{ vm.message }}</h3>
<div ng-repeat="item in vm.data">
<p>{{ item.name }}</p>
<ul>
<li ng-repeat="scale in item.scale | toArray">{{ scale }}</li>
</ul>
</div>
</div>
</div>
</body> | High | [
0.663608562691131,
27.125,
13.75
] |
Iran's Supreme Leader says the government's economic policies have fallen short and called for a new "resistance economy" to create jobs, piling pressure on President Hassan Rouhani before the presidential election in May. "I feel the pain of the poor and lower class people with my soul, especially because of high prices, unemployment and inequalities," Ayatollah Ali Khamenei said in his New Year's message on Monday. "The government has taken positive steps, but they do not meet people’s expectations and mine," he added, setting out a clear battle line before the presidential vote. READ MORE: Iran after Khamenei The New Year, or Nowruz, is the country's most important national event. Hardliners led by Khamenei have repeatedly criticised Rouhani, particularly for the terms of a nuclear deal he reached with world powers, which lifted economic sanctions and was supposed to boost the economy. Unemployment stood at 12.4 percent in this fiscal year, according to the Statistical Centre of Iran, up 1.4 percent from the previous year. About 3.2 million Iranians are jobless, out of a total population of 80 million. "I call the new year a year of resistance economy, production and employment," Khamenei said in the pre-recorded video broadcast on state television. Khamenei coined the term "resistance economy" to describe measures to make Iran's economy more self-sufficient, in contrast to Rouhani's policy of seeking to open Iran to more international trade and investment. 'Unprecedented' growth In his New Year's message, Rouhani touted the economic achievements of his government and called for citizens' rights to be respected, points likely to resonate with his supporters in the approaching election. "What we achieved in curbing inflation [and boosting] economic growth and jobs in the past year was unprecedented in the past 25 years," Rouhani said in a video message aired on state TV. Khamenei's latest criticism came as a number of prominent political figures, including Ayatollah Ahmad Jannati, the head of a body that selects Iran's supreme leader, also criticised Rouhani for his economic policies. But conservatives, who hope to stop Rouhani winning a second four-year term, have yet to identify their presidential candidate. "Mr Rouhani can't expect the Supreme Leader to take his side in the elections. The past has shown that the position of the Supreme Leader is more independent," said Saeed Leylaz, a Tehran-based political analyst who worked as an adviser to former president Mohammad Khatami. "After this new year period, Mr Rouhani can expect to face a lot of pressure and criticism." Despite the lifting of international sanctions, the world's top banks have refrained from doing business with Iran over fears of being penalised by US sanctions that have remained in place despite the nuclear deal. This has slowed Iran's efforts to rebuild its foreign trade and lure investment. Although inflation dropped to single digits and real GDP grew by as much as 7.4 percent, the IMF reported in February that "growth in [Iran's] non-oil sector averaged 0.9 percent ... reflecting continued difficulties in access to finance". "Aware of people's economic woes, Ayatollah Khamenei is trying to distance himself from [Rouhani's] government and move to the people's side, minimising responsibility," said Hossein Rassam, former Iran adviser to Britain's Foreign Office. | Mid | [
0.56115107913669,
29.25,
22.875
] |
/* * Copyright (C) 2013 [email protected] * * This program is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program. If not, see <http://www.gnu.org/licenses/>. */ package service; import burp.IInterceptedProxyMessage; import burp.IProxyListener; import gui.SentinelMainApi; import model.SentinelHttpMessage; import model.SentinelHttpMessageOrig; import util.BurpCallbacks; /** * * @author [email protected] */ public class SentinelProxyListener implements IProxyListener { private Boolean next2Repeater = false; private Boolean next2Sentinel = false; @Override public void processProxyMessage(boolean messageIsRequest, IInterceptedProxyMessage message) { if (messageIsRequest) { processRequest(message); } else { processResponse(message); } } private void processResponse(IInterceptedProxyMessage message) { } private void processRequest(IInterceptedProxyMessage message) { if (next2Repeater) { SentinelHttpMessage httpMessage = new SentinelHttpMessageOrig(message.getMessageInfo()); BurpCallbacks.getInstance().getBurp().sendToRepeater( httpMessage.getHttpService().getHost(), httpMessage.getHttpService().getPort(), (httpMessage.getHttpService().getProtocol().equals("http") ? false : true), httpMessage.getRequest(), ""); next2Repeater = false; } if (next2Sentinel) { SentinelHttpMessage httpMessage = new SentinelHttpMessageOrig(message.getMessageInfo()); //SentinelMainUi.getMainUi().addNewMessage(httpMessage); SentinelMainApi.getInstance().addNewMessage(httpMessage); next2Sentinel = false; } sentinelCheck(message); } private void sentinelCheck(IInterceptedProxyMessage message) { SentinelHttpMessage msg = new SentinelHttpMessageOrig(message.getMessageInfo()); String url = msg.getReq().getUrl().toString(); if (url.startsWith("http://sentinel")) { if (url.contains("nextToRepeater")) { next2Repeater = true; } if (url.contains("nextToSentinel")) { next2Sentinel = true; } if (url.contains("enableIntercept")) { BurpCallbacks.getInstance().getBurp().setProxyInterceptionEnabled(true); } if (url.contains("disableIntercept")) { BurpCallbacks.getInstance().getBurp().setProxyInterceptionEnabled(false); } // Removed, because did not really remove request // message.getMessageInfo().setRequest("GET http://burp/ HTTP1.1\r\nHost: burp\r\n\r\n".getBytes()); message.setInterceptAction(IInterceptedProxyMessage.ACTION_DROP); } } } | Low | [
0.5167652859960551,
32.75,
30.625
] |
Eosinophilia in infants with food protein-induced enterocolitis syndrome in Japan. Many Japanese infants with food protein-induced enterocolitis syndrome (FPIES) show eosinophilia, which has been thought to be a characteristic of food protein-induced proctocolitis (FPIP). To elucidate the characteristics of eosinophilia in Japanese FPIES patients, 113 infants with non-IgE-mediated gastrointestinal food allergy due to cow's milk were enrolled and classified into FPIES (n = 94) and FPIP (n = 19). The percentage of peripheral blood eosinophils (Eo) was increased in most FPIES patients (median, 7.5%), which was comparable with that in FPIP patients (9.0%). Among FPIES patients, Eo was the highest in patients who had vomiting, bloody stool, and diarrhea simultaneously (12.9%) and lowest in patients with diarrhea alone (3.2%). Eo showed a significant positive correlation with the incidence of vomiting (Cramer's V = 0.31, p < 0.005) and bloody stool (Cramer's V = 0.34, p < 0.0005). A significant difference was found in Eo between early- (≤10 days, n = 56) and late-onset (>10 days, n = 38) FPIES (median, 9.8% vs. 5.4%; p < 0.005). IL-5 production by peripheral blood T cells stimulated with cow's milk protein in early-onset FPIES was significantly higher than that in late-onset FPIES (67.7 pg/mL vs. 12.5 pg/mL, p < 0.01), and showed a significant positive correlation with Eo (rs = 0.60, p < 0.01). This study demonstrated two types of eosinophilia in Japanese FPIES infants: conspicuous and mild eosinophilia in early- and late-onset FPIES patients, respectively. Conspicuous eosinophilia in early-onset FPIES is suggested to be caused by abnormally high IL-5 production. | High | [
0.7038834951456311,
36.25,
15.25
] |
/**************************************************************************************** * 701 * MegaTronics v2.0 ****************************************************************************************/ //###CHIP #if DISABLED(__AVR_ATmega2560__) #error "Oops! Select 'Arduino Mega 2560' in 'Tools > Board.'" #endif //@@@ #define KNOWN_BOARD 1 //###BOARD_NAME #if DISABLED(BOARD_NAME) #define BOARD_NAME "Megatronics" #endif //@@@ //###X_AXIS #define ORIG_X_STEP_PIN 26 #define ORIG_X_DIR_PIN 27 #define ORIG_X_ENABLE_PIN 25 #define ORIG_X_CS_PIN NoPin //###Y_AXIS #define ORIG_Y_STEP_PIN 4 #define ORIG_Y_DIR_PIN 54 #define ORIG_Y_ENABLE_PIN 5 #define ORIG_Y_CS_PIN NoPin //###Z_AXIS #define ORIG_Z_STEP_PIN 56 #define ORIG_Z_DIR_PIN 60 #define ORIG_Z_ENABLE_PIN 55 #define ORIG_Z_CS_PIN NoPin //###EXTRUDER_0 #define ORIG_E0_STEP_PIN 35 #define ORIG_E0_DIR_PIN 36 #define ORIG_E0_ENABLE_PIN 34 #define ORIG_E0_CS_PIN NoPin #define ORIG_SOL0_PIN NoPin //###EXTRUDER_1 #define ORIG_E1_STEP_PIN 29 #define ORIG_E1_DIR_PIN 39 #define ORIG_E1_ENABLE_PIN 28 #define ORIG_E1_CS_PIN NoPin #define ORIG_SOL1_PIN NoPin //###EXTRUDER_2 #define ORIG_E2_STEP_PIN 23 #define ORIG_E2_DIR_PIN 24 #define ORIG_E2_ENABLE_PIN 22 #define ORIG_E2_CS_PIN NoPin #define ORIG_SOL2_PIN NoPin //###EXTRUDER_3 #define ORIG_E3_STEP_PIN NoPin #define ORIG_E3_DIR_PIN NoPin #define ORIG_E3_ENABLE_PIN NoPin #define ORIG_E3_CS_PIN NoPin #define ORIG_SOL3_PIN NoPin //###EXTRUDER_4 #define ORIG_E4_STEP_PIN NoPin #define ORIG_E4_DIR_PIN NoPin #define ORIG_E4_ENABLE_PIN NoPin #define ORIG_E4_CS_PIN NoPin #define ORIG_SOL4_PIN NoPin //###EXTRUDER_5 #define ORIG_E5_STEP_PIN NoPin #define ORIG_E5_DIR_PIN NoPin #define ORIG_E5_ENABLE_PIN NoPin #define ORIG_E5_CS_PIN NoPin #define ORIG_SOL5_PIN NoPin //###EXTRUDER_6 #define ORIG_E6_STEP_PIN NoPin #define ORIG_E6_DIR_PIN NoPin #define ORIG_E6_ENABLE_PIN NoPin #define ORIG_E6_CS_PIN NoPin #define ORIG_SOL6_PIN NoPin //###EXTRUDER_7 #define ORIG_E7_STEP_PIN NoPin #define ORIG_E7_DIR_PIN NoPin #define ORIG_E7_ENABLE_PIN NoPin #define ORIG_E7_CS_PIN NoPin #define ORIG_SOL7_PIN NoPin //###ENDSTOP #define ORIG_X_MIN_PIN 37 #define ORIG_X_MAX_PIN 40 #define ORIG_Y_MIN_PIN 41 #define ORIG_Y_MAX_PIN 38 #define ORIG_Z_MIN_PIN 18 #define ORIG_Z_MAX_PIN 19 #define ORIG_Z2_MIN_PIN NoPin #define ORIG_Z2_MAX_PIN NoPin #define ORIG_Z3_MIN_PIN NoPin #define ORIG_Z3_MAX_PIN NoPin #define ORIG_Z4_MIN_PIN NoPin #define ORIG_Z4_MAX_PIN NoPin #define ORIG_Z_PROBE_PIN NoPin //###SINGLE_ENDSTOP #define X_STOP_PIN NoPin #define Y_STOP_PIN NoPin #define Z_STOP_PIN NoPin //###HEATER #define ORIG_HEATER_HE0_PIN 9 #define ORIG_HEATER_HE1_PIN 8 #define ORIG_HEATER_HE2_PIN NoPin #define ORIG_HEATER_HE3_PIN NoPin #define ORIG_HEATER_HE4_PIN NoPin #define ORIG_HEATER_HE5_PIN NoPin #define ORIG_HEATER_BED0_PIN 10 #define ORIG_HEATER_BED1_PIN NoPin #define ORIG_HEATER_BED2_PIN NoPin #define ORIG_HEATER_BED3_PIN NoPin #define ORIG_HEATER_CHAMBER0_PIN NoPin #define ORIG_HEATER_CHAMBER1_PIN NoPin #define ORIG_HEATER_CHAMBER2_PIN NoPin #define ORIG_HEATER_CHAMBER3_PIN NoPin #define ORIG_HEATER_COOLER_PIN NoPin //###TEMPERATURE #define ORIG_TEMP_HE0_PIN NoPin #define ORIG_TEMP_HE1_PIN NoPin #define ORIG_TEMP_HE2_PIN NoPin #define ORIG_TEMP_HE3_PIN NoPin #define ORIG_TEMP_HE4_PIN NoPin #define ORIG_TEMP_HE5_PIN NoPin #define ORIG_TEMP_BED0_PIN NoPin #define ORIG_TEMP_BED1_PIN NoPin #define ORIG_TEMP_BED2_PIN NoPin #define ORIG_TEMP_BED3_PIN NoPin #define ORIG_TEMP_CHAMBER0_PIN NoPin #define ORIG_TEMP_CHAMBER1_PIN NoPin #define ORIG_TEMP_CHAMBER2_PIN NoPin #define ORIG_TEMP_CHAMBER3_PIN NoPin #define ORIG_TEMP_COOLER_PIN NoPin //###FAN #define ORIG_FAN0_PIN 7 #define ORIG_FAN1_PIN 6 #define ORIG_FAN2_PIN NoPin #define ORIG_FAN3_PIN NoPin #define ORIG_FAN4_PIN NoPin #define ORIG_FAN5_PIN NoPin //###SERVO #define SERVO0_PIN NoPin #define SERVO1_PIN NoPin #define SERVO2_PIN NoPin #define SERVO3_PIN NoPin //###SAM_SDSS #define SDSS NoPin //###MAX6675 #define MAX6675_SS_PIN NoPin //###MAX31855 #define MAX31855_SS0_PIN NoPin #define MAX31855_SS1_PIN NoPin #define MAX31855_SS2_PIN NoPin #define MAX31855_SS3_PIN NoPin //###LASER #define ORIG_LASER_PWR_PIN NoPin #define ORIG_LASER_PWM_PIN NoPin //###MISC #define ORIG_PS_ON_PIN 12 #define ORIG_BEEPER_PIN NoPin #define LED_PIN 13 //###UNKNOWN_PINS #define SHIFT_CLK 63 #define SHIFT_LD 42 #define SHIFT_OUT 17 #define SHIFT_EN 17 //@@@ //###IF_BLOCKS #if TEMP_SENSOR_HE0 == -1 //thermocouple with AD595 or AD597 #define ORIG_TEMP_HE0_PIN 4 #else #define ORIG_TEMP_HE0_PIN 13 #endif #if TEMP_SENSOR_HE1 == -1 //thermocouple with AD595 or AD597 #define ORIG_TEMP_HE1_PIN 8 #else #define ORIG_TEMP_HE1_PIN 15 #endif #if TEMP_SENSOR_BED0 == -1 //thermocouple with AD595 or AD597 #define ORIG_TEMP_BED0_PIN 8 #else #define ORIG_TEMP_BED0_PIN 14 #endif #if HAS_GRAPHICAL_LCD #if ENABLED(U8GLIB_ST7920) #define LCD_PINS_RS 56 #define LCD_PINS_ENABLE 51 #define LCD_PINS_D4 52 #define BTN_EN1 44 #define BTN_EN2 45 #define BTN_ENC 33 #endif #else #define LCD_PINS_RS 32 #define LCD_PINS_ENABLE 31 #define LCD_PINS_D4 14 #define LCD_PINS_D5 30 #define LCD_PINS_D6 39 #define LCD_PINS_D7 15 #define SHIFT_CLK 43 #define SHIFT_LD 35 #define SHIFT_OUT 34 #define SHIFT_EN 44 //buttons are directly attached using keypad #define BTN_EN1 44 #define BTN_EN2 45 #define BTN_ENC 33 #define BLEN_C 2 #define BLEN_B 1 #define BLEN_A 0 #endif //@@@ | Low | [
0.5343680709534361,
30.125,
26.25
] |
Vitamin D receptor and growth inhibition by 1,25-dihydroxyvitamin D3 in human malignant melanoma cell lines. The expression of vitamin D receptors (VDR) and growth inhibition induced by 1,25-dihydroxyvitamin D3 have been noted in certain human malignant melanoma cell lines. In this study, widely disparate levels of VDR mRNA expression were demonstrated in a panel of eight human malignant melanoma cell lines. Quantitation of receptor level by ligand binding assay showed a similar pattern. Proliferation and growth curve analysis was performed in two cell lines: RPMI 7951 (high VDR) and SK-MEL-28 (low VDR). Significant growth inhibition was noted in RPMI 7951 cells at 10(-9) M 1,25-dihydroxyvitamin D3. SK-MEL-28 cells, which express much lower levels of VDR, did not show any growth inhibition except at extremely high concentrations of 1,25-dihydroxyvitamin D3, namely 10(-5) M. These findings suggest a receptor-mediated mechanism of growth inhibition for 1,25-dihydroxyvitamin D3 and a role for this hormone in the growth of malignant melanoma cells. | High | [
0.6682926829268291,
34.25,
17
] |
The present disclosure relates generally to electronic displays. This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. Liquid crystal displays (LCDs) are commonly used as screens or displays for a wide variety of electronic devices, including consumer electronics such as televisions, computers, and handheld devices (e.g., cellular telephones, audio and video players, gaming systems, and so forth). Such LCD devices typically provide a flat display in a relatively thin package that is suitable for use in a variety of electronic goods. In addition, such LCD devices typically use less power than comparable display technologies, making them suitable for use in battery powered devices or in other contexts where it is desirable to minimize power usage. Typically, LCD panels include an array of pixels for displaying images. Image data related to each pixel may be sent by a processor to the LCD panel through a driver integrated circuit (IC). The driver IC then processes the image data and transmits corresponding voltage signals to the individual pixels. Typically, the method by which the driver IC receives and processes the image data is well suited for receiving certain types of image data, such as video images for example, but not as well suited for receiving other types of image data, such as still images. | Mid | [
0.5647058823529411,
36,
27.75
] |
Opioid Addiction Resources Opioids can be abused. Addiction refers to a problematic or unhealthy use of a substance. The harms from abusing opioids can range from mild to severe. Tolerance and addiction are not the same. Tolerance is when an individual requires more of a medication to get the same result as their body has become used to it. Tolerance happens with many differnet types of medications, not just opioids. 4 people found this helpful Print Share Save Addiction can be explained using the 4 C. Craving. An individual craves the use of the drug. This is not the same as wanting to reduce their pain level. Control. A individual loses control over the amount and frequency of use. They are not able to take a prescription as prescribed and would consistency run out of pills early. Compulsion. An individual has a compulsion to use the drug. This would be using the mediation even if there were no pain or no breakthrough pain. Consequences. An individual continues to use the medication despite the consequences of use. So, they continue to use it despite family issues, despite no longer being able to get the medication from a doctor or in any legal way. Addiction occurs as a result of many factors. These factors include: genetics, environment, mental health issues, coping with difficult situations and how the medication interacts with the brain. An individual may turn to illicit sources when they are refused by their doctor. The danger of illegal drugs is that they may contain contaminants and much stronger opioids. Other concerning activities includes consuming the medication in a different way from how it would be normally prescribed. Crushing the pill so that it can be snorted or injected are examples and have lead to the development of abuse-resistant medications. Finding resources for individuals who have chronic pain and have concerns about opioid addiction can be difficult. The Substance Abuse & Mental Health Services Administration National Helpline is a free, confidential, 24/7, 365-day-a-year treatment referral and information service (in English and Spanish) for individuals and families facing mental and/or substance use disorders. 1-800-662-HELP (4357) | High | [
0.6716049382716051,
34,
16.625
] |
IN THE SUPERIOR COURT OF THE STATE OF DELAWARE DOUGLAS S. DREWS, Appellant, v. C.A. Nl6A-03-001 AML DIVISION OF UNEMPLOYl\/[ENT INSURANCE & UNEMPLOYMENT INSURANCE APPEAL BOARD, Appellees. Submitted: January 12, 2017 Decided: April l9, 2017 ORDER On appeal from the Unemployment Insurance Appeal Board: AFFIRMED l. This is one of two appeals Douglas S. Drews has taken from two separate Unemployment Insurance Appeal Board (the “Board”) decisions after remand The Board’s decision found that the claimant received an overpayment of unemployment benefits The claimant argues, as he did to the Board, that he did not receive an overpayment of benefits based on his calculations. The question is Whether the Board’s decision is supported by substantial evidence and free from legal error. For the reasons that follow, l conclude it is. 2. On March 4, 2015, a claims deputy determined Drews received a “non-fraudulent overpayment” totaling $135.00 over a five-Week period.l Drews timely appealed that decision on March 9, 2015.2 On April 27, 2015, an appeals referee held a hearing.3 3. On April 27, 2015, the appeals referee issued a decision affirming the claims deputy’s determination that Drews Was overpaid by 3135.00.4 The appeals referee determined that although Drews contended he fully reported his earnings, his calculations “do[] not match With the requirement that the overall amount be divided equally over the Weeks at issue, in accordance With the regulations.”5 DreWs timely appealed the appeals referee’s decision to the Board on April 29, 2015.6 4. The Board held a hearing on June 10, 2015.7 On July 6, 2015, the Board affirmed the appeals referee’s decision, finding Drews liable for the $135.0() overpayment8 Drews timely appealed the Board’s decision to this Court. 5. Drews’ appeal Was assigned to another member of this Court, Who affirmed the Board’s decision that Drews is liable to repay the overpayment of ' R. at l. 2 1a ar 3. 3 Id. at 13. 4 ld. at 26-28. 5 1a at 27. 6 1a at 37. 7 Id. at 40. 8 ld. at48. unemployment benefits that he received, but reversed and remanded the case back to the Board to specify how the $135.00 overpayment Was calculated9 6. On remand, the Board determined Drews received an overpayment of $130.00 in unemployment benefits.lo The Board’s March 3, 2016 decision details its calculations, indicating Drews Was overpaid $26.00 a Week, rather than 51327.00.ll The Board explained the discrepancy Was “due to an error in rounding the original calculation.”12 7. On March 4, 2016, Drews again timely appealed the Board’s decision 3 to this Court.' Drews continues to dispute the manner in Which the overpayment should be calculated and maintains he does “not owe any money [because] all earned income Was noted/claimed.”14 In response, the Division of Unemployment Insurance (the “Division”) argues that this Court already rejected Drews’ Way of calculating the benefits he received and therefore the only issue on remand is Whether the record supports the calculation of the overpayment amount. The Division contends that the Board’s March 3, 2016 decision specifies how the 9 ld. 3170-71. '0 la at 72. " 1a at 73. 12 Id. See 19 Del. C. § 3313(m), requiring: “Such sum, if not an even dollar, shall be rounded down to the next Whole dollar.” 13 R. at 78. Due to a conflict that arose for the judge who heard Drews’ first appeal, this second appeal after remand Was re-assigned. D.I. lO. ' R. at 79. overpayment amount was calculated, and therefore the decision should be af`firmed.15 8. This Court’s review of the Board’s decision is limited to whether the Board’s findings were supported by substantial evidence and whether the decision 6 Substantial evidence is “relevant evidence that a is free from legal error.1 reasonable mind might accept as adequate to support a conclusion.”17 The Court will not weigh evidence, determine questions of credibility, or make its own factual findings and conclusions18 9. This appeal is limited to calculating the overpayment amount. Drews does not dispute the Board’s calculations based on the statute’s equation. Rather, he continues to maintain that his way of calculating unemployment benefits makes more sense under his circumstances and therefore is the correct way. That argument, however, previously was considered and rejected by this Court.19 I therefore only am considering whether the Board’s calculation of overpayment benefits is supported by substantial evidence and free from legal error. 15 Division’s Answering Br. 2. The Board did not file an answering brief, asserting that the “underlying case was decided on the merits” and “the Appellant raises only challenges to the Board’s decision on the merits.” D.I. 9. 16 Thompson v. Christiana Care Heallh Sys., 25 A.3d 778, 781-82 (Del. 2011); Deysher v. Unemployment Ins. Appeal Ba’., 2011 WL 7063475, at *1 (Del. Super. Sept. 28, 2011) (citing Olney v. Cooch, 425 A.2d 610, 614 (Del. 1981)) (defining substantial evidence as “evidence from which the Board could fairly and reasonably reach its conclusion”). '7 Murphy & L¢ma'@n, P.A. v. Pemzc, 121 A.3d 1215, 1221 (De1.2015). ’8 Thompson, 25 A.3d 31782. '° R. 3170. 10. To keep things in perspective: the Division has opposed appeals in this matter twice over a $130.00 non-fraudulent overpayment One begins to wonder if it is in the State’s best interest to expend this level of resources to recoup a relatively small sum, Nevertheless, this Court must decide the cases that come before it. On remand, the Board specifically illustrated how unemployment benefits are calculated under 19 Del. C. § 3313(m).20 Using the weekly compensation Drews reported ($295.00), and the weekly compensation he should have reported ($321.43), the Board determined Drews was overpaid by $26.00 a week. The Board also explained how an error in rounding in the original calculation resulted in $27.00 a week for a total of $135.00 for five weeks.21 Based on the present record, the Board’s decision is supported by substantial evidence and free from legal error. For the foregoing reasons, the Unemployment lnsurance Appeal Board’s l\/Iarch 3, 2016 decision is AFFIRMED. IT IS SO ORDERED. M Abigzi`rl M. LeGrow, Jiidge Original to Prothonotary cc: Paige J. Schmittinger, Deputy Attorney General Victoria W. Counihan, Deputy Attorney General l\/lr. Douglas S. Drews, pro se (via First Class Mail) 201¢1. a173. 21 Id | Low | [
0.5375302663438251,
27.75,
23.875
] |
Attack Tories not Corbyn, Unison union left challenger John Burgess hits out by Raymie Kiernan Published Tue 24 Nov 2015 Issue No. 2481 John burgess, the left candidate for Unison union general secretary, has criticised incumbent Dave Prentis’ “thinly veiled attack” on Labour leader Jeremy Corbyn. Prentis told the Sun on Sunday newspaper, “Divisive rows over Trident or shoot to kill are distractions no one needs. “Arguing against austerity is what Labour should have been doing this week”. John questioned Prentis “providing ammunition to Corbyn’s enemies in the pages of the Murdoch empire’s flagship paper”. He said, “Perhaps Mr Prentis has forgotten News International’s smashing of the print unions at Wapping.” He asked if Prentis had “suddenly discovered the Sun supporting our members against the Tories’ attacks?” As general secretary John said he would have different priorities. He would be questioning why the Tories can suddenly find money for 2,000 extra spies and bomb Syria while slashing fire and ambulance services. | Mid | [
0.544303797468354,
32.25,
27
] |
Q: Difference between LEA and MOVE.L? Are there any differences between LEA $1000,A0 and MOVE #$1000,A0 to put an address in the address registry? A: In this case, there will be no observable difference (unlike the accepted answer claims - the MOVE example will assemble as MOVEA which does not alter the CCR, see M68K Reference Manual Pg 4-116 to 4-120). A: The lea instruction does not affect flags, where the move instruction does. Specifically Z and C will be cleared after the move #$1000,a0. A: Durandal is correct, operations involving an address register have generally no impact on the processor flags, in this particular case the two instructions will behave the same and take the exact same cpu time (8 cycles using short addressing mode or 12 using long mode). MOVE xx,an is not a real instruction, it's something assemblers allow but if you look at the disassembled result you will see that that the actual instruction is MOVEA. | Mid | [
0.6132075471698111,
32.5,
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Mario Tozzi Mario Tozzi (30 October 1895 – 8 September 1979) was an Italian painter. He was awarded the Legion of Honour by the French government. Biography Tozzi studied at the Accademia di Belle Arti di Bologna in Italy where he met Giorgio Morandi and Osvaldo Licini. He graduated in 1916. After the First World War, he moved to Paris, France and founded the Groupe des Sept (also known as Les Italiens de Paris ) with Massimo Campigli, Giorgio de Chirico, Filippo de Pisis, Renato Paresce, Alberto Savinio and Gino Severini. Tozzi returned to Rome in 1936. His work was exhibited at the Venice Biennale in 1938, 1942, 1948, 1952 and 1954. He returned to France in 1971, dying there in 1979. A catalogue raisonné of his paintings was published In 1988 by Giorgio Mondadori Editore and edited by Marilena Pasquali. Public collections Centre Georges Pompidou, Paris, France Museum of Fine Arts of Lyon, Lyon, France Museum of Fine Arts Bern, Bern, Switzerland Pushkin Museum, Moscow, Russia Museo del Novecento, Milan, Italy Bologna Museum of Modern Art, Bologna, Italy Galleria Nazionale d'Arte Moderna, Rome, Italy References Further reading External links Archives of the Works of Mario Tozzi Category:1895 births Category:1979 deaths Category:20th-century Italian painters Category:Italian male painters Category:Recipients of the Legion of Honour Category:People from the Province of Pesaro e Urbino Category:Accademia di Belle Arti di Bologna alumni | High | [
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Q: Making Google Talk messages appear on all logged in clients We're using Google Talk as our unofficial-official chat client around the office at work. One thing that poses a big problem almost every day is the fact that Google Talk only sends a message to the clients that you last used. Even though you may be logged into GTalk on 3 different machines, if you start talking on one machine, that becomes your "active" machine, and if you go to another machine, you will still only get messages on the last active machine. Is there a way that you can force Google Talk to send messages to ALL logged in clients, regardless of which client you are actively using? That way, you don't miss any messages during the time between when you get up from the active machine and then make the new client "active". A: Google Talk speaks the Jabber Protocol. Perhaps a different jabber client would work better for your purposes. For example, I use Empathy, but if I happen to have a Gmail page open, I see the conversation in both places. | Mid | [
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/* * Copyright 2020 the original author or authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.gradle.api.internal.file.archive; import java.io.IOException; import java.io.InputStream; public interface ZipEntry { boolean isDirectory(); String getName(); /** * This method or {@link #getInputStream()} can be called at most once per entry. */ byte[] getContent() throws IOException; /** * This method or {@link #getContent()} can be called at most once per entry. */ InputStream getInputStream(); /** * The size of the content in bytes, or -1 if not known. */ int size(); } | Mid | [
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Menu Monday! I have been CRAVING a BBQ sandwich with pickles! Luckily, I found a Boston Butt on sale this weekend and cooked it in the crockpot today (Sunday) R and I had a sandwich when we got home from church (well, he had 3!!) and it was SOO good. I honestly can not tell you how yummy it was. I’m sure it’s more of a pregnancy thing than a great sandwich thing though. I am so glad that we have tons left so that I can eat it tomorrow and probably some Tuesday too! It was sooo easy. I rubbed the meat down with a blend of spices: garlic, onion, salt, black pepper and a little red pepper. I put it in the crock pot and cooked it on high for about three and a half hours. Then before church I turned it down to low. When we got home I shredded it and mixed it with almost a whole bottle of BBQ sauce. It hit the spot! 🙂 We have so much though that I may actually freeze some, if it lasts! There is a link to the Honeyed Pork Chops recipe below. I have never tried it but I have heard that it’s good. I’ll let you know how it turns out. As always, the days may change. I may flip flop them according to how I feel! I have been doing great with our food budget though since I’ve started my menus back up! And now that I’m ‘planning’ snacks, I actually do even better with our money! Instead of buying tons of stuff to snack on, I buy a few things and nothing goes wasted. (And we are eating a lot better too.) I, of course, don’t limit ourselves strictly to this. I just don’t want whoever might be out there reading this to think that I’m strict about what we eat. It’s not like Luke can’t have raisins with his lunch.. or can’t have one of my granola bars for a snack! I just like to have it laid out there because it helps me! I mean he had oatmeal for lunch one day because that’s what he wanted! I was just glad that he actually ate a decent amount of it! I’m seriously not that uptight about it. I am what you would call a ‘list maker’ … it is my therapy. So, I list it out, whatever it may be.. because it’s just what I do! I may never look at the list again.. and if it’s a “To Do” list, many things may never get done.. but at least I made a list for it. Well, that’s something about me that you may not have known! Now, I must go make a list before I go to bed! 🙂 Share this: Like this: Related Post navigation 2 thoughts on “Menu Monday!” Great menu, everything sounds so good 🙂 Thanks for the recipes!Have a great week!Rachel xxxA Juggling MumPS – I have a competition running at the moment for a free blog design. If you win you can use it yourself or give it to a friend 🙂 | Low | [
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Q: How to Create Custom PopUpView in ios8 & ios7? I try to create subview inside a view but view is get full screen present view so Can any one guide me through that Whether its possible to Customised Subview As PopupView? A: You can do it by AlertViewController. Here is my Forgot Password method, you can get help from that. @IBAction func forgotpwd(sender: AnyObject) { let alertController = UIAlertController(title: "Forgot Password", message: "Enter Your Email.", preferredStyle: .Alert) alertController.addTextFieldWithConfigurationHandler { (textField) in textField.placeholder = "Enter your Email" textField.keyboardType = .EmailAddress } var yesAction = UIAlertAction(title: "YES", style: UIAlertActionStyle.Default) { UIAlertAction in //Do you Success button Stuff here } var noAction = UIAlertAction(title: "NO", style: UIAlertActionStyle.Cancel) { UIAlertAction in //Do you No button Stuff here, like dismissAlertView } alertController.addAction(yesAction) alertController.addAction(noAction) self.presentViewController(alertController, animated: true) { } } May It help you, HTH, Enjoy Coding!! | High | [
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Silanediols: a new class of hydrogen bond donor catalysts. Silanediols are introduced as a new class of hydrogen bond donor catalysts for the activation of nitroalkenes toward nucleophilic attack. Excellent yields of product are obtained for the conjugate addition of indole to β-nitrostyrene catalyzed with a stable, storable dinaphthyl-derived silanediol. The preparation and structural characterization of a C(2)-symmetric chiral silanediol is also reported along with its ability to catalyze the conjugate addition reaction. | High | [
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Q: Need to call twice a setter to force GUI refresh in MFC I'm using a MFC ComboBox control to change some parameter which has constituencies on the IP range available ( only/ no broadcast IP for example). I need to call the range modification function twice to force the refreshing on the showed values : why ? Behaviour : One call to range modification Two calls to range modification Source code : void CIPAddressBugDlg::OnChangeCombo() { UpdateData(TRUE); ChangeIPRange(); //ChangeIPRange(); } void CIPAddressBugDlg::ChangeIPRange() { BYTE nField0, nField1, nField2, nField3; if ( Combo.GetCurSel() ) { IpAddress.GetAddress(nField0, nField1, nField2, nField3); if ( nField0 < (BYTE) 224 ) nField0 = 224; IpAddress.SetAddress(nField0, nField1, nField2, nField3); IpAddress.SetFieldRange(0, 224 , 232 ); } else { IpAddress.GetAddress(nField0, nField1, nField2, nField3); if ( nField0 >= (BYTE) 224 ) nField0 = 223; IpAddress.SetAddress(nField0, nField1, nField2, nField3); IpAddress.SetFieldRange(0, 0 , 223 ); } } Combo is a ComboBox control and IpAddress a CIPAddressCtrl. I'm compiling on VS C++ 6.0 (yes I know -_- ) running Windows XP. ( I can also upload the whole toy project if necessary ) A: Try moving SetFieldRange before SetAddress else Windows will ignore the SetAddress because it's out of range. | Mid | [
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What's on the ham radio bands today? WA4STO This weekend is above-average in the way of long-distance contacts on the amateur radio bands. At least, if you're into the ham radio digital modes. Note in the graphic above from my logbook that most of these QSOs were made via RTTY or Radioteletype. An ancient mode, relatively speaking, and no error-correction like some of the modes offer, but there sure are a LOT of overseas DX stations that enjoy RTTY. It was a nice surprise to see 10 meters open today. Ten is usually an "iffy" band and certainly not at all reliable to anywhere, normally. For all newcomers: please note that these millions and millions of frequencies are available to you at no charge for their use and that for those of you here in the USA, we publish all the questions and all the answers to the tests, so as to make it super easy for you to begin a lifelong and very enjoyable hobby. WA4STO When you press a PC keyboard key, it produces a "code" of sorts that the sound card spits out to the radio (by way of the ham radio software) and thus to the world, or perhaps to your BOL across the street. Most of the digital modes are like being in a in Internet chatroom. You 'text' back & forth by keyboard and read it on the screen. The GREAT part about doing this via ham radio, is that it works without internet. Your computers 'talk' over radio - no wires, no phones. As long as you can keep things running, like powering your radio and computer, there is no commercial infrastructure required at all. I love Morse CW because it's so much less complicated, not requiring a computer to be 'interfaced' into your radio transceiver. However, it does take a bit of learning, which should be a major joy of life anyway. 73 de RadioRay ..._ ._ "When we cannot do the good we would, we must be ready to do the good we can." ~ Matthew Henry To monitor digital communications and even download weather charts off the air from marine radio, you do NOT require a SignaLink or anything like that as long as you are only listening. :) All that you need is a shortwave receiver capable of receiving SSB. There are several of these under $100. Here is an article showing how to couple to your radio using a common set of ear-bus type earphones, to a low grade laptop running FREEware software from the internet. To monitor digital communications and even download weather charts off the air from marine radio, you do NOT require a SignaLink or anything like that as long as you are only listening. :) All that you need is a shortwave receiver capable of receiving SSB. There are several of these under $100. Here is an article showing how to couple to your radio using a common set of ear-bus type earphones, to a low grade laptop running FREEware software from the internet. WA4STO The HF bands are doing pretty well today with 10 and 12 meters being quite the surprise: White Tiger note! The second one down is from Bradenton. He's aware that you're just getting things going, about 40 miles from you. Check out his nifty "green antenna" at http://www.qrz.com/db/ad4wg Added bonus: he absolutely LOVES his Ten Tecs. Well, but who wouldn't? WA4STO Most of the contacts have been on JT65, a mode that was developed with moon-bounce and meteor trails in mind. Meteor trails? Yes, as it turns out, the military has known for decades that you can bounce your transmitted signals off of the ionized trails that meteors tend to have. Now, amateur radio operators can do the very same thing, thanks to the software development efforts of some very talented amateurs. Lots of fun and games, provided to you for free, on millions and millions of radio frequencies. WA4STO Yes, it's always interesting to me that ten meters is open so well during the daytime. On the one hand, I'm always babbling about how poor the CB band is, and yet 10 (and 12!) meters is open. On the other hand, for prepping purposes, it's probably useful to admit that reliability only happens a VERY small percentage of the day, if at all. Sure, I can work Outer Slobovia (populated by many of my relatives) once in a given month, maybe. Whoopie. What we need is a ham radio method of obtaining 85% reliability. My best guess is that we could accomplish that with a system that scans at least five bands and utilizes ARQ error-correction. WA4STO In case you're wondering about the word "HELL" in the mode column, no that doesn't refer to the difficulty of working stations on that mode but, rather, the name of the mode itself, FELD HELL. FH is an interesting mode in that it's very unique; VERY few FH signals can be heard on the bands. It may also prove to be useful to the group assembled here; its OPSEC capabilities are excellent for several reasons: 1. It's a 'visual' mode that doesn't lend itself well at ALL to intercept 2. It's frequently found (when it's found at all...) right in the busiest parts of the digital frequencies. Meaning that an automated intercept tool would be hard pressed to zero in on it, rather than the plethora of other signals so very nearby. 3. It requires very little transmit power One of the downsides of Feld Hell is that it's fine for very short texts but lousy for sending prepping-related data of any substantial amount. For that, we use Winmor, which can squish the data by 80 percent before sending, which also of course means that nobody else is going to intercept it. Plus, FH is slow and really offers no error correction. What is you send is -- maybe -- what you get, just like CW and SSB. So if you want high OPSEC and low interception likelihood, FH may work just fine. Imagine the following brief transmission: "See you on Olivia 16/500 usual freq" which would convey a huge amount of information. | Mid | [
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Q: Is my HDD the reason my PC got slow? My pc really got slow some months ago just like that. And I am trying to narrow the reason down. I have downloaded CrystalDisk to try and have information about the disk. But I don't even know what info it is giving me. So I come here to ask you if you know if any info of the following could tell if the disk is the reason for the slowness or not. I have also reinstalled windows on the disk and the problems continue. A: The problem turned out to be the power setting being set at Power Saver not High Performace. My face when the games regained their usual performance levels had to be priceless. Thank you. | Low | [
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“STEAM+ Arts Integration is the future of education. It’s a proven, more holistic approach to both enticing and educating students and preparing them for the workforce of the future,” Cofield contends. Margaret Sergent, Second Vice President of the RTA union, provided opening remarks, including a statement about her previous participation in a J Rêve International global Arts & Culture program in Paris, France, 2016. Dr. Sue Lane, Elementary Art & STEAM teacher at Clyde-Savannah Central School District gave closing remarks, sharing examples from the STEAM program she leads in the CSCS District. Cofield’s presentation includes examples from the anthology she co-authored on the subject, STEAM+ Arts Integration. She has been featured speaker across the nation in cities including Dallas, Queens, NY, Pittsburgh, Washington, DC, among others. The book has received favorable feedback from educators who attended the July conference. “It is an excellent intro to STEAM+ with research, case studies, and strategies,” says Susan Bardenhagen Region IV Director of Virginia Association of Science Teachers. J Rêve International aims to foster collaboration between interdisciplinary artists, programmers, policy makers and educators on issues relating to development, learning and the implementation of STEAM (STEM+Arts) and arts education. Dedicated to engaging students in STEAM+,J Rêve International has impacted more than 40,000 people in 10 countries including Cuba, Mozambique, Haiti, India, Burkina Faso, France, Dubai and US. They’ve enjoyed a strong relationship with 1000 educators, 50 community partners and schools, 85% k-12 teachers, 15% school administrators, museums and art studios & galleries and supported them since incorporation. | High | [
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22 Session Management for Clustered Applications Clustered applications require reliable and performant HTTP session management. Unfortunately, moving to a clustered environment introduces several challenges for session management. This article discusses those challenges and proposes solutions and recommended practices. The included session management features of Oracle Coherence*Web are examined here. 22.1 Basic Terminology An HTTP session ("session") spans a sequence of user interactions within a Web application. "Session state" is a collection of user-specific information. This session state is maintained for a period, typically beginning with the user's first interaction and ending a short while after the user's last interaction, perhaps thirty minutes later. Session state consists of an arbitrary collection of "session attributes," each of which is a Java object and is identified by name. "Sticky load balancing" describes the act of distributing user requests across a set of servers in such a way that requests from a given user are consistently sent to the same server. Coherence is a data management product that provides real-time, fully coherent data sharing for clustered applications. Coherence*Web is a session management module that is included as part of Coherence. An HTTP session model ("session model") describes how Coherence*Web physically represents session state. Coherence*Web includes three session models. The Monolithic model stores all session state as a single entity, serializing and deserializing all attributes as a single operation. The Traditional model stores all session state as a single entity but serializes and deserializes attributes individually. The Split model extends the Traditional model but separates the larger session attributes into independent physical entities. The applications of these models are described in later sections of this article. "Select the Appropriate Session Model" in the Coherence FAQ provides more information on the Monolithic, Traditional, and Split Session models. It also describes how to configure Coherence to use a particular model. 22.2 Sharing Data in a Clustered Environment Session attributes must be serializable if they are to be processed across multiple JVMs, which is a requirement for clustering. It is possible to make some fields of a session attribute non-clustered by declaring those fields as transient. While this eliminates the requirement for all fields of the session attributes to be serializable, it also means that these attributes will not be fully replicated to the backup server(s). Developers who follow this approach should be very careful to ensure that their applications are capable of operating in a consistent manner even if these attribute fields are lost. In most cases, this approach ends up being more difficult than simply converting all session attributes to serializable objects. However, it can be a useful pattern when very large amounts of user-specific data are cached in a session. The J2EE Servlet specification (versions 2.2, 2.3, and 2.4) states that the servlet context should not be shared across the cluster. Non-clustered applications that rely on the servlet context as a singleton data structure will have porting issues when moving to a clustered environment. Coherence*Web does support the option of a clustered context, though generally it should be the goal of all development teams to ensure that their applications follow the J2EE specifications. A more subtle issue that arises in clustered environments is the issue of object sharing. In a non-clustered application, if two session attributes reference a common object, changes to the shared object will be visible as part of both session attributes. However, this is not the case in most clustered applications. To avoid unnecessary use of compute resources, most session management implementations serialize and deserialize session attributes individually on demand. Coherence*Web (Traditional and Split session models) normally operates in this manner. If two session attributes that reference a common object are separately deserialized, the shared common object will be instantiated twice. For applications that depend on shared object behavior and cannot be readily corrected, Coherence*Web provides the option of a Monolithic session model, which serializes and deserializes the entire session object as a single operation. This provides compatibility for applications that were not originally designed with clustering in mind. Many projects require sharing session data between different Web applications. The challenge that arises is that each Web application typically has its own class loader. Consequently, objects cannot readily be shared between separate Web applications. There are two general methods for working around this, each with its own set of trade-offs. Place common classes in the Java CLASSPATH, allowing multiple applications to share instances of those classes at the expense of a slightly more complicated configuration. Use Coherence*Web to share session data across class loader boundaries. Each Web application is treated as a separate cluster member, even if they run within the same JVM. This approach provides looser coupling between Web applications (assuming serialized classes share a common serial Version UID), but suffers from a performance impact because objects must be serialized-deserialized for transfer between cluster members. 22.3 Reliability and Availability An application must guarantee that a user's session state is properly maintained to exhibit correct behavior for that user. Some availability considerations occur at the application design level and apply to both clustered and non-clustered applications. For example, the application should ensure that user actions are idempotent: the application should be capable of handling a user who accidentally submits an HTML form twice. With sticky load balancing, issues related to concurrent session updates are normally avoided, as all updates to session state are made from a single server (which dramatically simplifies concurrency management). This has the benefit of ensuring no overlap of user requests occurs even in cases where a user submits a new request before the previous request has been fully processed. Use of HTML frames complicates this, but the same general pattern applies: Simply ensure that only one display element is modifying session state. In cases where there may be concurrent requests, Coherence*Web manages concurrent changes to session state (even across multiple servers) by locking sessions for exclusive access by a single server. With Coherence*Web, developers can specify whether session access is restricted to one server at a time (the default), or even one thread at a time. As a general rule, all session attributes should be treated as immutable objects if possible. This ensures that developers are consciously aware when they change attributes. With mutable objects, modifying attributes often requires two steps: modifying the state of the attribute object, and then manually updating the session with the modified attribute object by calling javax.servlet.http.HttpSession.setAttribute(). This means that your application should always call setAttribute() if the attribute value has been changed, otherwise, the modified attribute value will not replicate to the backup server. Coherence*Web tracks all mutable attributes retrieved from the session, and so will automatically update these attributes, even if setAttribute() has not been called. This can help applications that were not designed for clustering to work in a clustered environment. Session state is normally maintained on two servers, one primary and one backup. A sticky load balancer will send each user request to the specified primary server, and any local changes to session state will be copied to the backup server. If the primary server fails, the next request will be rerouted to the backup server, and the user's session state will be unaffected. While this is a very efficient approach (among other things, it ensures that the cluster is not overwhelmed with replication activity after a server failure), there are a few drawbacks. Because session state is copied when the session is updated, failure (or cycling) of both the primary and backup servers between session updates will result in a loss of session state. To avoid this problem, wait thirty minutes between each server restart when cycling a cluster of server instances. The thirty-minute interval increases the odds of a return visit from a user, which can trigger session replication. Additionally, if the interval is at least as long as the session timeout, the session state will be discarded anyway if the user has not returned. This cycling interval is not required with Coherence*Web, which will automatically redistribute session data when a server fails or is cycled. Coherence's "location transparency" ensures that node failure does not affect data visibility. However, node failure does impact redundancy, and therefore fresh backup copies must be created. With most Coherence*Web configurations, two machines (primary and backup) are responsible for managing each piece of session data, regardless of cluster size. With this configuration, Coherence can handle one failover transition at any time. When a server fails, no data will be lost if the next server failure occurs after the completion of the current failover process. The worst-case scenario is a small cluster with large amounts of session data on each server, which may require a minute or two to rebalance. Increasing the cluster size, or reducing the amount of data storage per server, will improve failover performance. In a large cluster of commodity servers, the failover process may require less than a second to complete. For particularly critical applications, increasing the number of backup machines will increase the number of simultaneous failures that Coherence can manage. The need for serialization in clustered applications introduces a new opportunity for failure. Serialization failure of a single session attribute will ordinarily prevent the remaining session attributes from being copied to the backup server and can result in the loss of the entire session. Coherence*Web works around this by replicating only serializable objects, while maintaining non-serializable objects in the local server instance. One last issue to be aware of is that under heavy load, a server can lose session attribute modifications due to network congestion. The log will contain information about lost attributes, which brings up the most critical aspect of high-availability planning: Be sure to test all of your application components under full load to ensure that failover and failback operate as expected. While many applications will see no difficulties even at 99-percent load, the real test of application availability occurs when the system is fully saturated. 22.4 Scalability and Performance Moving to a clustered environment makes session size a critical consideration. Memory usage is a factor regardless of whether an application is clustered or not, but clustered applications also need to consider the increased CPU and network load that larger sessions introduce. While non-clustered applications using in-memory sessions do not need to serialize-deserialize session state, clustered applications must do this every time session state is updated. Serializing session state and then transmitting it over the network becomes a critical factor in application performance. For this reason and others, a server should generally limit session size to no more than a few kilobytes. While the Traditional and Monolithic session models for Coherence*Web have the same limiting factor, the Split session model was explicitly designed to efficiently support large HTTP sessions. Using a single clustered cache entry to contain all of the small session attributes means that network traffic is minimized when accessing and updating the session or any of its smaller attributes. Independently deserializing each attribute means that CPU usage is minimized. By splitting out larger session attributes into separate clustered cache entries, Coherence*Web ensures that the application only pays the cost for those attributes when they are actually accessed or updated. Additionally, because Coherence*Web leverages the data management features of Coherence, all of the underlying features are available for managing session attributes, such as near caching, NIO buffer caching, and disk-based overflow. Figure 22-3 illustrates performance as a function of session size. Each session consists of ten 10-character Strings and from zero to four 10,000-character Strings. Each HTTP request reads a single small attribute and a single large attribute (for cases where there are any in the session), and 50 percent of requests update those attributes. Tests were performed on a two-server cluster. Note the similar performance between the Traditional and Monolithic models; serializing-deserializing Strings consumes minimal CPU resources, so there is little performance gain from deserializing only the attributes that are actually used. The performance gain of the Split model increases to over 37:1 by the time session size reaches one megabyte (100 large Strings). In a clustered environment, it is particularly true that application requests that access only essential data have the opportunity to scale and perform better; this is part of the reason that sessions should be kept to a reasonable size. Another optimization is the use of transient data members in session attribute classes. Because Java serialization routines ignore transient fields, they provide a very convenient means of controlling whether session attributes are clustered or isolated to a single cluster member. These are useful in situations where data can be "lazy loaded" from other data sources (and therefore recalculated in the event of a server failover process), and also in scenarios where absolute reliability is not critical. If an application can withstand the loss of a portion of its session state with zero (or acceptably minimal) impact on the user, then the performance benefit may be worth considering. In a similar vein, it is not uncommon for high-scale applications to treat session loss as a session timeout, requiring the user to log back in to the application (which has the implicit benefit of properly setting user expectations regarding the state of their application session). Sticky load balancing plays a critical role because session state is not globally visible across the cluster. For high-scale clusters, user requests normally enter the application tier through a set of stateless load balancers, which redistribute (more or less randomly) these requests across a set of sticky load balancers, such as Microsoft IIS or Apache HTTP Server. These sticky load balancers are responsible for the more computationally intense act of parsing the HTTP headers to determine which server instance will be processing the request (based on the server ID specified by the session cookie). If requests are misrouted for any reason, session integrity will be lost. For example, some load balancers may not parse HTTP headers for requests with large amounts of POST data (for example, more than 64KB), so these requests will not be routed to the appropriate server instance. Other causes of routing failure include corrupted or malformed server IDs in the session cookie. Most of these issues can be handled with proper selection of a load balancer and designing tolerance into the application whenever possible (for example, ensuring that all large POST requests avoid accessing or modifying session state). Sticky load balancing aids the performance of Coherence*Web but is not required. Because Coherence*Web is built on the Coherence data management platform, all session data is globally visible across the cluster. A typical Coherence*Web deployment places session data in a near cache topology, which uses a partitioned cache to manage huge amounts of data in a scalable and fault-tolerant manner, combined with local caches in each application server JVM to provide instant access to commonly used session state. While a sticky load balancer is not required when Coherence*Web is used, there are two key benefits to using one. Due to the use of near cache technology, read access to session attributes will be instant if user requests are consistently routed to the same server, as using the local cache avoids the cost of deserialization and network transfer of session attributes. Additionally, sticky load balancing allows Coherence to manage concurrency locally, transferring session locks only when a user request is rebalanced to another server. 22.5 Conclusion Clustering can boost scalability and availability for applications. Clustering solutions such as Coherence*Web solve many problems for developers, but successful developers must be aware of the limitations of the underlying technology, and how to manage those limitations. Understanding what the platform provides, and what users require, gives developers the ability to eliminate the gap between the two. | Mid | [
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Characterization of an analphoid, neocentromere-positive inv dup 8p marker chromosome using multiplex whole chromosome and sub-telomere FISH analyses. A 30-year-old male patient with mild mental retardation was found to have a small supernumerary marker chromosome (SMC) in 90% of his peripheral blood cells and in 100% of his fibroblast cells. Multiplex whole chromosome and sub-telomere FISH analyses were used to determine that this SMC is an inverted duplicated distal chromosome 8p fragment. Although it was negative for alpha-DNA sequences, this marker had a functional kinetochore (neocentromere) demonstrated by a positive signal with a CENP-C antibody. Apparently intact 8p telomeres at the marker's ends were demonstrated by using a telomere repeat FISH probe. The patient's phenotypically normal mother on G-banding analysis had a small marker chromosome in 8% of her peripheral blood cells in two cultures of the first specimen studied. The marker was not seen in any subsequent maternal peripheral blood or fibroblast specimens. Although it was impossible to further characterize the maternal SMC, it was suggested that the mother had the same marker as the one seen in the proband. Inverted duplicated chromosomal fragments are the most frequent type of analphoid markers. Stable inverted duplicated 8p marker chromosomes were previously reported in three other patients. They all apparently occurred de novo and were found to be positive for kinetochore-associated proteins. Evidence for the possible inheritance of an inverted-duplicated, analphoid SMC was not shown to-date. This study also demonstrates a practical, straightforward approach for analphoid marker characterization in clinical laboratory settings, using whole chromosome multiplex and subtelomere-specific FISH analyses. FISH probes for all sub-telomere chromosomal regions are commercially available and the large majority of analphoid marker chromosomes involve telomere regions. | High | [
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Q: Apache - Files directive does not work HI guys. when i configure Files in this way: <Files ~ "\.png$"> deny from all </Files> it works. but when defining in this way it doesn't work: <Files /var/www/test/file.png> deny from all </Files> Directives are not inside Directory directive. Could someone help? A: If you read the apache manual it says that Files directive should be coupled with the Directory directive. Therefore to achieve the functionality you are looking for use <Directory /var/www/test> <Files ~ "file\.png"> deny from all <Files> </Directory> http://httpd.apache.org/docs/2.0/mod/core.html#files | High | [
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<?xml version="1.0" encoding="UTF-8"?> <table xmlns="http://query.yahooapis.com/v1/schema/table.xsd"> <meta> <author>Sebastian Spier (http://twitter.com/#!/sebastianspier/)</author> <description>Coderwall Profile API</description> <documentationURL>http://coderwall.com/api</documentationURL> <sampleQuery>SELECT * FROM {table} WHERE user=spier</sampleQuery> </meta> <bindings> <select itemPath="json" produces="JSON"> <urls> <url>http://coderwall.com/{user}.json</url> </urls> <inputs> <key id="user" type="xs:string" paramType="path" required="true"/> </inputs> </select> </bindings> </table> | Mid | [
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Estimating adult mortality from a census based method. "In this paper a simple method is presented to derive current adult mortality level. The sensitivity of estimates to various forms of data error is considered, and procedures are proposed for removing errors resulting from differential census coverage completeness and from age misstatement. The estimated life expectancy at age 5 derived from the method seems plausible." The method is applied to census data for Bangladesh to estimate adult mortality for the period 1974-1981. (summary in FRE, ITA) | High | [
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<?xml version="1.0"?> <!DOCTYPE test [ <!ENTITY ampproblem "&"> ]> <t a="&problem;">a</t> | Low | [
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Q: Wireless drivers failing to build when make command is run I'll have to start by saying I'm new to ubuntu, and linux in general. I have set up a dual boot on my pc with windows and linux. Due to positioning in my house, I'm unable to get ethernet access, so I use an external wireless adapter that functions fine in windows. There ARE linux drivers, which I have downloaded on the system. So far, I've entered: cd /usr/src/8812au-4.2.2 make However, this fails to build. It returns with this: make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/4.2.0-27-generic/build M-/usr/src/8812au-4.2.2 modules make[1]: Entering directory '/usr/src/linux-headers-4.2.0-27-generic' Building modules, stage 2. MODPOST 0 modules make[1]: Leaving directory '/usr/src/linux-headers-4.2.0-27-generic' From here, I'm not entirely sure where to go. If I try to continue, it finds that it doesn't build the 8812au.ko that I need. Are there any ideas about what I could do from here? EDIT: I downloaded the drivers from here: https://github.com/abperiasamy/rtl8812AU_8821AU_linux The drivers DO have instructions on using dkms, which also failed to work properly. Would you like to see what is returned when I try to install it through that? A: This driver is included in Ubuntu repositories for Ubuntu 15.10 and 16.04. It can be also installed to Ubuntu 14.04.4 with 4.2 kernels (see the offline guide). Most likely it will install on the previous kernels, but that is not guaranteed. It can be installed for wily or xenial by sudo apt-get install rtl8812au-dkms You need to uninstall all other drivers for this adapter first. You can install this driver offline this way: Download these files to your Home directory http://mirrors.kernel.org/ubuntu/pool/main/d/dkms/dkms_2.2.0.3-1.1ubuntu5.14.04.5_all.deb http://mirrors.kernel.org/ubuntu/pool/universe/r/rtl8812au/rtl8812au-dkms_4.3.8.12175.20140902+dfsg-0ubuntu1_all.deb Run in terminal sudo dpkg -i dkms*.deb rtl8812au-dkms*.deb | Mid | [
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Even though not really a mall (I don't think it classifies as one having only 4 shops) I enjoy shopping here as you can be quick about it. It hits 3 major areas: houseware (Super Home), groceries (Carrefour) and gifts/clothes (Debenhams/Oviesse).It also has a Venue Cafe for quick meals and a recently added Cinnabon. | Mid | [
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First Ledger Nano X Shipment To Start Next Week After the initial delay caused by a production quality issue that had surfaced on the last minute, the first batch of Ledger Nano X’s (Genesis Editions) will be shipped on May 15th, bringing the next generation of hardware wallets to the public. The rest of the pre-orders will be shipped the week of the 20th of May, enabling general availability from May 27th. As announced in March, those who pre-ordered before March 21st will also receive one free Nano S per order. We would like to thank you for your patience and understanding, we wanted to ensure delivering a top-quality product, which we are now able to provide. We are incredibly excited to bring what we believe to be a game-changer to crypto owners all around the globe. The Ledger Nano X brings innovation in many different ways. In this article, we would like to present some of these new or enhanced features to you. Bluetooth Enabled: Accessing Your Crypto Assets, Everywhere You Go. Thanks to the wireless connection of a Bluetooth enabled device, the Ledger Nano X can effortlessly communicate with mobile phones. Combined with the Ledger Live Mobile app (released end of January), this allows you quick access to your crypto assets anywhere you want. You will be able to perform the exact same operations on your Ledger Live Mobile app as had been the case with the desktop version, meaning installing apps, verifying receiving addresses and creating transactions for natively supported cryptocurrencies. Cryptocurrencies that are not supported natively yet can be managed through their compatible third party wallet – you can see the matching wallet on this page. While no sensitive data is transferred through it, we have taken the security of the Bluetooth communication into consideration. You can read more about this here. Increased Storage: As the Ledger Nano X uses a Secure Element with enhanced storage, it will be able to store up to 100 applications at once. This provides easier access to many more crypto assets. As of today, all cryptocurrency apps that are available on the Ledger Nano S are equally compatible with the Ledger Nano X. This allows it to be useable with over 1100 different cryptocurrencies that were already supported on the Ledger Nano S. We are also looking into making utility apps, such as Recovery Check, compatible with the Ledger Nano X soon. Improved Architecture: Providing You a Secure Experience, Everywhere You Go. Much like the Ledger Nano S, the Nano X features a certified Secure Element (CCEAL5+). This secure chip is resistant to many types of attacks, effectively protecting your hardware wallet against a variety of physical attacks. Secure Elements are used in high-end solution for storing critical, sensitive data such as credit cards and passports. Improved User-Experience: The Ledger Nano X has several features to provide its users with an enhanced experience. The screen size has been increased so that scrolling addresses will be a thing of the past. The buttons are larger and on the sides rather than the top and to round it all off we have improved the navigation. Today marks the start of a new era cryptocurrency security in the mobile market. We’re extremely excited and proud to bring the next generation of hardware wallets to you. We would like to once more apologize for the delay caused by a production issue and thank you for your patience. That said, we are excited to start shipping the Ledger Nano X and provide you with a secure crypto experience, everywhere you go. | Mid | [
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[Essential thrombocythemia in transformation from myelodysplastic syndrome to acute myeloid leukemia with inv(3) after treatment for gastric cancer]. In March 1990, a 61-year-old man was given a diagnosis of essential thrombocythemia with a normal karyotype and subsequently treated with hydroxyurea. In November 1995, he underwent surgery for gastric cancer with thereafter received tegafur/uracil for 2 years. Refractory anemia with excess of blasts in transformation and chromosomal abnormalities including -5, -7, 20q-developed in August 1998. Combined chemotherapy with daunorubicin, cytarabine, mercaptopurine, and prednisolone, had only limited effectiveness. Acute myeloid leukemia was finally diagnosed in October 1998, and chromosomal analysis disclosed inv(3) in addition to -5 and -7. The appearance of inv(3) might be related to leukemic transformation of hematopoietic stem cell disease with an increase in the number of megakaryocytes and platelets. | Mid | [
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1995 Murcian regional election The 1995 Murcian regional election was held on Sunday, 28 May 1995, to elect the 4th Regional Assembly of the autonomous community of the Region of Murcia. All 45 seats in the Regional Assembly were up for election. The election was held simultaneously with regional elections in twelve other autonomous communities and local elections all throughout Spain. Former president Carlos Collado had been formed to resign in April 1993 by his own party, the Spanish Socialist Workers' Party (PSOE), as a result of the ongoing struggle between the guerristas and renovadores factions within the PSOE and a political scandal over the purchase of the Casa Grande estate. He was replaced by María Antonia Martínez, the first woman presiding over a Spanish autonomous community as well as the only one to date holding the office in the Region of Murcia. The crisis resulting in Collado's resignation was among the factors said to contribute to the opposition People's Party (PP) spectacular gains in that year's June general election, overcoming the PSOE as the most voted party in the region for the first time in democracy; a feat which was confirmed in the 1994 European Parliament election. The regional election resulted in the PP consolidating its gains, winning by a landslide as the vote for the ruling PSOE plummeted. PP leader Ramón Luis Valcárcel would become the new President of the Region of Murcia, with the PP remaining in government ever since. The PP would also remain the prime party of Murcian politics until 2019. Overview Electoral system The Regional Assembly of Murcia was the devolved, unicameral legislature of the autonomous community of Murcia, having legislative power in regional matters as defined by the Spanish Constitution and the Murcian Statute of Autonomy, as well as the ability to vote confidence in or withdraw it from a President of the Region. Voting for the Regional Assembly was on the basis of universal suffrage, which comprised all nationals over eighteen, registered in the Region of Murcia and in full enjoyment of their political rights. The 45 members of the Regional Assembly of Murcia were elected using the D'Hondt method and a closed list proportional representation, with a threshold of 5 percent of valid votes—which included blank ballots—being applied regionally. Parties not reaching the threshold were not taken into consideration for seat distribution. Seats were allocated to constituencies, which were established by law as follows: I–Lorca II–Cartagena III–Murcia IV–Northwest V–Plateau Each constituency was entitled to an initial minimum of one seat, with the remaining 40 allocated among the constituencies in proportion to their populations. The electoral law provided that parties, federations, coalitions and groupings of electors were allowed to present lists of candidates. However, groupings of electors were required to secure the signature of at least 1 percent of the electors registered in the constituency for which they sought election. Electors were barred from signing for more than one list of candidates. Concurrently, parties and federations intending to enter in coalition to take part jointly at an election were required to inform the relevant Electoral Commission within ten days of the election being called. Election date The term of the Regional Assembly of Murcia expired four years after the date of its previous election. Elections to the Regional Assembly were fixed for the fourth Sunday of May every four years. The previous election was held on 26 May 1991, setting the election date for the Regional Assembly on Sunday, 28 May 1995. The Regional Assembly of Murcia could not be dissolved before the date of expiry of parliament except in the event of an investiture process failing to elect a regional President within a two-month period from the first ballot. In such a case, the Regional Assembly was to be automatically dissolved and a snap election called, with elected deputies merely serving out what remained of their four-year terms. Opinion polls The table below lists voting intention estimates in reverse chronological order, showing the most recent first and using the dates when the survey fieldwork was done, as opposed to the date of publication. Where the fieldwork dates are unknown, the date of publication is given instead. The highest percentage figure in each polling survey is displayed with its background shaded in the leading party's colour. If a tie ensues, this is applied to the figures with the highest percentages. The "Lead" column on the right shows the percentage-point difference between the parties with the highest percentages in a given poll. When available, seat projections are also displayed below the voting estimates in a smaller font. 23 seats were required for an absolute majority in the Regional Assembly of Murcia. Results Overall Distribution by constituency Aftermath Notes References Opinion poll sources Other Category:1995 in Murcia (region) Murcia Category:Elections in the Region of Murcia Category:May 1995 events in Europe | Low | [
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Wednesday, December 22, 2010 I jumped through the racket-filled hoops of the RI DMV this week. One such money-hoop was a VIN check. You had to go to a dude at a special police station that is open every other 3rd full moon for like 3 hours in the middle of the day. Next, pay him 10-30 bucks cash, and he'd check you car VIN vs your title. At this point you could now go find a person to notarize the friggin' application for a new registration. Yay! Anywho, the place had a special row of parking garage spots. The signs don't indicate anything about being towed or fined if you park there too long, just that you will be tagged. And given the many vibrant non-tax dollar funded murals that surrounded the place, I'd not park there for more than 15 minutes... Monday, December 13, 2010 I've been told to go check out this place up the road by Jess2 and her knowledgeable beerman. It's like a whole 3 miles away - which is light years in this town. So I've been going instead to the one that's 2 miles away. But I was driving back from some coupon fueled errand (how does Michael's stay in business?) and saw the neon lights beckoning, so I swerved in for a looksee. Hoooooooooooray. Place is loaded. Isles of crazy stuff. Coolers of good stuff. Mountains of crap stuff. The rest of the place is an alcoholics delight as well. Plus there's a can and bottle collection thingie attached. So in the parking lot I get to dodge station-wagons full of bottles and cans that are driven by hobos (all the windows are broken). Sunday, December 12, 2010 After a bunch of effort and lots of cursing, the hellish area that is my day-prison has finally been painted. I've been locked in this room, day-in/day-out staring at the institution green walls with a crap pile behind me that awaits a painted room. The mental downer this has been can finally be blocked. It's painted, I have purpose in here now.Have you gotten the idea that this room is painted and I'm stoked? New desk mat for my chair! Corner shelves for nerd shit! I even cut a hole in the outer desk wall for the radiator to poke through and warm my feet! Wheeeeee! Sunday, December 5, 2010 Not too much of the zombie outbreak was explained, as most of the facts were fuzzy and the dude didn't know what he was doing. The rest of the world is still a large enough mystery since the power/communication gird went down and no one seems to know what the deal is anywhere. The CDC exploded and is gone. No goofy new plot lines were developed. The cast has been whittled down to the canon group, with the welcome bonus of Darryl. The whisper thing was lame, but is easy enough to puzzle out if you think about it. Merle is still running around and will most certainly be back as an evil d-bag. Essentially, they built themselves a big fat reset button so that come second season they can plot a decent story arc or two. Smart move? However, the ending didn't really leave any openings or tantalizing bits to get you stoked for more, besides basic survival. Ya know? It could theoretically just end here with a well placed "and there were nooooo survivors". Switching to something that should've ended a long while back, but like a stubborn zombie keeps lurching forward - I leave you with this balsphemous nightmare that aired tonight. Saturday, December 4, 2010 Oooooooooook. Here I go. It's been a hit or miss batch of episodes with this series. A series I want to succeed reeeeeeeal bad. And it has, given the numbers and second season green light. But it is not living up to its potential. I know it was taking a chance and a short season and nothing was guaranteed during shooting and the budget was limited - but that's all the more reason you shouldn't fuck around with an equation that's been slingin' the bestest zombie fiction in comicdom. I've, for the most part, been fine with the minor deviations acquired during the comic to TV transition. New throw away characters are fine, so long as you toss them. And they have! A few new conflicts, like the "vatos" in the hospital thing, was no big deal and resolved itself. However. HOWEVER. Breaking canon by actually making it to the CDC and then developing a reason for the zombie plague itself is not cool. It's stupid and rushed. This is the one thing the comics never ever reveal over 80 issues, leaving lots of questions and venues to explore. So, there's no damn need to reveal it here either. It adds nothing and only, honestly, detracts from the stories that did so well in the first place to land a TV show. This changes everything. So many plotlines from the source material can't be used anymore with this shit floating around out there. I'm cool with new adventures and what have you, but this isn't a side trip. It's the answer. The potential for fail is so great at this point. It's almost like they're chickening out on what needs to be done ie the killing what needs doing. Shedding light on the virus subject is a very bad move. Fuck, they even named it! Isn't it better to have the charcaters guessing about how it spreads? Bites only? Scrapes? Can you get zombie juice in your mouth and become one? Or if the USA is alone in this? If it's just Georgia or the South? All that gets flushed tomorrow when the brother from The Truman Show ruins the surprise (how ironical!). And Merle. The wacky, now one handed, racist dude is still out there. A loose string is cool, but this loose string is bad for a pair of reasons. One: the hand cutting. Given events that will transpire down the line (hopefully), this injury will become Seinfeldian and the retribution will actually be deserved. Two: If Merle follows the trajectory he appears ot be on, then one of the best villians in the comics has just been explained away and now isn't so scary. So Kirkman, take care of Merle now. Basically, why mess with it at all really? Lighting in a bottle twice? Hard to do. Essentially, a small ass percentage of folks watchin the show have read the comics, so it's not like you're spoiling anything for them, in fact that's all we want is the stuff we love, but on TV. Is that so much to ask for? I guess so. Oh well. All in all, it's a fine show. The gore levels are exceptional and I'm liking Dale a bunch, he's spot on. It is after all a friggin' TV show about zombies and swinging axes at zombie's heads so I should just calm down. But I can't! Maybe they'll fix it up tomorrow. Perhaps the dude in the CDC is full of shit and this is a red herring. I have faith in this Kirman guy, he's led the story down some questionable paths in the comics, but always pulled it off and managed to shock me along the way. So, here's to hopin'... You're 8, you've only got 30 cents (in pennies and a nickel) for the ice cream man. So when you ask for the fakie lolipop up on the shelf behind him (cost: $.20) as a distraction, what do you steal from the cooler up front? If you were in chanrge of the NFL and were a crazyperson, which item would you force everyone to play football with? | Low | [
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[A phase II study of irinotecan combined with cisplatin in non-small cell lung cancer. CPT-11 Lung Cancer Study Group]. Based upon the results of phase I study of irinotecan (CPT-11) combined with cisplatin (CDDP) on non-small cell lung cancer (NSCLC), a combination phase II study on NSCLC was carried out from Feb., 1992 to Sep., 1992. CPT-11 (60 mg/m2) and CDDP (80 mg/m2) were administered by i.v. drip infusion, with administration schedules of Days 1, 8, 15 and only Day 1, respectively. This therapy course was repeated every 4 weeks. Subjects were NSCLC patients of stage III B or IV disease. Those without prior chemotherapy (Group A) and those with prior therapy (Group B) were enrolled separately. Seventy patients were entered into Group A and 32 patients into Group B. One of the patients of Group A was ineligible. The characteristics of the eligible cases of Group A were: male/female, 51/18; median age, 61 years old; PS 0/1/2, 18/39/12; stage IIIB/IV, 26/43; and adeno/squamous/large, 51/15/3. Those of group B were: male/female, 20/12; median age, 62 years old; PS 0/1/2, 5/18/9; stage I/IIIB/IV, 1/7/24, adeno/squamous/large/ad-sq, 28/2/1/1. Thirty-three patients (47.8%) responded in Group A and B patients (25.0%) responded in Group B. Major adverse reactions (grade 3 or higher) of Group A/Group B were neutropenia (80.3%/73.3%), anemia (35.3%/34.4%), diarrhea (18.8%/28.1%) and nausea/vomiting (34.8%/34.4%). Median survival times for Group A and Group B were 308 and 295 days, respectively. CPT-11 in combination with CDDP is effective against NSCLC, suggesting that further studies are needed to determine the usefulness of this therapy. | High | [
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The proposed case-control study is designed to investigate dietary factors which may inhibit cancer of the colon and rectum. These include vitamin C, vitamin E, vitamin A (retinol), beta carotene, selenium and protease inhibitors. Dietary intake of fats and fibers will additionally be assessed. The cases will be about 350 newly diagnosed colorectal cancer patients at three hospitals. A series of 350 patients with non-neoplastic disease from these hospitals will serve as controls. An additional population-based control group will also be obtained. Questionnaire information will be obtained on non-dietary risk factors for colon cancer and on sociodemographic variables. Dietary intake will be assessed by an extensive dietary interview which will be directed toward recall of intake 2-3 years ago (preceding symptomatic disease). Nutrient intakes will be calculated from an extensive and up-to-date food composition database for most nutrients. In order to confirm the validity of dietary intake information and to ascertain more physiologically-relevant parameters, bilogical assays will be conducted for about 100 cases and 100 controls. Fecal samples will be obtained and assayed for levels of protease inhibitors. Hair, which provides a temporally-integrative measure of various trace metals, will be assayed for levels of selenium. Since several of the dietary factors in question have been shown to have joint potentiating or compensating effects, interactions among them will be investigated in addition to their separate inhibitory effects. Finding a reduction in risk associated with some or all of these dietary factors would point to dietary modification as a potential preventive measure for cancer of the colon and rectum. | Mid | [
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UFO ROUNDUP Volume 5 Number 41 October 12, 2000 Editor: Joseph Trainor UFO Roundup and the UFOINFO site are operated on a "Not For Profit" basis. You can help to keep UFO Roundup operating by making a donation. CHEMTRAILS CAUSE WEIRD PHENOMENON IN MICHIGAN A strange incident involving chemtrails and two white helicopters occurred in Brighton, Michigan on Sunday, October 8, 2000, around 8 a.m. Commercial artist Michael reported, "My mother, who lives on a lakefront property, looked out the large picture window overlooking the lake. She noticed in the sky planes making contrails into a huge checkerboard shape. She had a disposable camera which she received free in the mail and was able to take of the most incredible event she had ever seen." "It was a partly cloudy day, and the sky was very blue, and within 15 minutes she said the sky had turned pitch black. There in the photo you can see the reddish- brown thick fog move across the lake in the same window. She took (several) photos from the large window and it was so black that the lake was not visible." "Around 10 a.m., the smoke/fog cleared, and she saw two copters painted white with no markings hovering over the lake and unfortunately she does not have a photo of this. They left soon, and (looking up) she noticed the huge Xs formed from contrails." (Editor's Note: United Nations helicopters are usually painted white.) After she phoned her son Michael, "I went over there to visit and look at the photos and to help calm her down. I'm an artist by trade, and I have a gift for seeing very clear and have a keen eye for detail." While examining his mother's photos, Michael noticed that the camera had picked up a very strange object in the sky above the lake. "While looking at the photos, I noticed a small white/blue light about 20 feet (6 meters) above tree level. I looked close to see if it was some glitch or flash from the camera, but it was not...I was totally in awe so I went to take the photo and have it enlarged. What we got back shocked me so much--that's why I'm writing now." The blue/white UFO "was like one of those plasma balls where you touch the glass globe and the lightning inside responds. It's a very clear and sharp image of blue lightning contoured into an egg shape. I can see the streaks binding and forming the egg shape. I thought maybe ball lightning, but what's strange about the image is (that) I discovered that the egg shape is not formed by the lightning but appears to be formed by the surrounding atmosphere." "This may sound strange but when you look close, the sky is a darker shade outside the egg shape and within the egg shape the sky is much lighter, and images such as the trees also seem to bend as if putting a magnifying glass on the photo." "I examined it for three hours, trying to come up with an answer. I have none!" Brighton is on Interstate Highway I-96 about 30 miles (48 kilometers) east of Detroit. (Email Form Report) (Editor's Comment: Filaments of an electrical nature have already been reported precipitating from the chemtrails. The phenomenon at Brighton is clearly electrical. Perhaps some physicist can explain what's going on. Weather modification, perhaps?) CHUPACABRA SPOTTED ON A ROOFTOP IN CHILE "Janitor Jesus Barrientos is the latest victim of the mythic Chupacabra. He was left shaking with fear and his hair standing up after having seen the strange beast up close, as he states, on the rooftop of the four-story building where he works. The 42-year-old resident of Iquique cannot be disabused of the notion that what he saw was indeed the strange Chupacabra, although some may not believe him." "Still on the nervous side, he told La Cuarta (newspaper) that 'around 10:30in the evening, he went up to the roof to arrange some boxes. It was well-lit, between the moonlight and the light coming from the Calle Tarapaca (street). Then I turned halfway around and saw that there was some kind of bird on top of the doorway.'" "Barrientos thought at first it was a jote (a large bat indigenous to northern Chile--J.T.) 'But when I tried to shoo it away, because jotes leave their droppings on the walls, I realized it was an animal with an elongated face, bulging eyes, sharp teeth and makes squealing sounds like a puppy,' he recalled." "He then froze, unable to do anything. This allowed him to get a better look at it." "'It had long ears and was black in color, measuring a meter (3 feet, 4 inches) long and had large wings like those of a bat.'" "He thought the creature was about to pounce on him, but as he broke into a run, the creature spread its wings and flew off over Iquique." "'I don't know how, but three seconds later, I was in the building's lobby. I told what had just happened to some children who were outside playing ball and they ran away in terror,' explained the frightened janitor." "Although he acknowledged that it was the first time he had seen the bloodthirsty Chupacabra up close, Jesus Barrientos remarked that others in the northern city claimed to have seen it standing in top of the dome of the city's cathedral." Iquique is a large city located about 150 kilometers (90 miles) south of Chile's border with Peru. (See the Chilean newspaper La Cuarta for October 8, 2000. Muchas gracias a Scott Corrales, autor de los libros Chupacabras and Other Mysteries y Forbidden Mexico para eso articulo de diario.) THREE UFOs CAVORT OVER WESTERN PENNSYLVANIA On Saturday, October 7, 2000, at 9 p.m., Mr. and Mrs. Alan Yost ""drove up on the hill above our place in the trailer court" in Portersville, Pennsylvania "to see if any thunderstorms were headed in our direction from the north. I was outside our van, checking the electrostatic meter I had made when my wife called me back inside to see what she had been observing through her binoculars." ""Using my binoculars, I was able to clearly see a small but brilliant point of light which was flicking about in an extremely unusual manner, changing color as it did so. It would be crimson red in one spot, then blink out only to re-appear in the same instant in another but would now be brilliant green, or a silver blue/white. I observed this one for a few minutes, then I checked for a reference point of land so I could make sure that its (the UFO's) movement was not caused by my binoculars. I was able to put the tree line just inside the bottom of the lens and still see the object. It was definitely doing the moving as the tree line remained perfectly still." "Then I was able to see that there was not only one but three or more of these 'objects' all doing the same 'dance in the sky.' I also noticed that whenever they blinked out and re-appeared they would form a perfect triangle. The size of the triangle was constantly changing as they darted about." The UFOs "remained in the same quadrant of the sky--a couple of miles due west" of the hilltop. "Many airplanes were also coming into and out of Pittsburgh International Airport. One of their main flight paths goes straight over the hill where we were, and I was able to track the airplanes quite well with my binoculars." All during the time of observation, the UFOs formed triangular formations in the same quadrant of sky. "We were able to view the objects doing their 'dance' for 25 minutes, and then they suddenly disappeared." (Many thanks to Alan Yost for this report.) MYSTERIOUS BLUE METEOR SIGHTED IN MAINE On Saturday, October 7, 2000, at 10 p.m., Jean C. and her daughter were driving on Interstate Highway I-95 between Howland and Lincoln, Maine when the daughter spotted something unusual in the dark night sky. "About 10 p.m., my daughter and I saw a meteorite burn up in the atmosphere," Jean reported, " "This meteorite had a long tail. We believe that it exploded because there was a flash of blue, then it disappeared. There were other people on the road at the time so it must have been seen by more people than just us. We were heading towards the Lincoln area in Maine." (Email Form Report) UFOs SIGHTED IN SOUTHERN ITALY AND SARDINIA On Tuesday, September 26, 2000, "a strange light was photographed hovering over Avellino," a city in Italy's Campania province about 120 kilometers (72 miles) east of Napoli (Naples). "Witnesses noticed 'a rod of light illuminating the mountainside.' The UFO moved sharply in a horizontal motion, then straight up in a vertical motion before 'flying away at a tremendous velocity.'" (See the Italian newspaper Il Mattino for September 27, 2000.) Four days earlier, on Friday, September 22, 2000, at about 10 p.m., "several motorists driving up a mountain near Bosa," a town on the Mediterranean island of Sardinia located 100 kilometers (60 miles) southeast of Sassari, "spotted an elongated object (hovering) above the pass." "The object seemed to be rotating slowly (on its longitudinal axis--J.T.) and it changed colors while emitting a very bright and intense light. People stopped their cars, got out and observed the object for nearly one hour. A few motorists with cameras took photos of the OVNI (Italian acronym for UFO--J.T.)" (See the newspaper L'Unione Sarda for September 25, 2000. Grazie a Edoardo Russo, Antonio Cuccu e Gildo Persone di Centro Italiano di Studi Ufologici per questi rapporti.) DISCOVERY LAUNCH BESET BY TECHNICAL PROBLEMS ""The heralded 100th launch of the space shuttle program was scrubbed Tuesday," October 10, 2000, "by a human goof. Someone had left an 8-ounce metallic pin in a perilous place--on an oxygen line between the shuttle and its huge external fuel tank." "Spotted during a final inspection, with the seven astronauts strapped into the shuttle Discovery, the extraneous part forced NASA to cancel the launch. Engineers feared that the pin could ricochet between the shuttle and the fuel tank, possibly detonating an explosion." "NASA spokesman Joel Wells said the part, used to secure handrails and platforms for shuttle maintenance crews, was left behind 'in a hard-to-reach location.'" "It was found by 'the inspection team,' a crew that inspects the entire shuttle assembly--the orbiter, its booster rockets and the external fuel tank--three hours before launch. The crew had been looking for ice formed by gases released by the spacecraft on the launch pad." This was the latest in a series of delays that have postponed the launch of Discovery, which was scheduled to fly last week. Discovery and its crew of seven astronauts had been scheduled to lift off Thursday evening," October 5, 2000, "from Cape Canaveral on a mission to add two segments to the International Space Station." "NASA scrubbed the launch of Discovery for at least 24 hours, citing concerns about the shuttle's large external fuel tank...The space agency says it was not sure whether a problem existed with Discovery's tank, but film from the launch of space shuttle Atlantis in September revealed that an explosive bolt used to separate the tank from the orbiter was protruding." Bad weather over the weekend, and "gusty wind at Cape Canaveral forced NASA to delay Monday (October 9, 2000) night's launch of space shuttle Discovery...The flight was already four days late because of mechanical problems which were resolved over the weekend." "The wind limit (for shuttle launches) is 48 miles per hour; (Monday's) gusts reached more than 51 miles per hour, NASA spokesman Bruce Buckingham said." "During the 11-day mission, the astronauts will add two new segments to the International Space Station. Until that is completed, no one can move in." (See the Chicago Tribune for October 11, 2000, "8-ounce pin causes expensive new delay for shuttle launch," page 3; and USA Today for October 6, 2000, "NASA postpones 100th shuttle launch," page 4A, and for October 10, 2000, "Wind delays shuttle again," page 3A.) CHINESE SPACE AGENCY LAUNCHES MOON PROGRAM "China's budding space program plans to explore the moon for commercially-useful resources and hopes to some day take part in an international expedition, members of the Chinese space agency said Wednesday," October 4, 2000. "Although details are few, the experts made one thing clear: China sees manned space flight as the key to securing its international status and economic revival." "'If China since the 1960s had not had the atomic bomb and the hydrogen bomb, nor launched its own satellites, China would not be regarded as an influential, powerful country,' Luan Enjie," director of China's State Aerospace Bureau, "told the audience of foreign dignitaries and Chinese schoolchildren at the start of the UN-declared World Space Week." "Started in the 1970s, the Chinese space program successfully built a spacecraft for manned exploration putting the Shenzou (Chinese for Sacred Vessel--J.T.) into orbit last November (1999)." "China hopes to send astronauts aloft, joining the United States and Russia as the only nations with domestic manned space programs." Previous Chinese "media reports indicated a second test flight would come before the year's end and a manned mission may soon follow. Luan revealed little about a timetable, saying only that several missions will follow 'successful flight of an unmanned experimental spacecraft.'" "But he was specific about the program's long-term goals. 'We will conduct exploration of the moon and actively join international activities for Mars exploration.'" "China's manned space program, given the secret designation Project 921, has gathered momentum in recent years, getting help from more experienced Russia and bigger budgets from a government eager not to fall further behind the West." (Many thanks to Steve Wilson for this report.) GEOLOGISTS SAY "BIG WAVE" COULD HIT THE USA "This is not science fiction. It could happen tomorrow or several decades from now--an insignificant piece of time, geologically speaking--but it will happen. The volcano Cumbre Vieja (Spanish for Old Woman's Peak- J.T.), located on the Atlantic Ocean island of La Palma, is thoroughly unstable and could collapse at any moment." La Palma is the largest of the Canary Islands, located west of Morocco. "The island will split in two. Half a trillion tons of rock will fall into the sea within seconds and form a colossal wave measuring some 560 meters )1,868 feet) in height traveling westwards at a speed of 720 kilometers per hour (432 miles per hour). A gigantic tsunami will devastate the islands of the Caribbean and the Eastern Seaboard of the USA. Water from the wave will penetrate more than 20 kilometers (12 miles) inland." "This would seem to be the plot of a disaster movie, but they are in fact the computations of of a team of Swiss scientists concerning measurements taken and then incorporated into an advanced geological profiling program. The results have been published in the Journal of Vulcanology and Geothermal Research." "'It could happen at any time, within 10 years or 10 decades. But please note this: if I lived in Miami or New York, and I heard that Cumbre Vieja was erupting, I wouldn't listen to the news a second longer,' Dr. Simon Bay of London's University College told the BBC." "Scientific fears are based not only on the geophysical computations which indicate that the current island of La Palma, which has only 706 square kilometers of surface area and is 2,406 meters (7,940 feet) in height, is in a precarious geotechnical balance,, they are also concerned about a new eruption of the Cumbre Vieja volcano, which isn't far-fetched considering that it has exploded a dozen times in the last 100,000 years, according to Bay's calculations, and the last eruption on La Palma occurred in 1971." "'This is a much more vivid danger than having an asteroid fall. This could be a catastrophe not only for the island's residents but for the people on the other side of the ocean who have never heard of La Palma,' Bay said." (See the Spanish newspaper Sociedad for October 6, 2000, "Scientists say the island of La Palma will collapse and devastate the Caribbean." Muchas gracias a Scott Corrales para eso articulo.) (Editor's Comment: Remember all those strange "Big Wave" dreams people were having, which have been reported here in UFO Roundup? Maybe they're picking up psychic emanations of this future disaster. For more on "Big Wave" dreams, see this week's feature story.) READER FEEDBACK: DUBYA'S NO SATANIST Glen E. Zook of Texas writes, "The photograph of Gov. George W. Bush on page 9 of 'The Globe' does NOT show him making a pagan sign, etc. What he is doing is making the 'Hooked Horns' sign of the University of Texas. The team name of the University of Texas is the Texas Longhorns (a breed of cattle--G.E.Z.) and the mascot is a longhorn named 'Bevo.' This hand gesture is made at football games, etc." "I moved to Texas after I graduated from Georgia Tech in Atlanta, Ga. However, I have lived in the state for 33 years and have seen this gesture many, many times." ANN ARBOR UFO COULD HAVE BEEN A BLIMP Greg Andrews of Michigan writes, "I'm going out on a limb here, but I'll bet those people were looking at one of the many sport blimps that show up to provide aerial coverage of the University of Michigan football games. Some of these blimps have impressive lights on them for night advertising, which look really odd if you see it at an angle or from a distance." "I'm not saying that it wasn't something more exotic, but it's a pretty good guess that it was a blimp." from the UFO Files... 2060: SECOND NOAH!? This week's article in the Journal of Vulcanology and Geothermal Research has rekindled interest in the recent spurt of "Big Wave" dreams experienced by some of the psychics. Since 1987, your editor has had six dreams about a monstrous tidal wave hitting the eastern shores of the USA. Some were truly frightening, but the most vivid, most detailed and most memorable dream dealt with the aftermath of the "Big Wave." I had this dream in April of 1996. I dreamed I was sitting at a desk in a darkened room. In front of me was a very odd-looking desktop computer. I groped for the on-switch, but I couldn't find it. Then I accidentally moved my hand across the screen, and it came on. A curved keyboard automatically came out of a panel of what I thought was the CPU. Figuring to access AOL, I typed "Menu" and hit what I thought was the Enter tab. The computer began beeping and making weird geometric patterns onscreen. The keyboard went in and out of its aperture like a cuckoo clock. I thought, I need some technical assistance with this thing, and, waving my hand in front of the screen, I shut it down and left the room. I found myself in a darkened upstairs hallway. I groped for a light switch, found it and flicked it. Nothing. (Editor's Note: Apparently the computer had its own built-in power pack.) Making my way downstairs, I saw that the first floor was a complete shambles. Overturned furniture, debris, patches of silt and muck on the floor. An overwhelming damp, dank scent like seawater. I went outside. Instantly I recognized the neighborhood. I was on the east side of Peck Street, in my childhood hometown of Attleboro, Massachusetts, about midway between North Main and Bank Streets. There was no mistake. This was Peck Street, the same street I had walked on my way to school for 12 years. Like Dickens, I could walk it blindfolded. But Peck Street had changed a bit. The Roman Catholic and Episcopalian churches still stood sentinel on each corner of Peck and North main. But they looked like stone islands in a vast lake. The whole corner was underwater. A similar "lake" occupied the wetlands north of the street, running along Bank Street. The Duffy-Poole Funeral Home, at the corner of Peck and Danforth Streets, was gone, replaced by a garden apartment complex with a first-floor cafe and gift shop. Same story across the street, where the old Victorian homes stood. Then I spotted the ranch house. Different paint scheme but the same house, only now it looked like one of the oldest homes on the street. Now, I remember when that house was built. It was back in 1957, when I was in the second grade. The following spring, the owner planted maple saplings in the yard. Today they're mature maples. But in my dream, the remaining trees looked about a century old. Meaning I was seeing Peck Street in about 2060 A.D. I figured that out later, though. My initial reaction was one of horrified shock. What happened to Attleboro!? The area looked as if it had been hit by a massive tidal wave of hurricane. Flood damage was everywhere. Shattered walls, overturned cars, downed trees, ponds littered with debris. The earth was sodden underfoot as I made my way across the lawn toward the sidewalk. There was no sign of any other humans. Where is everybody? I wondered. Looking toward a downed maple tree, I saw what I at first thought was a bundle of clothes in the water. Then I realized it was a man. I plunged into the thigh-deep water on the street and pulled him up onto the lawn. I rolled him over. He was a man in his early twenties, with a gold stud in each ear lobe and a forked beard and a curious haircut--slight bangs with a curled ponytail. Denim jacket and dark slacks. I put my hand on his throat. No pulse. He was dead. Rigor had come and gone, so I guess he was in the water for a day or two. Just then, I heard a soft whirring noise. Looking up I saw an unusual white craft flying from west to east at an altitude of about 2,000 feet. I gaped in astonishment. I don't believe it! A UFO! The object stopped. Some kind of canopy slid open and a man in black stood up. All at once, a light began winking at me. I heard a sound like angry bees on my left, and vertical fountains erupted in the water all around me. He's shooting at me! Grabbing a quick breath, I did a belly flop into the water. Went under and stayed under, gripping sunken rocks and debris to keep myself submerged. My lungs began to burn, but I didn't dare surface. Then I remembered the fallen maple tree just ahead. Doing a tadpole crawl along the bottom, I reached the branches, then pulled myself along into deeper water until I was close to the trunk. My face poked out of the water, and I drank in long breaths of air. Peering through the leaves, I could see the unusual aircraft fifty feet above. It was some kind of hybrid airplane/hovercraft. The studdy white fuselage was like an A-6 but with a huge, broad, bell-shaped rotorfan underneath it. There was a conventional empennage--upright tail and stabilizers, and thrust was provided by two small turbofan engines on outrigger pylons near the tail. On the tail I saw the black wreathed globe symbol of the United Nations with a logo underneath reading World Air Service. It was a two-seater, side-by-side cockpit. The bubble canopy was up. Both men wore black flight suits with large sky-blue helmets with Polaroid sun visors. One handled the controls; the other stood upright, toting what looked like a bull[up-style automatic weapon with a banana clip. The World Air Service hovercraft drifted around overhead for another five minutes. Its rotor raised ripples on the pond, and I got a few mouthfuls of brackish saltwater. Then the clear canopy descended, and it resumed its eastward flight. I gave it another five minutes and staggered out of the street pond. They must have thought I was a looter, I reflected, shivering as the wind began to pick up. (Editor's Comment: Or perhaps the flying UN police of 2060 don't bother to arrest and question suspects. Perhaps they merely gun them down.) Seeking shelter, I wandered through backyards. Most of the doors I tried were locked. But then I got lucky. The house I entered had severe flood damage on the first floor, but the second-story bedrooms were dry. I found a bedroom, doffed my soaked clothes, wrung the water out of them with my bare hands, and let them air-dry while I warmed myself beneath the bed's blankets. I must have dozed for awhile, because the next thing I knew, a Pomeranian dog hopped onto the bedspread and began barking. Sitting up, I ruffled the fur on the back of his neck and asked, "Where did you come from?" Suddenly, I heard a woman's voice on the first floor. "Honey, I think somebody's up there." Then a but louder from the stairwell. "Hello? Who's there?" And I woke up. Reading about the Cumbre Vieja volcano in the Canary Islands I wonder if I was given a glimpse of the aftermath of that disaster. Attleboro is about 15 miles north of Narragansett Bay, the nearest arm of the Atlantic Ocean, so it's conceivable that the city might fall within the flood zone. Even if it does get a bit banged up, it's comforting to know that Attleboro will still be there sixty years from now. I wish I could say the same about the Temple Mount. The way things are going, by the year 2060, they're liable to be calling that place Radioactive Crater Lake. O JERUSALEM DEPT.: No jokes this week, readers. The situation is too serious for that. The death toll is already over one hundred, and the wounded number in the thousands. Today it's a platoon-level war, with mobs rioting on the side. But it could escalate into heavy weapons and big battalions any time now. Here are a few things the Zionist sympathizers in mass media had withheld from the USA public. (1) On Sunday, October 8, thousands of Hasidic Jews attacked an upscale restaurant in Tel Aviv, setting it on fire and threatening to burn the Arab waiters alive. (2) On Tuesday, October 10, Ehud Barak made common cause with the Likud, inviting them to join a coalition government. Yes, that's the same Likud whose poster boy, Gen. Ariel Sharon, led his merry band of goat molesters into the Haram as-Sharif September 28 and desecrated the Al-Aqsa mosque, thereby setting off the current war of religion. (3) Also on Tuesday, October 10, Jews firebombed the Mahmoudin Mosque in Jaffa, presumably in retaliation for the Muslims' destruction of Joseph's Tomb. (4) Jews also firebombed the Hassan Ben Mosque. While these incidents have not been mentioned on American network TV, let me assure you, they are the Number One topic of conversation at the bazaar in Quetta, Pakistan. Eleven weeks ago, Tackanash, Francisco Marto and Jacinta Marto came to me in a dream and warned that "a major war will soon break out in the Middle East." Will these dream-predictions all come true? We'll know for certain on November 8, 2000. Until then, readers, keep hoping and praying and working for peace. Join us in seven days for more UFO and paranormal news from around the planet Earth, brought to you by "the paper that goes home--UFO Roundup." See you next week! UFO ROUNDUP: Copyright 2000 by Masinaigan Productions, all rights reserved. Readers may post news items from UFO Roundup on their websites or in newsgroups provided that they credit the newsletter and its editor by name and list the date of issue in which the item first appeared. | Mid | [
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From Exit 16 on I81 take 9W toward Berkeley Springs. Mountain Lake Road is approximately 7 miles down on left. The Woods Road is ~2 miles down on right. Take left onto Bald Eagle Trail. Turn left onto Pileated Woodpecker and house on left. Financial Considerations Association Fee:$271 Quarterly Ownership Type:Fee Simple Tax/Property ID: 020412F010800000000 Tax Amount:$618 Tax Year: 2016 Market Activity Listing Price History HEDGESVILLE Real Estate HEDGESVILLE is located in West Virginia. HEDGESVILLE, West Virginia 25427 has a population of 292. The median household income in HEDGESVILLE, West Virginia 25427 is $50,500. The median household income for the surrounding county is $53,332 compared to the national median of $53,046. The median age of people living in HEDGESVILLE 25427 is 31.3 years. | Low | [
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A hot air balloon floats over farm fields south of Washington, Ill., as the sun slips behind clouds on the autumn afternoon of Wednesday, Sept. 24, 2014. (AP Photo/Peoria Journal Star, Ron Johnson) (Newser) – A romantic ride in a hot air balloon turned into a rescue operation, with lifeguards and surfers saving three people after the basket dipped into the ocean off a Southern California beach. A man was proposing to his girlfriend during their sunset ride yesterday when the balloon drifted off course and hovered over the water near Cardiff-by-the-Sea, KNSD-TV reported. A crowd of people watched as the balloon drifted toward the beach in northern San Diego County and skimmed the water. Eric Barretto said he and his fiancee threw a rope to the water below and several surfers pulled the balloon back to shore. "It's unforgettable. That's all I can say," Barretto told the station. "I don't know if we'll do it again." The pilot stayed with the balloon and kept it inflated while it was tugged onto the beach. The balloon basket landed in the surf and took in several waves, said a local marine safety official. Nobody was injured. voice in balloon to woman below "I need to get to the game, but I'm off course, where am I?" Woman below "you're in a balloon" "you must be a woman" "why yes, how did you know?" "I asked you for information, your answer doesn't help one bit, and now I'll miss the game" "you must be a man" "why yes I am, how can you tell?" "You're trying something that won't work, ask me a question that makes no difference, and somehow missing the game is now my fault." BikeNEPA Oct 6, 2014 12:25 PM CDT Now that is a proposal they will never forget. Glad it worked out for them and no one got hurt. | Low | [
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[The suppression of the contractile activity of the cardiomyocytes by dermorphin in a heart culture of newborn rats]. Opioid peptides exert ino- and chronotropic effects on the heart. Paraopioid dermorphine (Y-dA-F-G-Y-P-S) was earlier shown to act as negative inotropic agent in isolated frog's hearts. In this study, the same effect was investigated in cultured myocardiac cells of the newborn rats. Dermorphine (10(-4)-10(-9) M) dose-dependently attenuated the contraction amplitude with the latency of 5-10 min. The peak of the response appeared in 30-45 min after application of dermorphine. The mu-opiate-receptor antagonist naloxone (10(-5) g/ml) blocked this effect. Dermorphine seems to exert its negative inotropic action through the opiate receptors, presumably of the mu-subtype. | Mid | [
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How to control an intracellular proteolytic system: Coordinated regulatory switches in the mycobacterial Pup-proteasome system. Intracellular proteolysis is critical for the proper functioning of all cells, owing to its involvement in a wide range of processes. Because of the destructive nature of protein degradation, intracellular proteolysis is restricted by control mechanisms at almost every step of the proteolytic process. Understanding the coordination of such mechanisms is a challenging task, especially in systems as complex as the eukaryotic ubiquitin-proteasome system (UPS). In comparison, the bacterial analog of the UPS, the Pup-proteasome system (PPS) is much simpler and, therefore, allows for insight into the control of a proteolytic system. This review integrates available information to present a coherent picture of what is known of PPS regulatory switches and describes how these switches act in concert to enforce regulation at the system level. Finally, open questions regarding PPS regulation are discussed, providing readers with a sense of what lies ahead in the field. | Mid | [
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Q: How Virtual Memory isolate different processes? Lets say I have two processes, process A and process B When the system is in Process A, CPU generates a virtual address let's say 0x800000. And the it switches to process B via context switch, the CPU also generates a same virtual address 0x800000. so if we write something to the page, how OS know it should be a page in Process B need to be modified rather than Process A? A: It is logical memory translation that separates processes; not virtual memory. Processes see logical memory addresses and have no access to the underlying physical memory. Each process has tables that tell the CPU how to translate logical addresses to physical addresses. The operating system maintains these tables. The location the tables are identified using protected hardware registers. When Process A switches out and Process B switches in, the operating system (assisted by the underlying hardware) changes the value of the registers so that B's tables are used. After that, the logical address 0X800000 no longer refers to "A"s physical memory location and instead points to "B"'s. | High | [
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This post was originally titled, “Asleep at the wheel: Junk science gets promoted by Bill Gates, NPR, Ted, University of California, Google, etc.,” but I decided the above quote had better literary value. We’ve had a few posts now about discredited sleep scientist Matthew Walker; see here and here, and here, with the disappointing but unsurprising followup that his employer, the University of California, just doesn’t seem to care about his research misconduct. According to his website, Walker is employed by Google as well. Heart attacks Also disappointingly but unsurprisingly, further exploration of Walker’s work reveals further misrepresentations of research. Markus Loecher shared this investigation of some attention-grabbing claims made in the celebrated Ted talk, “Sleep is your superpower.” Here’s Walker: I could tell you about sleep loss and your cardiovascular system, and that all it takes is one hour. Because there is a global experiment performed on 1.6 billion people across 70 countries twice a year, and it’s called daylight saving time. Now, in the spring, when we lose one hour of sleep, we see a subsequent 24-percent increase in heart attacks that following day. In the autumn, when we gain an hour of sleep, we see a 21-percent reduction in heart attacks. Isn’t that incredible? And you see exactly the same profile for car crashes, road traffic accidents, even suicide rates. “Isn’t that incredible?”, indeed. This reminds me of the principle that, if something is being advertised as “incredible,” it probably is. Loecher decided to look into the above claim: I [Loecher] tend to be sensitive to gross exaggerations disguised as “scientific findings” and upon hearing of such a ridiculously large effect of a one-day-one-hour sleep disturbance, all of my alarm bells went up! Initially I was super excited about the suggested sample size of 1.6 billion people and wanted to find out how exactly such an incredible data set could possibly have been gathered. Upon my inquiry, Matthew was kind enough to point me to the paper, which was the basis for the rather outrageous claims from above. Luckily, it is an open access article in the openheart Journal from 2014. Imagine my grave disappointment to find out that the sample was limited to 3 years in the state of Michigan and had just 31 cases per day! On page 4 you find Table 1 which contains the quoted 24% increase and 21% decrease expressed as relative risk (multipliers 1.24 and 0.79, respectively): Loecher notes the obvious multiple comparisons issues. But what I want to focus on is the manipulation or incompetence (recall Clarke’s Law). To start with, here’s the summary from the above-linked article: Now, we could argue about whether the data really show that daylight savings time “impacts the timing” of acute myocardial infarction—arguably, the data here are consistent with no effect on timing at all! But let’s set that aside and focus on the other point of their summary: daylight savings time “does not influence the overall incidence of this disease.” This completely contradicts Walker’s theme of sleep deprivation being dangerous. It did not influence the overall incidence of the disease! Presumably Walker realized this: even if he didn’t read the whole article, he must have read the abstract, at least to pull out those 24% and 21% numbers. (Or maybe Walker’s research assistant did it, but no matter. If Walker gets credit for the book and the Ted talk, he also gets blame for the errors and misrepresentations that he puts out under his name.) So . . . he read a paper claiming that, at most, daylight time is associated with some time-shifting of heart attacks, and he misrepresents that as being associated with an increase. Also, he says is “a global experiment performed on 1.6 billion people,” but he’s reporting results on one U.S. state. He must have realized that too, no, that this was not a N = 1.6 billion study??? But wait, there’s more. We switch to daylight time 2am on Sunday. So you might expect the largest effects to occur on Sunday—that day with the sleep deprivation. Or maybe Monday, the first day back at work. All sorts of things are possible. The point is that that, by saying it as “that following day,” Walker is hiding the choice. If it’d been Sunday, it would’ve been “the very day of,” etc. And then when he talks about autumn, he doesn’t say “that following day,” just leaving the (false) impression that it’s the same pattern both seasons. Tuesday, huh? I also wonder about Walker’s other claim, that at the switch to daylight or standard time “you see exactly the same profile for car crashes, road traffic accidents, even suicide rates.” Exactly the same, huh? I’ll believe it when I see the data, and not before. Testicles Loecher also looks into Walker’s claim that “Men who sleep five hours a night have significantly smaller testicles than those who sleep seven hours or more.” There seems to be no good evidence for that one either. Ted and Edge and all the rest I hate the whole Ted talk, Edge foundation, Great Man model of science. It can destroy people. As I wrote last year: Don’t ever think you’re too good for your data. . . . Which reality do we care about? The scientific reality of measurement and data, or the social reality that a Harvard [or University of California] professor can get caught falsifying data and still be presented as an authority on science and philosophy. Ultimately, both realities matter. But let’s not confuse them. Let’s not confuse social power with scientific evidence. Remember Lysenko. . . . OK, why am I picking on these guys? Marc Hauser and the Edge foundation: are these not the deadest of dead horses? But remember what they say about beating a dead horse. The larger issue—a smug pseudo-humanistic contempt for scientific measurement, along with an attitude that money plus fame = truth—that’s still out there. An always-relevant quote From Dan Davies: Good ideas do not need lots of lies told about them in order to gain public acceptance. A message to Bill Gates, NPR, Ted, University of California, Google, etc. It’s not your fault that you got scammed. I mean, sure, it’s kind of your fault for not checking, but that’s easy to say after the fact. Anyone can get scammed. I’ve been scammed! My political scientist colleague Don Green got scammed! Harvard got scammed by that disgraced primatologist. Cornell got scammed . . . George Schultz got scammed . . . maybe you’ve heard about that one. People get scammed. Scammers scam people, that’s what they do. You got scammed. That’s in the past, now. The question is: Are you gonna continue to let yourself get scammed? I’ll break that down into 2 questions: 1. Do you now, at last, realize you’ve been scammed? (If not, what would it take? An actual manipulated graph?? No, I guess not; we already have one of those!) 2. If your answer to the first question is Yes, then are you gonna decide that it’s worth your while to continue to get scammed, because the cost in effort and bad publicity is worse than the cost of continuing to promote this stuff? If the answer to question 1 is No, that’s just sad, that people could see all this evidence and still not get the point. If the answer to question 1 is Yes and the answer to question 2 is No, that’s even sadder. A quick google search appears to reveal six separate appearances by Walker on NPR, with the most recent being this June, several months after Guzey’s takedown of Why We Sleep. But I’m guessing that, once NPR had Walker on once or twice, he became a known quantity for them, so they just put him in the Expert category. Ted? They’ve had iffy talks before, I guess it comes with the territory. They’re probably focusing on scheduling and promoting new talks, not on problems with talks they’ve already posted. Bill Gates? He endorsed Walker’s book and now he’s moved on. Gates probably doesn’t care about an endorsement that’s sitting in the past. The University of California? They know about the problems with Walker’s work but they’ve carefully looked away. I think they’re basically Yes on question 1 and No on question 2, except that they’ve tried really hard to avoid answering question 1. At some level, they must know they’ve been scammed, but as long as they avoid looking at Walker’s work carefully (even to the extent of carefully reading a few blog posts), they can maintain a facade of uncertainty. Google? I have no idea. I don’t know what Walker does for Google. Maybe he’s doing great work for them. Yes, he has a problem with exaggerating research claims in publications and public talks, but maybe he does excellent work when the lights of publicity are not shining. In that case, he’s not scamming Google at all. Also, Walker could well be scamming himself. I’m not trying to paint him as some cackling villain here. I could well imagine he’s a true believer in the healing power of sleep, and that when he misrepresents the evidence, in his view that’s just because he doesn’t have all the data at hand. Sure, they didn’t really have data on 1.6 billion people, but if they did, it would undoubtedly confirm his views. He has a direct line to the truth, and he’d be remiss if he didn’t shout it from the treetops. The trouble is, people who think they have a direct line to the truth, often’t don’t. Recall the above quote from Dan Davies. Tony Blair probably thought those WMDs were real too, at some point—or, if they weren’t, they could’ve been, right? And the war was a good idea anyway, right? Etc. To return to sleep studies: the data support the theory, and once you believe the theory, you don’t need the data anymore. As always, I’d have no problem if this guy were to just straight-up give inspirational talks and write inspirational books. He could just say that he personally believes in the importance of sleep, and his broad reading and experience has lead him to this conclusion. It’s when he misrepresents data, that’s where I have the problem (even though the University of California doesn’t seem to mind). | Low | [
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Only 25% of Brits complain when subjected to poor customer service 55% feel confident complaining about a utility company such as an energy provider There is perhaps nothing quite as exasperating as bad customer service, and a recent survey carried out by uSwitch shows that Brits get more than their fair share of it: 65% of consumers say they regularly experience poor customer service. While the number of people being subjected to long lines, bad attitudes, or shoddy service isn’t surprising, the number willing to speak up about it is. Only 27% of consumers say that they will ‘complain without fail’ when dissatisfied, and 10% rarely or never complain at all. Letting them get away with it The reasons consumers claim they do not bother voicing their unhappiness are varied: 60% don’t complain because they say there is no point, and that their complaint won’t make a difference; 58% can’t be bothered, saying it’s not worth the hassle. A quarter of consumers don’t speak up out of fear, either due to lack of confidence, feeling intimidated or because of a previous bad experience involved with complaining. Is anybody listening? Exactly half (50%) report having had their problems resolved right away ‘at times’. Meanwhile, 36% say they had to persevere with their complaint because they were initially dismissed. About 20% had to pull out the big guns — including taking their issue to an Ombudsman or arbitrator. One per cent went so far as to take legal action. Almost half of consumers report facing some obstruction from a company when trying to complain, while another 32% had to endure rudeness. Almost a quarter of survey respondents say a member of staff refused to provide their name. The impact of poor service Back in February, it was reported that only four in 10 trusted their energy supplier. This number had dropped by 5% in less than two years, with poor customer service being noted as contributing to this decrease. Customers said their energy supplier was ‘unhelpful’ and ‘guilty of poor communication’ when it came to important information about their energy bill. Know your rights Many consumers’ willingness to complain has to do with the kind of company they are dealing with. Nearly 70% ‘feel confident’ about complaining to a retailer, including high street shops and supermarkets. That number drops to just 55% when it comes to complaining about utility companies. And less than 40% will speak up when dissatisfied with a Government department. uSwitch Limited is authorised and regulated by the Financial Conduct Authority (FCA) under firm reference number 312850. You can check this on the Financial Services Register by visiting the FCA website. | Mid | [
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Tuesday, 21 October 2008 We're busy producing the next issue of New Humanist (I'm proofing things as I write this) but I just wanted to give you a quick update on the Atheist Bus Campaign, because what's happened since midnight last night is extraordinary. The target was £5,500, which Richard Dawkins agreed to match, but they hit that at 10am. Right now it's up to £20,882, but that's rising every time I click refresh on the donation page. The higher the amount gets, the more time and more buses there'll be displaying the positive message of "There's probably no God. Now stop worrying and enjoy your life", so do get involved and donate some cash. 4 comments: d earlier I am now going to sit back and wait for the first christian, hindu, muslim, etc etc bus driver to refuse to drive one of the buses- you can't buy that kind of publicity :)Although- my American friends do admit that the buses wouldn't survive intact very long in their country I suspect there may well be some religious graffitti and/or protests of some kind over here too :) Then again- I wonder what would happen if 'god' was changed to 'allah'? Having come to know and love the One who loved me into life and loves me moment by moment into life, and you too,I simply cannot understand the message on this bus. What on earth has lack of enjoyment or worry to do with Christ? It is Christ who reveals who God is. All honour and glory to Him. | Low | [
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MORRISTOWN, N.J., March 13, 2019 (GLOBE NEWSWIRE) -- Melinta Therapeutics, Inc. (NASDAQ: MLNT), a commercial-stage company, developing and commercializing novel antibiotics to treat serious bacterial infections, today reported financial results and provided a business update for the fourth quarter and full-year ended December 31, 2018. In 2018, Melinta achieved several key milestones within its commercial, development and business development operations critical to positioning the company for long-term growth. “We are pleased with the decisive actions we took in 2018 to realign the business and help position Melinta for future growth and stockholder value creation. In the past year, the Company has made significant strides to streamline operations and strengthen its balance sheet, while at the same time executing against our sales and clinical goals,” said John H. Johnson, chief executive officer of Melinta. “As a result, we delivered revenues of $96.4 million, driven by $46.6 million in net product sales. In addition, the positive results we reported in 2018 give us confidence in the commercial potential of our products and pipeline.” “We have several upcoming milestones in 2019, including opportunities to potentially expand product labels and increase our marketing territory. We believe that the Company’s efforts over the past year coupled with our strategic initiatives underway position Melinta to continue leading the global fight against antimicrobial resistance and delivering anti-infective solutions to patients,” continued Johnson. Fourth Quarter and Full-Year Results -- In the fourth quarter, sales of commercial products increased 32% compared to the third quarter of 2018, driven by strong Vabomere® (meropenem and vaborbactam) and Orbactiv® (oritavancin) performance -- Delivered full-year 2018 revenues of $96.4 million, including $46.6 million in net product sales -- Melinta ended the year with $81.8 million of cash and cash equivalents Portfolio Updates -- Vabomere received European Commission approval in November 2018 for the following indications in adult patients: -- Complicated intra-abdominal infections (cIAI) -- Complicated urinary tract infections (cUTI) -- Hospital-acquired pneumonia including ventilator associated pneumonia (HAP/VAP) -- Bacteraemia that occurs in association with any of these infections -- Infections due to aerobic Gram-negative organisms where treatment options are limited -- Reported positive top-line results from the Phase III trial of Baxdela® (delafloxacin) for the treatment of adult patients with community-acquired bacterial pneumonia (CABP) in October 2018 -- Began preparation of supplemental new drug application (sNDA) to the U.S. Food and Drug Administration (FDA) for Baxdela in CABP, which is expected to be filed in the second quarter of 2019 -- Entered into a commercial agreement with Menarini Group to commercialize Vabomere, Orbactiv and Minocin®(minocycline) for injection in 68 countries outside of the U.S. in October 2018 Business Highlights -- John H. Johnson named permanent chief executive officer -- Closed the initial $75 million disbursement under the previously announced $135 million convertible loan facility from Vatera Healthcare Partners, LLC on February 22, 2019 -- Implementation of operating cost reduction initiatives expected to deliver significant cost savings in 2019 -- Strengthened Board of Directors and senior leadership team through new appointments adding beneficial experience and expertise to Melinta -- Effected a one-for-five reverse stock split of the Company’s common stock on February 22, 2019 “We were pleased to announce the closing and receipt of the initial $75 million disbursement of the $135 million convertible loan facility from Vatera in February 2019,” said Peter Milligan, chief financial officer of Melinta. “We believe this funding, along with existing cash and cash from future revenue, will provide valuable liquidity to support the Company’s operations as we continue to take steps to become cash-flow positive. We will continue to exercise disciplined post-integration stewardship of cash resources and spending to achieve significant operating expense savings in 2019.” 2019 GuidanceThe Company provides guidance for the full-year 2019 as follows: -- Net product sales of approximately $65 million -- Gross margin of approximately 55%, including intangible assets amortization -- Operating expenses of approximately $140 million Upcoming Potential Catalysts -- Expected sNDA submission to FDA for Baxdela for treatment of CABP -- European Commission approval decision for delafloxacin (to be marketed under the brand name Quofenix) for acute bacterial skin and skin structure infections (ABSSSI) -- Country approvals for Baxdela in South America and Central America -- Execute Latin America commercialization agreement for Vabomere, Orbactiv and Minocin for injection Fourth Quarter and Full-Year 2018 Financial ResultsMelinta reported revenue of $35.5 million and $96.4 million, respectively, for the fourth quarter and full-year ended December 31, 2018. Revenue from product sales was $14.6 million for the quarter and $46.6 million for the full-year, representing the first year of product sales in the Company’s history. Cost of goods sold (“COGS”) was $9.0 million and $41.1 million, respectively, for the fourth quarter and full-year ended December 31, 2018, of which $3.9 million and $16.4 million was comprised of non-cash amortization of intangible assets. In addition, for the fourth quarter and full-year ended December 31, 2018, we recorded $1.0 million and $8.0 million, respectively, in charges related to inventory that is approaching shelf life, primarily driven by product launches. There were no product sales and therefore no costs of goods sold in the prior year period. Research and development (“R&D”) expenses were $10.4 million and $55.4 million, respectively, for the fourth quarter and full-year ended December 31, 2018, compared to $11.6 million and $49.5 million for the same periods in 2017. Selling, general and administrative (“SG&A”) expenses were $29.5 million and $133.3 million for the fourth quarter and full-year ended December 31, 2018, compared to $37.3 million and $63.3 million for the same periods in 2017. R&D and SG&A expenses increased primarily as a result of the additional costs associated with the acquisition of The Medicines Company infectious disease business (“IDB”) and the Cempra merger. In addition, SG&A included severance-related costs of $8.9 million and $12.3 million, respectively, for the fourth quarter and full-year ended December 31, 2018, as well as an offsetting gain of $8.8 million from the remeasurement of contingent consideration associated with the acquisition of the IDB from The Medicines Company in January 2018. Also, during the fourth quarter of 2018, we recognized goodwill impairment charges of $25.1 million related to the acquisition of the IDB in the first quarter of 2018. Net loss was $44.1 million, or $3.94 per share, for the fourth quarter of 2018, compared to a net loss of $20.9 million, or $7.40 per share, for the fourth quarter of 2017. Net loss was $157.2 million, or $17.12 per share, for the year ended December 31, 2018, compared to a net loss of $78.2 million, or $109.28 per share, for 2017. Net loss per share year-over-year was impacted by changes in share count as a result of the Cempra merger and financing related to the acquisition of the IDB, as well as a one-for-five reverse stock split effective on February 22, 2019. Conference Call and WebcastMelinta’s earnings conference call for the fourth quarter and full-year ended December 31, 2018 will be broadcast at 4:30 p.m. ET on March 13, 2019. The live webcast can be accessed under “Events and Presentations” in the Investor Relations section of Melinta’s website at www.melinta.com. A live webcast of the call will be available online from the Investor Relations section of the company website at www.melinta.com and will be archived there for 30 days. A telephone replay of the call will be available by dialing 855-859-2056 for domestic callers or 404-537-3406 for international callers and entering the conference ID # 1698998. About Melinta TherapeuticsMelinta Therapeutics, Inc. is the largest pure-play antibiotics company, dedicated to saving lives threatened by the global public health crisis of bacterial infections through the development and commercialization of novel antibiotics that provide new therapeutic solutions. Its four marketed products include Baxdela® (delafloxacin), Vabomere® (meropenem and vaborbactam), Orbactiv® (oritavancin), and Minocin® (minocycline) for Injection. This portfolio provides Melinta with the unique ability to provide providers and patients with a range of solutions that can meet the tremendous need for novel antibiotics treating serious infections. Visit www.melinta.com for more information. As more fully described in our Annual Report on Form 10-K for the year ended December 31, 2017, the former private company Melinta was determined to be the accounting acquirer in our November 2017 reverse merger with Cempra and, accordingly, historical financial information for the fourth quarter and full year 2017 presented in this press release reflects the standalone former private company Melinta until November 3, 2017, and, therefore, period-over-period comparisons may not be meaningful. Non-GAAP Financial MeasuresTo supplement our financial results presented on a U.S. generally accepted accounting principles, or GAAP, basis, we have included information about non-GAAP adjusted EBITDA, a non-GAAP financial measure, as a useful operating metric. We believe that the presentation of this non-GAAP financial measure, when viewed with our results under GAAP and the accompanying reconciliation, provides supplementary information to analysts, investors, lenders, and our management in assessing the Company’s performance and results from period to period. This non-GAAP measure closely aligns with the way management measures and evaluates the Company’s performance. This non-GAAP financial measure should be considered in addition to, and not a substitute for, or superior to, net income or other financial measures calculated in accordance with GAAP. Non-GAAP Adjusted EBITDA is not based on any standardized methodology prescribed by GAAP and represents GAAP net income (loss), which the Company believes is the most directly comparable GAAP measure, adjusted to exclude interest income, interest expense, depreciation and amortization, stock based compensation expense, changes in the fair value of our warrant liability, impairment charges, bargain purchase gains, gains or losses on extinguishment of debt, acquisition-related costs, gains on the reversal of loss contracts, and other adjustments, including the remeasurement of contingent consideration related to our acquisition of IDB and launch-related excess and obsolete inventory. Non-GAAP financial measures used by us may be calculated differently from, and therefore may not be comparable to, non-GAAP measures used by other companies. Cautionary Note Regarding Forward-Looking StatementsCertain statements in this communication constitute “forward-looking statements” within the meaning of Section 27A of the Securities Act and Section 21E of the Securities Exchange Act and are usually identified by the use of words such as “anticipates,” “believes,” “estimates,” “expects,” “intends,” “may,” “plans,” “projects,” “seeks,” “should,” “will,” and variations of such words or similar expressions, including statements related to guidance. We intend these forward-looking statements to be covered by the safe harbor provisions for forward-looking statements contained in Section 27A of the Securities Act and Section 21E of the Securities Exchange Act and are making this statement for purposes of complying with those safe harbor provisions. These forward-looking statements reflect our current views about our plans, intentions, expectations, strategies and prospects, which are based on the information currently available to us and on assumptions we have made and include statements regarding: expectations with respect to our financial position, results and performance. Although we believe that our plans, intentions, expectations, strategies and prospects as reflected in or suggested by those forward-looking statements are reasonable, we can give no assurance that the plans, intentions, expectations, strategies or prospects will be attained or achieved. Furthermore, actual results may differ materially from those described in the forward-looking statements and will be affected by a variety of risks and factors that are beyond our control. Risks and uncertainties for Melinta include, but are not limited to, the fact that we have incurred significant operating losses since inception and will incur continued losses for the foreseeable future; our limited operating history; our need for future capital and risks related to our ability to obtain additional capital to fund future operations; risks related to the satisfaction of the closing conditions for the remaining two disbursements under the loan agreement with Vatera, including any consequences of a failure to close on the two disbursements under the Vatera loan financing; risks related to compliance with the covenants under our facilities with Vatera and Deerfield; uncertainties of cash flows and inability to meet working capital needs as well as other milestone, royalty and payment obligations, including as a result of the outcome of the pending litigation with respect to, and any requirement to make, payments potentially due to The Medicines Company; risks that may arise from the consummation of the Vatera loan financing and the effectiveness of the amendment to the Deerfield facility agreement, including potential dilution to our stockholders and the fact that Vatera will beneficially own a substantial portion of our common stock; the fact that our independent registered public accounting firm’s report on the Company’s 2016, 2017, and 2018 financial statements contains an explanatory paragraph that states that our recurring losses from operations and our need to obtain additional capital raises substantial doubt about our ability to continue as a going concern; our substantial indebtedness; risks related to the commercial launches of our products and our inexperience as a company in marketing drug products; the degree of market acceptance of our products among physicians, patients, health care payors and the medical community; the pricing we are able to achieve for our products; failure to obtain and sustain an adequate level of reimbursement for our products by third-party payors; inaccuracies in our estimates of the market for and commercialization potential of our products; failure to maintain optimal inventory levels to meet commercial demand for any of our products; risks that our competitors are able to develop and market products that are preferred over our products; our dependence upon third parties for the manufacture and supply of our marketed products; failure to achieve the benefits of our recently completed transactions with Cempra and The Medicines Company; failure to establish and maintain development and commercialization collaborations; uncertainty in the outcome or timing of clinical trials and/or receipt of regulatory approvals for our product candidates; undesirable side effects of our products; failure of third parties to conduct clinical trials in accordance with their contractual obligations; our ability to identify, develop, acquire or in-license products; difficulties in managing the growth of our company; the effects of recent comprehensive tax reform; risks related to failure to comply with extensive laws and regulations; product liability risks related to our products; failure to retain key personnel; inability to obtain, maintain and enforce patents and other intellectual property rights or the unexpected costs associated with such enforcement or litigation; risks relating to third party infringement of intellectual property rights; our ability to maintain effective internal control over financial reporting; unfavorable outcomes in any of the class action and shareholder derivative lawsuits currently pending against the Company; and the fact that a substantial number of shares of common stock may be sold into the public markets by one or more of our large stockholders in the near future. Many of these factors that will determine actual results are beyond Melinta’s ability to control or predict. Other risks and uncertainties are more fully described in our Annual Report on Form 10-K for the year ended December 31, 2018, our Revised Definitive Proxy Statement filed January 29, 2019, and in other filings that Melinta makes and will make with the SEC. Existing and prospective investors are cautioned not to place undue reliance on these forward-looking statements, which speak only as of the date hereof. The statements made in this press release speak only as of the date stated herein, and subsequent events and developments may cause our expectations and beliefs to change. While we may elect to update these forward-looking statements publicly at some point in the future, we specifically disclaim any obligation to do so, whether as a result of new information, future events or otherwise, except as required by law. These forward-looking statements should not be relied upon as representing our views as of any date after the date stated herein. | Mid | [
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Search Lee backs crackdown; Avalos: "I stand with Occupy SF" One of several trucks leave with Occupy SF belongings after the camp was unexpectedly raided in the middle of the night. Quinn Norton Mayor Ed Lee has just released a statement on last night's police raid of the Occupy San Francisco encampment – claiming to basically support the movement but also support the harsh police crackdown and seizure of tents, food, and other personal property – that offers a sharp contrast to the position of his mayoral rival, John Avalos, who is condemning the SFPD's actions. On both issues, Lee mouthed the meaningless “jobs” defense, claiming that he was trying to help working people by letting their employers raid their health care funds, allowing restaurants to fraudulently jack up their bills, or directing the police to seize their tents and food. That's not just pandering, it's insulting. I've tried unsuccessfully to get Lee's office to offer more detailed explanations of his positions, but they're so far sticking to prepared statements that are riddled with contradictions. So we're just going to run the full statements by Lee and Avalos and let you decide who makes more sense and best reflects San Francisco values. Lee wrote: “I understand and sympathize with the anxiety and frustration felt by so many in our country caused by a lingering recession and joblessness. That’s why I am doing everything I can to create jobs, get people back to work and make our families stronger here in San Francisco. I support the spirit of the Occupy Wall Street movement that calls for peacefully assembling to protest and bring national attention to disparity issues in our country. “In San Francisco, protesters are acting within their First Amendment right to free speech and freedom to assemble. While allowing for peaceful protests, we also must ensure that our streets and sidewalks remain safe and accessible for everyone. I will continue to work closely with our Police Chief to ensure San Francisco responds appropriately to these demonstrations. “San Francisco is a city that embraces free speech and freedom to assemble like no other city.” Indeed, no other city among the 60 or so that have followed the Occupy Wall Street example of occupying public spaces has sent police and trucks in to raid encampments in the middle of night, so San Francisco is indeed alone in its treatment of the movement that Lee shamelessly claims to support. And now Avalos: “Last night I gathered in solidarity with the protesters Occupying San Francisco. Like many people all over the country, I have been watching this protest gather strength and grow as more and more of us, more of the 99 percent, demand accountability from the corporations and people who are responsible for the destruction of our economy and devastation of our families. “I came to down to observe the protest last night in response to summons from protesters and a notice from the police accusing their encampment of a number of minor infractions, ranging from open flames on a city street or sidewalk to serving food without a permit. I observed and negotiated with police in good faith to keep the peace and allow the encampment to remain, only to hear of a crackdown shortly after I left. “This is not the San Francisco that I know. This is not the San Francisco I love. This City has served as a sanctuary for free speech and assembly for generations, and we must protect that legacy. With our unemployment rate nearing 10 percent, we have a responsibility to be a sanctuary for the 99 percent. "Instead, last night we witnessed that 99 percent being detained, arrested, and intimidated with force. “My vision is of a true sanctuary city - one that protects our right to free speech and assembly, and one that holds real criminals accountable. This should be a city for the rest of us - for the 99 percent. I stand with Occupy SF.” | Mid | [
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Q: PHP - Get range either side of integer In PHP, I am getting a range like this... $number = range(0,50,10); This is working, but now I am trying to modify it so that given a number, it will get the range 5 digits either side of that number. So, for example, given the number 25, I would like... 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 To further slightly complicate things, I would only like these numbers to be positive, so if the start number was 3, then it would only get the range 1-8 A: Just subtract and add to the number in the center. Use the max() function to restrict the beginning to at least 1. $n = 25; $numbers = range(max(1, $n-5), $n+5) | Mid | [
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Q: Configure ports in WebStorm - React + Node Express app I am going to do a fullstack implementation with WebStorm IDE. I use react.js and node-express for this. I can do this in separate projects. But I want to know how to implement both backend and frontend in WebStorm project while configuring ports. When starting the frontend we can give start html file in package.json file under "start": "parcel index.html". When starting backend we can give "node app.js" But this can be done when we are doing the implementation in two different projects. But if we are doing both frontend and backend how can I start react part and node-express part on two different ports? For example: - react app > localhost:1234 - node-express > localhost:3000 "start": "parcel index.html" "start": "node app.js" // in package.json we can set only one start A: You can use a package like npm-run-all to achieve this. Install it then have two separate scripts (like start-front-end and start-server) in your package.json that npm-run-all runs both of e.g. "scripts": { "start-front-end": "parcel index.html --open", "start-server": "node app.js", "start": "npm-run-all start-server start-front-end", } | High | [
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Utility meters are used to determine the amount of a utility, such as electricity, gas or water, consumed at a given site. In particular, conventional residential electric meters are watt-hour meters which measure total energy consumed at the site and indicate the usage in standard kilowatt hours. Modern residential electric meters typically include solid-state electronics for monitoring, storing and displaying utility usage data over time. Total energy consumed, as well as other data, is digitally displayed. For billing and management purposes, a utility provider periodically sends a meter reader to the site to directly view and report the meter display. Data from the meter may also be downloaded from the meter into a handheld device. This is a time-consuming and costly process which has produced a growing demand for more cost-efficient methods of utility accounting. In response to the growing demand, automatic meter reading (AMR) technologies have been introduced, including radio-based, telephone line based, and power line based systems. Known radio-based apparatus and methods include meters equipped with low power radio frequency transmitters to transmit utility usage data from the meter to a central location such as a mobile van unit, or a central building. Optimal transmission efficiency requires an antenna equal in length to about 1/4 the wavelength of the transmission frequency. In particular, at the low frequencies typically used in remote meter assemblies, optimal transmission efficiency requires the use of antennas having lengths which are difficult to incorporate within a standard meter housing. Known radio meter assemblies address this problem by using a non-standard meter housing having towers or projections to accommodate an antenna projecting from the meter assembly. However, the manufacture of such specially designed, non-standard meter housings is costly. Further, the towers or projections can present obstacles for individuals passing or working near the meter assembly. Thus it would be desirable to provide a utility meter apparatus which includes a suitable antenna within a standard type meter housing. It would be further desirable to provide such apparatus which is simple and inexpensive to manufacture. In addition, it is generally desirable in providing meter apparatus to minimize the number and size of components and mounting hardware to minimize costs and labor. It would also therefore be desirable to provide utility meter apparatus which integrates a suitable antenna with other meter components, to minimize costs and labor. | Mid | [
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Smaradahana Smaradahana is an old Javanese poem (kakawin) written by Mpu Dharmaja as a eulogy for King Kameçvara of Kediri in early-12th century East Java. The story describes the disappearance of Kamajaya (the Hindu god of love) and Kamaratih (the Hindu goddess of love) from Svargaloka after being burnt by fire that burst from the third eye of Shiva. Their spirits fall upon the earth where, incarnated as human beings, their spirits seduce and inspire lovers' hearts. Etymology Smaradahana is a Sanskrit word from smara (love) and dahana. Dhana itself can be translated as "thirst" or "yearning", also as dahana ("fire"). Smaradhana is thus sometimes translated as "the fire of love". Smaradhanas themes have inspired many works of art and literature in Indonesia, including stories, poems and love songs. The story The story begins when the goddess Parvati was feeling lonely. She missed and longed for her husband Lord Shiva, who at that time was meditating somewhere on a sacred mountain top. She decided to send Kamadeva, a lesser love god known in ancient Java as Kamajaya, to search for Shiva. His task was to inspire love in Shiva's heart, to make him yearn for his wife. Using the bow and arrow of love tipped with a flower, Kamajaya shot the meditating Shiva. Suddenly Shiva felt the desire to see his wife. His heart was filled with memories of past love-making with Parvati, so he promptly stopped his meditation. However, when Shiva opened his eyes, he caught sight of Kamajaya hiding behind a rock. Angered by the fact that Kamajaya, the lesser god, had dared to disturb his meditation, fire burst out from his third eye and burnt Kamajaya to ashes. Kamajaya's wife, the goddess Rati, known in ancient Java as Kamaratih, out of her love, devotion and loyalty, jumped into Shiva's fire to follow her husband. They both died in the flames, disappeared from Svargaloka and vanished from the realm of gods. The spirits of the couple, the divine lovers Kamajaya and Kamaratih, fell upon earth, into the realm of human beings. Frequently incarnated as two lovers, constantly searching for each other on earth, the spirits of Kamajaya and Kamaratih symbolize love, lust, desire and the yearning that inspires, seduces and is suffered by all lovers on earth. History Mpu Dharmaja wrote Smaradahana during the reign of Kameçvara, the second king of Kediri during the second quarter of the 12th century. Historians believe that in addition to Dharmajaya's intention to transmit the Hindu mythology of Kamadeva being burnt by Shiva's fire (interpreted by the Sanskrit poet Kalidasa in Kumārasambhava), it was also intended to explain the essence of love and desire in human beings. It is strongly suggested that the poem was also Dharmaja's eulogy for the king. Smaradahana celebrated Kameçvara as a strikingly handsome man, while his queen consort Çri Kirana was noted for her extraordinary beauty. The poem portrayed the king as the incarnation of Kamajaya, the Hindu god of love, and proclaimed that his capital city Dahana (or Daha) was admired throughout the known world. Kameçvara's wife, Çri Kirana, was celebrated as the incarnation of Kamaratih, the Hindu goddess of love and passion. The Smaradhana became a predecessor to the Panji cycle tales, where Raden Inu Kertapati (or Panji Asmoro Bangun) is portrayed as the incarnation of Kamajaya, while Dewi Chandra Kirana (or Sekartaji) is depicted as the incarnation of Kamaratih. The Panji tales spread throughout Southeast Asia as far as Malaya, Siam and Cambodia. References External links Kakawin Smaradhana (in Indonesian) Category:Kakawin Category:Hinduism in Indonesia Category:Hindu texts | Mid | [
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Consider the Man-Beast: Combining of the intelligence of humanity in one million years time with the power of the wolves of a thousand millennia hence, he has advance knowledge of future science and martial arts, psionic abilities, raw physical strength, and a hate of all life. He can destroy an adversary’s time sense, he possesses a field of mental repulsion so strong that Thor’s hammer cannot pierce it, and he can create anti-matter barriers. The Man-Beast is a pretty serious threat. The High Evolutionary tries to get the drop on the Man-Beast with his Discordion, a horn that is a gun, producing sounds scaled to bring instant death to wolves. The Man-Beast is injured by this sonic assault, but he retreats to the High Evolutionary’s genetic laboratory. Sealing himself in, he uses the equipment found in the lab to build himself his own army of evil New Men. There is an epic battle between the noble Knights of Wundagore with Thor fighting on their side, against the New-Men of the Man-Beast. It all comes down to a mano-a-mano fight between Thor and the Man-Beast, which Thor wins by punching really hard. Having defeated the New-Men, the Knights of Wundagore corral their fallen foes into the Star Chamber, a space-pod that they shoot into the uninhabited Dromisana galaxy, where they can form their own society, free from the need to destroy all life on Earth. Once the villains have been dispatched, the High Evolutionary decides that his mad science, how ever well intentioned, is too dangerous for Earth and so he reveals to Thor and Jane that Wundagore is in fact a giant rocket ship. As he bids Thor and Jane Foster farewell, he and his Knights depart to the unknown reaches of the universe. Several months prior to this story, in the pages of Stan and Jack’s other fantasti-classic series, Fantastic Four, a character named Galactus was introduced. Galactus is a giant cosmic presence beyond good and evil from the other side of the center of the universe. This being travels from world to world, feeding on the energy of planets, reducing them to lifeless husks. Galactus had intended to feed upon Earth in this manner, but Reed Richards of the Fantastic Four threatened to destroy the universe if Galactus tried, and so the cosmic devourer agreed to forever leave Earth in peace. Thor and his buddy the Recorder return to Rigel, where the Collectors honor their agreement to mark the Earth as off-limits. As they leave the Black Galaxy, they unwittingly pass Galactus as he heads into the Black Galaxy, intending to feed upon Ego. Thor returns to Earth as Tana Nile departs it. She may have lost the Earth, but she returns to Rigel, where she has been chosen by the High Commissioner to be his wife. Thor, meanwhile, has been left with a Psyche-Search Gauge with which to find his hypnotized beloved. He finds her in a bizarre compound in Europe known as Wundagore, which is guarded by animal-people riding rocket sleds. The leader of these people is known as the High Evolutionary, a man who has developed a technique to re-write the genes of animals, advancing their evolution one million centuries, which turns them into humanoids with animal heads. Since this is not remotely how evolution actually works, I would suggest that that this explanation is meant as a metaphor for the actual process at work. A lie-to-idiots, if you will. The Knights of Wundagore attempt to restrain Thor from barging into their compound, but the God of Thunder will not be restrained. Thor finds Jane, who has taken a job teaching the animal-folk created by this weird science. Thor mistrusts this science stuff, but Jane is a woman of science, and assures him that there is nothing inherently evil about experimenting on animals to create a race of New-Men. Good on her. Thor’s breaking and entering and shouting and fighting has distracted the High Evolutionary at a critical moment, and he has accidentally over-evolved a wolf! This combination of supreme man and supreme beast has created a hate-fuled Man-Beast, enemy of all that is living! First Appearance: The High Evolutionary, Wundagore, the New-Men, The Man-Beast, Psyche-Search Gauge This one’s strange. Thor and his new android buddy land on a sentient planet and fight it. It is a visual spectacle in full-on Kirby weirdness mode. Ego is a planet who had decided to leave the Black Galaxy and conquer the outside universe. However, after Thor unleashes the full power of the storm upon him, Ego has second thoughts and decides never to leave his little secluded corner. While Thor fights an entire planet, Jane Foster has found herself in Europe, compelled to send herself there by her ne’er do well roommate. She ends up in the company of two men named Porgia and Tagar. They ask her to be part of some larger scheme to solve the eternal secret of life itself, at which point she realizes that these guys might be nuts. Meanwhile Tana Nile is notified that her claim on Earth has been revoked. | Low | [
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The victims were on their way home after attending a wedding ceremony. PHOTO: AFP KARACHI: In a new spate of violence in Karachi, the wife and daughter of Balochistan MPA Mir Bakhtiar Domki were shot dead near Gizri flyover early Tuesday morning. The deceased were also the sister and niece of Baloch Republican Party (BRP) leader Baramdagh Bugti. “A black-coloured Toyota car, with the victims on board, was parked outside a house when two men riding on motorcycles opened fire on the car,” said Superintendent of Police Clifton Tariq Dharejo, while talking to The Express Tribune. “The victims were on their way home after attending a family wedding,” he added. The driver was also killed in the incident. Eyewitnesses said that the assailants had circled the area once or twice before attacking their target, and fled after the attack. The bodies were shifted to the Jinnah Postgraduate Medical Complex (JMPC) after the incident. Domki, who is a grandson of Nawab Akbar Bugti, belongs to Sibi. Police believe that the incident could be a case of target killing based on personal enmity. They are investigating the incident. Domki, while talking to Express News, said that they [his family] do not expect justice from the government of Sindh and that all it could do was form a few judicial committees. “They used to kill the men of our family, now they have started killing our women as well,” he said. “We have been sacrificing for our country, and will continue doing so.” Reader Comments (22) So tragic! When will the killing stop in this so called Muslim country! There is absolutely no remorse in taking a Human Life! When will the wrath of Almighty Allah fall on these heartless & souless criminals so that they understand that they will never succeed in bleeding this country to death by their secetarian, personal enmity or in the name of honor violence! Almighty Allah, help us out of this quagmire! “Domki, while talking to Express News, said that they [his family] do not expect justice from the government of Sindh and that all it could do was form a few judicial committees” Anohter wake up call and a strong rejoinder of no confidence on existing system of governance and judiciary. Innal lillahi Wa inna Alaihi Rajiyon.. Now that the women are killed, I’m sure the Domkis’ and Bugtis’ will blame Pakistan for it, and again start abusing the Pak Fauj. It’s not the Pak Fauj, it’s their own family enmities and fights with other feudal families, that have caused these deaths. @Ali Nawaz Magsi: First get information about tribal customs and then talk. In Baloch society women are the most sacred after Holy Quran, and women and children are exempted in tribal conflicts. Women of eVen enemies are treated as mothers and sisters of one’s own. The victims know which brutal forces are behind this incident and history is also witness whatever they did in Bangladesh to crush there freedom movement. @ali Get your mind and attention exactly to what I have said and I’m saying. You seem to lack in effective communication. Sorry for that, but you do. What I had said, has come true, now they have blamed Pakistan for it, including Sindh Government. I know each and every tribal custom very well, you please don’t teach me that. I never said that it was any Baloch who killed them(R.I.P), that you have started supporting baloch. Why do you seem to be seemed as a defensive, while I said nothing against the Baloch? Whoever you are talking about, they did in Bangladesh, go find out what does Mujib-ur-Rehman’s daughter, who is current PM of Bangladesh, says about Pak Fauj and her own father. Go, Run, Find out!! These people are like Mir Jafer and Mir Sadiq.They are playing in the hands of India , USA and all the enimies of Islam for some money .Sham for them they will have bad rewards in this life and the next. But no body should kill there women. | Low | [
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'Collateral': The Best Movie Tom Cruise Will Probably Ever Make By Petr Knava | Film | April 20, 2018 | A taxi glides forward on deserted nighttime streets. We see it from above and behind as the camera tracks it. Slowly we pull in closer, tightening the frame as glimpses of neon slide past. Billboards and shop signs and parking lots. A lone silver car enters the scene, heading in the opposite direction. It makes a turn, away from our taxi, and is gone just as quickly as it appeared. The effect is palpable: Whoever is inside that cab is alone, isolated in the stillness of these anonymous streets, bathed in intermittent light but seen by no one. The whole sequence only takes up six seconds but even in such a short sliver of time the fingerprints of its creator are immediately apparent. Michael Mann shoots Los Angeles like nobody else on Earth. There are not many people who can shoot anything the way Mann shoots L.A. The Chicago-born filmmaker has an affinity with the Southern Californian city that allows him to transform it onscreen in ways other directors can only dream of. He finds banal and unknown corners and makes them into landmarks. He traces roads and alleyways like nerve fibres running through a living organism. He levitates his camera above the sprawling and disconnected city in such a way so as to transform it, the chaotic and roiling metropolis becoming a serene constellation of lights in his hands, a dreamlike background both integral and distant. Mann’s other movie—his gem of gems, Heat—is a masterclass in how to use an urban setting to invoke feeling. Whether it’s the disorienting angular array of lights and fun house mirror-like reflections of Vincent Hanna’s skyscraper-slaloming helicopter ride, or the view from Eady’s house on the hillside from where the city appears as if a lake of fireflies glimpsed through a haze, the director casts Los Angeles almost a separate character in its own right, sometimes beautiful and enchanting, but often apathetic, if not outright hostile. In 2004’s Collateral, L.A. fits this description perhaps even better than in Heat. The effect Mann goes for here is one of isolation, anonymity. Indeed that is the crux of Collateral’s thesis: That the city—all cities in a way, but more specifically this city—can be incredibly indifferent to the struggles of those who inhabit it; that the humans living there are fundamentally alone, despite their vast number. That connection is rare. In short: That nobody cares. It all comes across as an oddly melancholy and affecting description for a movie the plot of which sounds like a high concept elevator pitch: ‘A silver haired assassin called Vincent, played by Tom Cruise, arrives in Los Angeles for one night. He has five targets on his list that he must take out before dawn, so he hires a cab for the night to ferry him between stops. The initially unwitting cabbie, played by Jamie Foxx, soon realises what’s going on, effectively finding himself both a hostage as well as an accomplice. Will he be able to save himself, and perhaps some of the potential victims, before the night is out?’ But while the pitch itself may sound hokey, the movie itself is anything but. A thriller on the face of it, Collateral is a piece of work that runs on genuine human feeling, more akin to a drama than anything else. This is in part due to Mann’s precise direction and evocative camerawork, but also thanks to the work he did on Stuart Beattie’s script. Originally set in New York and trading a lot more in cultural stereotype, Australian Beattie’s initial screenplay was a bit of a diamond in the rough before Mann got a hold of it. Said Mann of Beattie’s script: I didn’t like the screenplay, I didn’t like the dialogue, I didn’t like [the] writing, but if you took the screenplay, and put it under an MRI, or an X-ray machine, and took a look at it, you realize this thing has beautiful, beautiful bones. It’s one of the most beautifully constructed stories I’d had ever run into. And it was gemlike, and it all took place in one night, and the roles each guy played in the other’s realization of himself, and it was just a beautiful piece of writing by [Stuart] Beattie. But I loved the story structure of it, so I rewrote it. Michael Mann is a director often praised for his technical ability—and rightfully so, as he remains one of the finest craftsmen of his time—but it should never be forgotten that he, like David Fincher, has a deep understanding of what makes people tick. He knows how to write stories grounded in humanity, in our hopes and dreams and fears, and he is intuitively aware of how important it is to connect that way with the audience. The mechanics of the plot and the methods of telling it are important, but they are nothing without characters we care about. In Collateral, both aspects of this virtuous kind of filmmaking are supremely evident. On the one hand you have that gorgeous cinematography, a portion of it filmed on traditional celluloid, but much of it done with digital, using the Viper FilmStream High-Definition Camera. 2004 is not that long ago, but it was a quite dramatically different time in cinema to the one we see today. The vast majority of movies were still being shot on film, and while the industry was already slowly adapting to what would eventually become the new visual norm, it was Mann and his cinematographers, Dion Beebe and Paul Cameron, who were responsible for putting forward one of the landmark cases for digital. Their work on Collateral would garner an American Society of Cinematographers (ASC) nomination for outstanding achievement in cinematography—an unprecedented mark of industry acceptance for digital work at the time and a harbinger of things to come. Camera tech has moved on since then, but the digital shooting in Collateral still looks amazing to this day. Beebe hit the nail on the head when he said, years later: We have seen an emergence of what I think is a digital aesthetic. It’s a beautiful aesthetic, and it plays to the strength of that medium, which is the very open bottom of the curve. It can look into shadows; it’s got an amazing range. Digital gives us the ability to work from a base of ambient light, essentially. Because of that, you tend to light in a very different way. And I do think ‘Collateral’ helped launch that because it played to the strengths of the format. We never set out to replicate a film look, but rather to discover a digital one…Film has a unique texture and tone, and digital has its own unique texture and tone. It would be a sad day if we lost the ability to choose between them. Indeed we have now in 2018 arrived at a time when digital has almost totally eclipsed film in industry uptake, but to look at Collateral is to look at a piece of work that stands out as one of the prime examples of how good it can be when the two are used together, with the painterly celluloid compositions playing off the more urgent and gritty digital work that often washes out the Los Angeles skyline in the background, providing the sense of floating isolation that the movie needs. Collateral’s wonderful cinematography is matched by a pair of pitch-perfect performances. Tom Cruise and Jamie Foxx deliver some of the finest turns of their careers here. But the movie’s production was not straightforward, and one of the twists in that story is that Adam Sandler was originally attached to play Max, the unfortunate cabbie who is forced into enabling Vincent’s bloody itinerary. Now, Adam Sandler gets a lot stick. Deservedly so, I might add, as the vast majority of his output is lazy, offensive, offensive in its laziness, and lazy in its offensiveness. But we’ve all seen Punch-Drunk Love. We know that—when harnessed by the right director—the man can act. There’s no way to tell how things might have been, but it’s likely that Michael Mann could have coaxed one of those once-in-decade performances out of Sandler. Nevertheless that remains pure speculation, because Sandler passed on the project due to other commitments. We will never know if Sandler would have brought the goods for Collateral. All we do know, is that the man who ended up in the role instead completely owns it. Jamie Foxx knocks it out of the goddamn park as Max. Here is a man with whom we are with for almost the entirety of the movie’s running time, much of it in the cramped confines of his meticulously maintained cab. To sell his character, and his transformation, requires a great deal of control and understanding—and Foxx delivers with aplomb. We feel his journey intensely. Foxx’s Max is a deeply sympathetic and relatable character, trapped as he is in a holding pattern of life by his own fears. Max is stuck and unhappy, somewhat resigned to his fate, but at the same time he is quick, empathetic, and still has dreams, although we meet him at a time in his life when he seems to be slowly becoming content with letting them stay just that. Then along comes Vincent, and suddenly the stupor of Max’s years is shaken, violently, in far more terrifying and immediate ways than any paralysing anxiety he may have felt over his potential future before. Through this mortal threat, Max is vivified. Vincent, a cold-blooded killer with a penchant for nihilist repartee, brings out something in Max. As the night wears on, his fear transmutes into defiance. His personal safety stops mattering to him. At one point, he tosses Vincent’s mission-vital briefcase onto a freeway, and stands, scared but resolute, to meet the assassin’s fury. Later, near the climax of the movie, he calls out Vincent’s bullshit and vacant speechifying while speeding faster and faster down downtown L.A. The tipping point has been reached and Max can take no more. Suddenly the tables are turned and it is Vincent who’s scared. What has he unleashed in this mild-mannered cabbie? ‘Go fuck yourself!’ Max spits at Vincent, as he throws the car into a barrier at high speed, all sense of self-preservation now gone, putting his life into the hands of fate. It’s a tremendously heroic moment on Max’s part, and it only works because the character’s journey to this place has been so fully fleshed out. Jamie Foxx deserves all the credit for taking a fantastic script and making it sing. Which brings us to Vincent. Tom Cruise’s greatest role, in what is probably the best film he will ever make. Hey, don’t worry, I see you, Magnolia. I’m not taking anything away from you, and I understand that direct comparisons between such wildly different movies are fundamentally silly, but there is just something about Vincent. Perhaps a better way to put it is not that Vincent is Tom Cruise’s greatest role, but that it is his most Tom Cruise role. Cruise is not exactly an actor with a dazzlingly wide range, or the most subtlety. His is a style of acting that relies heavily on physicality, charisma, and a certain dead-eyed intensity, and he brings all of that to Vincent—whose way of carrying and handling himself immediately sells the notion that this is more of a walking weapon rather than a man—but there’s something more here too. A hidden reservoir of internal conflict, starting to bubble slowly as the night goes on, and the nuanced way Cruise manages to portray these layers is quite unprecedented in his body of work. Vincent is meticulous in how he presents himself to world, priding himself on clinical detachment and cool professionalism. Yet something changes in him on his journey with Max, just as much as Max is transformed by Vincent. The two seem to have a genuine connection, and through a sort of two-way Stockholm syndrome, they bond, and though it all ends as it must, their impact on each other is undeniable. This co-evolution is one of the most compelling parts of Collateral, and Tom Cruise is a huge part of why it works. Where Cruise goes as an actor after he has aged past the point of being physically capable of leaping across roofs and grabbing onto planes will be an interesting thing to see. Whether he has it in him to transition into a different type of ‘serious’ performer is anyone’s guess. Collateral proves that he definitely had it in him once, and that seeing it coupled with his raw physicality was once a formidable sight indeed. The movie is stacked with an excellent supporting cast too. Bruce McGill, Barry Shabaka Henley, Jada Pinkett Smith, Javier Bardem—they all flesh out Michael Mann’s L.A. beautifully, and they make Vincent and Max’s quasi-peripatetic quest a colourful and vibrant one. I am contractually obliged at this point to also highlight the star supporting player in all this: the Greatest Movie Detective of His Generation, Mark Ruffalo, who plays Detective Fanning, the one man who comes close to matching Vincent, and who almost rescues Max after one of the best shootouts in modern American cinema. There’s a real deliciousness to the way Collateral’s plot unfolds—a lean, relentless march of consequence and cause and effect, starting with the sheer chance that brings Vincent to Max’s cab—and Detective Fanning’s side of the story is a great illustration of that. It’s nothing new of course: Cop follows clues unwittingly left by criminal. But the urgency of the night, the fact that Vincent has everyone but Fanning fooled, and the intensity of Ruffalo’s performance makes it feel fresh. Despite the fact that I’ve spoken of Collateral largely as if it was a drama, the actual experience of watching it leaves you in no doubt of its thriller bonafides. The action is visceral, the suspense palpable. I want to come back to that scene I mentioned at the start. Max’s taxi gliding through deserted streets. After that brief establishing shot, we cut into the cab, and a conversation between Vincent and Max. It’s a tense one, and the camera stays on Max in the front seat, with Vincent in the back, re-focusing on whoever is speaking. Max has just destroyed Vincent’s briefcase, and Vincent has told him the price to pay: Max is to go into a club to meet his contact, and to get a replacement for the briefcase’s content. It will be dangerous, possibly fatal, but Vincent leaves no doubt: Max has no choice here. On the drive to the club, Vincent is trying to establish a bit of normalcy, and he is waxing philosophical, but Max is taciturn. Something has shifted in him, and his relationship with Vincent is not what it was. The potential for agency has been glimpsed, and Max has been pushed almost as far as he will go. Vincent finishes his little speech, and you can tell he is discomfited by Max’s lack of engagement. Max, who previously had been hanging on his every word thanks to fear, now sits quiet, inscrutable. Uncharacteristically, Vincent trails off into silence with an uncertain, ‘…anyway…’ and we regard these two solitary people, adrift in a city that does not care, who had bonded, albeit perversely, through incredible circumstance. Now that bond has changed, and the loneliness of the metropolis reasserts itself. The taxi glides on, neon flits by, and suddenly things reach a perfect stillness. The car slows, and out of nowhere, two coyotes run across the road. One dashes across Max and Vincent’s way without pause. The second one slows as it passes and turns its head, its eyes glowing in the reflection of Max’s headlights. Both Max and Vincent stare, lost in the moment completely, as the coyote makes uncanny eye contact, appearing less of a physical form and more a manifestation of something mystical and unknown, something alive and vital in this city where a corpse can ride a train without anyone noticing. The coyote moves on and Chris Cornell’s mournful vocal comes onto the soundtrack. Max and Vincent carry on to the club, but they do so as if they had momentarily passed through another dimension. It’s an absolutely magical moment, and its poetic nature speaks to the kind of movie that Collateral is: A soulful, emotive, thrilling modern classic. Petr is a staff contributor. You can follow him on Twitter. | Mid | [
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New Delhi, Aug 19: Offering help to the agitated students of FTII, Delhi CM Arvind Kejriwal on Wednesday said that he was shocked to see the plight of the students and has offered temporary space to them to conduct their classes. Kejriwal tweeted and said that till the time the Central government agrees to their demand, they can conduct classes in the Capital. | Mid | [
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Safety doesn't happen by accident. - Unknown Life's a game but Bridge is serious. - Unknown The bridge to the future in the phallus. - D.H. Lawrence Praise the bridge that carried you over. - George Colman In Seine: Those who jump off a Paris bridge - Daffynitions joe-ks.com My alone time is for everyone's safety. - Unknown Defendit numerus: There is safety in numbers. - Unknown Care shouldn't start in the emergency room. - James Douglas Safety is a cheap and effective insurance policy. - Unknown In skating over thin ice our safety is in our speed. - Ralph Waldo Emerson Obedience is the mother of success and is wedded to safety. - Aeschylus My wife made me join a bridge club. I jump off next Tuesday. - Rodney Dangerfield Safety Belt: The one you don't drink before driving home - Daffynitions joe-ks.com Mistakes are the usual bridge between inexperience and wisdom. - Unknown Coward: One who, in a perilous emergency, thinks with his legs. - Ambrose Bierce The best car safety device is a rear-view mirror with a cop in it. - Dudley Moore The traveler with empty pockets pursues his journey in perfect safety. - Ovid Your own safety is at stake when your neighbor's house is in flames. - Horace Stress is an ignorant state. It believes that everything is an emergency. - Natalie Goldberg The hardest thing in life is to know which bridge to cross and which to burn. - David Russell There is nothing so strong or safe in an emergency of life as the simple truth. - Charles Dickens Having hope will give you courage. You will be protected and will rest in safety. - Bible If I was the governor of New Jersey, the George Washington Bridge would not have been shut. - Donald Trump Bridge is a game that separates the men from the boys. It also separates husbands and wives. - George Burns If you're not paying for it through the health plan, you pay for it in the emergency room. - David Lehman Politicians are the same all over. They promise to build a bridge even where there is no river. - Nikita Khrushchev One of the tests of leadership is the ability to recognize a problem before it becomes an emergency. - Arnold H. Glasow My husband is so good at home repairs that they have a special VIP area for him in the emergency room. - Unknown Individuality is either the mark of genius or the reverse. Mediocrity finds safety in standardization. - Frederick Crane To say I'm an overrated troll, when you have never even seen me guard a bridge, is patently unfair. - Tina Fey Your problem is to bridge the gap which exists between where you are now and the goal you intend to reach. - Earl Nightingale Faith is a fine invention When Gentlemen can see - But Microscopes are prudent In an Emergency. - Emily Dickinson I have left orders to be awakened at any time in case of national emergency, even if I'm in a cabinet meeting. - Ronald Reagan Those who would give up essential liberty to purchase a little temporary safety, deserve neither liberty nor safety. - Benjamin Franklin He that cannot forgive others breaks the bridge over which he must pass himself, for every man has need to be forgiven. - Thomas Fuller If this humor be the safety of our race, then it is due largely to the infusion into the American people of the Irish brain. - William Howard Taft Faithfulness is essential to the character of a friend: without this there can be no safety in intimacy with and confidence in him. - Samuel Hopkins Everyone needs a coach. It doesn't matter whether you're a basketball player, a tennis player, a gymnast or a bridge player. - Bill Gates The best way to meet a woman is in an emergency situation - if you're in a shipwreck, or you find yourself behind enemy lines, or in a flood. - Mark Helprin He that cannot forgive others breaks the bridge over which he himself must pass if he would ever reach heaven; for everyone has need to be forgiven. - George Herbert | Mid | [
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? 9 Suppose 0 = m + 6*m - 294. Calculate the greatest common factor of m and 56. 14 Suppose -6*b + b = -105. Suppose -w + 2*w = b. What is the highest common factor of 3 and w? 3 Suppose 2*y = 5*y - 2*g - 21, 0 = -g - 3. Suppose -210 = 2*b - y*b. Calculate the greatest common factor of 10 and b. 10 Suppose -4*m + 110 + 33 = -5*f, 0 = -m + 4*f + 22. Calculate the greatest common divisor of 28 and m. 14 Suppose -d - 5*w = 10, 0 = -5*d - 0*d - w + 70. Let b = d - 12. Calculate the highest common divisor of 6 and b. 3 Let p be (576/45)/((-2)/20*-2). Calculate the greatest common factor of 32 and p. 32 Let w be 6/15 + 8/5. Let k be (1*-1)/(w/(-4)). Calculate the greatest common factor of 6 and k. 2 Suppose w - 2*t = 6, 5*w - 4*t - 50 = t. Let x be (1 - (-1)/2)*w. Suppose 0 = -16*n + 20*n - 56. What is the highest common factor of x and n? 7 Let q = 0 + 7. Calculate the greatest common factor of 56 and q. 7 Let b be 23/2 - 2/4. Suppose 7 = n - b. What is the highest common divisor of 12 and n? 6 Suppose 2*x - 5 = 1. Suppose 4*d = r + 10, -x*d = d + 4*r. What is the greatest common factor of 2 and d? 2 Let h(c) = c**2 - 14*c - 20. Let b be h(16). Calculate the highest common factor of b and 36. 12 Let h(p) = p**3 - 16*p**2 - 18*p + 20. Let w be h(17). Calculate the highest common factor of w and 33. 3 Suppose -3*k - k = 0. Suppose -3*i + 4*t = -11, k = 3*i + 2*t + 1. What is the highest common factor of 11 and i? 1 Let z(a) = a**2 - 7*a - 8. Let t be z(-4). Let f be -1 + (2 - 6/(-3)). Suppose -f*w = -5*w + 8. Calculate the greatest common divisor of t and w. 4 Suppose 4 = -4*r + 3*p, -p = -3*r + p - 2. Suppose -4*j - 27 = -2*g + 9, 36 = r*g + 4*j. What is the greatest common factor of g and 144? 18 Let l(z) = 2*z**3 + 2*z**2 + 1. Let k be l(3). Suppose 23 = -5*y + k. Let u be (-50)/(6/(-2) + 2). Calculate the highest common divisor of y and u. 10 Suppose 4*t - 11 - 49 = 0. Let p = -14 - -29. What is the greatest common divisor of p and t? 15 Let q be ((-5)/(-10))/((-3)/(-6)) + 10. Let t(i) = -i**3 - i**2 - i + 22. Let f be t(0). Calculate the greatest common divisor of f and q. 11 Let j(h) = -h**2 - 3*h - 1. Let y be j(-2). Let g(q) = 5 + 2*q**2 - q + 7*q + y. Let l be g(-5). What is the greatest common divisor of l and 13? 13 Suppose 0 = w - 4*s - 12, 5*s + 9 + 1 = 0. What is the greatest common divisor of 40 and w? 4 Let r be 19/2 + (-51)/34. Let d(k) = -k**3 + 8*k**2 + k + 5. Let x be d(r). What is the highest common divisor of x and 52? 13 Let f(y) = 35*y**2 + 1. Let k be f(-1). Let r = 24 + -15. What is the greatest common factor of k and r? 9 Let r = 39 + -3. Suppose -2*b = -5*b + 51. Let s = b + -5. What is the highest common divisor of r and s? 12 Suppose 0*i = -3*q + 4*i + 30, -16 = -2*q + 4*i. Let s = 16 - q. Let h(a) = a**2 + 3*a + 4. Let z be h(-6). What is the greatest common divisor of s and z? 2 Suppose 53*g = 49*g + 164. What is the greatest common divisor of 287 and g? 41 Let m be 882/5 - 4/10. Suppose 3*x - 5*v = 572, -5*v = x - 316 + 112. Let p be 5/(-30) + x/12. Calculate the greatest common divisor of p and m. 16 Suppose -5*u + 4*u = 3. Let j be -10*(u/(-3) + -2). What is the greatest common divisor of j and 1? 1 Suppose -3*r + q - 16 = 6*q, 4*r = q + 17. What is the highest common divisor of r and 6? 3 Let x(v) = -24*v - 15. Let w be x(-5). What is the greatest common divisor of 70 and w? 35 Suppose 96 = 4*t - 0*t. Calculate the greatest common factor of 36 and t. 12 Let d(y) = -y + 16. Let t be d(0). Suppose 5*i = -10 - 0. Let q = i + 18. What is the highest common divisor of q and t? 16 Suppose s + 19 = 33. What is the greatest common factor of s and 21? 7 Let d = -28 + 11. Let p = -9 - d. Calculate the highest common divisor of p and 8. 8 Let n be (0 - (-844)/10) + 24/(-60). Calculate the greatest common factor of 12 and n. 12 Suppose 4*m = -5*j + 5 - 48, -25 = 3*j + 2*m. Let h = j - -8. Calculate the greatest common factor of h and 10. 1 Let w = -20 - -22. Suppose -q + 2*q - 63 = 0. Suppose -b + q = w*b. Calculate the greatest common divisor of 3 and b. 3 Suppose 16*j - 2*j = 84. What is the greatest common divisor of 12 and j? 6 Let c = -126 - -142. Let o = -26 - -42. Calculate the greatest common divisor of c and o. 16 Let k = 50 - -181. Calculate the highest common divisor of 21 and k. 21 Let a = 46 - 27. Let q = a + -10. What is the highest common factor of q and 6? 3 Let a be (-1 - -1*3) + -2. Suppose a*i = -3*r - i + 1, -4*i = 5*r + 10. Let o be r + 2 + -1 + 1. What is the highest common divisor of o and 32? 4 Let z(g) = -g**3 + 9*g**2 - 8*g + 6. Let j be z(7). Calculate the greatest common divisor of 12 and j. 12 Let g(r) = -7*r - 2. Let v be g(-6). Calculate the highest common factor of 16 and v. 8 Let m = 384 + -258. What is the highest common factor of 18 and m? 18 Suppose 8 = -2*u + 6*u. Suppose -u*m + 32 = -12. Calculate the greatest common divisor of 55 and m. 11 Suppose -6*x - 60 = -7*x. Calculate the greatest common factor of x and 45. 15 Let n(r) = 3*r - 2. Let v be n(3). Suppose 33 = 2*i - v. Let z = -62 + 82. What is the highest common divisor of z and i? 20 Suppose 4*c + 14 - 54 = -2*o, 0 = 3*o + 3*c - 60. Let r be (6/9)/(2/(-66)). Let q = r - -32. Calculate the highest common factor of q and o. 10 Suppose 0 = 3*r - 2*r - 22. Calculate the highest common divisor of r and 11. 11 Let t = 159 + -95. Let f(q) = -4*q + 8. Let j be f(0). What is the highest common divisor of t and j? 8 Suppose -23 = 4*b + 2*v - 83, -v = 0. What is the highest common divisor of 45 and b? 15 Let j = -122 - -173. Suppose -2*b + 8 = -0*b. Suppose -j = -3*n - c, c = 5*n + b*c - 85. Calculate the highest common factor of 85 and n. 17 Let a(l) = -5*l - 223. Let s be a(-48). Let u(o) = 18*o**2 - o. Let z be u(1). Calculate the greatest common factor of s and z. 17 Let b be (-110)/4*(-12)/15. Let m = 109 + 45. Calculate the highest common factor of b and m. 22 Let x(r) = -r + 18. Let b be x(15). Suppose 2*u - 4*k = -0*k - 4, u - 18 = -b*k. What is the greatest common divisor of 24 and u? 6 Let u be 10*1/1*1. Suppose u = 4*f - 10. What is the greatest common divisor of 25 and f? 5 Let f = -21 - -41. Calculate the highest common factor of f and 20. 20 Let j = -4 - -64. Let w(q) = q**2 - 9*q - 6. Let u be w(10). Suppose -z = -f - 5*z - u, 2*f = -3*z + 12. What is the greatest common divisor of j and f? 12 Suppose -16 = 2*h - 4*h. Let w be 806/h - 2/(-8). Suppose -5*k = 4*z - w, -2*z - k = -0*z - 49. Calculate the greatest common factor of z and 36. 12 Let z be (-1)/1*(-30)/2. Suppose -1830 = -41*o + 630. What is the greatest common divisor of z and o? 15 Suppose -27 = 2*b - 135. Let h = -3 + 6. Suppose x - 72 = -h*x. What is the greatest common divisor of b and x? 18 Let a be (2 - (-6)/(-3))*1. Let y be -2 + (14 - (-1 - a)). Suppose z - 2*r = -r + 28, -z - 2*r = -22. What is the greatest common divisor of z and y? 13 Let y be 133/(-21) - 1/(-3). Let u be -2*y/(-15)*-15. What is the highest common factor of u and 60? 12 Suppose 36 = 3*b - 99. What is the highest common divisor of 18 and b? 9 Suppose -2*s = -s - 3. Suppose -s*q + 454 = -167. What is the greatest common divisor of q and 23? 23 Suppose 0 = 2*n + 18 - 74. What is the greatest common divisor of n and 42? 14 Suppose 3*i + 4*u - 39 = 0, -59 - 6 = -5*i + u. Let m = 6 + -1. Suppose -m*w + 3*c = -121, -41 = -w - 7*c + 2*c. What is the highest common factor of w and i? 13 Let u(b) = 24*b**2 + b + 2. Let z be u(-2). Let g(r) = -r + 18. Let d be g(6). What is the greatest common factor of d and z? 12 Suppose 0 = 16*a - 17*a + 8. Calculate the highest common divisor of a and 72. 8 Let j = -6 + 31. Suppose 175 = 4*w - j. What is the highest common divisor of w and 20? 10 Let a = 8 + -4. Suppose -43 = -a*x - 11. What is the highest common divisor of 8 and x? 8 Let u(i) = i**3 + 13*i**2 + 13*i + 30. Let z be u(-12). What is the greatest common divisor of 9 and z? 9 Suppose 56 + 72 = 2*m. What is the greatest common factor of 8 and m? 8 Let f be (4 - -16) + -1 + 1. Let d be 2*(35/2)/5. Let g(u) = u**3 - 7*u**2 + 8*u - 6. Let s be g(d). Calculate the highest common divisor of f and s. 10 Suppose -296 = -3*j - 3*z + 157, -j + 142 = 4*z. Calculate the greatest common divisor of 14 and j. 14 | Low | [
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What ever happened to Andy Garcia? He was a next big thing that would take over for DeNiro, Pacino, Nicholson....now he's not done done mainstream in 10 years except a couple of Ocean's 11/13 series films. He's a voice actor now. Christian Slater died, Colin Farrell died too but that was due to a sex tape I think, my guess is Russel Crowe wanted out of the spotlight or got some type actors delima where he wants his work to mean something and be profound Indy spree. I thought Leonardo Dicaprio was falling like some of these guys, he was on his way to being a mega star even when he was in Growing Pains. And than What's Eating Gilbert Grape. After that you didn't here much about him for like 4-5 years and than BAM Titanic and The Man in the Iron Mask. Even those were '97 & '98 and there was a few years were he kind of disappeared again (at least from major movies). I thought he may be out of the major movie gig and than BAM again "Gangs of New York" in 2002 and he hasn't looked back On the thought of actors who were supposed to turn into big stars, I read somewhere that in the late 80s that Harry Hamlin was supposed to be the next big thing.... He does a lot Lifetime movies, or at least the ones my wife watches | Mid | [
0.5650557620817841,
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Bafing River The Bafing River runs through Guinea and Mali and is about long. It joins with the Bakoy River at Bafoulabé to form the Sénégal River in the Kayes Region of western Mali. In Manding languages, Bafing signifies 'black river' and Bakoye 'white river'. The Bafing forms part of the international border between Guinea and Mali. From 1895 to 1898 the railway bridge near the town of Mahina, designed by Gustave Eiffel, was built. The Manantali hydroelectric dam is located on the Bafing River upstream of Bafoulabé. It forms the largest artificial lake in Mali, Lake Manantali. The dam retains of water which is used to power the turbines during the dry season. As a result, the intensity of the maximum flood downstream of the dam has been reduced but during the dry season, a flow of between and is maintained. References Category:Rivers of Mali Category:Rivers of Guinea Category:French West Africa Category:Senegal River Category:International rivers of Africa Category:Guinea–Mali border | Mid | [
0.578158458244111,
33.75,
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import 'package:flutter_boost/container/boost_page_route.dart'; import 'package:flutter_test/flutter_test.dart'; import 'package:flutter/foundation.dart'; import 'package:flutter/material.dart'; import 'package:flutter/widgets.dart'; void main() { TestWidgetsFlutterBinding.ensureInitialized(); testWidgets('test iOS edge swipe then drop back at starting point works', (WidgetTester tester) async { await tester.pumpWidget( MaterialApp( theme: ThemeData(platform: TargetPlatform.iOS), onGenerateRoute: (RouteSettings settings) { return BoostPageRoute<void>( settings: settings, builder: (BuildContext context) { final String pageNumber = settings.name == '/' ? '1' : '2'; return Center(child: Text('Page $pageNumber')); }, ); }, ), ); tester.state<NavigatorState>(find.byType(Navigator)).pushNamed('/next'); await tester.pump(); await tester.pump(const Duration(seconds: 1)); expect(find.text('Page 1'), findsNothing); expect(find.text('Page 2'), isOnstage); final TestGesture gesture = await tester.startGesture(const Offset(5, 200)); await gesture.moveBy(const Offset(300, 0)); await tester.pump(); // Bring it exactly back such that there's nothing to animate when releasing. await gesture.moveBy(const Offset(-300, 0)); await gesture.up(); await tester.pump(); expect(find.text('Page 1'), findsNothing); expect(find.text('Page 2'), isOnstage); }); group('Try to get the BoostPageRoute in the ancestor node', () { testWidgets( 'obtain BoostPageRoute through the BoostPageRoute.of(context) method', (WidgetTester tester) async { BoostPageRoute<dynamic> boostPageRoute; BoostPageRoute<dynamic> boostPageRouteFindByOfMethod; await tester.pumpWidget( MaterialApp( onGenerateRoute: (RouteSettings settings) { boostPageRoute = BoostPageRoute<void>( settings: settings, builder: (BuildContext context) => Builder( builder: (BuildContext context) { return FloatingActionButton( onPressed: () { boostPageRouteFindByOfMethod = BoostPageRoute.of<dynamic>(context); }, ); }, ), ); return boostPageRoute; }, ), ); await tester.tap(find.byType(FloatingActionButton)); await tester.pump(const Duration(seconds: 1)); // The route obtained from the ancestor node through the `of` method should be the same BoostPageRoute // as the originally created BoostPageRoute expect(boostPageRoute, boostPageRouteFindByOfMethod); }); testWidgets( 'try to find BoostPageRoute through the BoostPageRoute.of(context) method, ' 'but it doesn\'t exist, the method should throw an Exception', (WidgetTester tester) async { BuildContext contextCache; await tester.pumpWidget( MaterialApp( onGenerateRoute: (RouteSettings settings) { return MaterialPageRoute<dynamic>( settings: settings, builder: (BuildContext context) => Builder( builder: (BuildContext context) => FloatingActionButton( onPressed: () { contextCache = context; }, ), ), ); }, ), ); await tester.tap(find.byType(FloatingActionButton)); await tester.pump(const Duration(seconds: 1)); expect(() => BoostPageRoute.of<dynamic>(contextCache), throwsException); }); testWidgets( 'obtain BoostPageRoute through the BoostPageRoute.tryOf(context) method', (WidgetTester tester) async { BoostPageRoute<dynamic> boostPageRoute; BoostPageRoute<dynamic> boostPageRouteFindByOfMethod; await tester.pumpWidget( MaterialApp( onGenerateRoute: (RouteSettings settings) { boostPageRoute = BoostPageRoute<void>( settings: settings, builder: (BuildContext context) => Builder( builder: (BuildContext context) { return FloatingActionButton( onPressed: () { boostPageRouteFindByOfMethod = BoostPageRoute.tryOf<dynamic>(context); }, ); }, ), ); return boostPageRoute; }, ), ); await tester.tap(find.byType(FloatingActionButton)); await tester.pump(const Duration(seconds: 1)); // The route obtained from the ancestor node through the `tryOf` method should be the same BoostPageRoute // as the originally created BoostPageRoute expect(boostPageRoute, boostPageRouteFindByOfMethod); }); }); testWidgets( 'try to find BoostPageRoute through the BoostPageRoute.tryOf(context) method, ' 'but it doesn\'t exist, the method should return null', (WidgetTester tester) async { BoostPageRoute<dynamic> boostPageRouteFindByOfMethod; await tester.pumpWidget( MaterialApp( onGenerateRoute: (RouteSettings settings) { return MaterialPageRoute<dynamic>( settings: settings, builder: (BuildContext context) => Builder( builder: (BuildContext context) { return FloatingActionButton( onPressed: () { boostPageRouteFindByOfMethod = BoostPageRoute.tryOf<dynamic>(context); }, ); }, ), ); }, ), ); await tester.tap(find.byType(FloatingActionButton)); await tester.pump(const Duration(seconds: 1)); expect(boostPageRouteFindByOfMethod, null); }); } | Low | [
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24,
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Influence of oxic/anoxic fluctuations on ammonia oxidizers and nitrification potential in a wet tropical soil. Ammonia oxidation is a key process in the global nitrogen cycle. However, in tropical soils, little is known about ammonia-oxidizing microorganisms and how characteristically variable oxygen regimes affect their activity. We investigated the influence of brief anaerobic periods on ammonia oxidation along an elevation, moisture, and oxygen availability gradient in wet tropical soils. Soils from three forest types were incubated for up to 36 weeks in lab microcosms under three regimes: (1) static aerobic; (2) static anaerobic; and (3) fluctuating (aerobic/anaerobic). Nitrification potential was measured in field-fresh soils and incubated soils. The native ammonia-oxidizing community was also characterized, based on diversity assessments (clone libraries) and quantification of the ammonia monooxygenase α-subunit (amoA) gene. These relatively low pH soils appear to be dominated by ammonia-oxidizing archaea (AOA), and AOA communities in the three soil types differed significantly in their ability to oxidize ammonia. Soils from an intermediate elevation, and those incubated with fluctuating redox conditions, tended to have the highest nitrification potential following an influx of oxygen, although all soils retained the capacity to nitrify even after long anoxic periods. Together, these results suggest that wet tropical soil AOA are tolerant of extended periods of anoxia. | High | [
0.656565656565656,
32.5,
17
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Megakaryocytic dysfunction in myelodysplastic syndromes and idiopathic thrombocytopenic purpura is in part due to different forms of cell death. Platelet production requires compartmentalized caspase activation within megakaryocytes. This eventually results in platelet release in conjunction with apoptosis of the remaining megakaryocyte. Recent studies have indicated that in low-risk myelodysplastic syndromes (MDS) and idiopathic thrombocytopenic purpura (ITP), premature cell death of megakaryocytes may contribute to thrombocytopenia. Different cell death patterns have been identified in megakaryocytes in these disorders. Growing evidence suggests that, besides apoptosis, necrosis and autophagic cell death, may also be programmed. Therefore, programmed cell death (PCD) can be classified in apoptosis, a caspase-dependent process, apoptosis-like, autophagic and necrosis-like PCD, which are predominantly caspase-independent processes. In MDS, megakaryocytes show features of necrosis-like PCD, whereas ITP megakaryocytes demonstrate predominantly characteristics of apoptosis-like PCD (para-apoptosis). Triggers for these death pathways are largely unknown. In MDS, the interaction of Fas/Fas-ligand might be of importance, whereas in ITP antiplatelet autoantibodies recognizing common antigens on megakaryocytes and platelets might be involved. These findings illustrate that cellular death pathways in megakaryocytes are recruited in both physiological and pathological settings, and that different forms of cell death can occur in the same cell depending on the stimulus and the cellular context. Elucidation of the underlying mechanisms might lead to novel therapeutic interventions. | High | [
0.6666666666666661,
34,
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A new prenylated flavanone glycoside from the seeds of Glircidia maculata. A new flavanone glycoside, 5,4'-dihydroxy-6-prenylflavanone 4'-O-beta-D-xylopyranosyl-(1-->2)-alpha-L-rhamnopyranoside (1), was isolated from the seeds of Glircidia maculata. | High | [
0.691751085383502,
29.875,
13.3125
] |
333 P.2d 607 (1958) 65 N.M. 119 William P. KEARNS, Jr., Chief of the Division of Liquor Control, Appellant, v. Juan P. ARAGON, d/b/a Juan's Beer Garden, Appellee. No. 6450. Supreme Court of New Mexico. December 15, 1958. Rehearing Denied January 16, 1959. Charles B. Barker, Santa Fe, for appellant. Chavez & Cowper, Belen, for appellee. COMPTON, Justice. This appeal is taken by the Chief of Liquor Control, hereinafter referred to as the Chief, from the order of the District Court of Santa Fe County setting aside his order revoking appellee's liquor license. *608 Appellee, the holder of dispenser's license No. 199 authorizing him to operate a bar in Valencia County, New Mexico, was charged with making a sale of intoxicating liquor on Sunday in violation of Section 46-10-14, NMSA, 1953 Compilation. At a hearing upon the complaint before the Chief, Eddleman, a state police officer, testified that appellee sold him a bottle of whiskey on Sunday, April 14, 1957. This testimony was partially corroborated by Daves, another state police officer. Appellee flatly denied making any such sale. In addition, appellee moved for dismissal on the ground that he had been entrapped into committing the offense. This motion was denied by the Chief. The Chief found that appellee had made the illegal sale as charged, and pursuant to the authority vested in him by Section 46-6-2(g), NMSA, 1953 Compilation, revoked his license. Appellee appealed the order of the Chief to the district court for Santa Fe County and the case was tried solely on the record made in the proceeding before the Chief. The district court reversed the decision of the Chief finding that the action of the state police in bringing about the alleged sale constituted entrapment. The court also concluded that the action of the Chief was arbitrary, capricious and unreasonable. Upon review, this court must determine whether the order or findings of the Chief were sustained by substantial, competent, relevant and credible evidence. Section 46-6-6, NMSA, 1953 Compilation. See Gonzales v. New Mexico State Board of Embalmers and Funeral Directors, 63 N.M. 13, 312 P.2d 541. We believe the order of the Chief was so supported. A portion of Officer Eddleman's testimony was as follows: "We drove up to the establishment of Juan's Beer Garden between the house and the bar. We got out of our car. At this time we noticed Juan and his wife and a little boy coming out of the bar. We approached them and went inside the bar and stopped right at the edge of the bar and asked if there would be any chance of buying any liquor. He then stated that it was Sunday and there would be no chance. We started out the door. He stated if one of you come later there might be a chance, so we got in our car and left. We fooled around town for a little while and then we went back at approximately 7 P.M. where at this time I left Officer Daves off about a half block from Juan's Beer Garden on the road. I approached the house. The house was dark and also the bar. I parked the car in the same place between the house and the bar and got out and knocked on the rear door of the house. Juan can to the door and I asked if there would be any chance of buying any liquor then. He stepped out of the door and on the steps and observed my car and he then stated, `You can buy some any time if you are by yourself.' So we went over to the bar. He unlocked the door and we went inside. He asked what kind I liked and how much and I said I would like to have a half-pint of Schenley's. He looked over the stock and told me he didn't have any Schenley's in stock and if H and H would be sufficient. I said it would. He gave me the bottle; I gave him a five dollar bill. He gave me back three dollars and a quarter. I then walked to the door, opened the door and stood right in front of the door holding the bottle in front of me where Officer Daves could see it, making conversation with Juan, Mr. Aragon. At this time he said he had to be very careful because there had been other raids from State Police and at this time I informed, I showed him my credentials and informed him I was a New Mexico State Police and that `You are under arrest' and he said `That's all right,' he said, `It's your word against mine.' I then said that Officer Daves was present and he then stated that he had *609 to go into the house. I told him to get in the car and he proceeded on in the house. I followed him in the first door and then turned around and came back out. At this time Officer Daves was there and I told him to go to the front door. I stood at the rear door. I moved my car from behind the house around to the north side of the house. I stood by the rear door. I heard, I don't know exactly what it was, it seemed like some drawers moving in the bedroom. I heard a screen open and about a minute later Officer Daves came around and told me the man had a gun sticking out the window. We then proceeded to get in my car and go over to the Town of Belen and phone Officer Stringfellow of the State Police. We then went to a Justice of the Peace and filed a complaint for illegal sale of liquor and resisting arrest, pending by Sergeant Vigil and Captain Bradford. We then called Sergeant Vigil at Albuquerque." Appellee makes much of the fact that the court reporter and perhaps others, first understood Witness Eddleman to say that the whiskey he purchased was H & H, while the bottle placed in evidence was Ancient Age. The witness explained on cross-examination that he had said Ancient Age. We attach no particular significance to this point in view of the fact that when H and H and Ancient Age are spoken it is somewhat difficult for the ear to distinguish between the two terms. Officer Daves testified in part as follows: "* * * He (appellee) stated for us to go on but if one of us come back, that he would sell us some whiskey, some liquor. We left then and drove around town and observed other bars until around 7 P.M., and I guess. We then went back to Juan's Beer Garden and I got out around a half a block to a block from the bar and Officer Eddleman drove his car on up into the yard there and after I got out, I started walking toward the bar. It wasn't dark yet, but it was kind of hazy, and when I got I saw I did see Officer Eddleman and Mr. Aragon go into the bar and I kept on walking toward the bar and when they come out shortly, they stood there at the door for a few seconds, I don't know how long, and all of this time I was walking toward them and while they were standing there I saw a bottle in Officer Eddleman's hand that he was holding up in front of him. * * *" The Chief who heard the testimony and had an opportunity to observe the demeanor of the witnesses, stated as follows in his order. "that the testimony of the State's witness instant violation was very convincing. * * *" After reviewing the testimony taken in the proceedings before the Chief we are of the opinion that the order was supported by substantial, competent, relevant and credible evidence. Even assuming that the action of the State police officers constituted entrapment, this fact alone does not render their testimony unsubstantial, incompetent, irrevelant or incredible. As we held in State v. Romero, 49 N.M. 129, 133, 158 P.2d 851, the mere circumstance, standing alone, that the State's witnesses were engaged in a species of entrapment does not render their testimony unworthy of belief. See In re Wellcome, 23 Mont. 450, 59 P. 445. The Chief contends that since the appellee took the stand and denied under oath that he had made the alleged Sunday sale, he is precluded from raising the defense of entrapment. Appellee of course urges to the contrary. We have found well reasoned cases supporting both views, but as will be seen it is unnecessary to decide this point. A proceeding before the Chief to revoke a liquor license is not a criminal proceeding; rather it is an administrative proceeding in the nature of a civil action. Bradley v. Texas Liquor Control Board, Tex.Civ.App., 108 S.W.2d 300; Commonwealth v. Lyons, 142 Pa.Super. 54, 15 A.2d *610 851; Kravis v. Hock, 137 N.J.L. 252, 59 A.2d 657. This is true even though the charge and ground for revocation is the violation of a penal statute. Keller v. Kentucky Alcoholic Beverage Control Board, 279 Ky. 272, 130 S.W.2d 821; Boyd v. Allen, 246 N.C. 150, 97 S.E.2d 864. Section 46-6-4(m), NMSA, 1953 Compilation, makes this quite clear in providing that no admission of guilt, admission against interest or transcript of testimony taken in hearings before the Chief is admissible in a criminal prosecution against a licensee. Nor is the object of an administrative proceeding to revoke a liquor license intended as a punishment of the licensee. The purpose is to insure so far as possible the decent and orderly conduct of a business affecting the public health, morals, safety and welfare. Flowers v. Benton County Beer Board, Tenn. 302 S.W.2d 335; Cornell v. Reilly, 127 Cal. App.2d 178, 273 P.2d 572. State control of the liquor business under the police power is so great as to range from complete prohibition to lesser degrees of regulation and constant surveillance. Boyd v. Allen, 246 N.C. 150, 97 S.E.2d 864. See Floeck v. Bureau of Revenue, 44 N.M. 194, 100 P.2d 225. Hence, revocation proceedings are not governed by the rules of law applicable to criminal prosecutions. In such proceedings the offense need not be established beyond a reasonable doubt. Pennsylvania Liquor Control Board v. Summit Hill Rod and Gun Club, 184 Pa.Super. 584, 135 A.2d 781; Kravis v. Hock, 137 N.J.L. 252, 59 A.2d 657. The constitutional defenses of unreasonable search and seizure and self-incrimination are not available in similar proceedings. Camden County Beverage Co. v. Blair, D.C., 46 F.2d 648. In liquor license revocation proceedings proof of general reputation is not treated as substantive evidence to air in determining guilt or innocence. Commonwealth v. Lyons, supra. Likewise, and decisive for purposes of this case, entrapment is not a defense in an administrative proceeding to revoke a liquor license. In a civil proceeding for the forfeiture of contraband liquor, the Missouri court held that the defense of entrapment was not available since the "defendant is not being tried here for a criminal offense." State v. Ward, 361 Mo. 1236, 239 S.W.2d 313, 320. Our decision goes no further than to hold that the defense of entrapment is not available in a proceeding to revoke a liquor license. Nonetheless, we wish to point out that many courts have gone considerably further in restricting the defense of entrapment. In some jurisdictions, notably Tennessee and New York, the defense of entrapment is not recognized in any criminal action. Goins v. State, 192 Tenn. 32, 237 S.W.2d 8; People On Complaint of Klein v. Schacher, Mag.Ct., 47 N.Y.S.2d 371. In a number of jurisdictions the defense of entrapment has no application in criminal prosecutions for violating liquor laws. The rationale of these decisions is that to constitute entrapment the criminal intent must originate in the mind of the entrapper, and since no intent is necessary to violate liquor laws, an essential element of entrapment is absent. French v. State, 149 Miss. 684, 115 So. 705; State v. Driscoll, 119 Kan. 473, 239 P. 1105; State v. Merklinger, 180 Kan. 283, 303 P.2d 152; State v. Varnon, Mo., 174 S.W.2d 146; State v. Sheeler, 320 Mo. 173, 7 S.W.2d 340. In the case of State v. Broaddus, 315 Mo. 1279, 289 S.W. 792, 795, the court stated this principle as follows: "Whatever may be the general rule in regard to the effect upon the right to convict a defendant who has been entrapped into the commission of a crime (18 A.L.R. 146, 149), it is usually held to have no application to cases involving the sale of intoxicating liquors or other violations of the Prohibition Laws. In this class of cases criminal intent is not, as a rule, a necessary element and need not be shown." In a similar vein is the following statement by the Virginia court in Bauer v. *611 Commonwealth, 135 Va. 463, 115 S.E. 514, 515: "But whatever may be said against enticing one to commit crime, the decided weight of authority is that one who makes an unlawful sale of liquor, or unlawfully transports it, is not excused from criminality by the fact that he was induced to do the criminal act for the sole purpose of prosecuting him for it. Initiative on the part of the perpetrator of an offense of this nature is not essential to charge him with criminal responsibility." In view of what has been said above, the judgment of the district court must be reversed and the cause remanded with a direction to set aside its judgment and enter another affirming the order of the Chief. It is so ordered. McGHEE and SHILLINGLAW, JJ., concur. LUJAN, C.J., and SADLER, J., not participating. | Mid | [
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Q: Multithreading - Is threadpool good choice? I have a c#(.Net 3.5) application which imports thousands of files. Right now, I create background worker for each file. It works good up to certain limit & then application dies out with System out of memory exception. I am assuming this is happening because of large number of threads. Is threadpool a good solution for this situation? Exception is : System.OutOfMemoryException | Exception of type 'System.OutOfMemoryException' was thrown. at System.Data.RBTree`1.TreePage..ctor(Int32 size) at System.Data.RBTree`1.AllocPage(Int32 size) at System.Data.RBTree`1.InitTree() at System.Data.Index.InitRecords(IFilter filter) at System.Data.Index..ctor(DataTable table, Int32[] ndexDesc, IndexField[] indexFields, Comparison`1 comparison, DataViewRowState recordStates, IFilter rowFilter) at System.Data.DataTable.GetIndex(IndexField[] indexDesc, DataViewRowState recordStates, IFilter rowFilter) at System.Data.DataColumn.get_SortIndex() at System.Data.DataColumn.IsNotAllowDBNullViolated() at System.Data.DataTable.EnableConstraints() at System.Data.DataTable.set_EnforceConstraints(Boolean value) at System.Data.DataTable.EndLoadData() at System.Data.Common.DataAdapter.FillFromReader(DataSet dataset, DataTable datatable, String srcTable, DataReaderContainer dataReader, Int32 startRecord, Int32 maxRecords, DataColumn parentChapterColumn, Object parentChapterValue) at System.Data.Common.DataAdapter.Fill(DataTable[] dataTables, IDataReader dataReader, Int32 startRecord, Int32 maxRecords) at System.Data.Common.DbDataAdapter.FillInternal(DataSet dataset, DataTable[] datatables, Int32 startRecord, Int32 maxRecords, String srcTable, IDbCommand command, CommandBehavior behavior) at System.Data.Common.DbDataAdapter.Fill(DataTable[] dataTables, Int32 startRecord, Int32 maxRecords, IDbCommand command, CommandBehavior behavior) at System.Data.Common.DbDataAdapter.Fill(DataTable dataTable) at Dms.Data.Adapters.DataTableAdapterBase`2.FillByCommand(TTbl table, DbCommand command) A: The problem is most likely that you're trying to load too many files at once time. Using a ThreadPool may help, as it could give you a means of limiting the processing. However, if you're importing and processing "thousands of files", the appropriate means may be to create a pipeline to handle your processing, and then fill the pipeline (or a certain number of them) with your files. This would let you control the amount of concurrency, and prevent too many individual files from being processed at the same time. It could keep your memory and processing requirements to a more reasonable level. Edit: Since you (now) mentioned that you're using C#... The BackgroundWorker actually does use the ThreadPool. Switching to using the thread pool directly may still be a good idea, but it likely won't solve the issue entirely. You may want to consider using something like BlockingCollection<T> to set up a producer/consumer queue. You could then have 1 or more threads "consume" the files and process them, and just add all of the files to the BlockingCollection<T>. This would give you control over how many files are handled at once (just add another thread for processing as you can). | Mid | [
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Do you think you would be more productive if you only had to go to the office for five hours? A B.C. tech company is hoping that by switching to shortened "core" hours it will boost performance – and attract new talent in the process. Digital marketing firm RingPartner, based in Victoria, requires employees to work in the office from 10 a.m. to 3 p.m., with any remaining work to be done where and when they choose. Mother of four Katie Hoffmann, the company's risk manager, says the shorter hours and later start time have been a "gift." With children aged between one and seven, getting ready for work at an early hour used to be super hectic. “(Before) I had two minutes to get dressed, grab my lunch if I remembered it and then I would get to work and brush my teeth,” Hoffmann said. Company CEO Mike Williams said the perk of working core hours has not only brought in attractive job candidates, it's also shown value because people are working harder. “It’s really about the value and the results that they can drive rather than the time that you put into the office,” said Williams. Companies in B.C.'s booming tech sector are having to get creative as demand for workers soars. By 2021, the B.C. Tech Association estimates there could be close to 30,000 unfilled positions. With a report from CTV Vancouver’s Bhinder Sajan | Mid | [
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In vitro antiplasmodial activity and chloroquine-potentiating action of three new isoquinoline alkaloid dimers isolated from Hernandia voyronii Jumelle. Three new isoquinoline alkaloid dimers with pavine and benzyl-tetrahydroisoquinoline moieties have been isolated, by bioassay-guided fractionation, from an alkaloid extract of Hernandia (= Hazomalania) voyronii Jumelle. All had inherent antiplasmodial activity in vitro and two enhanced chloroquine effectiveness in vitro in a dose-dependent manner. Some structure requirements for the chloroquine-potentiating action were identified in the isoquinoline series. These results, if confirmed in vivo, would account for the traditional use of H. voyronii as an adjuvant to complement chloroquine action in Malagasy herbal remedies. | High | [
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RV Trailers Denver RV Four Seasons has dealerships in both the US and Canada. We also offer a RV resort that hosts 400+ campsites, an 18-hole golf course, pools, convenience store, mini golf, live entertainment, full service marina and many other friendly amenities. for more details visit | Mid | [
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What You Should Remember When Changing Your Car's Oil Filter What You Should Remember When Changing Your Car’s Oil Filter Oil filters are important in keeping your engine clean. A clean engine is constantly a plus. That is why replacing oil filters in Australia is advised by professionals. Initially, you will be puzzled since many oil filters look alike. You need to identify whichoil filteryou have to utilize depending upon the size of your car. Know When Replacement is Due Just like every part of your vehicle, you should consider changing your oil filters. The most convenient way to determine if your oil needs changing is to examine under the bonnet. When you hire technicians to change your oil, they will typically examine it and let you understand if it’s beginning to get unclean. Know the Distinctions of Different Oil Filters Many individuals do not understand the intrinsic distinctions between various kinds of oil filters. It is not safe to think that any filter will do. Just about every oil filter or oil filter package looks precisely the same on the exterior. The truth is, quality does matter. While various oil filters may look basically similar on the outdoors, their interior qualities are where the majority of the distinctions lie. Various kinds of filtering media are used by filters to keep the oil in your car clean. Check Western Filters for more details. Steer Away from Inexpensive Oil Filters As you may anticipate, using more affordable oil filters is something that will have numerous undesirable repercussions in the long run. Often, when you purchase inexpensive oil filter packages, they do not do work to keep your oil clean. Hence, you will have to alter the oil in your automobile, truck or devices on a more regular basis. This is not a cost-effective solution for you. You can check with your user’s manual or a mechanic which oil filter is perfect for your vehicle. Concentrate on Quality A greater quality oil filter will trap 99% of foreign particles (if not more), keeping your oil cleaner for longer. As an outcome, you will have the ability to drive even more in between oil changes. You can also use your vehicle longer without needing to stress over draining pipes and changing out the oil. In addition, the cleaner oil will be much easier on the internal parts of your car. Select the Right Oil Filter You need to inspect your owner’s handbook to understand the kind of oil filters Australia has today which is perfect for your automobile. If you utilize the incorrect oil filter, it will trigger the oil to leak and put you and your family in danger. Prevent any severe damage by ensuring that you purchase the suggested oil filter replacement. These are just a few things you should remember when buying oil filters for your car. Changing oil filters regularly is one way to care for your car. A well-maintained vehicle can yield a higher price when you sell it. That is why if you want to find oil filters Australia shops offer, visit https://www.westernfilters.net.au/ for high-quality products. You can also consult trusted mechanics to inspect the auto for you. | High | [
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The US Senate voted on Friday evening to defeat a motion to bring new witnesses in the impeachment trial, likely ending the Democrats' campaign to remove President Donald Trump. The motion was defeated with a vote of 51 to 49. Senate Minority Leader Chuck Schumer (D-N.Y.) denounced the action and said it invalidated the impeachment trial. "The acquittal will have no value," he told reporters. Senate Majority Leader Mitch McConnell (R-Ky.) released his own statement calling the matter closed. "A majority of the U.S. Senate has determined that the numerous witnesses and 28,000-plus pages of documents already in evidence are sufficient to judge the House Managers' accusations and end this impeachment trial," the statement read. "There is no need for the Senate to re-open the investigation which the House Democratic majority chose to conclude and which the Managers themselves continue to describe as 'overwhelming' and 'beyond any doubt,'" he added. Democrats and other critics of the president were outraged when Sen. Lamar Alexander (R-Tenn.) announced on Thursday that the would be voting against new witnesses because he said it was already clear that the president acted inappropriately. They hoped that there might be a tie in the vote for the new witness motion and that Supreme Court Chief Justice Roberts might break the tie in favor of new witnesses, but the vote cut off that possibility. Here's the latest in the impeachment trial: | Low | [
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--- abstract: 'We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown [@Brown1963], with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.' author: - | Camille Aron$^{1}$, Daniel G. Barci$^2$, Leticia F. Cugliandolo$^3$,\ Zochil González Arenas$^4$, and Gustavo S. Lozano$^{3,5}$\ $^1$[Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA]{}\ [& Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA]{}\ $^2$[Departamento de F[í]{}sica Teórica, Universidade do Estado do Rio de Janeiro,]{}\ [Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil]{}\ $^3$[ Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France]{}\ $^4$ [Centro Brasileiro de Pesquisas Físicas]{}\ [& National Institute of Science and Technology for Complex Systems,]{}\ [Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil,]{}\ [on leave from Instituto de Cibernética, Matemática y Física, Cuba]{}\ $^5$[Departamento de Física, FCEYN Universidad de Buenos Aires & IFIBA CONICET,]{}\ [Pabellón 1 Ciudad Universitaria, 1428 Buenos Aires, Argentina]{} bibliography: - 'magn-FDT.bib' title: 'Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation' --- Introduction ============ The control of magnetic materials [@Hillebrands2002; @Mattis1988; @Mattis1985], already at the heart of the information technologies developed in the second half of the twentieth century, is undergoing a second revolution with the development of spintronics [@Johnson1985; @Brataas12]. In ferromagnetic materials, the spin degrees of freedom carried by localized electrons tend to spontaneously long-range order below the Curie (second order) transition temperature. The so-called micromagnetic description consists in studying the local order parameter, $\mathbf{M}(\mathbf{x},t)$, the expectation value of the magnetization per unit volume averaged over, typically, a few lattice cells. In most relevant cases, this macroscopic composite object can be treated classically. The spin-spin interaction is essentially due to the overlap of the electronic wave functions. Below the Curie temperature, this is the dominant interaction. The modulus of the local magnetization can be approximated by a temperature-dependent constant which takes the value of the spontaneous magnetization at the working temperature, [*i.e.*]{} $|\mathbf{M}(\mathbf{x},t)|=M_{{\rm s}}$. The direction of ${\mathbf M}$ is, instead, subject to the interactions and external forces, and it is non-uniform in space and varies in time. When a ferromagnet is used to store information, bits are encoded in the orientation of the local magnetization. Usually, the magnetization is manipulated by applying Oersted fields generated by electric currents. Very early, damping, *i.e.* the transfer of spin angular momentum from the magnetization of the macrospin $\mathbf{M}(\mathbf{x},t)$ to the environment, became a matter of fundamental but also applied interest. Indeed, this is an important limiting factor in the reduction of the remagnetization rate in magnetic recording devices. The complex environment of the macrospin offers many different mechanisms for damping (spin-orbit coupling, coupling to the lattice vibrations, spin-waves, *etc.*). In 1935, Landau and Lifshitz [@Landau-Lifshitz] (LL) proposed a phenomenological classical equation to account for all these processes through a unique damping coefficient. Though the LL equation yields reasonable results for small damping coefficient, it was initially taken to be unphysical as it predicts an acceleration of the magnetization precession at large damping. Some years later, Gilbert [@Gilbert55; @Gilbert04] cured this problem by proposing an equation in which damping enters in a different manner. Ultimately, the two equations are equivalent after a redefinition of the parameters. Today, the latter equation is known as the Landau-Lifshitz-Gilbert (LLG) equation. Its inherent non-linearity makes it a difficult problem to solve, but also the source of very rich phenomena. Explicit solutions can be obtained in some particular cases but the generic cases require numerical integration [@Bertotti-etal; @Cimrak2008]. The dynamics of magnetic moments ruled by the LLG equation have been the focus of considerable research over the last 60 years. For sufficiently small ferromagnetic particles, thermal fluctuations can become relevant in determining the magnetization dynamics. In 1963, Brown [@Fuller63] proposed a simple extension of the LLG equation in which thermal agitation is introduced *à la* Langevin, *i.e.*, *via* the addition of a random magnetic field the correlation of which is proportional to the temperature. As already shown by Brown, the stochastic magnetization dynamics can also be analyzed within the Fokker-Planck framework, that is, *via* the partial differential equation satisfied by the time-dependent probability distribution. Since then, thermal effects in the magnetization dynamics have been studied in great detail [@Bertotti-etal]. Moreover, progress in computational capabilities have now made possible numerical solutions of realistic situations [@Cimrak2008; @Aditi2012]. A new means to manipulate the magnetization of ferromagnetic devices *via* the spin-transfer torque effect has opened a new perspective into magnetic storage technologies. It has also renewed the interest in the study of magnetization dynamics. Pioneered by the theoretical work by Slonczewski [@Slonczewski1996] and Berger [@Berger1996], it was realized almost two decades ago that one could also manipulate the magnetization by exchanging angular momentum with a spin-polarized current of electrons. This proposal rapidly found some experimental evidence [@Tsoi1998; @Myers1999] and, since then, the rapid advances in the field of spintronics have led to everyday life applications such as high-density magnetic recording devices (see, for instance, [@Brataas12] for a short review). Although quantum in origin, the spin-transfer torque effect can be handled phenomenologically by an appropriate generalization of the LLG equation. The LLG equation also appears in the context of molecular spintronics as a semi-classical limit of a full quantum problem [@Brataas02; @Parcollet05; @Brataas08; @Bode11]. In the quest for smaller and smaller devices with higher storage density capabilities, it has recently become crucial to take into account the effect of thermal fluctuations on the magnetization dynamics. Indeed, smaller magnetic domains are more prone to thermally activated magnetization reversal because the energy barrier is proportional to the volume of the domain. Furthermore, as one seeks to reduce the intensity of the currents used in magnetic devices (to reduce both power consumption and Joule heating), thermal fluctuations limit the signal-to-noise ratio. Most of the existing literature dealing with thermal effects in the magnetization dynamics of nanoparticles and nano-devices analyze the problem either by direct numerical simulation of the stochastic LLG equation or *via* the study of the corresponding Fokker-Planck equation [@Coffey12]. Yet, within the study of general stochastic processes there exists also the possibility of approaching the problem *via* the path integral formulation of generating functionals [@Martin73; @Janssen76; @deDominicis76]. The use of generating functionals is an elegant and powerful method to derive generic properties of dynamical systems. Compared to the other approaches mentioned above, a path-integral is handy for computing moments, probability distribution functions, transition probabilities and responses. It is also particularly well suited when it comes to perturbation theory and renormalization group analysis, as one can easily set up a diagrammatic expansion. This approach has proven to be extremely useful to treat many physical systems. Two problems of current interest that have points in common with ours are the path-integral formulation of the motion of a Brownian particle confined to a finite volume [@Lubensky2007] and the path-integral formulation [@Andreanov05; @Velenich2008; @Kim2013] of a system of interacting Langevin processes [@Dean97]. In this manuscript, we build the framework for a path-integral description of the magnetization dynamics described by the stochastic LLG equation. The expert reader, eager to see the actions in their various forms, can jump to Eqs. (\[eq:S\_det\_cart00\]), (\[eq:S\_diss\_cart00\]) and (\[eq:S\_jac\_cart00\]) for the Landau action, and Eqs. (\[eq:SLLGjac-det\])-(\[eq:SLLGjac-jac\]) for the Gilbert action both in Cartesian coordinates; or to Eqs. (\[eq:action-det-sph-L2\])-(\[eq:esferica-jac\]) for the Landau action, and Eqs. (\[eq:action-det-sph-Gilbert-maintext\])-(\[eq:action-jac-sph-Gilbert-maintext\]) for the Gilbert action both in spherical coordinates. The manuscript is organized as follows. In Sec. \[sec:landau-lifshitz-gilbert\] we introduce the stochastic LLG equation in its Landau-Lifshitz and Gilbert formulations, and we discuss the physical significance of each of its terms. In Sec. \[sec:prescriptions\] we discuss the discretization of the stochastic integrals; the prescription used has to be carefully specified since it is a defining part of the dynamics in multiplicative random processes. We explain how the conservation of the magnetization magnitude imposes the Stratonovich discretization prescription if one persists in using the original LLG equation, or guides one into generalizations of it if the choice is to use other discretization schemes. This is particularly useful for numerical simulations for which the Itô prescription has been claimed to be simpler to implement. In Sec. \[sec:functional\], we derive the generating functional of the local magnetization by using the Martin-Siggia-Rose-Janssen-deDominicis (MSRJD) path integral [@Martin73; @Janssen76; @deDominicis76], which was originally introduced in the context of conventional Langevin equations. Although, the MSRJD formalism is well understood for systems with additive noise or with inertia (see, for instance, [@AronLeticia2010]), the stochastic LLG equation is a Markovian first order stochastic differential equation with multiplicative white noise bringing in extra difficulties such as a non-trivial Jacobian [@arenas2010; @arenas2012a; @arenas2012; @Lubensky2007; @Honkonen] that contributes to the action. In Sec. \[sec:spherical-coordinates\] we reset the general discretization scheme formulation of the stochastic LLG equation in the spherical coordinate system. *A priori*, this is the natural coordinate system for numerical simulations since the non-linear constraint on the modulus of the magnetization is built in, lowering the dimensionality of the problem from $3d$ to $2d$. However, the random noise transforms non-trivially to the new coordinate system and, in particular, it is correlated with the polar angles, a fact that has often been overlooked in the literature. We therefore correct the widespread but erroneous assumption stating that the two-dimensional random field in spherical coordinates is a simple Gaussian white noise with vanishing mean. We end this Section with the derivation of the generating functional in the spherical coordinate system. Finally, in Sec. \[sec:recap\] we recap our results and we announce a number of applications of the formalism here introduced that we plan to investigate in the future. Technical details are reported in the Appendices. Magnetization dynamics {#sec:landau-lifshitz-gilbert} ====================== Let ${\mathbf M}({\mathbf x},t)$ be the three-dimensional vector describing the local magnetization in a ferromagnet and let us assume that its modulus is constant, and equal to the spontaneous magnetization of the ferromagnet at the working temperature $T$: $|{\mathbf M}({\bf x},t)| \equiv M_{{\rm s}}$. For simplicity, we also assume that the space dependence can be neglected, that is to say, we work in the macro-spin approximation, and we later introduce the time-dependent unit vector ${\mathbf m}(t)$ through ${\mathbf M}(t)=M_{{\rm s}}{\mathbf m}(t)$. We will not follow the historic route in the presentation but rather give a presentation that we find more natural. Landau-Lifshitz-Gilbert (LLG) equation -------------------------------------- Whenever thermal fluctuations are negligible, the dissipative dynamics of the magnetization can be described by the Landau-Lifshitz-Gilbert (LLG) equation [@Gilbert55; @Gilbert04] $${{\rm d}}_t \mathbf{M} = - \gamma_0 {\mathbf{M}} \wedge \left( {\mathbf{H}}_{{\rm{eff}}} -\frac{\eta}{M_{{\rm s}}} {{\rm d}}_t \mathbf{M} \right) \; , \label{eq:Gilbert}$$ where ${{\rm d}}_t$ denotes the time derivative ${{\rm d}}/{{\rm d}}t$. The modulus of the magnetization is automatically conserved thanks to the cross product denoted $\wedge$. $\gamma_0\equiv\gamma \mu_0$ is the product of $\gamma$, the gyromagnetic ratio relating the magnetization to the angular momentum, and $\mu_0$, the vacuum permeability constant. The gyromagnetic factor is given by $\gamma=\mu_B g/\hbar$ (in our convention $\gamma>0$ for the electronic spin) with $\mu_B$ Bohr’s magneton and $g$ Lande’s $g$-factor. The first term in the [rhs]{} describes the magnetization precession around the local effective magnetic field $\mathbf{H}_{{\rm{eff}}}$, while the second term is a phenomenological description of the dissipative mechanisms, introduced by Gilbert, which slow down this precession and push ${\mathbf M}$ towards the magnetic field ${\mathbf H}_{\rm eff}$ while keeping the modulus $M_{{\rm s}}$ fixed. In principle, dissipation could enter the problem with a memory kernel because the feedback of the environment on the magnetization involves, *a priori*, retardation effects. In that perspective, the choice of $\eta \mathbf{M} \wedge {{\rm d}}_t \mathbf{M} /M_{{\rm s}}$ for the dissipative torque can then be understood as the first term of a derivative expansion. The damping constant $\eta$ takes into account several dissipative mechanisms (spin-orbit coupling, magnon-phonon, magnon-impurity, etc.). Dimensions are such that $[H]= [\gamma_0]^{-1} [t]^{-1}$ and $[\gamma_0\eta]=1$. In most relevant cases, such as magnetic recording, one has $\gamma_0\eta\ll 1$. The local effective magnetic field can be divided into conservative and non-conservative contributions, $$\mathbf{H}_{{\rm{eff}}}= \mathbf{H}_{{\rm{eff}}}^{\rm c} + \mathbf{H}_{{\rm{eff}}}^{\rm nc} \;.$$ The conservative contribution $\mathbf{H}_{{\rm{eff}}}^{\rm c}=-\mu^{-1}_0 \delta U/\delta {\mathbf{M}}$, with $U$ the energy per unit volume, can originate from an external (possibly time-dependent) magnetic field $\mathbf{H}_{{\rm{ext}}}$, and a crystal field $\mathbf{H}_{{\rm{ani}}}$ associated to the crystalline anisotropy, $$U=- \mu_0\mathbf{M} \cdot {\mathbf{H}}_{{\rm{ext}}} + V_{{\rm{ani}}}(\mathbf{M}) \; .$$ $V_{{\rm{ani}}}$ is here the anisotropy potential (per unit volume). Examples of anisotropy potentials are [@Bertotti-etal] $${V}_{{\rm{ani}}}(\mathbf{M}) = K \sum_{i\neq j} M^2_i M^2_j \; , \qquad\qquad i,j = x,y,z \; , \label{eq:cubic-anisotropy}$$ corresponding to a cubic crystalline structure (each of the three Cartesian axes is a minimum of this function), or $${V}_{{\rm{ani}}}(\mathbf{M}) = K (M_{{\rm s}}^2-M_{z}^2) \; , \label{eq:uniaxial}$$ associated to the uniaxial symmetry (having a minimum along the so-called easy axis, here the $z$-axis). We will give a very timely example of non-conservative ${\mathbf H}^{\rm nc}_{\rm eff}$, the spin-torque term, in Sec. \[sec:spin-torque\]. From the very structure of the equation, one sees that only the instantaneous component of the effective field, ${\mathbf H}_{\rm eff}= {\mathbf H}^\perp_{\rm eff} + {\mathbf H}^\parallel_{\rm eff}$, that is perpendicular to the magnetization, *i.e.* ${\mathbf H}_{\rm eff}^\perp$ such that ${\mathbf H}_{\rm eff}^\perp \cdot {\mathbf M} =0$, has an effect on its dynamics. Indeed, the field appears as $${\mathbf M} \wedge {\mathbf H}_{\rm eff} = {\mathbf M} \wedge {\mathbf H}^\perp_{\rm eff} \; .$$ The LLG equation can be written in the equivalent form [@Landau-Lifshitz] $${{\rm d}}_t {\mathbf{M}} = - \frac{\gamma_0}{1+\gamma_0^2 \eta^2} \mathbf{M} \wedge \left( {\mathbf{H}}_{{\rm{eff}}} + \frac{\eta \gamma_0}{M_{{\rm s}}} {\mathbf{M}} \wedge {\mathbf{H}}_{{\rm{eff}}} \right) \; , \label{eq:landau}$$ by simply factorizing the time-derivatives on the left-hand-side of Eq. (\[eq:Gilbert\]). In the rest of this manuscript, we shall refer to Eq. (\[eq:Gilbert\]) and Eq. (\[eq:landau\]) as the Gilbert and the Landau formulation of the same LLG equation, respectively.[^1] (We will come back to the passage from one to the other in Sec. \[sec:functional\].) Depending on the space dimension and the interactions, the LLG can exhibit a variety of non-linear structures (solitons, spatio-temporal patterns, etc.), see [@Lakshmanan2013] for a review. In some particular cases explicit solutions are known but the generic problem requires numerical integration [@Bertotti-etal; @Cimrak2008]. Stochastic LLG equation ----------------------- In 1963, Brown [@Fuller63] showed that thermal fluctuations can be taken into account by adding a random field, ${\mathbf H}$, [*à la*]{} Langevin in Eq. (\[eq:Gilbert\]) $${{\rm d}}_t {\mathbf{M}} = - \gamma_0 {\mathbf{M}} \wedge \left( \mathbf{H}_{{\rm{eff}}}+ \mathbf{H} - \frac{\eta}{M_{{\rm s}}}{{\rm d}}_t{\mathbf{M}} \right) \label{eq:sLLG1}$$ or, equivalently, by adding this field in Eq. (\[eq:landau\]) $${{\rm d}}_t {\mathbf{M}} = - \frac{\gamma_0}{1+\gamma_0^2\eta^2} \mathbf{M} \wedge \left[ (\mathbf{H}_{{\rm{eff}}} + \mathbf{H}) + \frac{\eta\gamma_0}{M_{{\rm s}}} \mathbf{M} \wedge ( \mathbf{H}_{{\rm{eff}}} +\mathbf{H}) \right] \; . \label{eq:sLL1}$$ Assuming that the thermal environment is composed of a large number of degrees of freedom and that the time-scale on which they relax is the shortest one in the problem, it is natural to consider Gaussian white noise statistics for the stochastic field. In formal terms, $$\label{eq:HhatD} \langle H_i(t) \rangle_{\mathbf H} = 0 \;, \qquad \langle H_i(t) H_j(t') \rangle_{\mathbf H} = 2 D \delta_{ij} \delta(t-t') \; ,$$ for all $i,j=x,y,z$. The parameter $D$ is such that the fluctuation-dissipation relation of the second kind (in Kubo’s terminology [@Kubo66]) is satisfied, that is to say, that the sLLG equation takes the magnetization to equilibrium, *i.e.* with a Gibbs-Bolztmann distribution function at the temperature $T$ of the environment. As we will show explicitly in Sec. \[sec:Fokker-Planck\], its relation to the parameters in the problem is $$D = \frac{\eta k_{\rm B}T}{M_{{\rm s}}V \mu_0} \; .$$ $V$ is the volume of the sample and $k_{\rm B}$ the Boltzmann constant. Dimensions are such that $[D] = [t] [H^2]$. In both Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]), the noise couples multiplicatively to the time-dependent magnetization. To completely define the Markovian dynamics of such a stochastic equation with multiplicative white noise, one needs to specify a prescription for the way in which the noise acts at a microscopic time level. As we will discuss in more detail in Sec. \[sec:prescriptions\], written as they are, Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]) have to be understood as Stratonovich equations, *i.e.* with a mid-point prescription [@Bertotti-etal; @Langevin-Coffey; @Martinez-etal], as this is the unique scheme consistent with the conservation of the modulus of the magnetization. Henceforth, we will refer to these equations as the [*stochastic Stratonovich*]{} Landau-Lifshitz-Gilbert equations. We will also show in Sec. \[sec:prescriptions\] how to generalize these equations to use other discretization schemes. It can be useful to work with adimensional variables and parameters. If one defines $\gamma_0 M_{{\rm s}}t \mapsto t$, $\mathbf{M}/M_{{\rm s}}\mapsto \mathbf{m}$, $\mathbf{H}_{{\rm{eff}}}/M_{{\rm s}}\mapsto \mathbf{h}_{{\rm{eff}}}$, $\mathbf{H}/M_{{\rm s}}\mapsto \mathbf{h}$, and $\eta\gamma_0 \mapsto \eta$ the dynamical equation becomes $${\rm d}_t {\mathbf{m}} =- {\mathbf{m}} \wedge \left(\mathbf{h}_{{\rm{eff}}} + {\mathbf{h}} - \eta \ {\rm d}_t{\mathbf{m}} \right) \;, \label{eq:sLLG1-adim}$$ or $${\rm d}_t {\mathbf{m}} =- \frac{1}{1+\eta^2} \ \mathbf{m} \wedge [(\mathbf{h}_{{\rm{eff}}}+ \mathbf{h}) + \eta \ {\mathbf{m}} \wedge(\mathbf{h}_{{\rm{eff}}}+ \mathbf{h} ) ] \; . \label{eq:sLL1-adim}$$ The Gaussian white noise ${\mathbf h}$ has zero average and correlations characterized by a new diffusion constant, $\gamma_0 D/M_{{\rm s}}\mapsto D$, $$\langle h_{i}(t) \rangle_{\mathbf h} = 0 \;, \qquad \langle h_{i}(t) h_{j}(t') \rangle_{\mathbf h} = 2 D \ \delta_{ij} \delta(t-t') \; .$$ All variables and parameters are now adimensional. Here again, the Gilbert and Landau stochastic Eqs. (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]) have to be understood as Stratonovich equations and are totally equivalent. Spin-torque {#sec:spin-torque} ----------- The LLG equation (\[eq:Gilbert\]) or its stochastic version (\[eq:sLLG1\]) can also be used to describe spin-transfer torque in magnetic multilayers [@Slonczewski1996; @Berger1996]. By means of this effect, a spin-polarized electric current flowing through the multilayer can affect the orientation of the magnetization in one of the layers (the free moving one). Although the origin of this effect is quantum mechanical, it can be phenomenologically studied by adding to the LLG equation an extra “torque" term which depends on the relative position of the layers, their polarization, the electrical current, and other properties of the material. This effect has been the topic of a tremendous amount of work during the last 15 years due to its many potential applications in the field of spintronics. In its simpler form, the Landau-Lifshitz-Gilbert-Slonczewski equation reads [@Stiles2006] $${{\rm d}}_t {\mathbf{M}} = - \gamma_0 {\mathbf{M}} \wedge \left(\mathbf{H}_{{\rm{eff}}} + {\mathbf H} - \frac{\eta}{M_{{\rm s}}} {{\rm d}}_t \mathbf{M} \right) - \frac{g \mu_B J {\cal P}}{2 M_{{\rm s}}^2 d e} \mathbf{M} \wedge (\mathbf{M} \wedge \mathbf{p}) \; , \label{eq:sLLG1-spintorque-dim}$$ where we singled out from ${\mathbf H}_{\rm eff}$ the spin-torque term. Here, $g\mu_B = \gamma\hbar$ with $\gamma$ the gyromagnetic ratio, $J$ is the current per unit area, ${\cal P}$ represents the (dimensionless) polarization function of the fixed layer, ${\mathbf p}$ is a unit vector in the direction of the fixed layer magnetization, $d$ the interlayer separation, and $e$ is the electric charge of the carriers. (Recall that in the macromagnetic approach ${\mathbf M}$ is the magnetization per unit volume.) In dimensionless variables, this equation reads $${{\rm d}}_t {\mathbf{m}} = - {\mathbf{m}} \wedge \left( \mathbf{h}_{{\rm{eff}}} + {\mathbf h} - \eta {{\rm d}}_t \mathbf{m} \right) - \chi \mathbf{m} \wedge (\mathbf{m} \wedge \mathbf{p}) \label{eq:sLLG1-spintorque-adim}$$ with $$\chi=\frac{\hbar J}{2 M_{{\rm s}}^2 d e \mu_0} {\cal P} \; ,$$ a dimensionless parameter. The last terms in Eqs. (\[eq:sLLG1-spintorque-dim\]) and (\[eq:sLLG1-spintorque-adim\]) represent a torque that cannot be derived from a potential and provides a mechanism to exchange energy between the magnetic moment and the environment *via* the current that flows in the sample. Thus, a spin polarized current of electrons can be used to manipulate the dynamics of the magnetic moment, its spin flip rate and its precession frequency [@Brataas12]. Initial studies of spin-torque assisted dynamics focused on the zero temperature limit [@Stiles2006; @Berkov2008] while temperature effects were considered in [@Myers2002; @Koch2004; @Li2004; @Russek2005; @Apalkov2005; @Xiao2005]. Most of this literature addresses the problem [*via*]{} the numerical integration of the stochastic equation [@Cimrak2008] or the Fokker-Planck approach. A simple way to understand, at least qualitatively, thermal effects in spin-torque driven dynamics is by realizing that spin-torque effectively modifies the dissipation coupling. If the current is such that this dissipation is lowered, one can expect thermal effects to be more relevant than in the absence of spin torque. Even more so, spin torque may not only reduce the effective dissipation constant but also make it [*negative*]{} meaning that the system amplifies disturbances from equilibrium [@Koch2004]. Discretization prescriptions {#sec:prescriptions} ============================ In this Section, we discuss the time-discretization of the stochastic magnetization dynamics. Indeed, as in any stochastic differential equation, the discretization used to define the Wiener integral is a defining part of the model, and should be carefully taken into account to obtain sensible physical results [@Gardiner]. As we will show, in the way the stochastic equation is currently written \[either in the form in Eq. (\[eq:sLLG1\]) or in the one in Eq. (\[eq:sLL1\]), or in their adimensional versions\], it conserves the magnetization modulus [*only if*]{} the Stratonovich prescription is used. Although this is not a new result (see, e.g., [@Bertotti-etal]), one still finds quite confusing statements in the literature [@Martinez-etal; @Berkov2002]. In the following discussion, we first describe the discretization of generic stochastic equations and we later discuss the case of the stochastic LLG (sLLG) equation. We next show how Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]) have to be modified if one wishes to work with other stochastic calculi in order, notably, to ensure the conservation of the modulus of ${\mathbf M}$. Rules of stochastic calculus {#subsec:rules} ---------------------------- Let us consider a set of time-dependent random variables $x_a(t)$ satisfying a set of first order differential equations, $${{\rm d}}_t x_a(t) = f_a({\bf x}(t)) + g_{aj}({\bf x}(t)) h_j(t) \;, \label{eq.Langevin}$$ where the $x_a$, with $a=1,\dots, N$ are the components of the stochastic variable ${\bf x}$ and $h_j$, with $j=1,\dots, M$ are the components of the Gaussian white-noise process ${\bf h}$ satisfying $$\left\langle h_i(t)\right\rangle_{\mathbf h} = 0 \; , \qquad\qquad \left\langle h_i(t) h_j(t')\right\rangle_{\mathbf h} = 2D \delta_{ij}\delta(t-t') \;. \label{whitenoise}$$ Here and in what follows, we use the Einstein summation convention over repeated indices. In Eq. (\[eq.Langevin\]), $f_a({\bf x})$ and $g_{aj}({\bf x})$ are the so-called drift term and diffusion matrix, respectively, and are arbitrary smooth functions of ${\bf x}(t)$ (but not of its time-derivatives). Notice that, in general, the diffusion matrix is rectangular as the number of random variables is not necessarily equal to the number of random processes. Due to the fact that $h_j(t)$ has an infinite variance, Eq. (\[eq.Langevin\]) is ill-defined until the product $g_{aj}({\bf x}(t)) h_j(t)$ is given a proper microscopic meaning. This subtlety can be understood by looking at the integral $$\int g_{aj}({\bf x}(t)) h_j(t) \; {{\rm d}}t= \int g_{aj}({\bf x}(t))\; {{\rm d}}W_j(t) \ ,$$ where we have introduced the Wiener processes $W_j(t)$ as $h_j(t)={{\rm d}}W_j(t)/{{\rm d}}t$. The Riemann-Stieltjes integral is defined by using a set of times $t_0 < t_1 < \dots < t_N ={\cal T}$ in the interval $[t_0, {\cal T}]$ and constructing the sum $$\int_{t_0}^{\cal T} g_{aj}({\bf x}(t))\; {{\rm d}}W_j(t)= \lim _{N\to\infty} \sum_{n=0}^{N-1} g_{aj}(\bar {\bf x}_n) \left[ W_j(t_{n+1})-W_j(t_n) \right] \label{eq.Wiener}$$ where $\bar x_n$ is taken in the interval $[x_n,x_{n+1}]$ and the [rhs]{} of Eq. (\[eq.Wiener\]) converges in the mean-square sense[^2]. For a smooth measure $W_j(t)$ the limit converges to a unique value, regardless of the choice of the $\bar x_n$’s. However, a Wiener process $W_j(t)$ is not smooth; in fact, it is nowhere differentiable. Therefore, the value of the integral depends on the prescription used to choose the $\bar x_n$’s. There are several ways to define this integral that can be collected in the so-called “generalized Stratonovich prescription” [@Hanggi1978] or “$\alpha$-prescription” [@Janssen-RG], for which one uses $$\begin{aligned} \bar {\bf x}_n &=& \alpha {\bf x}_{n+1} + (1-\alpha) {\bf x}_{n} \; , \end{aligned}$$ with $0\le \alpha \le 1$, and $$g_{aj}(\bar {\bf x}_n)=g_{aj}(\alpha {\bf x}(t_{n+1}) + (1-\alpha){\bf x}(t_n)) \; . \label{eq.prescription}$$ The case $\alpha=0$ corresponds to the pre-point Itô prescription and $\alpha=1/2$ coincides with the mid-point Stratonovich one. The post-point prescription, $\alpha=1$, is also used [@Hanggi1978; @Hanggi1982; @Klimontovich]. For Markov processes with multiplicative white-noise, each choice of $\alpha$ corresponds to a different stochastic evolution. For any physical problem, the prescription is dictated by the order of limits when sending the time scales associated to inertia and the relaxation of the thermal bath to zero [@Kupferman]. Once the prescription is fixed, the stochastic dynamics are unambiguously defined. In the cases in which the time scale associated to inertia is much smaller than the relaxation time of the bath, Eq. (\[eq.Langevin\]) is given an unambiguous meaning by adding a little color to the Gaussian noise, *i.e* a finite variance [@Hanggi-shot], and by eventually taking the white-noise limit at the end of the calculations. This regularization procedure is equivalent to the Stratonovich prescription, $\alpha=1/2$ [@vanKampen; @Zinn-Justin]. In the present case of magnetization dynamics, there is [*a priori*]{} no term playing the role of inertia. The rules of calculus applied to the stochastic variables also depend on the prescription. In particular, the chain rule used to differentiate an arbitrary function $Y({\bf x}(t))$ of a set of stochastic variables reads [@arenas2010; @arenas2012a; @arenas2012] $${{\rm d}}_t Y({\bf x}(t))=\frac{\partial Y}{\partial x_a}\; {{\rm d}}_t x_a +(1-2\alpha) D\; \frac{\partial^2 Y}{\partial x_a\partial x_b}\; g_{ak} g_{bk} \; . \label{eq.chainrule}$$ Clearly, in the Stratonovich prescription ($\alpha=1/2$), Eq. (\[eq.chainrule\]) is the usual chain rule of conventional calculus. For $\alpha=0$, Eq. (\[eq.chainrule\]) is the so-called Itô formula. For the $\alpha=1$ prescription, the latter differentiation rule only differs from the Itô formula by the sign of the last term. In fact, these two prescriptions are related by a time reversal transformation $t\to -t$ and $\alpha\to (1-\alpha)$. Discretization scheme for the sLLG equation {#sec:sLLGprescription} ------------------------------------------- Let us start with the dimension-full Landau formulation of the sLLG equation, *i.e.*, with Eq. (\[eq:sLL1\]) that we recast in the generic form of Eq. (\[eq.Langevin\]) $${\rm d}_t M_i= g_{ij} \left(H_{{{\rm{eff}}}, j}+ H_j\right) \; , \label{eq:sLLG-functional-int}$$ where we introduced the $3\times 3$ diffusion matrix $$g_{ij}=\frac{\gamma_0}{1+\eta^2\gamma_0^2} \ [\epsilon_{ijk} M_k + \frac{\eta\gamma_0}{M_{{\rm s}}} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j)] \;. \label{Eq:gij}$$ The Latin indices take values $i, j=x,y,z$, $\epsilon_{ijk}$ is the completely antisymmetric Levi-Civita tensor and we are always assuming summation over repeated indices. $g_{ij}$ can be decomposed in symmetric and antisymmetric parts, $g_{ij} = g_{ij}^{{\rm s}}+g_{ij}^{{\rm a}}$, with $$\begin{aligned} && g_{ij}^{{\rm s}}= \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{\eta\gamma_0}{M_{{\rm s}}} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j) \; , \\ && g_{ij}^{{\rm a}}= \frac{\gamma_0}{1+\eta^2\gamma_0^2} \epsilon_{ijk} M_k \; .\end{aligned}$$ It is simple to show that $g$ is transverse in the sense that $$g_{ij} M_j = M_i g_{ij} = 0 \; .$$ Equation (\[eq:sLLG-functional-int\]) then yields $$\mathbf{M} \cdot {\rm d}_t \mathbf{M} =0\;. \label{eq:identity00}$$ Contrary to what it may seem, this result does not imply the conservation of the magnetization modulus, ${{\rm d}}(\mathbf{M}\cdot\mathbf{M}) /{{\rm d}}t = {{\rm d}}M_{{\rm s}}^2 /{{\rm d}}t =0$, for all discretization schemes. Indeed, using the appropriate generalized chain rule given in Eq. (\[eq.chainrule\]), replacing $$\label{eq.gg} g_{ik}g_{jk}= g_{ki}g_{kj} = \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}\left(M_{{\rm s}}^2 \delta_{ij}-M_i M_j \right) = \frac{M_{{\rm s}}}{\eta} g_{ij}^{{\rm s}}\;,$$ and choosing $Y({\bf M})=\mathbf{M}\cdot \mathbf{M} = M_{{\rm s}}^2$, one finds $${{\rm d}}_t M_{{\rm s}}^2 = 4D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2 \;,$$ where we used $M_i {\rm d}_t M_i =0$, Eq. (\[eq:identity00\]). Therefore, the physical constraint that the modulus of the magnetization be conserved by the dynamics can only be satisfied when giving a Stratonovich prescription ($\alpha =1/2$) to Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]). $\alpha$-covariant expression of the sLLG {#sec:alpha-covariantLLG} ----------------------------------------- If for any reason one prefers to work with a prescription with $\alpha\neq 1/2$ (for instance, to perform a numerical simulation with an algorithm based on the Itô calculus) while conserving the magnetization modulus, the equation has to be changed accordingly. An elegant way consists in replacing the time-derivative by the [*$\alpha$-covariant derivative*]{} $${\rm d}_t \mapsto {\rm D}^{(\alpha)}_t= {{\rm d}}_t + 2D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \;, \label{eq.covariant}$$ so that the $\alpha$-covariant expression of the sLLG equation, in its dimension-full Landau formulation, reads $${\rm D}^{(\alpha)}_t M_i= g_{ij} \left( H_{{{\rm{eff}}},j} + H_j \right) \;. \label{eq.LLG-covariant}$$ The same replacement in Eq. (\[eq:sLLG1\]) yields the $\alpha$-covariant expression of the Gilbert formulation of the sLLG equation. In both cases, this replacement is equivalent to adding a [*spurious drift term*]{} to the equation. Notice that the second term in Eq. (\[eq.covariant\]) is odd under time reversal as it should be for a time-derivative, since the time-reversal transformation includes the transformation $\alpha\to (1-\alpha)$ [@arenas2012]. Equation (\[eq.LLG-covariant\]) encodes a family of stochastic equations with different underlying prescriptions, *i.e.* different $\alpha$. The Stratonovich equation (\[eq:sLLG-functional-int\]) can naturally be recovered by setting $\alpha = 1/2$. We emphasize that the general-$\alpha$ Eq. (\[eq.LLG-covariant\]) is strictly equivalent to the Stratonovich equation (\[eq:sLLG-functional-int\]) and that the choice of $\alpha$ cannot have any consequence on the physical properties of the system. In particular, Eq. (\[eq.LLG-covariant\]) conserves the norm of the magnetization for any $\alpha$ since $M_i{\rm D}^{(\alpha)}_t M_i=0$, which implies, using the generalized chain-rule in Eq. (\[eq.chainrule\]), ${{\rm d}}_t M_{{\rm s}}^2 =0$, and ensure the approach to Boltzmann equilibrium in conservative cases as we show the in the next Subsection. The same kind of argument can be applied to the adimensional equations (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]). Fokker-Planck approach {#sec:Fokker-Planck} ---------------------- An alternative method to study the time evolution of a stochastic process is the Fokker-Planck (FP) approach, in which the system is characterized by the probability of finding ${\bf M}$ (or ${\mathbf m}$) at time $t$. The probability distribution $P({\bf M}, t)$ satisfies a [*deterministic*]{} partial differential equation, the solution of which completely describes the dynamics of the system. The FP equation associated to the sLLG equation in Gilbert’s formulation and for Stratonovich calculus was derived by Brown [@Fuller63], see also [@Bertotti-etal; @GarciaPalacios98]. We will show below that the $\alpha$-covariant stochastic equation (\[eq.LLG-covariant\]) leads to a FP equation that is [*independent*]{} of $\alpha$. The FP method allows one to prove that the stochastic process described by Eq. (\[eq.LLG-covariant\]) leads, at long times and under conservative time-independent forces, to the equilibrium Gibbs-Boltzmann probability distribution for any value of $\alpha$, provided that the noise correlation $D$ is set by an Einstein relation. ### Derivation of the Fokker-Planck equation In order to derive the Fokker-Planck equation, we begin with the identity $$P({\bf M},t+\Delta t) = \int {\hspace{-0em}\mathrm{d}{{\bf M}_0}\;} P({\bf M},t+\Delta t|{\bf M}_0,t)P({\bf M}_0,t) \; , \label{Eq.Identity}$$ where $P({\bf M},t+\Delta t|{\bf M}_0,t)$ is the conditional probability of finding ${\bf M}$ at the time $t+\Delta t$, provided the system was in the state ${\bf M}_0$ at the previous time $t$ (note that ${\mathbf M}_0$ is not necessarily the initial magnetization here). The integral in Eq. (\[Eq.Identity\]) runs over all accessible values of ${\bf M}_0$. This equation holds for any value of $\Delta t$ but we will later focus on infinitesimal time increments. To make contact with the stochastic process in the Langevin-like description, it is convenient to define the conditional probability in the following way: $$\label{eq.conditionalP} P({\bf M},t+\Delta t|{\bf M}_0,t) = \langle \delta({\bf M} - {\bf M}(t+\Delta t)) \rangle_{\mathbf H} \; ,$$ where the mean value is taken over the noise $\mathbf{H}$, and ${\bf M}(t+\Delta t)$ is determined by the stochastic equation (\[eq.LLG-covariant\]) with the initial condition ${\bf M}(t)={\bf M}_0$. Expanding Eq. (\[eq.conditionalP\]) in powers of $\Delta{\bf M}={\bf M}(t+\Delta t)-{\bf M}(t)={\bf M}(t+\Delta t)-{\bf M}_0$ we immediately obtain $$\begin{aligned} && P({\bf M},t+\Delta t|{\bf M}_0,t) = \delta({\bf M}-{\bf M}_0) - \partial_i\delta({\bf M}-{\bf M}_0) \ \langle \Delta M_i\rangle_{\mathbf H} \nonumber \\ && \qquad\qquad\qquad\qquad\qquad+ \frac{1}{2} \partial_{i}\partial_{j}\delta({\bf M}-{\bf M}_0) \ \langle \Delta M_i\Delta M_j\rangle_{\mathbf H} + \ldots \qquad \label{eq.delta_Cond}\end{aligned}$$ where $\partial_i \equiv \partial/\partial{M}_i$ and the ellipsis indicate terms involving higher order correlations. The idea is to compute the correlations $\langle \Delta M_i\rangle_{\mathbf H}$ and $\langle \Delta M_i\Delta M_j\rangle_{\mathbf H}$ to leading order in $\Delta t$ and then take the limit $\Delta t\to 0$. To do this, we integrate the sLLG equation (\[eq.LLG-covariant\]) in the interval $(t, t+\Delta t)$ obtaining $$\Delta M_i = f_i ({\bf M}_0)\Delta t + g_{ij}[{\bf M}_0+ \alpha \Delta {\bf M}(t + \Delta t)] \int_{t}^{t+\Delta t} {\hspace{-0em}\mathrm{d}{t'}\;} H_j(t')\;, \label{eq.deltam}$$ where we have used the $\alpha$-discretization procedure to define the last Wiener integral as explained in Sec. \[subsec:rules\], $W_j(t+\Delta t) - W_j(t) = \int_t^{t+\Delta t} dt' H_j(t')$, and $$\begin{aligned} \label{eq.f} f_i ( {\bf M}_0)&=&g_{ij}({\mathbf M}_0) H_{{{\rm{eff}}},j} - 2D \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}\; (1-2\alpha) {M_0}_i\;, \\ \label{eq.gij} g_{ij}( {\bf M}_0)&=&\frac{\gamma_0}{1+\eta^2\gamma_0^2} \ \left[\epsilon_{ijk} {M_0}_k + \frac{\eta\gamma_0}{M_{{\rm s}}} (M_{{\rm s}}^2 \delta_{ij} - {M_0}_i {M_0}_j)\right]\;,\end{aligned}$$ see Eq. (\[Eq:gij\]). Solving Eq. (\[eq.deltam\]) to order $\Delta t$ (by expanding $g_{ij}$ in powers of $\Delta{\bf M}$ and solving iteratively), and computing the mean values using $\langle H_i(t)H_j(t') \rangle_{\mathbf H}=2D\delta_{ij}\delta(t-t')$, we finally obtain $$\begin{aligned} \langle \Delta M_i\rangle_{\mathbf H} &=& f_i({\bf M}_0)\Delta t + 2D \alpha g_{k\ell}({\bf M}_0)\partial_k g_{i\ell}({\bf M}_0) \Delta t\,, \label{prom_deltax} \\ \langle \Delta M_i\Delta M_j\rangle_{\mathbf H} &=& 2 D g_{ik}({\bf M}_0)g_{jk}({\bf M}_0)\Delta t \,. \label{prom_deltaxdeltay}\end{aligned}$$ Interestingly enough, the mean value as well as the two point correlation are of order $\Delta t$. Higher momenta of the distribution such as $\langle \Delta M_i\Delta M_j\Delta M_k\rangle_{\mathbf H}$ are of higher order in $\Delta t$ and do not contribute to the expansion in Eq. (\[eq.Pm\]) for sufficiently small $\Delta t$. It is important to note that these results depend on ${\mathbf M}_0$. Replacing now Eq. (\[eq.delta\_Cond\]) into Eq. (\[Eq.Identity\]) and integrating over ${\bf M}_0$ we have $$\begin{aligned} && P({\bf M},t+\Delta t)-P({\bf M},t) = - \partial_i \ [ \langle \Delta M_i\rangle_{\mathbf H} P({\bf M},t) ] \nonumber \\ & & \qquad\qquad\qquad\qquad\qquad\qquad + \frac{1}{2} \partial_{i}\partial_{j} \ [\langle \Delta M_i\Delta M_j\rangle_{\mathbf H} P({\bf M},t) ] + \ldots \qquad\qquad \label{eq.Pm}\end{aligned}$$ Using the averages found in Eqs. (\[prom\_deltax\]) and (\[prom\_deltaxdeltay\]) and performing the continuum limit $\Delta t \to 0$ we finally find the desired partial differential equation for $P({\bf M},t)$, $$\begin{aligned} \label{eq.FP0} && \partial_t P({\bf M},t) = -\partial_i \left[ \left( f_i({\bf M})+ 2D \alpha g_{k\ell}({\bf M})\partial_k g_{i\ell}({\bf M}) \right) P({\bf M},t) \right] \nonumber \\ & & \qquad\qquad\qquad + \partial_i\partial_j \left[ D g_{ik}({\bf M})g_{jk}({\bf M}) \ P({\bf M},t) \right] \;. \label{eq:FP}\end{aligned}$$ It is instructive to rewrite Eq. (\[eq:FP\]) in the form of a continuity equation, $$\partial_tP({\bf M},t) +\boldsymbol{\nabla}\cdot \mathbf{J}({\bf M},t) = 0\;,$$ where the components of the current probability $\mathbf{J}({\bf M},t)$ are given by $$\begin{aligned} J_i&=& \left[ f_i + D (2\alpha-1) g_{k\ell}\partial_k g_{i\ell} - D g_{ik}\partial_j g_{jk} - D g_{ik}g_{jk}\partial_j \right] P \;.\end{aligned}$$ The two following properties of the diffusion matrix $g$ $$\begin{aligned} g_{k\ell}\partial_k g_{i\ell} &=& -\frac{2 \gamma_0^2}{1+\eta^2 \gamma_0^2} {M_0}_i \;,\\ g_{ik}\partial_j g_{jk}&=&0 \; ,\end{aligned}$$ and the explicit form of $f_i$ given in Eq. (\[eq.f\]) allow us to arrive at the simpler expression, $$\begin{aligned} J_i= \left( g_{ij} H_{{\rm eff},j} - D g_{ik}g_{jk}\partial_j \right) P\;.\end{aligned}$$ Thus, the Fokker-Planck equation, related with the stochastic process governed by the $\alpha$-covariant sLLG equation (\[eq.LLG-covariant\]), is given by $$\label{eq:FP333} \partial_tP({\bf M},t) =\partial_i \left\{ \left[ g_{ij} H_{{\rm eff},j} - D g_{ik}g_{jk}\partial_j \right] P({\bf M},t) \right\} \;.$$ Note that, as anticipated, this differential equation is $\alpha$-independent. Thus, the $\alpha$-covariant sLLG equation (\[eq.LLG-covariant\]) leads to a unique time evolution for the magnetization probability for any value of the parameter $\alpha$. Also, from $g_{ij} M_j=0$, it is immediate to check that the current probability is transverse, $ {\bf J} \cdot {\bf M}=0$, meaning that there is no dynamics in the direction of the magnetization and, consequently, the time evolution preserves the magnetization modulus. ### Approach to equilibrium With the Fokker-Planck equation defined in Eq. (\[eq:FP333\]), we can study the asymptotic probability distribution. Any stationary state at long times, $$P^{\rm st}({\bf M})=\lim_{t\to\infty} P({\bf M},t)\;,$$ has an associated stationary current that satisfies $\partial_i J^{\rm st}_i=0$. However, solutions to this equation do not necessarily represent equilibrium distributions as they could be non-equilibrium steady states with non-vanishing probability current. Indeed, the equilibrium distribution is defined as a stationary solution of the Fokker-Planck equation with zero current, ${\mathbf J}_{\rm eq}={\mathbf 0}$, and it is expected to be reached asymptotically in the absence of explicit time dependent or non-potential forces. Considering the [*Ansatz*]{} $P_{\rm eq}({\bf M})= N \exp(-{\cal V}[{\bf M}])$ for the equilibrium probability, where $N$ is a normalization constant, the condition $J^{\rm eq}_i=0$ implies $$g_{ij} H_{{\rm eff},j} + D g_{ik}g_{jk}\partial_j {\cal V} =0\;.$$ In order to solve it for ${\cal V}({\bf M})$, we assume that the effective magnetic field can be obtained from a potential energy density $H_{{\rm eff},i}=H^c_{{\rm eff},i} = -\mu_0^{-1} \partial_i U[{\bf M}]$. Then, $$-\mu_0^{-1} g_{ij} \partial_j U + D g_{ik}g_{jk}\partial_j {\cal V} =0\;.$$ We can further simplify this equation by noting that the antisymmetric part contributes with a topological divergence-less term since $\partial_ i \left(g^{{\rm a}}_{ij} \partial_j U\right)= 0$ for symmetry reasons. Also, from Eq. (\[eq.gg\]), $g^{{\rm s}}_{ij}=(\eta/M_{{\rm s}}) g_{ik}g_{jk}$. Then the null stationary current condition takes the very simple form, $$g^{{\rm s}}_{ij} \partial_j \left( \frac{U}{\mu_0} - \frac{DM_{{\rm s}}}{\eta} {\cal V}\right) =0\;,$$ with obvious solution ${\cal V}=\eta/(DM_{{\rm s}}\mu_0) \ U$. The equilibrium solution of the Fokker-Planck equation is of the Gibbs-Boltzmann type $P_{\rm GB}=N\exp(-\beta U V)$ provided we choose $$D=\eta k_{\rm B}T/(M_{{\rm s}}V \mu_0) \label{eq:D}$$ which is the Einstein relation or, more generally, a consequence of the fluctuation-dissipation theorem of the second kind in Kubo’s terminology [@Kubo66]. Generating functional {#sec:functional} ===================== It is a well established fact that stochastic process can be analyzed with the help of path integrals. Janssen [@Janssen76] introduced such a description for stochastic processes, a very convenient formalism to manipulate correlation and response functions, that is close in spirit to the operator approach of Martin-Siggia-Rose [@Martin73]. The formalism was later applied to quenched disorder by De Dominicis [@deDominicis76; @deDominicis78] and is often referred as the MSRJD formalism. Over the years, there have been numerous attempts to generalize the work of Janssen to the case of multiplicative noise, [*i.e.*]{}, the case in which the diffusion matrix depends on the stochastic variable. The literature on this problem is rather extensive and in many cases also confusing. No attempt will be made here to review this literature (the interested reader can look at [@Tirapegui82] for a thorough description of path integral methods in the stochastic context). Instead, we will focus on the specific problem at hand, the stochastic dynamics of the magnetization in the Cartesian and spherical coordinate systems. Let us consider that the system is prepared at an initial time, $t_0$, and subsequently let evolve until the final time of the experiment, $\mathcal{T}$. It is common to consider the limit $\mathcal{T}\to \infty$, but we prefer to keep the final time arbitrary. In the rest of this manuscript, we will encounter many time-integrals of the form $\int_{t_0}^{\cal T} {\hspace{-0ex}\mathrm{d}{t}\;} \ldots $ and, for the sake of simplicity, we will most frequently simply denote them $\int{\hspace{-0em}\mathrm{d}{t}\;} \ldots$ The generating functional of observables averaged over thermal histories is defined as $$\begin{aligned} \mathcal{Z}[\boldsymbol{\lambda}] = \langle \ \langle \ \exp \int_{t_0}^{\cal T} {\hspace{-0ex}\mathrm{d}{t}\;} \boldsymbol{\lambda}(t) \cdot \mathbf{M}_{\mathbf H}(t) \ \rangle_{{\rm i}}\ \rangle_\mathbf{H} \;, \label{eq:uno}\end{aligned}$$ where $ \langle \cdots \rangle_{{\rm i}}= \int {{\rm d}}\mathbf{M}_0 \cdots P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)] $ is the average over the initial conditions, ${\mathbf M}_0 \equiv {\mathbf M}(t_0)$ with $|\mathbf{M}_0| = M_{{\rm s}}$, distributed with the probability distribution function $P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)]$ which is normalized to unity. The average over the realizations of the thermal noise, which are distributed according to the probability distribution functional $P_{\rm n}[\mathbf{H}]$, is denoted $$\begin{aligned} \langle \cdots \rangle_\mathbf{H} \equiv \int{\mathcal{D}}{[\mathbf{H}]} \cdots P_{\rm n}[\mathbf{H}] \; .\end{aligned}$$ $P_{\rm n}[\mathbf{H}]$ is also normalized to unity. In the rest of the manuscript, we use the notation $$\begin{aligned} \langle \cdots \rangle \equiv \langle\langle \cdots \rangle_{{\rm i}}\rangle_\mathbf{H} \;.\end{aligned}$$ $\boldsymbol{\lambda}$ is a vector source that couples linearly to the fluctuating magnetization configuration $\mathbf{M}_{\mathbf H}(t)$ which is the unique solution to the sLLG equation for a given initial condition $\mathbf{M}_0$ and a given history of the noise $[\mathbf{H}]$. By construction ${\cal Z}[\boldsymbol{\lambda} = \mathbf{0}]=1$. In the rest of this Section, we construct the MSRJD representation of the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ according to the following steps. The first one is to exchange the dependence on the unique solution $[\mathbf{M}_{\mathbf{H}}]$ with a sum over all trajectories by imposing the equation of motion written in the form $\mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}]=\mathbf{0}$ *via* a delta functional: $$\begin{aligned} && {\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{H}] \ P_{\rm n}[\mathbf{H}] \ \int {\cal D}[\mathbf{M}]\ P_{\rm i}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)] \nonumber\\ && \qquad\;\; \times \ \delta\Big{[} \mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}] \Big{]} \ |{\cal J}[\mathbf{M},\mathbf{H}]| \ \exp \int_{ t_0}^{\cal T} \! {\hspace{-0em}\mathrm{d}{t}\;} {\boldsymbol{\lambda}}(t) \cdot \mathbf{M}(t) \;. \label{eq:generatingZ}\end{aligned}$$ The measure ${\cal D}[\mathbf{M}] $, defined precisely in App. \[app:discrete\], has to be understood as the sum, at each time step, over vectors $\mathbf{M}(t)$ in the entire $\mathbb{R}^3$ space. In particular, it includes the integration over the initial conditions at time $t_0$. As discussed in Sec. \[sec:sLLGprescription\], the constraint $|\mathbf{M}(t)| = cst$ is encoded in the equation of motion (see later Sec. \[sec:conservation\_modulus\]). Notice that, at the level of the path integral, this allows one to consider $M_x$, $M_y$ and $M_z$ as unconstrained variables, *i.e.* $|\mathbf{M}(t)| \neq \mbox{cst}$. The Jacobian ${\cal J}[\mathbf{M},\mathbf{H}]$ ensures that the [rhs]{} of Eq. (\[eq:generatingZ\]) does not depend on the particular formulation of $\mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}]$: $$\begin{aligned} \mathcal{J}[\mathbf{M},\mathbf{H}] \equiv \det_{ij;uv} \begin{array}{c} \displaystyle \frac{\delta {\rm{Eq}}_{\it i}[\mathbf{M},\mathbf{H}](u)}{\delta M_{j}(v)} \end{array}\end{aligned}$$ with the coordinate indices $i,j=x,y,z$ and the times $u,v$. (If one thinks in terms of discrete time, the equation is imposed by a product of $\delta$-functions starting at time indexed $n=1$ and ending at time indexed $n=N$. We next exponentiate the functional Dirac delta with the help of a Lagrange multiplier $[{{\rm i}}\hat{\mathbf{M}}]$. Afterwards, we average over the initial conditions $\mathbf{M}_0$ and the noise realizations $[\mathbf{H}]$. Finally, we obtain a path integral representation of $\mathcal{Z}[\boldsymbol{\lambda}]$ in which the trajectories are weighted by the exponential of an action functional $S[\mathbf{M},{{\rm i}}\hat{\mathbf{M}}]$: $${\cal Z}[{\boldsymbol{\lambda}}] = \int {\cal D}[{\mathbf M}] {\cal D}[{{\rm i}}\hat {\mathbf M}] \ \exp\left[ S[{\mathbf M}, {{\rm i}}\hat {\mathbf M}] + \int {{\rm d}}t \ {\boldsymbol{\lambda}}(t) \cdot {\mathbf M}(t) \right] \; .$$ Landau formulation {#sec:MSRDJ} ------------------ In Sec. \[sec:landau-lifshitz-gilbert\], we presented two formulations of the same sLLG equation (Gilbert and Landau) with generic discretization prescriptions. These different starting points lead to distinct formulations of the generating functional that describe the same physics. In the presentation below, we choose to start with the dimension-full Landau formulation of the $\alpha$-covariant sLLG equation, *i.e.* with Eq. (\[eq.LLG-covariant\]) $$\begin{aligned} {\rm{Eq}}_{Li}[\mathbf{M},\mathbf{H}] &\equiv& {\rm D}_t^{(\alpha)} M_i - g_{ij}( H_{{{\rm{eff}}},j}+H_j ) = 0 \; , \label{eq:def-Eq}\end{aligned}$$ and we construct a formalism that is valid in any $\alpha$-prescription. The subscript $L$ stands for Landau formulation here and in the rest of this Section. We collected in the magnetic field ${\mathbf H}_{\rm eff}$ all contributions from conservative as well as non-conservative origin, including the possible spin-torque terms. We discuss the generating functional obtained when starting from the Gilbert formulation, and its equivalence to the Landau formulation, in Sec. \[sec:Landau2Gilbert\] and App. \[app:path-integral:Gilbert\]. In Sec. \[sec:observables\] we recall how these generating functionals enable one to compute all cumulants and linear responses of the magnetization. The operator in the determinant can be worked out explicitly and put into the form $$\frac{\delta {\mbox{Eq}}_{Li}(u)}{\delta M_j(v)} = \delta_{ij} {\rm d}_u \delta(u-v) + A_{ij}(v) \delta(u-v)\;,$$ with $$\begin{aligned} A_{ij} = 2 D(1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \delta_{ij} - \frac{\partial g_{ik}}{\partial M_j} ( H_{{{\rm{eff}}},k}+H_k ) - g_{ik} \frac{\partial H_{{{\rm{eff}}},k}}{ \partial M_j}\end{aligned}$$ where we assumed that ${\mathbf H}_{\rm eff}$ is ultra-local in time in the sense that it involves only the magnetization evaluated at time $u$ but no time-derivatives, [*i.e.*]{} the effective magnetic field can be of the form ${\mathbf H}_{\rm eff}({\mathbf M}(u), u)$. From now on we will use the notation $\partial_i = \partial /\partial M_i$ as in Sec. \[sec:Fokker-Planck\]. Using that the inverse of $\delta_{ik} {\rm d}_u \delta(u-w)$ is proportional to the Heaviside function $ \delta_{ik}\Theta(w-v)$, the Jacobian becomes $$\begin{aligned} \mathcal{J}_L[\mathbf{M}, \mathbf{H}] & = \; \det_{ik;uw} \left[ \delta_{ik}(u) {\rm d}_u\delta(u-w)\right] \nonumber\\ & \qquad\qquad \times \det_{kj;wv} \left[ \delta(w-v) \delta_{kj} + \Theta(w-v) A_{kj}(v) \right] \; . \label{sec:discussRVsA} \end{aligned}$$ We treat the second determinant in the way described in App. \[sec:determinants\]. Notice that $C_{kj}(w,v) = \Theta(w-v) A_{kj}(v)$ is causal. Usually, the expansion stops at the first order due to the causality of the operator $C$. However, when there is a white-noise dependence in this operator, as it is the case here, one has to be careful and consider the possible contribution of the second order term, $C^2$ [@Arnold2000; @Lubensky2007]. This is explained in App. \[sec:determinants\]. In the Cartesian framework, the contribution of the second order term is an irrelevant constant and only the first term has a non-trivial dependence on the magnetization field. We obtain $$\begin{aligned} \label{eq:jacjacjac} \mathcal{J}_L[{\mathbf M}, {\mathbf H}] \propto \; & \exp\ [ \alpha \int{} {\hspace{-0em}\mathrm{d}{t}\;} A_{ii}(t) ] \;, \end{aligned}$$ where the factor $\alpha$ comes $\Theta(0)=\alpha$ in the $\alpha$-prescription. Indeed, when working with continuous-time notations, it can be shown [@Gardiner] that the $\alpha$ discretization prescription introduced in Sec. \[sec:prescriptions\] translates into the prescriptions $\int_{t_1}^{t_2}{\hspace{-0ex}\mathrm{d}{t}\;} G(t) \delta(t-t_1) = (1-\alpha) G(t_1)$ and $\int_{t_1}^{t_2}{\hspace{-0ex}\mathrm{d}{t}\;} G(t) \delta(t-t_2) = \alpha G(t_2)$ for any $G(t)$ that is a causal functional of the random field. In particular, for $G(t)=1$, this can be conveniently collected into $\Theta(0) \equiv \alpha$. The integrand in Eq. (\[eq:jacjacjac\]) is $$A_{ii}(t) = 2 D(1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \delta_{ii} + \frac{2\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{M_i}{M_{{\rm s}}} (H_{{{\rm{eff}}},i}+H_i ) - g_{ik} \partial_i H_{{{\rm{eff}}},k} \;.$$ Finally, dropping all terms that are constant in the overall normalization, we obtain $$\begin{aligned} \mathcal{J}_L[{\mathbf M}, {\mathbf H}] & \!\! \!\! \propto \!\! \!\! & \exp \left\{ \frac{\alpha\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{1}{M_{{\rm s}}} \int{} {\hspace{-0em}\mathrm{d}{t}\;} \Big{[} 2 \eta \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}} \right. \nonumber\\ && \qquad\qquad + \eta (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{{\rm{eff}}},i} \nonumber\\ && \qquad\quad\;\;\; \left. + M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc} + 2 \eta \ \mathbf{M} \cdot {\mathbf{H}} \Big{]}\! \right\} \; . \label{eq:Jcart-L} \end{aligned}$$ Coming back to the generating functional ${\cal Z}[\boldsymbol{\lambda}]$, we now exponentiate the delta functional that imposes the sLLG equation as $$\begin{aligned} \delta \Big{[} \mbox{\textbf{Eq}}_L[\mathbf{M},\mathbf{H}] \Big{]} \propto \int {\cal D}[\hat{\mathbf{M}}] \ \exp \int{} {\hspace{-0em}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}} \cdot\mbox{\textbf{Eq}}_L[\mathbf{M},\mathbf{H}] \; ,\end{aligned}$$ in which $\hat{\mathbf{M}}$ is integrated over the entire $\mathbb{R}^3$ space at each time slice and has dimension $[{{\rm i}}\hat {\mathbf M}] = [{\mathbf M}]^{-1}$. The integration over the Gaussian white noise $\mathbf{H}$ yields $$\begin{aligned} && \int {\cal D}{[\mathbf{H}}] \ \displaystyle \exp \left\{ \int{} {\hspace{-0em}\mathrm{d}{t}\;} \left( {\frac{ 2\alpha \eta\gamma_0^2}{1+\eta^2\gamma_0^2} M_j H_j -{{\rm i}}\hat{M}_i g_{ij} H_j - \frac{1}{2} \frac{H_j H_j}{2D}} \right) \right\} \nonumber\\ && \qquad\qquad \propto \exp \left\{ D \int{} {\hspace{-0em}\mathrm{d}{t}\;} \ g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k \right\} \; ,\end{aligned}$$ where the cross term vanishes thanks to the property $g_{ij} M_j =0$. We will also drop a factor that depends only on $M_{{\rm s}}^2$ in the overall normalization. Accordingly, the effect of the random field contribution coming from the Jacobian disappears. Altogether, we recast the generating functional in the form $${\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{M}] {\cal D}[\hat{\mathbf{M}}] \ \exp \left\{ S_L+\int{} \! {\hspace{-0em}\mathrm{d}{t}\;} \boldsymbol{\lambda} \cdot \mathbf{M} \right\} \; .$$ The action $S_L$ is a functional of the histories of the magnetization $[\mathbf{M}]$ and the auxiliary field $[{{\rm i}}\hat{\mathbf{M}}]$. It reads $$\begin{aligned} S_L =&\; \; \ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)] \nonumber \\ & + \int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat M_i \left( {\rm D}^{(\alpha)}_t M_i - g_{ij} H_{{{\rm{eff}}}, j} \right) + D \int{} {\hspace{-0em}\mathrm{d}{t}\;} g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k \nonumber \\ & + \frac{\alpha\gamma_0}{1+\eta^2 \gamma_0^2 } \frac{1}{M_{{\rm s}}} \int{} {\hspace{-0em}\mathrm{d}{t}\;} \Big{[} 2 \eta\gamma_0 \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}} + \eta\gamma_0 (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{\rm eff}, i} \nonumber\\ & \qquad\qquad\qquad\qquad\qquad + M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc} \Big{]}\! \; . \label{eq:generating-functional0}\end{aligned}$$ Notice that we identified $\mathbf{M}_0$ with $\mathbf{M}(t_0)$ and we included the integral over the initial conditions, $\int{{\rm d}}\mathbf{M}_0$, into the functional integral $\int{\mathcal{D}}[\mathbf{M}]$ and their probability distribution, $P_{{\rm i}}(\mathbf{M}_0),$ into the action functional. One identifies the contribution of the deterministic dynamics, $\widetilde S_{L,{\rm det}}$, the dissipative and thermal effects, $\widetilde S_{L,{\rm diss}}$, and the Jacobian $$S_L = \widetilde S_{L,{\rm det}} + \widetilde S_{L,{\rm diss}} + S_{L,{\rm jac}}\;. \label{eq:SLandau}$$ Using the decomposition of $g_{ij}$ in symmetric and antisymmetric parts, $g_{ij} = g_{ij}^{{\rm s}}+g_{ij}^{{\rm a}}$, already used in Sec. \[sec:Fokker-Planck\], and renaming indices conveniently one has $$\begin{aligned} \widetilde S_{L,{\rm det}} = & \;\; \ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)] + \int {\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{M_i} \cdot \left( {\rm D}_t^{(\alpha)} M_i -g^{{\rm a}}_{ij} {H_{\rm eff}}_j \right) \; , \label{eq:S_det_cart00} \\ \widetilde S_{L,{\rm diss}} =& \;\; \int {\hspace{-0ex}\mathrm{d}{t}\;} \ g_{ij}^{{\rm s}}\ {{\rm i}}\hat{M_i} \left( \frac{DM_{{\rm s}}}{\eta} \ {{\rm i}}\hat{M_j} - {H_{\rm eff}}_j \right) \;, \label{eq:S_diss_cart00} \\ S_{L,{\rm jac}}=& \;\; \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{M_{{\rm s}}} \int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[} 2 \eta\gamma_0 \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}} + \eta\gamma_0 (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{\rm eff}, i} \nonumber\\ & \qquad\qquad\qquad\qquad\;\;\; + M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc} \Big{]}\! \; . \label{eq:S_jac_cart000}\end{aligned}$$ Remembering that $D$ is proportional to $\eta$ \[see Eq. (\[eq:D\])\], one sees that $\widetilde S_{L,{\rm diss}}$ vanishes at $\eta=0$ while the remaining deterministic and Jacobian parts, $\widetilde S_{L,{\rm det}}+S_{L,{\rm jac}}$, yield what one would have obtained starting from the equation without dissipation. This writing of the Landau action, shows that $g^{{\rm s}}$ contains the information on the dissipative aspects of the dynamics. Note that $g^{{\rm s}}$ does not have an inverse. This is related to the “gauge invariance" of the action, that retains the same form under the parallel translation ${{\rm i}}\hat {\mathbf M} \to {{\rm i}}\hat {\mathbf M} + a {\mathbf M}$, with $a$ generic. ### Rewriting of the Jacobian {#sec:rewriting-Jacobian} As mentioned in the introduction, one should distinguish the parallel and perpendicular components of the effective field ${\mathbf H}_{\rm eff}={\mathbf H}^\perp_{\rm eff} + {\mathbf H}^\parallel_{\rm eff}$. We will write them as $$H_{{\rm eff},i} = H_{{\rm eff}, i}^\parallel + H_{{\rm eff}, i}^\perp = f M_i + \epsilon_{ilk} M_l T_k \; ,$$ where $f$ and ${\mathbf T}$ can be functions of ${\mathbf M}$. This separation is different from the separation in conservative and non-conservative contributions. Notice that ${\mathbf T}$ is not defined uniquely as any translation parallel to ${\mathbf M}$ leaves this relation unchanged. Using this separation, one proves that the Jacobian contribution to the action, $S_{L,{\rm jac}}$, is independent of the parallel component of the effective field, more precisely, it is independent of $f$. This arises due to the cancellation of the first term with one stemming from the second one. The Jacobian contribution to the action then reads $$\begin{aligned} && S_{L,{\rm jac}} = \;\; \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{M_{{\rm s}}} \int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[} \eta\gamma_0 (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H^\perp_{{{\rm{eff}}}_i} \nonumber\\ && \qquad\qquad\qquad\qquad + M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H^\perp_{{{\rm{eff}}}_i} \Big{]} \; . \label{eq:S_jac_cart00}\end{aligned}$$ As expected, we conclude that the full action does not depend on ${\mathbf H}_{\rm eff}^\parallel$. ### Conservation of the modulus {#sec:conservation_modulus} The decomposition of the auxiliary field $ {{\rm i}}\hat{\mathbf{M}} = {{\rm i}}\hat {\mathbf M}_\parallel + {{\rm i}}\hat {\mathbf M}_\perp$ into a sum of parallel and perpendicular components to the magnetization ${\mathbf M}$ (*i.e.* ${{\rm i}}\hat{\mathbf{M}}_\perp \cdot {\mathbf M} = 0$ and ${{\rm i}}\hat{\mathbf{M}}_\parallel \wedge {\mathbf M} = {\mathbf 0}$) will allow us to show that the modulus $M_{{\rm s}}$ is conserved by the dynamics and to derive the Gilbert formulation of the action functional (see Sec. \[sec:Landau2Gilbert\] for the latter). As $M_i g_{ij} = 0$, then $${{\rm i}}\hat M_i g_{ij} = \frac{\gamma_0}{1+\eta^2\gamma_0^2} [ \epsilon_{jkl} M_k {{\rm i}}\hat M_l + \eta\gamma_0 M_{{\rm s}}{{\rm i}}\hat M_j ] \; .$$ Therefore, we find $ g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k = M_{{\rm s}}^2 \gamma_0^2/ (1+\eta^2\gamma_0^2) \ {{\rm i}}\hat{\mathbf{M}}_\perp \cdot {{\rm i}}\hat{\mathbf{M}}_\perp$. This property allows us to rewrite the action in (\[eq:generating-functional0\]) in an equivalent form: $$S_L= {S}_{L,{\rm det}} + {S}_{L,{\rm diss}} + S_{L,{\rm jac}}\;,$$ with $$\begin{aligned} {S}_{L,{\rm det}} = & \ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)] + \int {\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} \mathbf{M} \nonumber \\ &+ \frac{1}{1+\eta^2\gamma_0^2} \int {\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \Big{[} {{\rm d}}_t \mathbf{M} - \eta \gamma_0^2 M_{{\rm s}}\ \mathbf{H}_{{\rm{eff}}} \nonumber\\ & \qquad\qquad\qquad\; - \left( \eta\gamma_0 M_{{\rm s}}^{-1} \ {{\rm d}}_t \mathbf{M} \wedge \mathbf{M} + \gamma_0 \ {\mathbf M} \wedge \mathbf{H}_{{\rm{eff}}} \right) \Big{]} \;, \label{eq:S_det_cart0} \\ {S}_{L,{\rm diss}} =& \frac{1}{1+\eta^2\gamma_0^2 } \int {\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \Big{[} D \gamma_0^2 \, M_{{\rm s}}^2 \ {{\rm i}}\hat{\mathbf{M}}_\perp \nonumber\\ & \qquad\qquad\qquad + \left( \eta\gamma_0 M_{{\rm s}}^{-1} \ {{\rm d}}_t \mathbf{M} \wedge \mathbf{M} + \eta^2\gamma_0^2 {{\rm d}}_t \mathbf{M}\right) \Big{]} \; . \label{eq:S_jac_diss0}\end{aligned}$$ The Jacobian contribution, $S_{L,{\rm jac}}$, is again given by Eq. (\[eq:S\_jac\_cart00\]) as it does not involve ${{\rm i}}\hat{\mathbf M}$. We added and subtracted a term in what we called deterministic and dissipative contributions for later convenience. The dissipative part, ${S}_{L,{\rm diss}}$, only regroups terms that involve the interactions with the environment such as thermal effects and the dissipative torque. It does not depend on the deterministic forces acting on the problem, grouped in ${\mathbf H}_{\rm eff}$, that appear only in ${S}_{L,{\rm det}}$. At $\eta=0$, ${S}_{L,{\rm diss}}$ vanishes while the remaining deterministic part, ${S}_{L,{\rm det}}$, again yields what one would have obtained starting from the equation without dissipation. This cutting up will take a clear meaning in the Gilbert formulation of the generating functional (see Sec. \[sec:Landau2Gilbert\]). The sector of the formalism that involves ${{\rm i}}\hat{{\mathbf M}}_\parallel$, the component of ${{\rm i}}\hat{\mathbf{M}}$ which is parallel to $\mathbf{M}$, encodes the conservation of the modulus of the magnetization. Indeed, the only term involving ${{\rm i}}{\hat{ \mathbf{M}}}_\parallel$ in the action functional given in Eqs. (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]) is $$\begin{aligned} \int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{{\mathbf M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M} = \int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{M}_\parallel \ \frac{\mathbf{M}}{M_{{\rm s}}} \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \;.\end{aligned}$$ If one were to integrate over $\hat M_\parallel$, this would yield a delta functional $$\begin{aligned} \delta\left[ \mathbf{M} \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \right]\;,\end{aligned}$$ that imposes the constraint ${\mathbf M} \cdot {\rm D}_t^{(\alpha)} {\mathbf M} = 0$ at all times, simply expressing the conservation of the modulus, ${{\rm d}}_t M_{{\rm s}}^2 = 0$, as we explained in Sec. \[sec:alpha-covariantLLG\]. Gilbert formulation {#sec:Landau2Gilbert} ------------------- As we stressed in Sec. \[sec:landau-lifshitz-gilbert\], the Gilbert and Landau formulations of the sLLG equation, Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]), or their adimensional form in Eqs. (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]), are strictly equivalent. In Sec. \[sec:MSRDJ\], we constructed a prescription-covariant functional formalism starting from the $\alpha$-covariant expression of the Landau formulation of the sLLG equation, namely Eq. (\[eq.LLG-covariant\]). Starting from the $\alpha$-covariant expression of Eq. (\[eq:sLLG1-adim\]) and following a similar route (see App. \[app:path-integral:Gilbert\]), one can construct another action functional corresponding to the Gilbert formulation of the problem. The ensuing Gilbert action functional reads (the subscript $G$ stands for Gilbert formulation): $$\begin{aligned} S_G = S_{G,{\rm det}} + S_{G,{\rm diss}} + S_{G,{\rm jac}} \label{eq:total-action-Gilbert}\end{aligned}$$ with $$\begin{aligned} S_{G,{\rm det}} \! &\! = \! & \! \ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)] + \int{\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \nonumber \\ & & + \int{\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \left( \frac{1}{ M_{{\rm s}}^2} {\rm D}^{(\alpha)}_t \mathbf{M} \wedge \mathbf{M} + \gamma_0 \mathbf{H}_{{\rm{eff}}} \right) \; , \;\;\;\;\; \label{eq:SLLGjac-det} \\ S_{G,{\rm diss}} \! &\! = \! & \! \int {\hspace{-0ex}\mathrm{d}{t}\;} \gamma_0{{\rm i}}\hat{\mathbf{M}}_\perp \cdot \left( D \gamma_0 {{\rm i}}\hat{\mathbf{M}}_\perp - \frac{\eta}{M_{{\rm s}}} \ {\rm D}^{(\alpha)}_t \mathbf{M} \right) \; . \label{eq:SLLGjac-diss} \\ S_{G,{\rm jac}} \! &\! = \! & \! \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{M_{{\rm s}}} \int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[} \eta\gamma_0 (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H^\perp_{{{\rm{eff}}}_i} \nonumber\\ && \qquad\qquad\qquad\qquad + M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H^\perp_{{{\rm{eff}}}_i} \Big{]} \; . \label{eq:SLLGjac-jac}\end{aligned}$$ The Jacobian contribution, $S_{G,{\rm jac}}$, is identical to Eq. (\[eq:S\_jac\_cart00\]), $S_{G,{\rm jac}}=S_{L, {\rm jac}}$. The equivalence between the Landau and the Gilbert formulations simply corresponds to a transformation of the auxiliary field ${{\rm i}}\hat{\mathbf{M}}$. One passes from the Landau action functional given in Eqs. (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]) to the Gilbert formulation in Eqs. (\[eq:SLLGjac-det\]) and (\[eq:SLLGjac-diss\]) *via* the following change $$\begin{aligned} \label{eq:Trans_L2G} {{\rm i}}\hat{\mathbf{M}}_\perp \mapsto -\frac{1}{M_{{\rm s}}} \left( \frac{1}{M_{{\rm s}}} {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} + \eta\gamma_0 \ {{\rm i}}\hat{\mathbf{M}}_\perp \right)\;,\end{aligned}$$ which is a linear transformation with a constant Jacobian that can be dropped into the overall normalization. Conversely, one passes from the Gilbert action functional to the Landau formulation *via* the inverse transformation $$\begin{aligned} \label{eq:Trans_G2L} {{\rm i}}\hat{\mathbf{M}}_\perp \mapsto \frac{1}{1+\eta^2\gamma_0^2} \left[ {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} - \eta\gamma_0 M_{{\rm s}}\ {{\rm i}}\hat{\mathbf{M}}_\perp \right]\;.\end{aligned}$$ Observables {#sec:observables} ----------- The generating functional can be used to evaluate the average of functions of the magnetization, in particular its $n$-times correlation functions, cumulants, and linear responses, by taking variations with respect to sources conveniently introduced in the action through linear couplings to the magnetization and the auxiliary field. We list a number of these observables below. The averaged magnetization is given by $$\begin{aligned} \langle M_i(t)\rangle = \frac{1}{\mathcal{Z}[\boldsymbol{\lambda}=0]} \frac{\delta \mathcal{Z}[\boldsymbol{\lambda}]}{\delta \lambda_i(t)}\Big{\rvert}_{\boldsymbol{\lambda}=0} \; . \end{aligned}$$ The two-time correlations can be obtained from the variation of the ${\mathcal Z}$ with respect to two sources: $$\begin{aligned} \langle M_i(t)\, M_j(t')\rangle = \frac{1}{\mathcal{Z}[\boldsymbol{\lambda}=0]} \frac{\delta \mathcal{Z}[\boldsymbol{\lambda}]}{\delta \lambda_i(t) \, \delta \lambda_j(t')}\Big{\rvert}_{\boldsymbol{\lambda}=0} \; . \end{aligned}$$ Similarly, one derives the $n$-times correlation functions by taking variations with respect to $n$ factors $\lambda_i$ evaluated at different times. The cumulant generating functional is defined as $W[\boldsymbol{\lambda}] \equiv \ln \mathcal{Z}[\boldsymbol{\lambda}]$. For instance, one generates the second order cumulant as $$\left. \frac{\delta^2 W[\boldsymbol{\lambda}]}{\delta \lambda_i(t) \delta \lambda_j(t')} \right|_{{\mathbf \lambda} = {\mathbf 0}} = \langle M_i(t) M_j(t') \rangle - \langle M_i(t)\rangle \langle M_j(t') \rangle \; .$$ The linear response is the result of the effect of a linear perturbation of the local effective magnetic field, $\mathbf{H}_{\rm eff} \mapsto \mathbf{H}_{\rm eff} + \widetilde{\mathbf{H}}$, performed at a time $t'$ on the observable of choice. The equation of motion and the dynamic action do not depend on $H_{\rm eff}^\parallel$. Therefore, the only variation that may have an effect on the averaged observables is the one on $H_{\rm eff}^\perp$. The linear response of the magnetization component $M_i$ measured at a later time $t$, in the Landau formulation, is $$\begin{aligned} R_{ij}(t,t') = & \left. \frac{\delta \langle M_i(t)\rangle_{S_L} }{\delta {\widetilde{H}_j(t')}} \right|_{\widetilde{\mathbf H}={\mathbf 0}} \!\!\! = \left. \frac{\delta \langle M_i(t)\rangle_{S_L} }{\delta {\widetilde{H}^\perp_j(t')}} \right|_{\widetilde{\mathbf H}^\perp={\mathbf 0}} \nonumber\\ = & \;\; \langle M_i(t) {{\rm i}}\hat M_k(t') g_{kj}[{\mathbf M}(t')] \rangle_{S_L}\;. \nonumber\end{aligned}$$ The average has to be taken with the weight $\exp S_L$ with the Landau formulation of the action functional, $S_L$, given in Eqs. (\[eq:S\_jac\_cart00\]), (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]). The presence of the auxiliary field ${{\rm i}}\hat{\mathbf{M}}$ in the expression of the response is the reason why it is often referred to as the “response field”. This “classical Kubo formula” can be generalized to the response of any observables $A$: $$\begin{aligned} R_{A\,j}(t,t') \equiv & \left. \frac{\delta \langle A(t) \rangle_{S_L}}{\delta \widetilde{H}_j(t')} \right|_{\widetilde{\mathbf{H}}=0} = \left. \frac{\delta \langle A(t) \rangle_{S_L}}{\delta \widetilde{H}^\perp_j(t')} \right|_{\widetilde{\mathbf{H}}=0} \;\; \nonumber\\ = & \;\; \langle A(t) \, {{\rm i}}\hat M_k(t') g_{kj}[{\mathbf M}(t')] \rangle_{S_L} \;.\end{aligned}$$ The trivial case in which $A$ is set to be a constant, gives $R_{A\,j}(t,t') = 0$ for all $t$ and $t'$, yielding the identity $$\begin{aligned} \label{eq:KuboID0} \langle {{\rm i}}\hat{M}_k(t) g_{kj}[{\mathbf M}(t')] \rangle_{S_L} = 0 \; . \end{aligned}$$ Within the Gilbert formulation of the $\alpha$-covariant generating functional, one can also compute the linear response function. Another classical Kubo formula expressing the linear response as a two-time correlator is found $$\begin{aligned} R_{ij}(t,t') & = \left. \frac{\delta \langle M_i(t) \rangle_{S_G}}{\delta \widetilde{H}_j(t')} \right|_{\widetilde{\mathbf{H}}=0} = \left. \frac{\delta \langle M_i(t) \rangle_{S_G}}{\delta \widetilde{H}^\perp_j(t')} \right|_{\widetilde{\mathbf{H}}^\perp=0} \nonumber\\ & = \;\; \langle M_i(t) \,\gamma_0 {{\rm i}}\hat{M}_{\perp\,j}(t') \rangle_{S_G} \; , \end{aligned}$$ where the averages are weighted by $\exp S_G$ given in Eqs. (\[eq:total-action-Gilbert\]) with the contributions (\[eq:SLLGjac-det\]), (\[eq:SLLGjac-diss\]) and (\[eq:S\_jac\_cart00\]). Applied now to any observable $A$ this relation reads $$\begin{aligned} R_{A\,j}(t,t') = & \;\; \langle A(t) \, \gamma_0 {{\rm i}}\hat{M}_{\perp\,j}(t') \rangle_{S_G} \; . \end{aligned}$$ The trivial case in which $A$ is set to be a constant, gives $R_{A\,j}(t,t') = 0$ for all $t$ and $t'$, yielding the identity $$\begin{aligned} \label{eq:KuboID0G} \langle {{\rm i}}\hat{\mathbf{M}}_\perp(t) \rangle_{S_G} = 0 \; . \end{aligned}$$ Equilibrium dynamics {#sec:equilibrium_cond} -------------------- The magnetization undergoes equilibrium dynamics if it is prepared in and let evolve under equilibrium conditions. More specifically, initial conditions at temperature $T$ have to be drawn from a Gibbs-Boltzmann distribution in a potential $U$ (per unit volume), the system has to evolve with the same (time-independent) potential $U$ with no additional non-potential fields, ${\mathbf H}_{\rm eff}^{\mathrm{nc}}={\mathbf 0}$, and it has to be in contact with a thermal bath in equilibrium at the same temperature. Thermal initial conditions in the potential $U$ correspond to the Gibbs-Boltzmann probability distribution $$P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{{\rm{eff}}}(t_0)] = {{\rm e}}^{\displaystyle -\beta V U[\mathbf{M}_0, \mathbf{H}_{{\rm{ext}}}(t_0)]-\ln Z[\mathbf{H}_{{\rm{ext}}}(t_0)]}$$ with $Z[\mathbf{H}_{{\rm{ext}}}(t_0)] \equiv \int{\hspace{-0em}\mathrm{d}{\mathbf{M}_0}\;} {{\rm e}}^{\displaystyle -\beta V U[\mathbf{M}_0, \mathbf{H}_{{\rm{ext}}}(t_0)]}$. The deterministic contribution to the Landau action functional in Eqs. (\[eq:S\_det\_cart00\])-(\[eq:S\_jac\_cart00\]) reads $$\begin{aligned} S_{L,{\rm det}} = & \; \ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)] + \int {\hspace{-0ex}\mathrm{d}{t}\;} {{\rm i}}\hat{M_i} \left( {\rm D}_t^{(\alpha)} M_i -g^{{\rm a}}_{ij} H^c_{{\rm eff},j} \right) \; , \end{aligned}$$ with ${\mathbf H}^c_{\rm eff} = -\mu_0^{-1} \partial U/\partial {\mathbf M}$. The Jacobian can be expressed in terms of $U$ by using $H^c_{{\rm eff},i} = -\mu_0^{-1} \partial_i U$ in Eq. (\[eq:S\_jac\_cart000\]) or $H^c_{{\rm eff},i} = -\mu_0^{-1} P_{ij} \partial_j U$ in Eq. (\[eq:S\_jac\_cart00\]) with $P_{ij}$ the projector onto the direction perpendicular to the magnetization, $P_{ij} = \delta_{ij} - M_i M_j /M_{{\rm s}}^2$. The dissipative part, $S_{L,{\rm diss}}$, remains unchanged. Spherical coordinate formalism {#sec:spherical-coordinates} ============================== As the modulus of the magnetization $\mathbf{M}$ is constant, the vector rotates on a sphere of radius $M_{{\rm s}}$, and it is natural to work in a spherical coordinates system. In this Section, we present an equivalent functional formalism for the dynamics of the magnetization, that uses a system of spherical coordinates. In Sec. \[sec:sph\_LLG\_cov\] we present the sLLG equation in spherical coordinates and in any discretization prescription. We stress in Sec. \[sec:sph\_random\_field\] that the statistics of the random field are not as trivial as they are in a Cartesian description. Although the non-trivial character of the noise has been correctly treated in some references (see, for instance, [@Fuller63] and Sec. 4.4.5 in [@Gardiner]), this subtlety has led to mistaken statements [@Langevin-Coffey] and omission or lack of clarity in the literature [@Bertotti-etal; @Martinez-etal]. We hope to clarify this matter once and for all here. It is also important to note that the transformation from Cartesian to spherical coordinates is non-linear and one cannot naively apply it to the generating functional. We construct the corresponding path integral formalism starting from the dynamic equations in the spherical coordinate system in Sec. \[sec:contruct\_spherical\]. The resulting action functional is given by the sum of the terms in Eqs. (\[eq:action-det-sph-L2\]), (\[eq:action-diss-sph-L\]) and (\[eq:esferica-jac\]). We introduce the usual coordinates $M_{{\rm s}}$, $\theta$ and $\phi$ where $M_{{\rm s}}$ is the radial component, $\theta$ the polar angle, and $\phi$ the azimuthal angle (see App. \[app:conventions\] for more details on the conventions used). The vector $\mathbf{M}$ defines the usual local basis ($\mathbf{e}_{M_{{\rm s}}}, \mathbf{e}_\theta, \mathbf{e}_\phi$) with $$\begin{aligned} \mathbf{M}(M_{{\rm s}},\theta,\phi) &\equiv& M_{{\rm s}}\, \mathbf{e}_{M_{{\rm s}}}(\theta,\phi) \nonumber\\ &=& M_{{\rm s}}\left( \sin\theta \cos\phi \ {\mathbf e}_x + \sin \theta \cos \phi \ {\mathbf e}_y + \cos \theta \ {\mathbf e}_z \right) \; . \end{aligned}$$ Here and after, Greek indices such as $\mu$ or $\nu$ label the spherical coordinates $M_{{\rm s}}, \ \theta, \ \phi$, and Latin indices continue to label the Cartesian coordinates $x, \ y, \ z$. We collect the spherical coordinates in a vector $\Omega_\mu$. The rotation matrix is called $R$ and we give its explicit form in App. \[app:conventions\]. $\alpha$-covariant sLLG equation {#sec:sph_LLG_cov} -------------------------------- Similarly to what was done in the Cartesian coordinate system, the Stratonovich sLLG equation in spherical coordinates should be modified to work in a generic $\alpha$-prescription, while maintaining the physics unchanged. We wish to find the equation satisfied by the spherical coordinates $M_{{\rm s}}, \theta, \phi$ knowing that the Cartesian components of the magnetization vector ${\mathbf M}$ satisfy the sLLG given in Eq. (\[eq.LLG-covariant\]) in the Landau formulation, $$\begin{aligned} \mathbf{Eq}_L[\mathbf{M},\mathbf{h}] \equiv {\rm D}^{(\alpha)}_t \mathbf{M} - g \left( \mathbf{H}_{{\rm{eff}}} + \mathbf{H} \right) = {\mathbf 0} \label{eq:LLG-recall} \, ,\end{aligned}$$ and that the Cartesian chain rule in Eq. (\[eq.chainrule\]) applied to our problem reads $$\begin{aligned} \label{eq:cr11} {{\rm d}}_t & = {{{\rm d}}_t} M_i \ \partial_i + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left(M_{{\rm s}}^2 \delta_{ij} - M_i M_j \right) \, \partial_i \partial_j \; .\end{aligned}$$ We start by re-writing the chain rule in spherical coordinates. We first work out the first term in Eq. (\[eq:cr11\]) as $$\begin{aligned} {{{\rm d}}_t} M_i \ \partial_i & = -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}} \nonumber\\ & \;\;\;\;\; + \frac{1}{M_{{\rm s}}} \left[ g_{\theta \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\theta + \frac{1}{\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\phi \right] \nonumber\end{aligned}$$ (see App. \[app:metric\]). The relevant elements of $g_{\mu\nu}$ are $$\begin{aligned} g_{\theta\theta} = g_{\phi\phi} = \eta\gamma_0 g_{\theta\phi} = - \eta\gamma_0 g_{\phi\theta} = \frac{\eta\gamma_0^2 M_{{\rm s}}}{1+\eta^2\gamma_0^2} \label{eq:g-elements-spherical}\end{aligned}$$ while $g_{M_{{\rm s}}\mu}=g_{\mu M_{{\rm s}}}=0$. In order to treat the second term of Eq. (\[eq:cr11\]) we notice that $$\begin{aligned} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j ) \partial_i \partial_j &= M_{{\rm s}}^2 \nabla^2 - M_i M_j \, \partial_i \partial_j \;, \nonumber\end{aligned}$$ where $\nabla^2$ is the Laplacian operator that in spherical coordinates reads $$\begin{aligned} \nabla^2 = \frac{1}{M^2_{{\rm s}}} \left( M_{{\rm s}}^2 \partial^2_{M_{{\rm s}}} + 2 M_{{\rm s}}\partial_{M_{{\rm s}}} + \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \;.\end{aligned}$$ We also have $ M_i M_j \, \partial_i \partial_j = M^2_{{\rm s}}\ \partial_{M_{{\rm s}}}^2 $. Therefore, the second term in Eq. (\[eq:cr11\]) becomes $$\begin{aligned} \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2 \left( \nabla^2 - \partial_{M_{{\rm s}}}^2 \right)\;.\end{aligned}$$ Altogether we have $$\begin{aligned} \label{eq:cr22-maintext} {{\rm d}}_t & = \frac{1}{M_{{\rm s}}} \left[ g_{\theta \nu_\perp} H_{\nu_\perp} \partial_\theta + \frac{1}{\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\phi \right] \nonumber\\ & \;\;\;\;\; + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left( \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right)\;.\end{aligned}$$ We now apply the differential operator (\[eq:cr22-maintext\]) to $M_{{\rm s}}$, $\theta$ and $\phi$, respectively, to obtain the equations of motion in spherical coordinates $$\begin{aligned} {{\rm d}}_t M_{{\rm s}}&= 0\;, \\ {{\rm d}}_t \theta &= \frac{1}{M_{{\rm s}}} g_{\theta \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \;, \\ {{\rm d}}_t \phi &= \frac{1}{M_{{\rm s}}\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \; ,\end{aligned}$$ and we use these identities in Eq. (\[eq:cr22-maintext\]) to re-write the time-differential operator in a form that is explicitly independent of the external and random fields $$\begin{aligned} {{\rm d}}_t &= \ {{\rm d}}_t \Omega_{\mu_\perp} \ \partial_{\Omega_{\mu_\perp}} + \ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta} \ \partial^2_\phi \right) \;.\end{aligned}$$ This is the chain-rule in spherical coordinates. Introducing the covariant derivatives $$\begin{aligned} {\rm D}_t^{(\alpha)} M_{{\rm s}}&\equiv {{\rm d}}_t M_{{\rm s}}\; , \label{eq:covDMs}\\ {\rm D}^{(\alpha)}_t(\theta) &\equiv {{\rm d}}_t \theta-\frac{D(1-2\alpha)\gamma_0^2}{(1+\eta^2\gamma_0^2)} \cot\theta \; , \label{eq:covDtheta} \\ {\rm D}^{(\alpha)}_t(\phi) &\equiv {{\rm d}}_t \phi \; , \label{eq:covDphi}\end{aligned}$$ we now recast Eqs. (\[eq:covDMs\])-(\[eq:covDphi\]) as $$\begin{aligned} \mbox{Eq}^{\rm sph}_{L,M_{{\rm s}}}[M_{{\rm s}},\theta,\phi] &\equiv {\rm D}_t^{(\alpha)} M_{{\rm s}}= 0 \; , \label{eq:ralpha} \\ \mbox{Eq}^{\rm sph}_{L,\theta}[M_{{\rm s}},\theta,\phi] &\equiv M_{{\rm s}}\ {\rm D}^{(\alpha)}_t(\theta) - g_{\theta\nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) = 0 \; , \label{eq:thetaalpha} \\ \mbox{Eq}^{\rm sph}_{L,\phi}[M_{{\rm s}},\theta,\phi] &\equiv M_{{\rm s}}\sin\theta\, {\rm D}^{(\alpha)}_t(\phi) - g_{\phi\nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) =0\;. \label{eq:phialpha} \end{aligned}$$ Equation (\[eq:ralpha\]) encodes the conservation of the modulus. Using the explicit form of $g_{\mu\nu}$ given in Eq. (\[eq:g-elements-spherical\]), Eqs. (\[eq:thetaalpha\]) and (\[eq:phialpha\]) become $$\begin{aligned} && {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ H_{{\rm eff},\phi} + H_\phi + \eta\gamma_0 ( H_{{\rm eff},\theta} + H_\theta) \right] = 0 \;, \label{eq:spherical-Landau1} \\ && \sin\theta \ {\rm D}_t^{(\alpha)}(\phi) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ \eta\gamma_0 ( H_{{\rm eff},\phi} + H_\phi ) - ( H_{{\rm eff},\theta} + H_\theta) \right] = 0 \; . \qquad \label{eq:spherical-Landau2}\end{aligned}$$ Had we started from the Gilbert formulation of the sLLG equation in Cartesian coordinates, we would have naturally obtained $$\begin{aligned} {\rm D}^{(\alpha)}_t(\theta) + \eta\gamma_0 \ \sin \theta \ {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 \left( H_{{\rm{eff}}, \phi} + H_\phi \right) = 0 \; , \label{eq:thetaalpha-Gilbert} \\ - \sin\theta\, {\rm D}^{(\alpha)}_t(\phi) + \eta\gamma_0 \ {\rm D}^{(\alpha)}_t(\theta) -\gamma_0 \left( H_{{\rm{eff}}, \theta} + H_\theta \right) =0 \;. \label{eq:phialpha-Gilbert} \end{aligned}$$ In this form, the random field $H_\theta, H_\phi$ may be erroneously interpreted as being additive, and that all discretization prescriptions are equivalent in spherical coordinates. This is not the case as the time-derivative of $\phi$ in Eqs. (\[eq:phialpha\]) and (\[eq:phialpha-Gilbert\]) are multiplied by a function of $\theta$. Moreover, we will see in Sec. \[sec:sph\_random\_field\] that, in the local coordinate system, the random field has a non-trivial distribution that depends on the discretization. Summarizing, we have shown how to write the sLLG equation in spherical coordinates in a generic $\alpha$-prescription. For each prescription the stochastic equations are [*different*]{} and one can simply encode the dependence on $\alpha$ by introducing $\alpha$-covariant time-derivatives. When treated with the correct rules of stochastic calculus, all equations yield the same physical results. An interesting observation is that in the case of a planar ferromagnet, *i.e.* when the magnetization is bound to live on the plane (moving on a circle), the equations no longer have any explicit dependence on $\alpha$. In this case, one can project the equations on the $x,y$ plane by setting $\theta=\pi/2$ and the $\alpha$-covariant time-derivatives reduce to the usual time-derivatives. This means that the sLLG equation is the same for all discretization schemes. We will see in Sec. \[sec:sph\_random\_field\] that in the case $\theta=\pi/2$, the noise in polar coordinate is a usual Gaussian white noise with vanishing mean. In other words, the stochastic evolution in two dimensions is driven by an effective [*additive*]{} noise, despite its original multiplicative character. However, this property only holds in two dimensions and it is not true in general. Random field statistics {#sec:sph_random_field} ----------------------- The probability distribution function of the random noise in the Cartesian coordinate system is Gaussian with zero average. This statistics does not directly translate into another coordinate system. The distribution in the transformed system has to be carefully studied if one wishes to use the rotated components of the random field. As we found some misconceptions in the literature regarding this point, in this Subsection we derive this distribution in spherical coordinates. The reader who is just interested in the generating functional construction can jump over this Subsection and go directly to Sec. \[sec:contruct\_spherical\]. The equations of motion do not involve the radial component of the random field, $H_{M_{{\rm s}}}$. We are then naturally interested in deriving the probability distributions of the orthoradial components, $P^{\rm sph}_{\rm n}[H_\theta,H_\phi]$. Let us start with the statistics of the random field in the Cartesian basis. The probability distribution of histories for such an isotropic Gaussian white noise is given by $$P_\mathrm{n}[H_x,H_y,H_z] \propto \exp\left\{-\frac{1}{4D} \int{} {\hspace{-0em}\mathrm{d}{t}\;} \left[ H_x(t)^2+ H_y(t)^2 + H_z(t)^2 \right] \right\}\;.$$ The rotation to the spherical coordinate system, $$\begin{aligned} P^{\rm sph}_{\rm n}[H_{M_{{\rm s}}}, H_\theta, H_\phi] = |\mathcal{J}^{\rm rot}| \ P_\mathrm{n}[R^{-1}_{x\mu} H_\mu,R^{-1}_{y\mu} H_\mu,R^{-1}_{z\mu} H_\mu]\;,\end{aligned}$$ with $$R^{-1}_{i\mu}(\mathbf{M}) = R^{-1}_{i \mu}(\theta,\phi) = \!\! \begin{array}{cc} \left[ \begin{array}{ccc} \sin\theta\cos\phi & \cos\theta\cos\phi & -\sin\phi \\ \sin\theta\sin\phi & \cos\theta\sin\phi & \cos\phi \\ \cos\theta & -\sin\theta & 0 \end{array} \right] \; , \end{array} \label{eq:inverse-rotation-matrix0}$$ involves the Jacobian $$\begin{aligned} \mathcal{J}^{\rm rot} \equiv \mathrm{det}_{i\nu,tt'} \frac{\delta R^{-1}_{i\mu}(t) H_\mu(t)}{\delta H_\nu(t')} \; . \label{eq:Jacobian-rot}\end{aligned}$$ After a series of transformations detailed in App. \[app:rotation-noise\] we set the calculation of the determinant in a form that allows us to use the identity (\[eq:identity\]) with a causal $C_{\mu\nu}(w,v)$. In the present case, the noise dependence in the operator $C$ requires to keep the second-order contribution in the expansion, but all higher order terms vanish [@Arnold2000; @Lubensky2007]. We therefore use Eq. (\[eq:identity-random-field\]). After a lengthy computation detailed in App. \[app:rotation-noise\] the Jacobian ${\cal J}^{\rm rot}$ is found to be $$\begin{aligned} \ln\mathcal{J}^{\rm rot} &= \int{\hspace{-0ex}\mathrm{d}{t}\;} R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\nu_\perp}} \frac{\delta \Omega_{\nu_\perp}(t)}{\delta H_{\mu}(t)} H_\rho(t) \nonumber\\ & -\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} R_{\mu_\perp j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu_\perp}(t')} R_{\nu_\perp k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu_\perp}(t)} \nonumber\\ & \qquad\qquad\qquad \times H_\rho(t) H_\sigma(t') \; . \nonumber\end{aligned}$$ The “responses" $ {\delta \Omega_{\tau_\perp}(t)}/{\delta H_{\nu_\perp}(t')}$ are causal, making the integrand in the last term vanish for all $t'\neq t$. However, as it involves two random field factors (which are delta correlated) it may still yield a non-trivial contribution at $t=t'$. We will see that in cases in which the “equal-time responses” $ {\delta \Omega_{\tau_\perp}(t)}/{\delta H_{\nu_\perp}(t)}$ vanish (as in, [*e.g.*]{}, non-Markovian processes) the Jacobian turns out to be trivial and equals one, $ \mathcal{J}^{\rm rot} = 1$. This is the case for the Itô convention. However, the sLLGs in spherical coordinates and generic discretization prescription yield finite and non-vanishing equal-time responses and, hence, a non-trivial ${\mathcal J}^{\rm rot}$. Using a more compact notation, the probability distribution function reads $$\begin{aligned} && \ln P^{\rm sph}_{\rm n}[H_\mu] = -\frac{1}{4D} \int {\rm d} t \ H^2_\mu(t) + \int{\hspace{-0em}\mathrm{d}{t}\;} L_\rho(t) H_\rho(t) \nonumber\\ && \;\;\;\qquad - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') H_\rho(t) H_\sigma(t') \; ,\end{aligned}$$ with $$\begin{aligned} L_\rho(t) &\equiv& R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\mu}(t)} \; , \\ Q_{\rho\sigma}(t,t') &\equiv& R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu}(t')} R_{\nu k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu}(t)} \; . \end{aligned}$$ The responses can be computed by first formally recasting the solutions of the equations of motion (\[eq:thetaalpha-Gilbert\]) and (\[eq:phialpha-Gilbert\]) into $$\begin{aligned} \theta(t) &= \theta_0 + \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \!\! \ldots + \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \left[ H_\phi(t') + \eta\gamma_0 H_\theta(t') \right]\,, \label{eq:integre_theta} \\ \phi(t) &= \phi_0 + \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \!\! \ldots + \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \left[ \eta\gamma_0 H_\phi(t') - H_\theta(t') \right]\,, \label{eq:integre_phi}\end{aligned}$$ where we only expressed explicitly the kernels involving the random fields. The argument exposed in App. \[app:rotation-noise\] allows one to recast the last term in a form in which the product of random fields $H_\rho(t) H_\sigma(t')$ is replaced by its average, $2D \delta_{\rho\sigma} \delta(t-t')$, contracting the indices of the factors $Q$ and cutting one of the time integrals. In short, one only needs the equal-time responses of the polar coordinates with respect to variations of the random fields. These read, using $\int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \delta(t'-t) = \Theta(0) = \alpha$, $$\begin{aligned} \frac{\delta \theta(t)}{\delta H_\theta(t)} &= \frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \delta(t'-t) = \frac{\alpha\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \,, \label{eq:equal-time1} \\ \frac{\delta \theta(t)}{\delta H_\phi(t)} & \ = \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t {\rm d} t' \ \delta(t-t') = \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \; , \\ \frac{\delta \phi(t)}{\delta H_\theta(t)} &= -\frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \delta(t-t') = - \frac{1}{\sin\theta(t)} \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \,, \\ \frac{\delta \phi(t)}{\delta H_\phi(t)} &= \frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \delta(t-t') = \frac{1}{\sin\theta(t)} \frac{\alpha\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \,. \label{eq:equal-time4}\end{aligned}$$ The first terms in Eqs. (\[eq:integre\_theta\]) and (\[eq:integre\_phi\]) give vanishing contributions since their integrands are finite at all times. Using these results one calculates $L_\rho$ and $Q_{\rho\rho}$: $$\begin{aligned} L_\rho(t) &=& \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \left[ 2\eta\gamma_0 \delta_{\rho M_{{\rm s}}} + \eta\gamma_0 \cot\theta \delta_{\rho\theta} + \cot\theta \delta_{\rho\phi} \right] \; , \\ Q_{\rho\rho}(t,t) &=& \frac{\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2} \left(1+\frac{1}{\sin^2\theta} \right) \; , \end{aligned}$$ and, after another lengthy calculation detailed in App. \[app:rotation-noise\], we obtain the following expression for $P_{\rm n}^{\rm sph}$ in terms of the random field components and the magnetization polar angles: $$\begin{aligned} P_{\rm n}^{\rm sph}[H_\theta,H_\phi] \propto & \exp \int{\hspace{-0em}\mathrm{d}{t}\;} \!\! \left\{ -\frac{1}{4D} H^2_{\mu_\perp} \! (t) + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta(t) \ [\eta\gamma_0 H_\theta(t) + H_\phi(t) ] \right. \nonumber\\ & \left. \qquad\qquad\qquad - \frac{\alpha^2\gamma_0^2 D}{1+\eta^2 \gamma_0^2} \cot^2\theta(t) \right\} \; .\end{aligned}$$ Itô calculus provides a special case in which a conventional Gaussian distribution is recovered. We stress that there is another special case in which this distribution boils down to a standard Gaussian distribution (with zero mean and delta correlations) for all discretization prescriptions: the case in which the magnetization is constrained to rotate on the plane $\theta=\pi/2$. Fokker-Planck approach {#fokker-planck-approach} ---------------------- Following steps similar to the ones in Sec. \[sec:Fokker-Planck\] and in [@Fuller63], now for the $\alpha$-scheme spherical equations of motion, one finds the $\alpha$-generic Fokker-Planck equation $$\begin{aligned} \partial_t P(\theta, \phi; t) \! \! & \! = \! & \! \! - \partial_\theta \left\{ [f_\theta + D(2\alpha-1) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \right. \nonumber\\ && \left. \qquad\qquad + D \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta ] P(\theta, \phi;t) \right\} \nonumber\\ && -\partial_\phi[f_\phi P(\theta, \phi; t)] \nonumber\\ && -\frac{D\gamma_0^2}{1+\eta^2\gamma_0^2} \left\{ \partial_\theta^2 P(\theta,\phi;t) +\partial_\phi^2 [ \frac{1}{\sin^2\theta} P(\theta,\phi;t) ] \right\}\end{aligned}$$ with $$\begin{aligned} f_\theta &=& \frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \ \cot \theta + \frac{\gamma_0}{1+\eta^2\gamma_0^2} (H_{{\rm eff}, \phi} + \eta\gamma_0 H_{{\rm eff},\theta} ) \; , \nonumber\\ f_\phi &=& \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} (\eta\gamma_0 H_{{\rm eff}, \phi} - H_{{\rm eff},\theta} ) \; . \end{aligned}$$ As in the Cartesian case one finds that the drift term in $f_\theta$ cancels the following term and all explicit $\alpha$ dependence disappears form the Fokker-Planck equation. One can check that in the conservative case $$H_{{\rm eff},\theta} = - (M_{{\rm s}}\mu_0^{-1}) \ \partial_\theta U \qquad\qquad H_{{\rm eff},\phi} = - (M_{{\rm s}}\mu_0^{-1}) \ \frac{1}{\sin\theta} \partial_\phi U$$ the stationary probability density $$P_{\rm eq}(M_{{\rm s}}, \theta,\phi) = N \sin\theta \ e^{-\beta V U(\theta,\phi)} \label{eq:equil-Pi-sph}$$ with $N$ a normalisation constant is a solution to the Fokker-Planck equation. as long as $D$ is given by Eq. (\[eq:D\]). Landau generating functional {#sec:contruct_spherical} ---------------------------- The purpose of this Subsection is to derive the generating functional in the spherical coordinate system. The steps performed in this Section are very similar to the ones performed in Sec. \[sec:functional\] when working with Cartesian coordinates. Given an initial condition ${M_{{\rm s}}}_0$, $\theta_0$ and $\phi_0$ that we collect in the vector notation ${\mathbf \Omega}_0 = \mathbf{\Omega}(t_0)$, and a particular realization of the Gaussian and zero-mean random variables $[{\mathbf H}]$ in the Cartesian coordinate system, there is a unique trajectory of the variables $[M_{{\rm s}}]$, $[\theta]$ and $[\phi]$, collected in $[{\mathbf \Omega}]$, that obeys the equations of motion. The generating functional is defined as $$\begin{aligned} \mathcal{Z}[\boldsymbol{\lambda}] = \langle \ \exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \boldsymbol{\lambda}(t) \cdot \mathbf{\Omega}_{\mathbf H}(t) \ \rangle \; ,\end{aligned}$$ where $ \langle \cdots \rangle $ denotes the average over initial conditions and random field realizations. $\boldsymbol{\lambda}$ is a source that couples linearly to the fluctuating magnetization configuration $\mathbf{\Omega}_{\mathbf H}(t)$. Similarly to the Cartesian case, we construct the MSRJD representation of the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ by imposing the equation of motion with a functional delta-function $$\begin{aligned} && {\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{H}] \ P_{\rm n}[\mathbf{H}] \ \int {\cal D}[\mathbf{\Omega}] \ P_{\rm i}[\mathbf{\Omega}(t_0), {\mathbf {H}}_{\rm eff}(t_0)] \nonumber\\ && \qquad\quad \ \times {\prod_{n=1}^N [M_{{\rm s}}^2\sin\theta_{n}]^{-1}} \delta\Big{[} \mbox{\textbf{Eq}}^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \Big{]} \nonumber\\ && \qquad\qquad \; \; \times \ \ |{\cal J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}]| \ \exp \int {\hspace{-0em}\mathrm{d}{t}\;} {\boldsymbol{\lambda}}(t) \cdot \mathbf{\Omega}(t) \;. \label{eq:generatingZ24}\end{aligned}$$ $P_{\rm n}[\mathbf{H}]$ is the probability distribution of the random field in Cartesian coordinates, that we still take to be Gaussian with zero mean, delta correlated and variance $2D$. For the moment we leave the initial probability density $P_{\rm i}$ general. A particular case is the one in which it is given by the equilibrium weight (\[eq:equil-Pi-sph\]). The measure over the spherical coordinates, ${\cal D}[\mathbf{\Omega}]$, is defined in App. \[app:conventions\] and includes a summation over the initial conditions at time $t_0$. The geometric factor $\prod_{n=1}^N |M_{{\rm s}}^2 \sin \theta_n |^{-1}$ accompanies the $\delta$ function in the spherical coordinate system, see also App. \[app:deltafunction\]. The Jacobian ${\cal J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}]$ is $$\begin{aligned} \label{eq:defjac} \mathcal{J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv \det_{\mu\nu;uv} \begin{array}{c} \displaystyle \frac{\delta {\rm{Eq}}^{\rm sph}_{\mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)} \end{array}\end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$. At this point we have the freedom to write the equation of motion in the Landau or Gilbert formulation. The advantage of the former lies in the fact that the time derivatives are well separated from the other terms, thus simplifying the analysis. We choose to use a modified Landau formulation that we compactly write as follows: $$\begin{aligned} & {\rm Eq}^{\rm sph}_{L,M_{{\rm s}}} = {{\rm d}}_t M_{{\rm s}}= 0 \; , \nonumber\\ & {\rm Eq}^{\rm sph}_{L,\theta} = {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ H_{{\rm eff},\phi} + H_\phi + \eta\gamma_0 (H_{{\rm eff}, \theta} +H_\theta)\right] = 0 \; , \nonumber\\ & {\rm Eq}^{\rm sph}_{L,\phi} = {\rm D}_t^{(\alpha)}(\phi) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} \left[\eta\gamma_0 (H_{{\rm eff}, \phi}+H_\phi ) - (H_{{\rm eff},\theta} +H_\theta ) \right] = 0 \; . \nonumber\end{aligned}$$ This form is convenient since, as the derivatives are separated from the rest, it is relatively simple to compute the Jacobian (as opposed to what has to be done in the Gilbert formulation that we develop in App. \[sec:construct\_spherical\_Gilbert\]). The operator in the determinant can be worked out explicitly as explained in App. \[app:MSRDJ-Jacobian-Gus\] $$\begin{aligned} && {\cal J}_L^{\rm sph} = \exp \left\{ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;} \left[ \frac{D(1-\alpha)\gamma_0}{\sin^2\theta} \right. \right. \nonumber\\ && \left. \left. \qquad\qquad - \partial_\theta \left[ H_{{\rm eff},\phi} + H_{\phi} + \eta\gamma_0 (H_{{\rm eff},\theta} + H_\theta) \right] \right. \right. \nonumber\\ && \left. \left. \qquad\qquad + \frac{1}{\sin\theta} \partial_\phi \left[ H_{{\rm eff},\theta} + H_\theta - \eta\gamma_0 (H_{{\rm eff},\phi} + H_\phi) \right] \right] \right\} \; . \label{eq:Jacobian-Landau-spherical}\end{aligned}$$ As found in the Cartesian calculation, it does not depend on the parallel component of the field, that in spherical coordinates means that ${\cal J}_L^{\rm sph}$ is independent of $H_{{\rm eff},M_{{\rm s}}}+H_{M_{{\rm s}}}$. We next introduce an adimensional Lagrange multiplier $[{{\rm i}}\hat{\mathbf{\Omega}}]$ to exponentiate the functional delta: $$\int {\mathcal{D}}{[{{\rm i}}\hat{\mathbf \Omega}]} \exp \left\{ - \int \! {\hspace{-0em}\mathrm{d}{t}\;} \left( {{\rm i}}\hat\Omega_{M_{{\rm s}}} \mbox{{Eq}}^{\rm sph}_{M_{{\rm s}}}[{\mathbf \Omega}] + {{\rm i}}\hat\Omega_\theta \mbox{{Eq}}^{\rm sph}_\theta[{\mathbf \Omega}, {\mathbf H}] + {{\rm i}}\hat\Omega_\phi \mbox{{Eq}}^{\rm sph}_\phi[{\mathbf \Omega}, {\mathbf H}] \right) \right\} \; .$$ We identify all the terms in the integrand of the exponent that involve the random field ${\mathbf H}$: $$\begin{aligned} && -\frac{1}{4D} H_i^2 + \frac{\gamma_0}{1+\eta^2\gamma_0^2} \left( {{\rm i}}\hat\Omega_\phi \frac{1}{\sin\theta} \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) + {{\rm i}}\hat\Omega_\theta \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) \right) H_i \nonumber\\ && \qquad + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \left( -\partial_\theta R_{\phi i} - \eta\gamma_0 \partial_\theta R_{\theta i} -\frac{\eta\gamma_0}{\sin\theta} \partial_\phi R_{\phi i} + \frac{1}{\sin\theta} \partial_\phi R_{\theta i} \right) H_i\;. \qquad\end{aligned}$$ The quadratic term in $H_i$ comes from its probability distribution. The first set of linear terms comes from imposing the equations of motion with the Dirac delta function. The third group of terms comes from the Jacobian. Contrary to the Cartesian case, the latter will yield non-trivial contributions to the action. After integration and a number of simplifications that use the explicit expression of the rotation matrix $R$ one finds that these terms give rise to $$\begin{aligned} \frac{D \gamma_0^2}{1+\eta^2\gamma_0^2} \left[ \frac{({{\rm i}}\hat\Omega_\phi)^2}{\sin^2\theta} + ({{\rm i}}\hat\Omega_\theta)^2 + 2\alpha {{\rm i}}\hat\Omega_\theta \cot\theta + \frac{\alpha^2}{\sin^2\theta} \right]\end{aligned}$$ (apart from an irrelevant additive constant). The last term is of the same form as the first term in ${\cal J}_L^{\rm sph}$ and we will combine them together when writing $\widetilde S^{\rm sph}_{{\rm jac}}$ below. We now perform the change of fields $$\begin{aligned} {{\rm i}}\hat\Omega_\phi \mapsto \sin\theta \, {{\rm i}}\hat\Omega_\phi \;,\end{aligned}$$ which comes with a Jacobian $$\begin{aligned} \prod_{n=0}^{N-1} | \sin\bar\theta_n |\;, \label{eq:detedete4}\end{aligned}$$ where we were careful to evaluate the factors on the intermediate points $\bar \theta_n \equiv \alpha \theta_{n+1} + (1-\alpha) \theta_n$. Notice indeed that the discretization matters here since there is no trivial continuous limit of this expression. See also the discussion in Sect. \[subsec:rules\]. The product above can be re-writen as $$\begin{aligned} \prod_{n=0}^{N-1} | \sin\bar\theta_n | = {{\rm e}}^{(1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| } \prod_{n=1}^{N} | \sin\theta_n | \;, \label{eq:detedetee4}\end{aligned}$$ where we used the development $$\begin{aligned} \sin\bar\theta_n = \alpha \sin \theta_{n+1} + (1-\alpha) \sin \theta_n\;,\end{aligned}$$ and the fact that we do not need to consider higher order terms because they vanish from Eq. (\[eq:detedete4\]) once the limit $\delta t \to 0$ is considered. The product $\prod_{n=1}^{N} | \sin\theta_n |$ in Eq. (\[eq:detedetee4\]) cancels exactely the geometric one accompanying the delta functions in Eq. (\[eq:generatingZ24\]). We now put all these results together to write the generating functional $$\mathcal{Z}[\boldsymbol{\lambda}] = \int {\mathcal{D}}[\boldsymbol{\Omega}] {\cal D}[\hat{\boldsymbol{\Omega}}] \ \exp\left( S_L^{\rm sph}[\boldsymbol{\Omega},\hat{\boldsymbol{\Omega}}] + \int{\hspace{-0em}\mathrm{d}{t}\;}\boldsymbol{\lambda} \cdot \boldsymbol{\Omega} \right)\;,$$ with the measure ${\cal D}[\boldsymbol{\Omega}] \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N {{\rm d}}{M_{{\rm s}}}_n {{\rm d}}\theta_n {{\rm d}}\phi_n \, {M_{{\rm s}}}_n^2 |\sin\theta_n|$ (that includes the initial time $t_0$), the full action $$S_L^{\rm sph}= S^{\rm sph}_{L,{\rm det}} + \widetilde S^{\rm sph}_{L,{\rm diss}} + \widetilde S^{\rm sph}_{L,{\rm jac}}$$ and $$\begin{aligned} S^{\rm sph}_{L,{\rm det}} \! & \! = \! & \! \ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] - \int {\rm d}t \ \left\{ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right. \nonumber\\ && \; + {{\rm i}}\hat\Omega_\theta \left[ {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \phi} \right] \nonumber\\ && \left. \; + {{{\rm i}}\hat\Omega_\phi} \left[ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \theta} \right] \right\} , \qquad \label{eq:action-det-sph-L} \\ \widetilde S^{\rm sph}_{L,{\rm diss}} \! & \! = \! & \! \frac{D \gamma_0^2}{1+\eta^2\gamma_0^2} \int {\rm d}t \left[ {({{\rm i}}\hat\Omega_\phi)^2} + ({{\rm i}}\hat\Omega_\theta)^2 + 2\alpha {{\rm i}}\hat\Omega_\theta \cot\theta \right] \nonumber\\ && \;\; + \frac{\eta\gamma^2_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \left({{\rm i}}\hat \Omega_\theta H_{{\rm eff}, \theta} + \frac{{{\rm i}}\hat \Omega_\phi}{\sin\theta} H_{{\rm eff}, \phi} \right) , \label{eq:action-diss-sph}\end{aligned}$$ $$\begin{aligned} \widetilde S^{\rm sph}_{L,{\rm jac}} \! & \! = \! &\! (1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| \nonumber \\ && + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;} \left[ \frac{D\gamma_0}{\sin^2\theta} - \partial_\theta \left( H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta} \right) \right. \nonumber\\ && \left. \qquad\qquad\qquad\qquad + \frac{1}{\sin\theta} \partial_\phi \left( H_{{\rm eff},\theta} - \eta\gamma_0 H_{{\rm eff},\phi} \right) \right] . \end{aligned}$$ The expressions above can be modified to obtain a slightly more compact, and eventually more convenient, form. $\widetilde S_{L,{\rm diss}}^{\rm sph}$ includes a linear term in ${{\rm i}}\hat\Omega_\theta$ that can be replaced with the help of the identity $$\begin{aligned} && \int d\phi \ \exp\left[ ({{\rm i}}\sigma \phi)^2 - {{\rm i}}\phi b - {{\rm i}}\phi a \right] \nonumber\\ && \qquad\qquad = \int d\phi \ \exp\left[ ({{\rm i}}\sigma \phi)^2 - {{\rm i}}\phi b - \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2} \right] \; . \label{eq:identity-Gus}\end{aligned}$$ We apply it to the functional integration over ${{\rm i}}\hat \Omega_\theta$ by choosing $$\begin{aligned} && \sigma^2 = \frac{D\gamma_0^2}{1+\eta^2\gamma_0^2} \; , \nonumber\\ && a=-\frac{2D\gamma_0^2\alpha}{1+\eta^2\gamma_0^2} \ \cot\theta \; , \nonumber\\ && b = {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} (H_{{\rm eff},\phi}+\eta\gamma_0 H_{{\rm eff}, \theta}) \; . \nonumber\end{aligned}$$ The integration generates the terms $$\begin{aligned} -\frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2} = & -\frac{\alpha^2 D \gamma_0^2}{1+\eta^2\gamma_0^2} \ \cot^2\theta \nonumber\\ & + \alpha\cot\theta \ [{\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} (H_{{\rm eff},\phi}+\eta\gamma_0 H_{{\rm eff}, \theta})] \; . \end{aligned}$$ We rewrite the full action as $S= S^{\rm sph}_{L,{\rm det}} + S^{\rm sph}_{L,{\rm diss}} + S^{\rm sph}_{\rm jac}$, with $S^{\rm sph}_{L,{\rm det}}$ given in Eq. (\[eq:action-det-sph-L\]) that we repeat here to ease the reading of the final result, $$\begin{aligned} S^{\rm sph}_{L,{\rm det}} \! & \! = \! & \! \ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] - \int {\rm d}t \ \left\{ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right. \nonumber\\ && \; + {{\rm i}}\hat\Omega_\theta \left[ {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \phi} \right] \nonumber\\ && \left. \; + {{{\rm i}}\hat\Omega_\phi} \left[ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \theta}) \right] \right\} , \qquad \label{eq:action-det-sph-L2} \\ S^{\rm sph}_{L,{\rm diss}} \! & \! = \! & \! \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int {\rm d}t \left[ D\gamma_0 \left( {{\rm i}}\hat\Omega_\phi \right)^2 + D\gamma_0 ({{\rm i}}\hat\Omega_\theta)^2 \right. \nonumber\\ && \left. \;\;\;\;\qquad\qquad + \eta\gamma_0 \left({{\rm i}}\hat \Omega_\theta H_{{\rm eff}, \theta} + {{{\rm i}}\hat \Omega_\phi} H_{{\rm eff}, \phi} \right) \right] , \label{eq:action-diss-sph-L} \\ S^{\rm sph}_{L,{\rm jac}} \! & \! = \! &\! (1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| + \alpha \int {{\rm d}}t \ \cot\theta \ {\rm D}_t^{(\alpha)}(\theta) \nonumber\\ && \;\; + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;} \! \left[ \frac{(1-\alpha)D\gamma_0}{\sin^2\theta} - \cot \theta (H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta}) \right. \nonumber\\ && \qquad\qquad\qquad\qquad - \partial_\theta \left( H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta} \right) \nonumber\\ && \left. \qquad\qquad\qquad\qquad + \frac{1}{\sin\theta} \partial_\phi \left( H_{{\rm eff},\theta} - \eta\gamma_0 H_{{\rm eff},\phi} \right) \right] . \label{eq:esferica-jac} \end{aligned}$$ This completes the construction of the generating functional for the Landau formulation of the dynamics in the spherical coordinate system. The construction of the Gilbert action reported in App. \[sec:construct\_spherical\_Gilbert\] leads to $$\begin{aligned} S^{\rm sph}_{G,{\rm det}} \!\! & \!\! = \! \! & \! \ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] - \int {\rm d}t \left\{ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}+ {{\rm i}}\hat\Omega_\theta [ {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi} ] \right. \nonumber\\ && \left. \!\! - {{\rm i}}\hat\Omega_\phi [ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta} ] \right\} , \label{eq:action-det-sph-Gilbert-maintext}\\ S^{\rm sph}_{G,{\rm diss}} \!\! & \!\! = \!\! & \!\! \int {\rm d}t \left[ D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2 - {{\rm i}}\hat\Omega_\theta \eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi) \right. \nonumber\\ && \left. \qquad\quad - {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta) \right] \;, \label{eq:action-diss-sph-Gilbert-maintext} \\ S^{\rm sph}_{G,{\rm jac}} \!\! & \!\! = \!\! & \! S^{\rm sph}_{L,{\rm jac}} \label{eq:action-jac-sph-Gilbert-maintext} \end{aligned}$$ and $S_G^{\rm sph} = S_{G, {\rm det}}^{\rm sph} + S_{G, {\rm diss}}^{\rm sph} + S_{G, {\rm jac}}^{\rm sph}$. One can easily check that one can go from the Landau to the Gilbert formalism and [*vice versa*]{} within the path-integral [*via*]{} a change of variables of the auxiliary fields, similarly to what we discussed in the Cartesian coordinate system around Eqs. (\[eq:Trans\_L2G\]) and (\[eq:Trans\_G2L\]): $$\begin{aligned} {{\rm i}}\hat \Omega^L_\theta &=& {{\rm i}}\hat \Omega^G_\theta + \eta\gamma_0 \ {{\rm i}}\hat\Omega^G_\phi \; , \\ {{\rm i}}\hat\Omega^L_\phi &=& \eta\gamma_0 \ {{\rm i}}\hat\Omega^G_\theta - {{\rm i}}\hat\Omega^G_\phi \; ,\end{aligned}$$ with inverse $$\begin{aligned} {{\rm i}}\hat \Omega_\theta^G &=& \frac{1}{1+\eta^2\gamma_0^2} \left[ {{\rm i}}\hat \Omega_\theta^L + \eta\gamma_0 \ {{{\rm i}}\hat \Omega_\phi^L} \right] \; , \nonumber\\ {{\rm i}}\hat \Omega_\phi^G &=& \frac{1}{1+\eta^2\gamma_0^2} \left[\eta\gamma_0 \ {{\rm i}}\hat \Omega_\theta^L - {{{\rm i}}\hat \Omega_\phi^L} \right] \; . \end{aligned}$$ Conclusions {#sec:recap} =========== In this manuscript we revisited the stochastic approach to the dynamics of a magnetic moment under the effect of thermal noise, dissipation, magnetic field of potential origin and, also, non-potential forces such as spin-torque terms. We used the stochastic Landau-Lifshitz-Gilbert (sLLG) equation as a phenomenological description of the dynamics and we constructed a functional generating functional for physical observables. We found rather confusing statements on the influence (or not) of the discretization scheme used to define the stochastic dynamics in discrete time in the literature [@Berkov2002]. Our first goal was to insist upon the fact that unless the Stratonovitch prescription is used to define the sLLG, a drift term has to be added to the equation of motion. The drift term ensures both the conservation of the magnetization modulus and the approach to Boltzmann equilibrium under conservative magnetic fields. We also formulated the problem in the spherical coordinate system. Although this is the most natural framework to work in, due to the explicit conservation of the modulus of the magnetization, it has been the source of many confusing statements in the literature. For instance, it is stated in [@Martinez-etal] that the random field in the spherical coordinate system is additive. In Sec. 7.3.1 in [@Langevin-Coffey] it is written that the spherical components of the random field is a Gaussian with zero mean. In this paper we showed that the polar coordinate field acquires a non-vanishing average. We clarified these issues not only in the standard Itô and Stratonovich schemes but also in the general $\alpha$ prescription. This is an important result for the correct numerical study of the magnetization dynamics. We then derived the drift term to be added to the equation for the polar angle. We showed that the evolution dictated by this $\alpha$ prescription stochastic equations leads to the equilibrium Gibbs-Boltzmann distribution independently of $\alpha$. Next, we focused on the construction of the generating functional. We stressed that physical results should be independent of the framework used to write the path-integral, this being the Landau [*vs.*]{} Gilbert formulation of the dynamics, the $\alpha$-prescription, or whether we use Cartesian or spherical coordinates. The equivalence between the Landau and Gilbert formulations at the level of the equations of motion was carefully discussed in several textbooks on this subject [@Bertotti-etal]. We showed explicitly how this equivalence is realized in the path-integral formalism. We proved the independence of the $\alpha$-prescription in Sec. \[sec:Fokker-Planck\] within the framework of the Fokker-Planck equation. The $\alpha$-invariance of physical results can also be shown within the generating functional formalism but, as the action depends explicitly on $\alpha$, this feature is less trivial to show in this set-up. One way to prove invariance is to use an underlying BRST symmetry [@arenas2010]. Another possibility is to construct a perturbative expansion and to show invariance in this way [@Honkonen]. In both cases, an interplay between the contributions of all parts in the action, including the Jacobian, are necessary to establish invariance. At the level of the stochastic equations of motion, one can go from Cartesian to spherical expressions by using the transformation rules for the change of basis and the generalized chain-rule for the time-derivative. In the Fokker-Planck formalism, a change of variables also allows one to relate Cartesian and spherical approaches. However, at the level of the path-integral, the equivalence is more subtle. As it is well-known from the results in [@Edwards64; @Jevicki76; @Tirapegui82; @Alfaro92], a non-linear change of variables in the path-integral generates non-trivial extra terms in the action (beyond the formal change of variables and the corresponding Jacobian). These are found also in this particular case. We have not discussed this issue in further detail in this manuscript since the more adequate scheme to do it is the BRST formalism [@Alfaro92] that we will develop elsewhere. Our work can be extended in different directions. For simplicity, we presented the path-integral for a single magnetic moment. The sLLG equation can be easily generalized to the case of a space-dependent magnetization by introducing a Ginzburg-Landau free-energy functional [@Bertotti-etal; @Langevin-Coffey; @Martinez-etal]. The generalization of the generating functional construction to this case is straightforward. It will be useful to treat micromagnetism [@Ralph2008] and, in particular, the dynamics of magnetic domains. A field in which the path-integral formulation of the stochastic dynamics has been specially successful is the one of systems with quenched randomness. As known since the work in [@deDominicis76], the average over quenched disorder is simple to perform within this functional framework and allows the analytic treatment of many interesting phenomena [@LesHouches]. Path integral measure {#app:discrete} ===================== The time interval $t\in [t_0,\mathcal{T}]$ is divided in $N$ discrete time intervals, $t_n \equiv t_0 + n \Delta t$ with $n=0, \ldots, N$ and increment $\Delta t \equiv (\mathcal{T}-t_0)/N$. The continuous time limit is performed by sending $N$ to infinity while keeping ${\cal T}-t_0$ finite. We define the path integral over functions defined on the time interval $[t_0,\mathcal{T}]$ as $$\begin{aligned} \int{\mathcal{D}}{[{\mathbf x}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{{\mathbf x}_n}\;} \; . \end{aligned}$$ When integrating over the magnetization, a 3-dimensional field in Cartesian coordinates, $$\begin{aligned} \int{\mathcal{D}}{[\mathbf{M}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{\mathbf{M}_n}\;} \;,\end{aligned}$$ the integration on each time-slice is performed over the $\mathbb{R}^3$ space, and the spherical constraint is imposed by the equation of motion. More specifically, it is imposed through the ${{\rm i}}\hat{M}_\parallel$ sector of the path-integral expression of the generating functional, see Sec. \[sec:conservation\_modulus\]. Gilbert Cartesian generating functional {#app:path-integral:Gilbert} ======================================= We start from the evolution equation in the $\alpha$-covariant Gilbert formulation in Cartesian coordinates, $$\mbox{\bf Eq}_G[ {\mathbf M}, {\mathbf H} ] \equiv {\rm D}_t^{(\alpha)} {\mathbf M} + \gamma_0 \left( {\mathbf H}_{\rm eff} + {\mathbf H} - \frac{\eta}{M_{{\rm s}}} {\rm D}_t^{(\alpha)} {\mathbf M} \right) = {\mathbf 0} \; , \label{eq:Gilbert-alpha-gen}$$ and we impose this equation in a path integral over ${\mathbf M}$ as described in Sec. \[sec:functional\]. The Jacobian that ensures that the integration over $\mathbf{M}$ equals one is given by $$\begin{aligned} \mathcal{J}_G[\mathbf{M},\mathbf{H}] \equiv \det_{ij;uv} \begin{array}{c} \displaystyle \frac{\delta {\rm Eq}_{Gi}(u)}{\delta M_{j}(v)} \end{array}\end{aligned}$$ with Eq$_G$ given in Eq. (\[eq:Gilbert-alpha-gen\]). The operator in the determinant can be worked out explicitly and put into the form $$\frac{\delta \mbox{Eq}_{Gi}(u)}{\delta M_j(v)} = X_{ij}(u) {\rm d}_u \delta(u-v) + A_{ij}(v) \delta(u-v)$$ with $$\begin{aligned} X_{ij}(u) &\equiv \delta_{ij} + \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u) \; , \\ A_{ij} &\equiv \gamma_0 \epsilon_{ijk} ( {H_{\rm eff}}_k + H_k) + \gamma_0 \epsilon_{ilk} M_l \partial_j {H_{\rm eff}}_k - \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} {\rm d}_t M_k \nonumber\\ & \;\;\;\; + 2D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2 \gamma_0^2} \delta_{ij} \;.\end{aligned}$$ Factorizing the operator $X_{ik}(u) {\rm d}_u \delta(u-w)$, with inverse $X^{-1}_{kj}(v) \Theta(w-v)$, $$\begin{aligned} X^{-1}_{ij}(u) = \frac{1}{1+\eta^2 \gamma_0^2} \left[\delta_{ij} - \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u) + \frac{\eta^2\gamma_0^2}{M_{{\rm s}}^2} M_i(u) M_j(u) \right] \; , \end{aligned}$$ we write $$\begin{aligned} \frac{\delta \mbox{Eq}_{Gi}(u)}{\delta M_j(v)} = & \int {\hspace{-0em}\mathrm{d}{w}\;} \ X_{ik}(u) {\rm d}_u \delta(u-w) \nonumber\\ & \qquad \times \left[ \delta_{kj} \delta(w-v) + \Theta(w-v) X^{-1}_{kl}(v) A_{lj} (v) \right] \; . \end{aligned}$$ The Jacobian becomes $$\begin{aligned} & \mathcal{J}_G[\mathbf{M}, \mathbf{H}] = \; \det_{ik;uw} \left[ X_{ik}(u) {\rm d}_u\delta(u-w)\right] \nonumber\\ & \qquad \times \det_{kj;wv} \left[ \delta(w-v) \delta_{kj} + \Theta(w-v) X^{-1}_{kr}(v) A_{rj}(v) \right] \; . \end{aligned}$$ \[sec:discussRVsA2\] Notice that the first factor is actually independent of $\mathbf{M}$. Indeed, using $\det_{ik;uw} [X_{ik}(u) {\rm d}_u \delta(u-w) ]= \det_{ij;uv} [X_{ij}(u) \delta(u-v)] \det_{jk;vw} [\delta_{jk} {\rm d}_v\delta(v-w)]$, one easily finds $\det_{ij;uv} [X_{ij}(u) {\rm d}_u \delta(u-v) ] \propto \prod_u \det_{ij} [\delta_{ij} + \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u)] = \prod_u [1 + \eta^2\gamma_0^2]$, a trivial constant. We treat the second determinant, that depends upon $A_{ij}$ and hence $\mathbf{H}$, with the identity (\[eq:identity\]) to obtain $$\begin{aligned} \mathcal{J}_G[{\mathbf M}, {\mathbf H}] \propto \; & \exp \left( \alpha \int {\hspace{-0ex}\mathrm{d}{t}\;} X^{-1}_{jr} A_{rj} \right) \;. \end{aligned}$$ In this case only the first term in the expansion yields a non-trivial contribution. Performing the contractions with $X^{-1}_{jr}$, we find $$\begin{aligned} \mathcal{J}_G[{\mathbf M}, {\mathbf H}] & \!\! \!\! \propto \!\! \!\! & \exp \left\{ \frac{\alpha\gamma_0}{1+\eta^2 \gamma_0^2} \int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[} \frac{2\eta\gamma_0}{M_{{\rm s}}} \ \mathbf{M} \cdot ({\mathbf{H}_{\rm eff}} +\mathbf{H}) \right. \nonumber\\ && \;\; \left. + \frac{\eta\gamma_0}{M_{{\rm s}}} (M_k M_j -\delta_{kj} M_{{\rm s}}^2)\partial_j {H_{\rm eff}}_k + \epsilon_{jlk} M_l \partial_j {H_{\rm eff}}_k \Big{]}\! \right\} \nonumber \end{aligned}$$ where we omitted a constant factor. This result coincides with the Jacobian in the Landau formulation, see Eq. (\[eq:Jcart-L\]), and $${\cal J}_G[{\mathbf M}, {\mathbf H}] = {\cal J}_L[{\mathbf M}, {\mathbf H}] \; .$$ Coming back to the generating functional ${\cal Z}[\boldsymbol{\lambda}]$, we now exponentiate the delta functional with an auxiliary field ${{\rm i}}\hat {\mathbf M}$ that imposes Eq. (\[eq:Gilbert-alpha-gen\]) as $$\begin{aligned} \delta \Big{[} \mbox{\textbf{Eq}}_G[\mathbf{M}, \mathbf{H}] \Big{]} \propto \int {\cal D}[\hat{\mathbf{M}}] \ \exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}} \cdot \mbox{\textbf{Eq}}_G[\mathbf{M},\mathbf{H}] \; . \nonumber\end{aligned}$$ From the very structure of the equation it is clear that after decomposing the auxiliary field in two components ${{\rm i}}\hat{\mathbf M}_\perp$ and ${{\rm i}}\hat {\mathbf M}_\parallel$ perpendicular and parallel to ${\mathbf M}$, respectively, one has $$\begin{aligned} \delta \Big{[} \mbox{\textbf{Eq}}_G[\mathbf{M}, \mathbf{H}] \Big{]} \propto & \int {\cal D}[\hat{\mathbf{M}}_\perp] {\cal D}[\hat{\mathbf{M}}_\parallel] \ \exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \mbox{\textbf{Eq}}_G[\mathbf{M},\mathbf{H}] \nonumber\\ & \qquad\qquad \times \exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \; . \nonumber\end{aligned}$$ The integration over the Gaussian white noise $\mathbf{H}$ involves the following terms in the exponential: $$\frac{2\alpha\eta\gamma_0^2}{(1+\eta^2\gamma_0^2) M_{{\rm s}}} \mathbf{M} \cdot \mathbf{H} + \gamma_0 {{\rm i}}\hat{\mathbf{M}}_\perp \cdot (\mathbf{M} \wedge \mathbf{H}) - \frac{\mathbf{H}^2}{2D} \; .$$ The Gaussian integral then yields $D [ 4\alpha^2\eta^2\gamma_0^4/(1+\eta^2 \gamma_0^2)^2 + \gamma_0^2 (\epsilon_{ijk} {{\rm i}}{\hat M}_{\perp_i} M_j)^2] $. The first term is just a constant while the second one is non-trivial. We then recast the generating functional into the form $${\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{M}] {\cal D}[\hat{\mathbf{M}}_\perp] {\cal D}[\hat{\mathbf{M}}_\parallel] \ \exp \left(S_G+\int {\hspace{-0ex}\mathrm{d}{t}\;} \ \boldsymbol{\lambda} \cdot \mathbf{M} \right) \; ,$$ where we neglected all trivial constant factors, with an action $S_G$ that reads $$S_G= \widetilde S_{G,{\rm det}} + \widetilde S_{G, {\rm diss}} + S_{{\rm jac}}\;,$$ and $$\begin{aligned} && \widetilde S_{G,{\rm det}} = \ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)] + \int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf M}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \nonumber\\ &&\qquad\qquad + \int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \left({\rm D}^{(\alpha)}_t{\mathbf{M}} + \gamma_0 \mathbf{M} \wedge \mathbf{H}_{\rm eff} \right) \; , \;\;\;\;\;\;\;\;\; \\ && \widetilde S_{G,{\rm diss}} = \int {\hspace{-0em}\mathrm{d}{t}\;} \left({{\rm i}}\hat{\mathbf{M}}_\perp \wedge {\mathbf{M}}\right) \cdot \left( D \gamma_0^2 \ {{\rm i}}\hat{\mathbf{M}}_\perp \wedge {\mathbf{M}} - \frac{\eta\gamma_0}{M_{{\rm s}}} {\rm D}^{(\alpha)}_t{\mathbf{M}} \right) \; , \label{eq:S_diss_cart} \qquad \\ && S_{\rm jac} = \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {\hspace{-0em}\mathrm{d}{t}\;} \Big{\{} \frac{2 \eta\gamma_0}{M_{{\rm s}}} \ \mathbf{M} \cdot \mathbf{H}_{\rm eff} \nonumber\\ && \qquad\qquad\qquad + \Big{[}\frac{\eta\gamma_0}{M_{{\rm s}}} (M_i M_j - \delta_{ij} M_{{\rm s}}^2) +\epsilon_{ijk} M_k) \Big{]} \partial_j {H_{\rm eff}}_i \Big{\}} \; . \;\;\;\;\;\; \label{eq:Sjac-cart}\end{aligned}$$ For reasons that should become clear when reading Sec. \[sec:Landau2Gilbert\], we perform the change of (dummy) auxiliary fields from ${{\rm i}}\hat{\mathbf{M}}_\perp$ to ${{\rm i}}\hat{\mathbf{M}}_\perp '\equiv {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} \ M_{{\rm s}}^{-1}$. The Jacobian of this change of variables is a constant and the action functional now reads $S_G= S_{G,{\rm det}} + S_{G, {\rm diss}} + S_{{\rm jac}}$ with $$\begin{aligned} S_{G, {\rm det}} &= \ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)] + \int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf M}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \nonumber\\ & \qquad + \int\! {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \! \left( \frac{1}{M_{{\rm s}}} {\rm D}^{(\alpha)}_t{\mathbf{M}} \wedge {\mathbf M} + \gamma_0 M_{{\rm s}}\ \mathbf{H}_{\rm eff} \right) \label{eq:S_det_cart-redef} \ , \\ S_{G, {\rm diss}} &= \int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}} _\perp \cdot \left( D \gamma_0^2 M_{{\rm s}}^2 \ {{\rm i}}\hat{\mathbf{M}}_\perp - \eta\gamma_0 {\rm D}^{(\alpha)}_t{\mathbf{M}} \right) \; , \label{eq:S_diss_cart-redef}\end{aligned}$$ where we used the identity ${{\rm i}}\hat{\mathbf{M}}_\perp \cdot {\rm D}_t^{(\alpha)}{\mathbf{M}} = - ({{\rm i}}\hat{\mathbf{M}}_\perp \wedge \mathbf{M}) \cdot (\mathbf{M} \wedge {\rm D}_t^{(\alpha)} {\mathbf{M}}) M_{{\rm s}}^{-2}$ and we dropped the prime: ${{\rm i}}\hat{\mathbf{M}}_\perp' \mapsto {{\rm i}}\hat{\mathbf{M}}_\perp$. $S_{\rm jac}$ is unchanged. In Sec. \[sec:Landau2Gilbert\] we presented the action functional given by the sum of the terms in Eqs. (\[eq:Sjac-cart\]), (\[eq:S\_det\_cart-redef\]) and (\[eq:S\_diss\_cart-redef\]) and we showed that it can be taken to the Landau form by a suitable change of the auxiliary field. We prove in this way that the functional representations of the Landau and Gilbert formulation of the stochastic dynamics are totally equivalent. Spherical coordinate conventions {#app:conventions} ================================ We are using the spherical coordinate system in which $\theta$ the polar angle, $\theta\in[0,\pi]$, and $\phi$ the azimuthal angle, $\phi \in [0,2\pi]$. The local orthogonal unit vectors are ${\mathbf e}_\mu = (\mathbf{e}_{M_{{\rm s}}}, \mathbf{e}_\theta, \mathbf{e}_\phi)$. The link to the Cartesian basis is given by $$\begin{aligned} M_x=M_{{\rm s}}\, \sin\theta \, \cos\phi \; , \qquad\quad M_y=M_{{\rm s}}\, \sin\theta \, \sin\phi \; , \qquad\quad M_z=M_{{\rm s}}\, \cos\theta \; .\end{aligned}$$ We use Latin indices to label Cartesian coordinates ($i=x,y,z$) while Greek indices refer to the local basis ($\mu = M_{{\rm s}},\theta,\phi$). The rotation matrix linking Cartesian to local coordinates, ${\mathbf e}_\mu = R_{\mu i } {\mathbf e}_i$, is $$R_{\mu i}(\mathbf{M}) = R_{\mu i}(\theta,\phi) = \begin{array}{cc} \left[ \begin{array}{ccc} \sin\theta\cos\phi & \sin\theta\sin\phi & \cos\theta \\ \cos\theta\cos\phi & \cos\theta\sin\phi & -\sin\theta \\ -\sin\phi & \cos\phi & 0 \end{array} \right] \end{array} \label{eq:rotation-matrix}$$ with $R_{\alpha i} R_{\beta i } = \delta_{\alpha\beta}$. Notice that $\mathrm{det} R = 1$ and $R^{-1} = \ ^t\!R$: $$R^{-1}_{i\mu}(\mathbf{M}) = R^{-1}_{i \mu}(\theta,\phi) = \begin{array}{cc} \left[ \begin{array}{ccc} \sin\theta\cos\phi & \cos\theta\cos\phi & -\sin\phi \\ \sin\theta\sin\phi & \cos\theta\sin\phi & \cos\phi \\ \cos\theta & -\sin\theta & 0 \end{array} \right] \; . \end{array} \label{eq:inverse-rotation-matrix}$$ and $R^{-1}_{i\alpha} R^{-1}_{i\beta} = \delta_{\alpha\beta}$. The following properties are useful $$\begin{aligned} && R_{\mu j} \frac{\partial R^{-1}_{j\rho} }{\partial \theta} = - \delta_{\mu M_{{\rm s}}} \delta_{\rho \theta} + \delta_{\mu\theta} \delta_{\rho M_{{\rm s}}} \; , \nonumber\\ && R_{\mu j} \frac{\partial R^{-1}_{j\rho} }{\partial \phi} = - \sin \theta \delta_{\mu M_{{\rm s}}} \delta_{\rho \phi} -\cos \theta \delta_{\mu\theta} \delta_{\rho \phi} + \sin\theta \delta_{\mu \phi} \delta_{\rho M_{{\rm s}}} + \cos \theta \delta_{\mu\phi} \delta_{\rho \theta} \; . \qquad\;\;\;\;\; \nonumber\end{aligned}$$ \[app:deltafunction\] The delta function is not a scalar in the sense that it transforms non-trivially under coordinate transformations. This can be simply seen by considering the property $$1 = \int{\hspace{-0em}\mathrm{d}{\mathbf{x}}\;} \delta^3(\mathbf{x}-\overline{\mathbf{x}})\;,$$ which after a coordinate change to the spherical basis reads $$1 = \int{\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} \delta^3(\mathbf{x}(M_{{\rm s}},\theta,\phi)-\mathbf{x}(\overline M_{{\rm s}},\overline \theta,\overline\phi))\;,$$ The measure is ${\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} = M_{{\rm s}}^2 \sin\theta \ {{\rm d}}M_{{\rm s}}\, {{\rm d}}\theta\, {{\rm d}}\phi$. The integrals run over $M_{{\rm s}}\geq 0$, $\theta\in[0,\pi]$ and $\phi\in [0, 2\pi]$. $\mathbf{x}(M_{{\rm s}},\theta,\phi)$ and $\mathbf{x}(\overline M_{{\rm s}},\overline\theta,\overline\phi)$ are the expressions for $\mathbf{x}$ and $\overline{\mathbf{x}}$ in terms of the spherical coordinates. Using the identity $$\delta(\mathbf{x}(M_{{\rm s}},\theta,\phi)-\mathbf{x}(\overline M_{{\rm s}},\overline\theta,\overline\phi)) = \left|\det_{i\mu} \frac{\partial \Omega_\mu}{\partial x_i}\right| \delta(M_{{\rm s}}-\overline M_{{\rm s}}) \delta(\theta-\overline\theta) \delta(\phi-\overline\phi)\;,$$ we get $$\begin{aligned} 1 &=& \int {\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} \frac{1}{M_{{\rm s}}^2 \sin \theta} \delta(M_{{\rm s}}-\overline M_{{\rm s}}) \delta(\theta-\overline\theta) \delta(\phi-\overline\phi) \nonumber\\ &=& \int\ {{\rm d}}M_{{\rm s}}{{\rm d}}\theta {{\rm d}}\phi \ \delta(M_{{\rm s}}- \overline M_{{\rm s}}) \delta(\theta - \overline\theta) \delta(\phi-\overline\phi) \; . \label{eq:delta-spherical-Jacobian}\end{aligned}$$ \[app:metric\] If $x_i$ are the Cartesian coordinates of the vector $\mathbf{x}$ and $x_\mu$ the coordinates of the same vector in another coordinate system, the Jacobian matrix of the coordinate change is $$\begin{aligned} J_{i\mu} \equiv \frac{\partial x_i}{\partial x_\mu} \; , \label{eq:Jacobian-matrix}\end{aligned}$$ and the Jacobian of the transformation is $ \mathcal{J} \equiv \det_{i\mu} J_{i\mu} $. We relate the derivatives with respect to Cartesian coordinates to those with respect to spherical coordinates as $$\partial_i = \frac{\partial x_\mu}{\partial x_i} \ \partial_\mu = J^{-1}_{\mu i} \ \partial_\mu \; .$$ For the vector ${\mathbf M}$ transformed to spherical coordinates, the Jacobian matrix (\[eq:Jacobian-matrix\]) reads $$\begin{aligned} J_{i\nu} = \left[ \begin{array}{ccc} \cos\phi\sin\theta & M_{{\rm s}}\cos\phi\cos\theta & -M_{{\rm s}}\sin\phi\sin\theta \\ \sin\phi\sin\theta & M_{{\rm s}}\sin\phi\cos\theta & M_{{\rm s}}\cos\phi\sin\theta \\ \cos\theta & -M_{{\rm s}}\sin\theta & 0 \end{array} \right]\end{aligned}$$ for $i=x,y,z$ and $\mu=M_{{\rm s}},\theta,\phi$. With spherical coordinates, the integration measure is understood as $$\begin{aligned} \int{\mathcal{D}}{[\mathbf{\Omega}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{M_{{{\rm s}}\,n}}\;} {\hspace{-0ex}\mathrm{d}{\theta_n}\;} {\hspace{-0ex}\mathrm{d}{\phi_n}\;} M_{{{\rm s}}\, n}^2 \, |\sin\theta_n| \;.\end{aligned}$$ Chain rule in spherical coordinates {#sec:chain-rule-sph} =================================== The matrices introduced in App. \[app:metric\] and the properties listed above allow one to derive the chain rule in spherical coordinates from the one in Cartesian coordinates, $$\begin{aligned} \label{eq:cr1} {{\rm d}}_t & = {{{\rm d}}_t} M_i \ \partial_i + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left(M_{{\rm s}}^2 \delta_{ij} - M_i M_j \right) \, \partial_i \partial_j \;.\end{aligned}$$ The first term can be re-written as $$\begin{aligned} {{{\rm d}}_t} M_i \ \partial_i & = {{{\rm d}}_t} M_i \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma} = \left[ -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_i + g_{ij} \overline H_j \right] \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma} \nonumber \\ & = -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}} + R_{i\mu} g_{\mu\nu} \overline H_\nu \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma} \nonumber \\ & = -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}} + \frac{1}{M_{{\rm s}}} \left( g_{\theta \nu_\perp} \overline H_{\nu_\perp} \partial_\theta + \frac{1}{\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \partial_\phi \right) \;, \nonumber\end{aligned}$$ where in the second line we introduced the equation of motion in Cartesian coordinates, in the third line we used $M_i \partial_i = M_{{\rm s}}\partial_{M_{{\rm s}}}$ and $g_{ij} \overline H_j = R_{i\mu} g_{\mu\nu} \overline H_\nu$, and in the last line we used the fact that $g_{M_{{\rm s}}\mu} = g_{\mu M_{{\rm s}}} = 0$. To shorten the notation we called $\overline {\mathbf H} = {\mathbf H}_{\rm eff} + {\mathbf H}$. In order to treat the second term of Eq. (\[eq:cr1\]), we notice that $$\begin{aligned} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j ) \partial_i \partial_j &= M_{{\rm s}}^2 \nabla^2 - M_i M_j \, \partial_i \partial_j \;, \nonumber\end{aligned}$$ with $\nabla^2$ the Laplacian operator in spherical coordinates $$\begin{aligned} \nabla^2 = \frac{1}{M^2_{{\rm s}}} \left( M_{{\rm s}}^2 \partial^2_{M_{{\rm s}}} + 2 M_{{\rm s}}\partial_{M_{{\rm s}}} + \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \;.\end{aligned}$$ We also have $$\begin{aligned} M_i M_j \, \partial_i \partial_j &= M_{{\rm s}}\ M_i \frac{\partial}{\partial M_{{\rm s}}} \partial_{i} = M_{{\rm s}}\ M_i \frac{\partial}{\partial M_{{\rm s}}} \left[ J^{-1}_{\sigma i} \frac{\partial}{\partial\Omega_\sigma} \right] \nonumber \\ & = M_{{\rm s}}\ M_i J^{-1}_{\sigma i} \ \frac{\partial^2}{\partial M_{{\rm s}}\partial\Omega_\sigma} + M_{{\rm s}}\ M_i \ \partial_{M_{{\rm s}}} J^{-1}_{\sigma i} \ \frac{\partial}{\partial\Omega_\sigma} \nonumber \\ & = M^2_{{\rm s}}\ \frac{\partial^2}{\partial M_{{\rm s}}^2} = M_{{\rm s}}^2 \ \partial^2_{M_{{\rm s}}}\;,\end{aligned}$$ where in the first line we used $M_i \partial_i = M_{{\rm s}}\partial_{M_{{\rm s}}} $ and we later used $M_i J^{-1}_{\sigma i} = M_{{\rm s}}\delta_{\sigma M_{{\rm s}}}$ and $M_i \partial_{M_{{\rm s}}} J^{-1}_{\sigma i} = 0$ to obtain the last line. Therefore, the second term in Eq. (\[eq:cr1\]) reads $$\begin{aligned} \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2 \left( \nabla^2 - \partial_{M_{{\rm s}}}^2 \right)\;.\end{aligned}$$ Altogether the chain rule in spherical coordinates is given by $$\begin{aligned} \label{eq:cr2} {{\rm d}}_t & = \frac{1}{M_{{\rm s}}} \left( g_{\theta \nu_\perp} \overline H_{\nu_\perp} \partial_\theta + \frac{1}{\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \partial_\phi \right) \nonumber\\ & \;\;\;\;\; + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left( \cot\theta \ \partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right)\;.\end{aligned}$$ Applying this differential operator to $M_{{\rm s}}$, $\theta$ and $\phi$ respectively, we obtain $$\begin{aligned} {{\rm d}}_t M_{{\rm s}}&= 0\;, \\ {{\rm d}}_t \theta &= \frac{1}{M_{{\rm s}}} g_{\theta \nu_\perp} \overline H_{\nu_\perp} + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \;, \label{eq:equation1} \\ {{\rm d}}_t \phi &= \frac{1}{M_{{\rm s}}\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \; . \label{eq:equation2}\end{aligned}$$ We now define the covariant derivatives $$\begin{aligned} {\rm D}^{(\alpha)}_t(\theta) &\equiv {{\rm d}}_t \theta-\frac{D(1-2\alpha)\gamma_0^2}{(1+\eta^2\gamma_0^2)} \cot\theta \; , \label{eq:covDtheta2} \\ {\rm D}^{(\alpha)}_t(\phi) &\equiv {{\rm d}}_t \phi \;.\end{aligned}$$ and we reintroduce the equations of motion (\[eq:equation1\]) and (\[eq:equation2\]) in Eq. (\[eq:cr2\]) to re-write the differential operator as $$\begin{aligned} {{\rm d}}_t &= {\rm D}^{(\alpha)}_t(\theta) \partial_\theta + {\rm D}^{(\alpha)}_t(\phi) \partial_\phi + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \nonumber \\ &= {{\rm d}}_t \theta \ \partial_\theta + {{\rm d}}_t \phi \ \partial_\phi + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \;.\end{aligned}$$ We finally obtain an expression for the chain rule in spherical coordinates that is independent of the external and random fields $$\begin{aligned} {{\rm d}}_t &= \ {{\rm d}}_t \Omega_{\mu_\perp} \ \partial_{\Omega_{\mu_\perp}} + \ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta} \ \partial^2_\phi \right) \;.\end{aligned}$$ Determinants {#sec:determinants} ============ We will be confronted to the task of calculating the determinant of an operator of the form $$\delta_{ab} \delta(u-v) + C_{ab}(u,v) \label{eq:operator-form}$$ where $u$ and $v$ are times and $a$ and $b$ are coordinate labels in a generic coordinate system. Using the identity $$\det(1+C) = \exp \mbox{Tr}\ln (1+C) \label{eq:identity}$$ and expanding $\ln(1+C)$ one has $$\det(1+C) = \exp \ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} \int \ {\hspace{-0ex}\mathrm{d}{u}\;} \ \left\{ \underbrace{C \circ C \circ ... \circ C}_{n \ \mathrm{times}} \right\}_{\mu\mu}\!(u,u)$$ The symbol $\circ$ indicates a matrix product and a time convolution. Typically, $C$ will be proportional to the Heaviside Theta function, $C_{ab}(u,v)=\Theta(u-v) A_{ab}(u,v)$, hence causal. In regular cases, $A$ does not diverge within the time interval and causality ensures that the terms with $n>1$ vanish. This simplification does not necessarily apply to the cases we deal with since the matrix $A$ depends on the white noise ${\mathbf H}$ and, roughly speaking, two such factors together are proportional to a temporal Dirac-delta function [@Arnold2000; @Lubensky2007]. Accordingly, we need to analyze each order in the expansion separately to decide which ones yield non-vanishing contributions. Let us take $A_{ab}(u) = A^1_{ab}(u) + A^2_{abc}(u) H_c(u)$ where $A^1$ and $A^2$ do not depend on the random field. For concreteness, let us assume that the field $H_a$ has zero mean and correlations $\langle H_a(u) H_b(v) \rangle = 2D \delta_{ab} \delta(u-v)$. These are the $A$’s we will work with in this manuscript. The first order term, $n=1$, in the series is $$1\mbox{st} = \Theta(0) \int {{\rm d}}u \ [A^1_{aa}(u) + A^2_{aac}(u) H_c(u) ] \;.$$ The second order term, $n=2$, in the series is $$\begin{aligned} & 2\mbox{nd} = \int {{\rm d}}u \int {{\rm d}}v \ \Theta(u-v) \Theta(v-u) [A^1_{ab}(v) + A^2_{abc}(v) H_c(v) ] \nonumber\\ & \qquad\qquad \times [A^1_{ba}(u) + A^2_{bad}(u) H_d(u) ] \; . \end{aligned}$$ Because of the two Theta factors, the only non-vanishing contribution may come from $u=v$ if the integrand diverged at this point. Let us now assume that one can replace a single random field factor by its average and two random field factors by their correlations: $H_a(u) \to \langle H_a(u) \rangle = 0$ and $H_a(u) H_b(v) \to \langle H_a(u) H_b(v) \rangle = 2D \delta_{ab} \delta(u-v)$. An argument to justify this procedure is given below. Thus, $$\begin{aligned} 2\mbox{nd} & = \int {{\rm d}}u \int {{\rm d}}v \ \Theta(u-v) \Theta(v-u) \ 2D\delta_{cd} \delta(u-v) \ A^2_{abc}(v) A^2_{bad}(u) \nonumber\\ & = \Theta^2(0) \ 2D \int {{\rm d}}u \ A^2_{abc}(u) A^2_{bac}(u)\end{aligned}$$ This term is non-vanishing. What about higher order terms? Fortunately, they all vanish. For instance, the third order term is $$\begin{aligned} 3\mbox{rd} = & \int {{\rm d}}u \int {{\rm d}}v\int {{\rm d}}w \ \Theta(u-v) \Theta (v-w) \Theta(w-u) \nonumber\\ & \qquad \times [A^1_{ab}(v) + A^2_{abc}(v) H_c(v) ] \ [A^1_{bd}(w) + A^2_{bde}(w) H_e(w) ] \nonumber\\ & \qquad \times [A^1_{da}(u) + A^2_{daf}(u) H_f(u) ] \nonumber\\ =& \int {{\rm d}}u \int {{\rm d}}v\int {{\rm d}}w \ \Theta(u-v) \Theta (v-w) \Theta(w-u) \nonumber\\ & \qquad \times A^1_{ab}(v) 2D \delta_{ef} \delta(w-u) A^2_{bde}(w) A^2_{daf}(u) +\dots \nonumber\\ = & \int {{\rm d}}u \int {{\rm d}}v \ \Theta(u-v) \Theta (v-u) \Theta(0) \nonumber\\ & \qquad \times A^1_{ab}(v) 2D A^2_{bde}(w) A^2_{dae}(u) +\dots \nonumber\\ = & \;\; 0 \; . \end{aligned}$$ Similarly, one can prove that there are no further contributions to the series. In conclusion, $$\det(1+C) = \exp \mbox{Tr} \ln (1+C) = \exp [ \ \mbox{Tr}\ C - \frac{1}{2} \mbox{Tr}\ C^2 \ ] \label{eq:identity-random-field}$$ We now justify heuristically the replacement of the random field and product of two random fields, in the exponentials, by their averages. Given a generic functional of the random field, $F[{\mathbf H}]$, multiplied by an exponential of the kind $${{\rm e}}^{ -\frac{1}{2} \int \int {{\rm d}}t {{\rm d}}t' \ Q_{ab}(t,t') H_a(t) H_b(t') }$$ with $Q_{ab}(t,t')$ a generic symmetric matrix in the $ab$ indices and the times $t$ and $t'$, let us consider its average over random field histories distributed according to a normal Gaussian pdf $$P_{\rm n}[{\mathbf H}] \propto {{\rm e}}^{-\frac{1}{4D} \int \int {{\rm d}}t \ H^2_a(t) }$$ that we indicate with $\langle \dots \rangle_0$. We now evaluate the average as $$\begin{aligned} \mbox{Ave} = \langle F[\mathbf{H}] \ {{\rm e}}^{- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{ab}(t,t') \ H_a(t) H_b(t') } \rangle_0 \nonumber\end{aligned}$$ With a Taylor expansion of the exponential, $$\begin{aligned} \mbox{Ave} = & \sum_{n=0} \frac{1}{n !\!} \left( - \frac12 \right)^n \iint{\hspace{-0em}\mathrm{d}{t_1}\,\mathrm{d}{t'_1}\;} \ldots \iint{\hspace{-0em}\mathrm{d}{t_n}\,\mathrm{d}{t'_n}\;} Q_{a_1b_1}(t_1,t_1') \ldots Q_{a_nb_n}(t_n,t_n') \\ & \qquad \times \langle F[\mathbf{H} ] \ H_{a_1}(t_1) H_{b_1}(t_1') \ldots H_{a_n}(t_n)H_{b_n}(t_n') \rangle_0\end{aligned}$$ we set the calculation in a way that we can use Wick theorem. Since $Q_{ab}(t,t') = 0 $ for all $t\neq t'$, most of the contractions of the fields on the right side of the average vanish, except for the ones that set $t_i=t_i'$ for all $i=1,\dots, n$. Therefore, the only non-vanishing contributions should be of the form $$\begin{aligned} & \langle F[{\mathbf H}] \rangle_0 \ \langle H_{a_1}(t_1) H_{b_1}(t'_1) \rangle_0 \; \ldots \; \langle H_{a_n}(t_n) H_{a_n}(t_n')] \rangle_0 \\ & \qquad\qquad = \langle F[{\mathbf H}] \rangle_0 \ (2D)^n \ \delta_{a_1 b_1} \ldots \delta_{a_n b_n} \ \delta(t_1-t_1') \ldots \delta(t_n-t_n') \;.\end{aligned}$$ This can be re-exponentiated to recast the average as $$\begin{aligned} & \langle F[\mathbf{H} ] \ {{\rm e}}^{- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{ab}(t,t') H_a(t) H_b(t')} \rangle_0 = {{\rm e}}^{-D \int{\hspace{-0em}\mathrm{d}{t}\;} Q_{aa}(t,t)} \ \langle F[\mathbf{H}] \rangle_0 \;. \end{aligned}$$ In short, the result of the calculation is equivalent to the replacement $$H_a(t) H_b(t') \to \langle H_a(t) H_b(t')\rangle_0$$ in the exponential. This argument can be easily generalized to the case in which the random field has a non-zero average. The line of reasoning followed in this Section is close in spirit to the one consider in [@Arnold2000]. A different but equivalent approach has been discussed in [@Lubensky2007] (see also [@Tirapegui-comment]). We remark, nevertheless, that we have not used the invertibility of the diffusion matrix $g$ as our $g$ is actually not invertible. Random field in spherical coordinates {#app:rotation-noise} ===================================== The probability distribution of the random field components, in the Cartesian coordinate system, is given by $$P_\mathrm{n}[H_x,H_y,H_z] \propto \exp\left\{-\frac{1}{4D} \int{} {\hspace{-0em}\mathrm{d}{t}\;} \left[ H_x(t)^2+ H_y(t)^2 + H_z(t)^2 \right] \right\}\;.$$ The rotation to the spherical coordinate system, $$\begin{aligned} P^{\rm sph}_{\rm n}[H_{M_{{\rm s}}}, H_\theta, H_\phi] = |\mathcal{J}^{\rm rot}| \ P_\mathrm{n}[R^{-1}_{x\mu} H_\mu,R^{-1}_{y\mu} H_\mu,R^{-1}_{z\mu} H_\mu]\;,\end{aligned}$$ involves the Jacobian $$\begin{aligned} \label{eq:Jacobian-rot-app} \mathcal{J}^{\rm rot} &\!\! \equiv \!\! & \mathrm{det}_{i\nu,tt'} \frac{\delta R^{-1}_{i\mu}(t) H_\mu(t)}{\delta H_\nu(t')} \; . \end{aligned}$$ The Jacobian ${\cal J}^{\rm rot}$ --------------------------------- A series of simple operations allow us to factorize the Jacobian of the change of basis from Cartesian to spherical, ${\cal J}^{\rm rot}$ defined in Eq. (\[eq:Jacobian-rot-app\]), in two factors: $$\begin{aligned} \mathcal{J}^{\rm rot} & \!\!\! = \!\! & \mathrm{det}_{i\nu,tt'} \left[ R^{-1}_{i\nu}(t) \delta(t-t') + \frac{\delta R^{-1}_{i\mu}(t)}{\delta H_\nu(t')} H_\mu(t) \right] \nonumber\\ &\!\!\! = \!\! & \mathrm{det}_{i\mu,tt''} \left[ R^{-1}_{i\mu}(t)\delta(t-t'') \right] \nonumber\\ && \qquad\qquad \times \ \mathrm{det}_{\mu\nu,t''t'} \left[ \delta_{\mu\nu}\delta(t''-t') + R_{\mu j}(t'') \frac{\delta R^{-1}_{j\rho}(t'')}{\delta H_\nu(t')} H_\rho(t'') \right]\;, \nonumber\end{aligned}$$ that we can now compute since the first term is identical to one and the second one takes the form in Eq. (\[eq:operator-form\]) with $$C_{\mu\nu}(t,t') \equiv R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} H_\rho(t) \; .$$ The factor $\frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')}$ is proportional to $\Theta(t-t')$. Due to the random field dependence in $C$ we need to use the result in (\[eq:identity-random-field\]) to express the determinant [@Arnold2000; @Lubensky2007]. The first term in the sum, $n=1$, is $$\begin{aligned} \ln \mathcal{J}^{\rm rot}_1 = \exp \int{\hspace{-0ex}\mathrm{d}{t}\;} R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\mu(t)} H_\rho(t) = \int{\hspace{-0ex}\mathrm{d}{t}\;} L_\rho(t) H_\rho(t) \; .\end{aligned}$$ The rotation matrix $R^{-1}_{j\rho}$ is a function of $\theta$ and $\phi$ (not of $M_{{\rm s}}$) and neither $\theta$ nor $\phi$ depend on the radial component of the noise $H_{M_{{\rm s}}}$. Therefore $$\begin{aligned} \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} \Rightarrow \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_\nu} \frac{\delta\Omega_\nu(t)}{\delta H_\mu(t)} = \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu_\perp}(t')} \end{aligned}$$ and $$\begin{aligned} L_\rho(t) = R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta\Omega_{\tau_\perp}(t)}{\delta H_\mu(t)} \; . \end{aligned}$$ The second term in the series, $n=2$, reads $$\begin{aligned} \ln {\cal J}_2^{\rm rot} = & -\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} H_\rho(t) R_{\nu k}(t') \frac{\delta R^{-1}_{k\sigma}(t')}{\delta H_\mu(t)} H_\sigma(t') \nonumber\\ = & -\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') H_\rho(t) H_\sigma(t')\end{aligned}$$ with $$Q_{\rho\sigma}(t,t') \equiv R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu}(t')} R_{\nu k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu}(t)} \; .$$ Random field distribution {#app:randomfield} ------------------------- Let us now collect all terms together in a compact notation such that the probability distribution of the random field reads $$\begin{aligned} \ln P^{\rm sph}_{\rm n}[H_\mu] =& -\frac{1}{4D} \int {\rm d} t \ H^2_\mu(t) + \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu(t) H_\mu(t) \nonumber\\ &- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') H_\rho(t) H_\sigma(t') \label{eq:pnoise1} \; ,\end{aligned}$$ that vanishes for $t' \neq t$ because of the response functions involved in its expression. Therefore, the integrand of the last integral above vanishes for $t\neq t'$ but the integral may still yield a non- trivial contribution at $t=t'$ due to the presence of the two random field factors (which are delta correlated). The quadratic weight can be given a usual form by completing the square between the first two terms under the integral $$\begin{aligned} && - \frac{1}{4D} H_\mu^2(t) + L_\mu(t) H_\mu(t) = - \frac{1}{4D} \left[ H_\mu(t) - 2D L_\mu(t) \right]^2 + D \ L^2_\mu(t),\end{aligned}$$ and the measure can be recast as $$\begin{aligned} && \ln P^{\rm sph}_{\rm n}[H_\mu] = \ln P^{{\rm sph},0}_{\rm n }[H_\mu] + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t) \nonumber\\ && \qquad\qquad\qquad - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \, H_\rho(t) H_\sigma(t')\end{aligned}$$ where we singled out the conventional Gaussian part of the measure $$\begin{aligned} \ln P^{{\rm sph},0}_{\rm n}[H_\mu] \equiv -\frac{1}{4D} \int {\rm d} t \ [H_\mu(t) - 2D L_\mu(t)]^2 \;. \end{aligned}$$ We now rewrite the last term in a way that the noises appear as $H_\rho(t) - 2D L_\rho(t)$. This rewriting introduces two new terms, one that is linear in $H_\rho(t) - 2D L_\rho(t)$, another one in which this factor does not appear: $$\begin{aligned} && - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ H_\rho(t) H_\sigma(t') \nonumber\\ && \qquad = - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ [H_\rho(t) - 2D L_\rho(t)] [H_\sigma(t') -2D L_\sigma(t')] \nonumber\\ && \qquad\;\;\;\; + \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ 2D L_\rho(t) [H_\sigma(t') -2D L_\sigma(t')] \nonumber\\ && \qquad\;\;\;\; - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ 2D A_\rho(t)2D L_\sigma(t')\end{aligned}$$ The last term vanishes identically since $Q_{\rho\sigma}(t,t')$ is equal to zero for $t\neq t'$ and the accompanying factors do not diverge. A similar argument can be applied to the second term as two factors $H_\rho(t)-2D L_\rho(t)$ are needed to get a divergence in the integrand. The noise pdf then reads $$\begin{aligned} && \ln P^{\rm sph}_{\rm n}[H_\mu] = \ln P^{{\rm sph},0}_{\rm n }[H_\mu] + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t) \nonumber\\ && \qquad\qquad - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ [H_\rho(t) -2DL_\rho(t)] [H_\sigma(t') - 2D L_\sigma(t')] \; . \end{aligned}$$ We conclude that the probability density of the random field is $$\begin{aligned} && \ln P^{\rm sph}_{\rm n}[H_\mu] = -\frac{1}{4D} \int {\rm d} t \ [H_\mu(t) - 2D L_\mu(t)]^2 + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t) \nonumber\\ && \qquad\qquad\qquad - D \int {\rm d} t \ Q_{\rho\rho}(t,t) \; . \end{aligned}$$ After a lengthy computation that uses the properties mentioned in App. \[app:conventions\] and the equal-time responses calculated in the main part of the text, Eqs. (\[eq:equal-time1\])-(\[eq:equal-time4\]), one derives $$L_\mu^2(t) = \frac{\alpha^2 \gamma_0^2 }{1+\eta^2\gamma_0^2} \left[ \frac{4\eta^2\gamma_0^2}{1+\eta^2\gamma_0^2} + \cot^2\theta(t) \right]\;, \label{eq:Acuadrado}$$ and $$\begin{aligned} & Q_{\rho\rho}(t,t) \nonumber\\ & \qquad = \left [\left( \frac{\delta \theta}{\delta H_\theta} \right)^2 + 2 \sin\theta \frac{\delta \theta}{\delta H_\phi} \frac{\delta \phi}{\delta H_\theta} + \left( \frac{\delta \phi}{\delta H_\phi} \right)^2 + \cos^2\theta \left( \frac{\delta \phi}{\delta H_\theta} \right)^2 \right] \nonumber\\ & \qquad = \frac{\alpha^2\gamma_0^2 }{1+\eta^2\gamma_0^2} \cot^2\theta +\dots\end{aligned}$$ with the dots being just constant terms. Therefore, apart from irrelevant additive constants we establish that $$\begin{aligned} L_\mu^2(t) =Q_{\rho\rho}(t,t) = \frac{\alpha^2 \gamma_0^2}{1+\eta^2\gamma_0^2} \cot^2\theta(t) \;. \label{eq:Acuadrado} \end{aligned}$$ In the end, the measure is $$P_{\rm n}^{\rm sph}[H_\mu] \propto \exp \left\{ -\frac{1}{4D} \int{\hspace{-0em}\mathrm{d}{t}\;} [H_\mu(t) - 2D L_\mu(t)]^2 \right\} \; .$$ One concludes that the random fields remain delta correlated but they acquire a mean-value in the spherical basis. It is also quite clear that the radial and angular sectors decouple: $$\begin{aligned} P_{\rm n}^{\rm sph}[H_\mu] \propto P_{\rm n}^{\rm sph}[H_{M_{{\rm s}}}] \ P_{\rm n}^{\rm sph}[H_{\mu_\perp}] \; . \end{aligned}$$ As the equations of motion do not depend on the longitudinal noise the first term is irrelevant in the context of the LLG equation. The explicit form of the perpendicular sector of the random field distribution is $$\begin{aligned} P_{\rm n}^{\rm sph}[H_{\mu_\perp}] \propto & \ \exp \int{\hspace{-0em}\mathrm{d}{t}\;} \left\{ -\frac{1}{4D} H^2_{\mu_\perp}(t) + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta(t) \ [\eta\gamma_0 H_\theta(t) + H_\phi(t) ] \right. \nonumber\\ & \left. \qquad\qquad\qquad - \frac{\alpha^2\gamma_0^2 D}{1+\eta^2 \gamma_0^2} \cot^2\theta(t) \right\} \; . \label{eq:Pn-random-noise-sph}\end{aligned}$$ The Jacobian ${\cal J}_L^{\rm sph}$ {#app:MSRDJ-Jacobian-Gus} =================================== We compute here the Jacobian needed for the construction of the generating functional in the spherical Landau formalism used in Sec. \[sec:contruct\_spherical\]. $$\begin{aligned} \label{eq:defjac2} \mathcal{J}_L^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv \det_{\mu\nu;uv} \begin{array}{c} \displaystyle \frac{\delta {\rm{Eq}}_{L \mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)} \end{array} \; , \end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$. From its definition one has $$\begin{aligned} \mathcal{J}_L^{\rm sph}[\mathbf{\Omega},\mathbf{H}] & = \det_{uv} \left[ {\rm d}_u \delta_{u-v} \right] \ \det_{\mu_\perp\nu_\perp;uv} \frac{\delta \mbox{Eq}_{L \mu_\perp}(M_{{\rm s}},\theta,\phi;u)}{\delta {\nu_\perp}(v)} \nonumber\\ & = \displaystyle \det_{uv} \left[ {\rm d}_u \delta_{u-v} \right] \ \det_{\nu_\perp\nu_\perp;uw} [\delta_{\mu_\perp \nu_\perp} {{\rm d}}_u \delta_{u-w} ] \nonumber\\ & \qquad \times \det_{\nu_\perp\nu_\perp;wv} [\delta_{\mu_\perp \nu_\perp} \delta_{w-v} + \Theta(w-v) A_{\mu_\perp\nu_\perp}(v) ]\end{aligned}$$ with $$\begin{aligned} && A_{\theta\theta}(v) = \frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i)\right] \; , \nonumber\\ && A_{\theta\phi}(v) = - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \partial_\phi \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \; , \nonumber\\ && A_{\phi\theta}(v) = - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} \left[ \partial_\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) \right. \nonumber\\ && \qquad\qquad\qquad\qquad\qquad\qquad \left. - \cot\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i}\right) \right] (H_{{\rm eff},i} + H_i) \; , \nonumber\\ && A_{\phi\phi}(v) = - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \; . \nonumber\end{aligned}$$ The first two factors contribute irrelevant constants. The last one can be treated with the identity (\[eq:identity\]) where the time-dependent $2\times 2$ matrix with entries is $C_{\mu_\perp\nu_\perp}(w,v)=\Theta(w-v) A_{\mu_\perp\nu_\perp}(v)$. The causal character of $C$ cuts the expansion at its second order. The first contribution is $\mbox{Tr}\ C = A_{\theta\theta}+A_{\phi\phi}$, $$\begin{aligned} \mbox{Tr} \ C &=& \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \right. \nonumber\\ && \left. \qquad\qquad\qquad\;\;\; - \frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \right] \; .\end{aligned}$$ The second order term is given by $\mbox{Tr}\ C^2 /2= (A^2_{\theta\theta}+2A_{\theta\phi} A_{\phi\theta} + A^2_{\phi\phi})/2$. Keeping only the terms that are proportional to two random fields, and using $H_i(t) H_j(t') \to \langle H_i(t) H_j (t') \rangle = 2 D \delta_{ij} \delta(t-t')$, see App. \[sec:determinants\], $$\begin{aligned} && \mbox{Tr} \ C^2 = \frac{2D\alpha^2\gamma_0^2}{(1+\eta^2\gamma_0^2)^2} \int {{\rm d}}t \ \Big{\{} [ \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) ]^2 \qquad \nonumber\\ && \qquad\qquad\qquad + \frac{1}{\sin^2\theta} [\partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right)]^2 + 2 \ \partial_\phi \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) \nonumber\\ && \qquad\qquad\qquad\qquad \times \left. \frac{1}{\sin\theta} \left[ \partial_\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) - \cot\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i}\right) \right] \right\} \qquad \nonumber\\ && \qquad = \mbox{cst} - \frac{2D\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \ \frac{1}{\sin^2\theta} \; . \end{aligned}$$ The two terms together yield $$\begin{aligned} {\mathcal J}_L^{\rm sph} &=& \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \ \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \right. \nonumber\\ && \left. \qquad\qquad\qquad\;\;\; - \frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i) \right] \nonumber\\ && + \frac{D\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \ \frac{1}{\sin^2\theta} \;. \end{aligned}$$ The first and last terms combine to yield a contribution proportional to $\alpha(1-\alpha)/\sin^2\theta$ and $$\begin{aligned} && {\mathcal J}_L^{\rm sph} = \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \left\{ \frac{D(1-\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta [ (H_{{\rm eff},\phi} + H_{\phi}) + \eta\gamma_0 (H_{{\rm eff},\theta} + H_{\theta}) ] \right. \nonumber\\ && \left. \qquad\qquad\qquad\qquad\qquad - \frac{1}{\sin\theta} \partial_\phi [ \eta\gamma_0 (H_{{\rm eff},\phi} + H_\phi) - (H_{{\rm eff},\theta} + H_\theta) ] \right\} \; . \end{aligned}$$ Gilbert spherical generating functional {#sec:construct_spherical_Gilbert} ======================================= We here construct the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ by imposing the equations of motion in the Gilbert formulation $$\begin{aligned} \mbox{Eq}^{\rm sph}_{G,M_{{\rm s}}} &\equiv {\rm d}_t M_{{\rm s}}= 0 \; , \label{eq:Ms-Gilbert-app} \\ \mbox{Eq}^{\rm sph}_{G,\theta} &\equiv {\rm D}^{(\alpha)}_t(\theta) + \eta\gamma_0 \ \sin \theta \ {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 \left( H_{{\rm{eff}}, \phi} + H_\phi \right) = 0 \; , \label{eq:thetaalpha-Gilbert-app} \\ \mbox{Eq}^{\rm sph}_{G,\phi} &\equiv - \sin\theta\, {\rm D}^{(\alpha)}_t(\phi) + \eta\gamma_0 \ {\rm D}^{(\alpha)}_t(\theta) -\gamma_0 \left( H_{{\rm{eff}}, \theta} + H_\theta \right) =0 \; . \label{eq:phialpha-Gilbert-app} \end{aligned}$$ The Jacobian $$\begin{aligned} \label{eq:defjac4} \mathcal{J}_G^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv \det_{\mu\nu;uv} \begin{array}{c} \displaystyle \frac{\delta {\rm{Eq}}^{\rm sph}_{G\mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)} \end{array} \; , \end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$, reads $$\begin{aligned} \mathcal{J}_G^{\rm sph} [\mathbf{\Omega},\mathbf{H}] & = \det_{uv} \left[ {\rm d}_u \delta_{u-v} \right] \nonumber\\ & \displaystyle \;\;\; \;\;\; \times \det_{\mu_\perp\nu_\perp;uv} \left[ X_{\mu_\perp\nu_\perp}(u) {\rm d}_u \delta_{u-v} + A_{\mu_\perp\nu_\perp}(u) \delta_{u-v} \right] \; . \nonumber\end{aligned}$$ The first factor is due to the $M_{{\rm s}}$ diagonal element and it can only yield a constant contribution. We next focus on the second factor. $$\begin{aligned} {\cal J}_G^{\rm sph} \displaystyle & \propto \det_{\mu_\perp\rho_\perp;uw} \left[ X_{\mu_\perp\rho_\perp}(u) {\rm d}_u \delta_{u-w} \right] \nonumber\\ & \qquad \times \det_{\mu_\perp\rho_\perp;wv} \left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v) A_{\sigma_\perp\nu_\perp}(v) \right] \nonumber\\ & \displaystyle = \det_{\mu_\perp \nu_\perp; uv} [X_{\mu_\perp \nu_\perp}(u)\delta (u-v)] \det_{\nu_\perp \rho_\perp; vw}[ \delta_{\nu_\perp \rho_\perp} {\rm d}_v\delta(v-w)] \nonumber\\ & \qquad \times \det_{\mu_\perp\rho_\perp;wv} \left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v) A_{\sigma_\perp\nu_\perp}(v) \right] \nonumber\\ & \displaystyle \propto \det_{\mu_\perp \nu_\perp; u,v} [X_{\mu_\perp \nu_\perp}(u)\delta (u-v)] \nonumber\\ & \qquad \times \det_{\mu_\perp\rho_\perp;wv} \left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v) A_{\sigma_\perp\nu_\perp}(v) \right] \;, \label{eq:factorized-jac}\end{aligned}$$ with $$\begin{aligned} X_{\mu_\perp\nu_\perp}(u) & \equiv \left[ \begin{array}{cc} 1 & \eta\gamma_0 \sin\theta_u \\ \eta\gamma_0 & -\sin\theta_u \end{array} \right]\;, \\ { X^{\,-1}_{\mu_\perp\nu_\perp}}(v) & \equiv \displaystyle \frac{1}{1+\eta^2\gamma_0^2} \left[ \begin{array}{cc} 1 & \eta\gamma_0\\ \displaystyle \frac{\eta\gamma_0}{\sin\theta_v} & \displaystyle -\frac{1}{\sin\theta_v} \end{array} \right]\;,\end{aligned}$$ and $$\begin{aligned} && A_{\theta\theta}= \frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta} - \gamma_0 \partial_\theta (H_{{\rm eff},\phi} +H_\phi) \\ && \qquad\qquad +\frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \left[ \eta\gamma_0 (H_{{\rm eff},\phi} +H_\phi) - (H_{{\rm eff},\theta} +H_\theta) \right] \; , \\ && A_{\theta\phi} = - \gamma_0 \partial_\phi (H_{{\rm eff},\phi} +H_\phi) \; , \\ && A_{\phi\theta} = + \eta\gamma_0 \ \frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta} - \gamma_0 \partial_\theta (H_{{\rm eff},\theta} +H_\theta) \\ && \qquad\qquad - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta \left[ \eta\gamma_0 (H_{{\rm eff},\phi} +H_\phi) - (H_{{\rm eff},\theta} +H_\theta) \right] \; , \\ && A_{\phi\phi} = - \gamma_0 \partial_\phi (H_{{\rm eff},\theta} +H_\theta) \; . \end{aligned}$$ where we used the equations of motion (\[eq:thetaalpha-Gilbert-app\]) and (\[eq:phialpha-Gilbert-app\]) to replace the occurrences of ${\rm D}_t^{(\alpha)}(\phi)$ by its corresponding expression in terms of the random field. Indeed, making explicit the random field dependence of the Jacobian is crucial as we shall see below. The absolute value of the first factor in Eq. (\[eq:factorized-jac\]) is $$\begin{aligned} & \Big{|} \det_{\mu_\perp \rho_\perp; uv} X_{\mu_\perp \rho_\perp}(u) \delta(u-v) \Big{|} = \prod_{n=0}^{N-1} | \sin\bar\theta_n |\;, \label{eq:detedete}\end{aligned}$$ where we were careful to evaluate the determinant factors on the intermediate points $\bar \theta_n \equiv \alpha \theta_{n+1} + (1-\alpha) \theta_n$. Notice indeed that the discretization matters here since there is no trivial continuous limit of this expression. See also the discussion in Sect. \[subsec:rules\]. The product above can be re-writen as $$\begin{aligned} \prod_{n=0}^{N-1} | \sin\bar\theta_n | = {{\rm e}}^{(1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| } \prod_{n=1}^{N} | \sin\theta_n | \;, \label{eq:detedetee45}\end{aligned}$$ where we used the development $$\begin{aligned} \sin\bar\theta_n = \alpha \sin \theta_{n+1} + (1-\alpha) \sin \theta_n\;,\end{aligned}$$ and the fact that we do not need to consider higher order terms because they vanish from Eq. (\[eq:detedete\]) once the limit $\delta t \to 0$ is considered. The product $\prod_{n=1}^{N} | \sin\theta_n |$ in Eq. (\[eq:detedetee45\]) cancels exactely the geometric one accompanying the delta functions in Eq. (\[eq:generatingZ24\]). In the following, we use this to drop it from the expressions. We treat the third factor in Eq. (\[eq:factorized-jac\]) with the identity (\[eq:identity\]) and we use the causality of $C_{\rho_\perp\nu_\perp}(w,v)=\Theta(w-v) X^{-1}_{\rho_\perp\sigma_\perp}(v) A_{\sigma_\perp\nu_\perp}(v)$ to keep only the first two terms of the expansion. Performing the contractions with $X^{-1}_{\rho_\perp\sigma_\perp}$ and dropping a constant term in the overall normalization, we obtain $$\begin{aligned} && \mbox{Tr} \ C = \alpha \int{\hspace{-0ex}\mathrm{d}{t}\;} X^{-1}_{\nu_\perp\sigma_\perp}(t) A_{\sigma_\perp\nu_\perp}(t) \nonumber\\ && \qquad\;\; = \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;} \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta (H_{{\rm eff},\phi} + H_{\phi}) \right. \nonumber\\ && \qquad\qquad\qquad\qquad\qquad \left. - \frac{\eta\gamma_0}{\sin\theta} \partial_\phi ( H_{{\rm eff},\phi} + H_\phi) -\eta\gamma_0 \partial_\theta ( H_{{\rm eff},\theta} + H_\theta) \right. \nonumber\\ && \qquad\qquad\qquad\qquad\qquad \left. + \frac{1}{\sin\theta} \partial_\phi ( H_{{\rm eff},\theta} + H_\theta) \right] \; . \end{aligned}$$ Note that the random field ${\mathbf H}$ is still present in this expression, as it was in the Cartesian framework calculation as well. The second order term in the expansion is a half of $$\mbox{Tr } C^2 = \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;} \Theta(t-t') \Theta(t'-t) X^{-1}_{\sigma_\perp \mu_\perp}(t) A_{\mu_\perp \nu_\perp}(t) X^{-1}_{\nu_\perp \rho_\perp}(t') A_{\rho_\perp \sigma_\perp}(t')$$ that making the sums over the $\perp$ components and using the explicit form of $X^{-1}$ reads $$\begin{aligned} \mbox{Tr } C^2 &= \frac{1}{(1+\eta^2\gamma_0^2)^2} \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;} \Theta(t-t') \Theta(t'-t) \nonumber \\ & \quad \times \Big{\{} \frac{1}{\sin\theta(t)} \left[ A_{\phi\phi}- \eta\gamma_0 A_{\theta\phi} \right](t) \frac{1}{\sin\theta(t')} \left[A_{\phi\phi}- \eta\gamma_0 A_{\theta\phi} \right](t') \nonumber\\ & \quad\quad + 2\frac{1}{\sin\theta(t)} \left[ \eta\gamma_0 A_{\phi\phi} + A_{\theta\phi} \right](t) \left[ \eta\gamma_0 A_{\theta\theta} -A_{\phi\theta}\right](t') \nonumber\\ & \quad\quad + \left[A_{\theta\theta} + \eta\gamma_0 A_{\phi\theta}\right](t) \left[A_{\theta\theta} + \eta\gamma_0 A_{\phi\theta} \right](t') \Big{\}} \nonumber \;. \end{aligned}$$ We now replace $A_{\mu_\perp\nu_\perp}$ by their explicit form. Since the two $\Theta$ functions make the integrand vanish for $t\neq t'$, the non-vanishing contributions can only come from divergent equal-time terms. Owing to the delta-correlated nature of the random field, we only keep the terms that are quadratic in the random field, see App. \[sec:determinants\]. We find $$\begin{aligned} & \mbox{Tr} \ C^2 = \frac{1}{(1+\eta^2\gamma_0^2)^2} \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;} \Theta(t-t') \Theta(t'-t) \ H_i(t) H_j(t') \nonumber \\ & \quad \times \left\{ \frac{\gamma_0}{\sin\theta(t)} \left[ \left( \partial_\phi R_{\theta i} + \eta\gamma_0 \partial_\theta R_{\phi i} \right) + \frac{\eta\gamma_0}{1+\eta^2\gamma_0^2}\cot\theta\left( \eta\gamma_0 R_{\phi i}- R_{\theta i}\right)\right](t) \right. \nonumber \\ & \quad \quad \times \frac{\gamma_0}{\sin\theta(t')} \left[\left( \partial_\phi R_{\theta j} + \eta\gamma_0 \partial_\theta R_{\phi j} \right) + \frac{\eta\gamma_0}{1+\eta^2\gamma_0^2}\cot\theta\left( \eta\gamma_0 R_{\phi j}- R_{\theta j}\right) \right](t') \nonumber\\ & \quad\quad - 2\frac{\gamma^2_0}{\sin\theta(t)} \left[ \eta\gamma_0\partial_\phi R_{\theta i} + \partial_\phi R_{\phi i} \right](t) \nonumber \\ & \qquad \qquad \times \left[ \cot\theta \left(\eta\gamma_0 R_{\phi j} - R_{\theta j} \right) + \left( \partial_\theta R_{\theta j} - \eta\gamma_0 \partial_\theta R_{\phi j} \right) \right](t') \nonumber\\ & \quad\quad + \eta^2\gamma_0^4 \left[ \partial_\theta R_{\theta i} + \partial_\theta R_{\phi i} \right](t) \left[\partial_\theta R_{\theta j} + \partial_\theta R_{\phi j} \right](t') \Big{\}} \; . \nonumber\end{aligned}$$ Following the same steps as in App. \[app:randomfield\], we now replace the product of random fields $H_i(t) H_j(t')$ by its average over the Gaussian measure, $2D \delta_{ij} \delta(t-t')$, see again App. \[sec:determinants\]. After a tedious but straightforward computation, dropping constant terms, we obtain $$\begin{aligned} -\frac{1}{2} \mbox{Tr } C^2 = \frac{D\gamma_0^2\alpha^2}{1+\eta^2\gamma_0^2} \int{\hspace{-0em}\mathrm{d}{t}\;} \frac{1}{\sin^2\theta} \; . \end{aligned}$$ Finally, putting all terms together, the Jacobian is $$\begin{aligned} && {\cal J}_G^{\rm sph} = \exp\left\{ (1-\alpha) \ln \left| \frac{\sin\theta(t_0)}{\sin\theta(t_N)} \right| \right\} \nonumber\\ && \qquad \times \exp \left\{\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;} \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta} - \partial_\theta (H_{{\rm eff},\phi} + H_{\phi}) \right.\right. \nonumber\\ && \qquad\qquad\qquad\qquad - \frac{\eta\gamma_0}{\sin\theta} \partial_\phi ( H_{{\rm eff},\phi} + H_\phi) -\eta\gamma_0 \partial_\theta ( H_{{\rm eff},\theta} + H_\theta) \nonumber\\ && \qquad\qquad\qquad\qquad \left.\left. + \frac{1}{\sin\theta} \partial_\phi ( H_{{\rm eff},\theta} + H_\theta) + \frac{\alpha\gamma_0 D}{\sin^2\theta} \right] \right\} \; . \end{aligned}$$ As found in the Cartesian calculation and in the spherical construction for the Landau formulation of the dynamics, the Jacobian ${\cal J}_G^{\rm sph}$ does not depend on the parallel component of the effective field, $H_{{\rm eff},M_{{\rm s}}}+H_{M_{{\rm s}}}$. Moreover, we find that the Landau and Gilbert Jacobian in spherical coordinates coincide. see Eq. (\[eq:Jacobian-Landau-spherical\]) and App. \[app:MSRDJ-Jacobian-Gus\] for the Landau calculation. We next introduce a Lagrange multiplier $[{{\rm i}}\hat{\mathbf{\Omega}}]$ to exponentiate the functional delta: $$\int {\mathcal{D}}{[{{\rm i}}\hat{\mathbf \Omega}]} \exp \left\{ - \int \! {\hspace{-0em}\mathrm{d}{t}\;} \left( {{\rm i}}\hat\Omega_{M_{{\rm s}}} \mbox{{Eq}}^{\rm sph}_{G,M_{{\rm s}}}[{\mathbf \Omega}] + {{\rm i}}\hat\Omega_\phi \mbox{{Eq}}^{\rm sph}_{G,\phi}[{\mathbf \Omega}, {\mathbf H}] + {{\rm i}}\hat\Omega_\theta \mbox{{Eq}}^{\rm sph}_{G,\theta}[{\mathbf \Omega}, {\mathbf H}] \right) \right\} \; .$$ We identify all the terms in the integrand of the exponent in the exponential that involve the random field ${\mathbf H}$: $$\begin{aligned} && -\frac{1}{4D} H_i^2 + \gamma_0 \left( {{\rm i}}\hat\Omega_\theta R_{\phi i} + {{\rm i}}\hat\Omega_\phi R_{\theta i} \right) H_i \nonumber\\ && \qquad + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \left( -\partial_\theta R_{\phi i} -\frac{\eta\gamma_0}{\sin\theta} \partial_\phi R_{\phi i} - \eta\gamma_0 \partial_\theta R_{\theta i} + \frac{1}{\sin\theta} \partial_\phi R_{\theta i} \right) H_i\;. \qquad\end{aligned}$$ After integration and a number of simplifications that use the explicit expression of the rotation matrix $R$ we find that these terms give rise to $$\begin{aligned} D \gamma_0^2 \left[ ({{\rm i}}\hat\Omega_\phi)^2 + ({{\rm i}}\hat\Omega_\theta)^2 + \frac{2\alpha}{1+\eta^2\gamma_0^2} \left( {{\rm i}}\hat\Omega_\theta + \eta\gamma_0 {{\rm i}}\hat\Omega_\phi \right) \cot\theta + \frac{\alpha^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta} \right]\end{aligned}$$ (apart from an irrelevant additive constant). Note that minus this form equals the terms in the exponential of the transverse random field measure in spherical coordinates, Eq. (\[eq:Pn-random-noise-sph\]), after the identification ${{\rm i}}\hat\Omega_\theta \to - H_\phi/(2\gamma_0 D)$ and ${{\rm i}}\hat\Omega_\phi \to - H_\theta/(2\gamma_0 D)$ (plus a constant). We put all these results together to write the generating functional $$\mathcal{Z}[\boldsymbol{\lambda}] = \int {\cal D}[\boldsymbol{\Omega}] {\cal D}[\hat{\boldsymbol{\Omega}}] \exp\left( S_G^{\rm sph}[\boldsymbol{\Omega},\hat{\boldsymbol{\Omega}}] + \int{\hspace{-0em}\mathrm{d}{t}\;}\boldsymbol{\lambda}(t) \cdot \boldsymbol{\Omega}(t) \right)\;,$$ the full action $$S_G^{\rm sph}= \widetilde S^{\rm sph}_{G,{\rm det}} + \widetilde S^{\rm sph}_{G,{\rm diss}} + \widetilde S^{\rm sph}_{G,{\rm jac}} \;,$$ and the terms $$\begin{aligned} \widetilde S^{\rm sph}_{G,{\rm det}} \! & \! = \! & \! \ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] - \int {\rm d}t \left[ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right. \nonumber\\ && \left. \;\; + {{\rm i}}\hat\Omega_\theta ( {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi} ) - {{\rm i}}\hat\Omega_\phi (\sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta}) \right] \;, \label{eq:action-det-sph-Gilbert-tilde}\\ && \nonumber\\ \widetilde S^{\rm sph}_{G,{\rm diss}} \! & \! = \! & \! \int {\rm d}t \left[ D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2 - {{\rm i}}\hat\Omega_\theta \eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi) - {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta) \right. \nonumber\\ && \;\; \left. + \frac{2\alpha\gamma_0^2 D}{1+\eta^2\gamma_0^2} ( {{\rm i}}\hat\Omega_\theta + \eta\gamma_0 {{\rm i}}\hat\Omega_\phi) \cot\theta \right]\;, \label{eq:action-diss-sph-Gilbert-tilde} \\ \widetilde S^{\rm sph}_{G,{\rm jac}} \! & \! = \! &\! (1-\alpha) \ln \left| \frac{\sin\theta(t_0)}{\sin\theta(t_N)} \right| + \frac{\alpha\gamma_0^2 D}{1+\eta^2\gamma_0^2} \int{\hspace{-0em}\mathrm{d}{t}\;} \frac{1}{\sin^2\theta} \nonumber\\ && + \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {\rm d}t \left[ - \partial_\theta H_{{\rm eff},\phi} - \frac{\eta\gamma_0}{\sin\theta} \partial_\phi H_{{\rm eff},\phi} \right. \nonumber\\ && \left. \qquad\qquad\qquad\qquad\qquad -\eta\gamma_0 \partial_\theta H_{{\rm eff},\theta} + \frac{1}{\sin\theta} \partial_\phi H_{{\rm eff},\theta} \right]\;. \end{aligned}$$ (We canceled the last term in the result from the integration over $H_i$ with one term from ${\cal J}^{\rm sph}_{G,{\rm jac}}$.) We now use the identity (\[eq:identity-Gus\]) to bring the action $S^{\rm sph}_{G}$ into a form that is closer to the one in the Landau formulation. We apply this identity to the integration over ${{\rm i}}\hat \Omega_\phi$ and ${{\rm i}}\hat \Omega_\theta$ separately with $$\begin{aligned} & \sigma^2= D\gamma_0^2 \nonumber\\ & a = - \frac{2\alpha \gamma_0^2 D}{1+\eta^2\gamma_0^2} \eta\gamma_0 \cot\theta \nonumber\\ & b = -\sin\theta {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 H_{{\rm eff},\theta} + \eta\gamma_0 {\rm D}^{(\alpha)}_t(\theta) \nonumber\end{aligned}$$ for ${{\rm i}}\hat \Omega_\phi$, and $$\begin{aligned} & \sigma^2 = D \gamma_0^2 \nonumber\\ & a = - \frac{2\alpha \gamma_0^2 D}{1+\eta^2\gamma_0^2} \cot\theta \nonumber\\ & b = {\rm D}^{(\alpha)}_t(\theta) - \gamma_0 H_{{\rm eff},\phi} + \eta\gamma_0 \sin\theta {\rm D}^{(\alpha)}_t(\phi) \nonumber\end{aligned}$$ for ${{\rm i}}\hat \Omega_\theta$. The new terms generated by the identity are $$\begin{aligned} - \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2} & \!\! = \!\! & - \frac{\alpha^2\gamma_0^2 D}{(1+\eta^2\gamma_0^2)^2} \eta^2\gamma^2_0 \cot^2\theta \nonumber\\ & & + \frac{\alpha}{1+\eta^2\gamma_0^2} \eta\gamma_0 \cot\theta \ [-\sin\theta {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 H_{{\rm eff},\theta} + \eta\gamma_0 {\rm D}^{(\alpha)}_t(\theta)]\end{aligned}$$ in the first case, and $$\begin{aligned} - \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2} & \!\! = \!\! & - \frac{\alpha^2\gamma_0^2 D}{(1+\eta^2\gamma_0^2)^2} \cot^2\theta \nonumber\\ & & + \frac{\alpha}{1+\eta^2\gamma_0^2} \cot\theta \ [ {\rm D}^{(\alpha)}_t(\theta) - \gamma_0 H_{{\rm eff},\phi} + \eta\gamma_0 \sin\theta {\rm D}^{(\alpha)}_t(\phi)]\end{aligned}$$ in the second case. Adding them up one finds the total contribution $$\begin{aligned} - \frac{\alpha^2\gamma_0^2 D}{1+\eta^2\gamma_0^2} \cot^2\theta + \alpha \cot\theta {\rm D}^{(\alpha)}_t(\theta) - \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta \ [\eta\gamma_0 H_{{\rm eff},\theta}+H_{{\rm eff},\phi} ] \; . \end{aligned}$$ We will add the first and last term to $\widetilde S_{G,{\rm jac}}$ to get $S_{L,{\rm jac}}^{\rm sph}$, see Eq. (\[eq:esferica-jac\]). In order to put together all terms in $1/\sin^2\theta$ we dropped an irrelevant constant. We are left with the rest of the contributions that we rearrange as $$\begin{aligned} S^{\rm sph}_{G,{\rm det}} \!\! & \!\! = \! \! & \! \ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] - \int {\rm d}t \left[ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}+ {{\rm i}}\hat\Omega_\theta ( {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi} ) \right. \nonumber\\ && \left. \!\! - {{\rm i}}\hat\Omega_\phi ( \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta} ) \right] , \label{eq:action-det-sph-Gilbert}\\ S^{\rm sph}_{G,{\rm diss}} \!\! & \!\! = \!\! & \!\! \int {\rm d}t \left[ D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2 - {{\rm i}}\hat\Omega_\theta \eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi) \right. \nonumber\\ && \left. \qquad\quad - {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta) \right] \;, \label{eq:action-diss-sph-Gilbert} \\ S^{\rm sph}_{G,{\rm jac}} \!\! & \!\! = \!\! & \! S^{\rm sph}_{L,{\rm jac}} \label{eq:action-jac-sph-Gilbert} \end{aligned}$$ and $S_G^{\rm sph} = S_{G, {\rm det}}^{\rm sph} + S_{G, {\rm diss}}^{\rm sph} + S_{G, {\rm jac}}^{\rm sph}$. [**Acknowledgements.**]{} We thank H. Hüffel and F. Romà for very useful discussions. We acknowledge financial support from ANR-BLAN-0346 (FAMOUS), PICT-2008-0516 (Argentina), NSF grants No. DMR-0906943 and DMR-1151810 (USA) and the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). DGB thanks the ICMP at the University of Illinois at Urbana-Champaign, where part of this work was developed. GSL thanks CNRS for an associate researcher position at LPTHE, Jussieu. LFC and GSL thank the ICTP Trieste for hospitality during the first steps of this investigation. ZGA is a CNPq fellow (Brasil). [^1]: We found some contradictions in the literature concerning the relation between the parameters in the two formulations. To be more precise, we find that the parameters transform as in [@Bertotti-etal; @Cimrak2008] but differently from what is shown in [@Berkov2007]. [^2]: A sequence of random variables $X_n$ converges in the mean-square sense to another random variable $X$ if $\lim_{n\to\infty} \langle (X_n - X)^2 \rangle = 0$ [@Gardiner]. | Mid | [
0.6296296296296291,
34,
20
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Archive | November 2013 This blog post is the second part of a 2-part series on the key highlights from ‘A Night of Hope’, an inspirational live event of worship and celebration, by bestselling author and transformational pastor, Joel Osteen. Some of the highlights of Joel and Victoria’s messages of hope, transformation and purpose (PART II): 1. Our first mission field is to our families. Everything flows from the family. Value your relationships. Agree to disagree respectfully. Everyone has different backgrounds, education, upbringing, belief system etc., so learn to accept and respect one another. Pick your fights. Know what’s worth fighting about and what to let go. Sometimes you have to keep your mouth shut and sow that act of compromise as a seed. 2. In life you’ve got to stand up and fight for what you want. Live a life of FAITH in action and focus on touching one life at a time. Everyday is an opportunity to do something different and better! 3. In pursuing your purpose in life, it is not how you start, it is how you finish. Take a step and tell yourself empowering stories. If the inner conversation is not taking you towards your goals, have a different conversation with yourself and make it louder! 4. Are you going to go forward or will you stay stuck staring behind through your rear view mirror? Let go and forgive all of yesterday’s pain. God made you to be free of excess baggage. His promise is to always make your burden lighter. 5. In life there are two types of bags that you get to carry around. It is either one or the other. The first is the special positive bag filled with joy, thanksgiving and service etc. While the other is the negative bag. Are you dragging around all the negative baggage from your past with you in the present? Which bag do you carry: Disappointment bag, Hurt bag, Regret bag, Anger bag, Bitter bag? Isn’t time to let go and let GOD? 6. Manage your happiness by managing your expectation, your sense of happiness is a choice. You have control over the type of relationships you wish to co-create. Only what you allow happens. Love yourself enough to honour God in you by giving and asking for the best. treat yourself with respect. 7. Speak words of faith and affirmation to any difficult situation and then take action in line with your words. “The tragedy of life is not death but what we let die inside of us while we live.” ~Norman Cousins~ Disclaimer: The highlights above are based on personal notes and understanding of Joel and Victoria Osteen’s messages. No intentional omission or error is intended. I hope something on this list resonates and plants an active seed in your life. Have an abundantly blessed day and an awesome life ahead! -Juliet ‘Kego Ume-Onyido, MBA Poet | Master-Certified Leadership Coach-Trainer -Consultant| ~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~ ———————————————————— Blogger Bio: The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]! She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook. Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” On the sidelines of the Port Harcourt Book festival, I caught up with festival headliner, Chika Unigwe, and engaged her in this interview where she talked about her life after winning the coveted NLNG prize. She spoke also on other sundry issues.How has life been since the NLNG prize? How has life been? It’s been a lot easier to convince other people that writing is a serious business and that’s what winning a big prize always does. Suddenly people who help baby sit your kids so you can go and gallivant round the world and do things start taking you seriously. It’s been such a great honour to be recognised in my country. Of everything I would want to win, the NLNG was top of the list simply because it is something from Nigeria. It’s been nice coming back to Nigeria as a writer some people have heard of… (Note, these are not the same as new year resolutions. Please refer to this previous post for more on the ‘I AM statements: http://wp.me/p1o3v6-1a). One of the many 50 statements that I wrote down was: “In 2014, I AM attending a live event of inspirational worship and celebration by bestselling author and pastor Joel Osteen.” Then, I simply stood in the flow gratitude and acceptance of allowing this statement to manifest and it did happen! Well, fast forward to a few months ago, when randomly, a friend of mine called me up excitedly to tell me the great new: Joel and Victoria Osteen were coming to Toronto for an evening of worship, music and motivation. The sad news was it was happening that night, intact 3 hours from the time she called me! The event was tagged: ‘A Night of Hope.’ First I made the conscious decision and voiced it out and wrote it down: ‘I AM attending this event tonight.’ And I held on to the hope that even though we were informed about this so late, there was still hope that our creator of midnight hours and crossover miracles would come to our rescue:-)After a frantic search online for any available, last minute ticket(s), a few phone calls to sort out babysitting, we were soon both Air Canada Centre, ACC-bound! It was a life-affirming day for me because even though the messages may not be new, Joel and victoria shared them with such authenticity and power that it resonated and stayed with me till today. The energy that filled ACC dome was deeply moving and so incredible! Apparently, I was not the only one who took copious notes. My friend had also sent me an email which contained her biggest take-aways from that evening. So we both collated our list of highlights and though we’d share, so here it goes! P.S: It would be done in a two-part series, so look out for part two tomorrow. Some of the highlights of Joel and Victoria’s messages of hope, transformation and purpose (PART I): 1. Let everyday be a new beginning for you. Forgive yourself and let go of the feelings of guilt and condemnation. Don’t sit on the sidelines of life, get back in the game and play at 100%! 2. God never allows you to experience difficulties without a divine purpose. Use your faith not to pray away difficulties but rather, surrender and allow the storm to lead you exactly where you should go. 3. Quit fighting back, relinquish control, surrender, so that God’s will may be done. Trust him and know that your storms are not a surprise to him. Burn up the limiting beliefs and shake off the self-pity! 4. You would not have been given a destiny without being equipped and empowered by God to fulfill it. Each day is a step forward towards your purpose and destiny. Start the day how you want the day to be. Set very clear intentions and be in tune with your attention. Be grateful everyday for the gifts of life and love. Shake off the bad ‘stuff’ by changing your internal recording and inner movie. Learn to change your dial/channels! 5. Affirm daily who you are1 Your ‘I AM’ statements are very powerful; ‘I am creative, I am fun, I am strong, I am healthy, I am wealthy, I am magnificent, I am a masterpiece.’ Indeed, you are God’s masterpiece, equipped, approved, blessed, forgiven, NOT average, not mediocre! 6. Stop the self-abuse and self-flagellation! You have enough people against you, you don’t have to be against yourself. There are lots of negative thoughts AND comments, from people that you have to ignore. Know how to take the learnings and corrections in criticism without attaching yourself to the negativity of its sting. You only have so much emotional energy each day. There are even some family members and ‘friends’ that you may have to sometimes distance yourself from. 7. Unforgiveness is like a poison inside you, Release yourself and release people. Write letters to everyone who’s ever hurt ou and who you’ve ever hurt. Do anything you can to help yourself. Know who you are and whose you are; victors and not victims! 8. Are you still tied to the victim mentality? Are you still choosing to be married to your pain? You CANNOT drag your baggage of pain over and over again, let it go! dream another dream. Quit thinking about it. Change the channel. Quit reliving negative memories. When you play negative movies in your mind, you will only feel negative emotions. Be disciplined in your thoughts. Think only pure thoughts, start changing the channels of your thoughts. 9. How you tell your stories of your wound matters. When you tell it, do you tell it from an empowered place, knowing the wound is already healed or when you talk about it, are you still stuck in the drama of reliving the pain? 10. Beauty for ashes! You have to decide and let go of the ashes before you can see and receive the beauty. It is an act of faith-let go of the pain and the blame. Do not live life looking in your rear view mirrors. 11. Seasons come and seasons go. A season of mourning does not equate to a LIFETIME of mourning! Shake off the pain of the past. Strain towards what lies ahead. The past is dead and gone, we can choose to be like the mountain climber, who cut of his infected arm so that he may live. Stop rehearsing and rehashing your old pains. 12. I BELIEVE AND DECLARE THAT THE REST OF YOUR LIFE WILL BE THE BEST OF YOUR LIFE! Disclaimer: The highlights above are based on personal notes and understanding of Joel and Victoria Osteen’s messages. No intentional omission or error is intended. I hope something on this list resonates and plants an active seed in your life. Have an abundantly blessed day and an awesome life ahead! ❤ -Juliet ‘Kego Ume-Onyido, MBA Poet | Master-Certified Leadership Coach-Trainer -Consultant| ~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~ ———————————————————— Blogger Bio: The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]! She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook. Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” On this site I talk about blocks to personal/spiritual growth and uncovering them so we are able to have an insight for living. Well, I’ve discovered a big core block for myself. Here’s how the discovery of it went: In the coaching group I’m leading, at the end of the call when it was her turn to share what she got out of the call, one of the members said that she see’s the little girl in each of us (5 women including me). Then I said, “You want to know what kind of little girl I was? I loved skirts that twirl. I put on shows in the neighborhood organizing the kids a little younger then I. We made and sold tickets. My mother hung an old bedspread on the clothesline and we put on some kind of show. I don’t remember the show but I do remember that… The pain and shock caused by a loss may lead to extreme, and sometimes unhealthy, new patterns of behaviour. If these patterns last beyond a temporary period of time, then perhaps, it is important to seek empathetic help and support from professionals and/or loved ones. (Various researches have shown that the presence, support and love from loved ones and even strangers, make a huge difference to the healing curve). Of the many emotions one experiences after a loss, perhaps the three really important ones to watch out for are Denial, Guilt and Shame. This is because other emotions-anger, sadness, fear hurt, regret and pain, which are warranted emotions, when expressed in a healthy way, may lead the person to a sense of release, acceptance and closure over time. On the other hand, feelings of denial, shame and guilt prolong the healing period and may make one sink in deeper into a prolonged, unhealthy spiral of mourning and grieving. To grief fully, without reservation, is itself, an important piece of the healing process. The loss of someone or something very dear to us, creates a shift in our perspective of the world and life in general. This is as it should be because we are not the same person we were before the loss and we can never go back to being that old person. Irrevocably, we are changed, for better or worse, by that singular experience. And it still comes down to the choices we make, either consciously or unconsciously. An interesting and empowering thing about the pain of loss is that if we pay close attention, the purpose of the death should compel us re-prioritize our lives. And it should also push us or inspire us to pursue only those things that give us the most joy, as well as adding the most value. The loss then simply acts as a boulder, and it’s role is to make us pause and reflect, as we are reminded that with every breath we take, death looms nearer, waiting in the shadows. Each day we wake up is a day closer to the end of the journey. What is the quality of the memories we wish to celebrate at the end? What is the life story we want told? Begin to live the future you dream of for yourself NOW, because the choices you make now, create the tomorrow you desire or despise! You get to tell your story, BE and LIVE the story you want told. Death offers us a chance to pause, take a deep breath, and recall shared memories of our loved ones. It allows us an opportunity to really stop everything, as we share our grief and connect with the deceased by building a legacy that upholds and reflects their values and purpose. Therefore, we must seek grace so that we do not waste the inherent power and beauty that our loss affords us. Everything has a purpose, nothing is an accident. Thus, the purpose of death becomes that of a jarring or gentle reminder, an alarm clock that wakes us up and draws the attention of the living towards their own path, their own purpose. Periods of grief are also a time to also take another hard look at our lives and course-correct our track, if necessary. It is a time to strengthen existing bonds or heal broken ones. Death is a destroyer of arrogance. It is in periods of intense sorrow that we ask the most important WHYs. The answers are already within us, we simply need the right questions to unlock what we already know. Death allows us to question what is truly important to us about living. There can be no greater opportunity for growth, learning and transformation than through death. It lends itself to such a literal and metaphoric finality that we are forced to pay immediate attention to the pain it elicits. And when we are courageous enough to face, feel and conquer ours fears/pains, we are in a better place. The more specific we get with our pain, the easier and faster it dis-integrates. “Sorrows are our best educators. A person can see further through a tear than a telescope.” ~Lord Byron~ To everyone and anyone experiencing intense sorrow over the loss of someone or something precious, I join others across our global WWN community in reaching out to you. We share our common connectedness and exchange our energy of understanding, of empathy, of unconditional love and of healing. Know that God walks with you, always, especially in the valleys, his light is there to comfort and guide your ways. We hold sacred space for the living survivors and also for the living who’ve moved on. Time in itself doesn’t heal, I’d like to think that we choose to heal, in time. We choose to heal and live and thus honour the spirit of the dead. If not, what difference would it then make if we either lived or die. Remember that death is itself a metaphor for life and vice versa. One journey starts when the other end, so loved ones never really die, they are merely transformed. Everything and everyone is energy and because we have shared the sacred space of living with them, they leave a part of themselves with us, the most important parts of them; their love, spirit, essence and core. As we grief and mourn for different reasons, let us reflect deeply on the truth that one of the greatest gifts of deep loss is the profound understanding that we must all learn to begin to surrender to life, be more accepting and allowing of letting go, while focusing on embracing both our nothingness and our majesty, both our humanity and our divinity. Blogger’s Note: This post was inspired by a dear friend who recently lost a beloved spouse. In the death of a loved one, we are all reminded of the precious gift of life. And even as we mourn, we hold firm in faith. We are strong believers; we believe in resurrection, we believe that the deceased are with us, even though we no longer physically see them. Also, we know and believe that this too shall pass and although the pain may sometimes be overwhelming, we have faith in the abiding grace of God to lead us through the storms. This is thanksgiving weekend in the USA, and so, we lift up our heartfelt prayers of love and thanksgiving. May the power of our collective wishes give healing and peace to those among us who mourn. For indeed, ALL things work together for those who believe. The task is to let go and believe! May the souls of the faithfully departed, Rest In Perfect Peace of our Lord. Through the pain and the storm of your loss, may you be willing, ready and open to love. In love were you created, with love were you moulded, through love were you redeemed. At your core, you are love! Are you or anyone you know experiencing intense sorrow over the passing of a loved one? Two (2) books that I highly recommend for anyone who’s grieving are: 1. A TIME TO GRIEVE: Meditations for healing after the death of a loved one, by Carol Staudacher; 2. HEALING AFTER LOSS: Daily Meditations for working through grief,by Martha Whitmore Hickman -Juliet ‘Kego Ume-Onyido, MBA Poet | Master-Certified Leadership Coach-Trainer -Consultant| ~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~ ———————————————————— Blogger Bio: The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]! She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook. Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” Today’s reflection is focused on the power of ASKING QUESTIONS. Sometimes, it is not the answers that we find that give us the biggest shifts and transformation. Often, it is the questions that we ask ourselves or are asked by others that open up our hearts and minds to possibilities we never imagined. The act of seeking the answers becomes a metaphor for the journey of life. Begin to pay attention to the questions that keep you awake at night, the questions that never seem too far from your mind, the questions that you run away from confronting. Those are probably the questions that have the biggest relationship with your life purpose and destiny. WWN Reflection DAY 27: Take ACTION and Transform Your Life! Here are some questions to reflect upon as you enjoy the rest of the week: 1. This mid-week, reflect and ask yourself: Am I on the ‘WOE me’ or ‘WOW me’ axis of life’s equation? WOE ME= Making excuses and having reasons to blame others for the drama and crap in your life! You are an expert at pointing fingers outwards, talking about other people’s limitations and never yours. You play the victim card. Failure and stagnation are guaranteed states in this zone. WOW ME=You take ownership and responsibility for both your awesomeness and your crap! You understand that you are a co-heir and co-creator with God. You focus on the learning in any situation, you seek to provide solutions and to add value. You are at cause for your life. You are in control of your results. You look inwards for answers. Success and purposeful living is guaranteed here. Note: You get to choose only one side at any given time….you cannot be in both! And if you’re in neither, you may be sitting on the ‘stuck’ fence, where life seems to be ‘happening’ to you. It is important to also note that as human beings, we will definitely find ourselves hanging out in the ‘woe me’ quadrant once in a while. The key is not to stay there for too long and also to celebrate the awareness of your lessons and learnings while you’re there or after you get out! So, be gentle with yourself and others, we’re all doing the very best we can with the resources we have. 2. Did you know that there’s a behavioural link between Self-Esteem, Over-Eating, Over-Spending, Over-Complaining and generally feeling ‘out of balance’ in life? They often have a common root and if you destroy the root cause, every thing else crumbles and life RE-ALIGNS back into shape! Are you aware of what your root cause is? Sometimes the manifesting ‘problem’ is simple a symptom of something deeper. 3. “Do you want a successful career or a close relationship with your family? Both! Do you want a focus on business or have fun and play? Both! Do you want money or meaning in your life? Both! Do you want to earn a fortune or do the work you love? Both! Unsuccessful people always choose one, successful people choose both. Do you realize that you always have options and indeed, by God’s grace and through hard work/working smart, you can have it all.” ~T. Harv Eker~ 4. “Are you stressed? Do you take time to relax? Do you take things so seriously? Laugh as much as you can! Play! When we’re adults, sometimes we forget to play and or we think we shouldn’t be wasting time on play when the opposite is true – PLAY! PLAY! PLAY! That’s where our true joy stems from, the most innocent part of who we are, our inner child that’s so excited about life and all its blessings! Are you letting your inner child out?” ~Patricia Grace Tomasi, Life Coach~ 5. Do you suffer because you think you do not have enough OR because you’ve accepted a fallacy that you can never have enough, and so you suffer? (Re-read this and ponder on it for a few minutes) 🙂 Do you realize that you have an innate ability to co-create everything you desire, want or need? Do you understand that you are enough and you always have enough? Do you play the compare and contrast game? Do you compare yourself against others or compare the present to the past or an imaginary future? Do you comprehend that this is the root cause of most unhappiness? Are you always looking at the other side and thinking the grass greener? Are you celebrating the beauty of NOW and looking inwards to find solutions unique to you or are you blindly following the dictates of the external world around you? 6. What if your problem is not YOUR problem? What if your problem is simply just a problem? What if you stopped taking your challenges and problems so personally? What if you could ‘remove’ yourself from your problem and look at them through someone else’s eyes? What if you took a new perspective, an ‘eagle-eyed’ overview of the problem and became open to new ways of ‘seeing’ them? What if the whole essence of the problems is to make you grow and transform into someone who resources creatively to resolve and solve said problems? What if all your problems have solutions and you role is to simply explore new ideas, perspectives and be open to others around you, in order to find the answers you seek? 7. What’s your purpose? Are you living in alignment with your purpose? What are your most important values in different spheres of life? What kind of life would you rather be living if you had an abundance of money, time, energy? LIVE IT NOW! Do you have the faith to believe in the formless and not in the formed physical reality? Are you speaking, feeling and living your truth? Do you realize that in order to manifest your dreams into reality, you MUST become the person who is capable of achieving those goals and dreams? WHAT you have and do flow directly from WHO you are BEING. The equation for the law of manifest ion is this: BE-DO-HAVE! Warmest Regards, Blessings & Cyber-hugs, -Juliet ‘Kego Ume-Onyido, MBA Poet | Master-Certified Leadership Coach-Trainer -Consultant| ~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~ ———————————————————— Blogger Bio: The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]! She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook. Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” “The secret of change is to focus all your energy, not on fighting the old, but on building the new.” ~Socrates~ WWN Reflection DAY 26: Take ACTION and Transform Your Life! Today’s focus is on revisiting some old sayings, quotes and proverbs and adapting them to become more aligned with this new value-based, empathy-driven economy. I think that perhaps sometimes we are so set in a particular model of the world that it holds us back from enjoying the fullness of life all around us. I love the idea of periodically ‘checking in’ on our existing value construct and even loosening our Model of the World (MOTW), in order to allow new perspectives and pathways of creative solutions. Sometimes, we hold beliefs and run unconscious programs that are in conflict with what we wish to manifest in life. Just because something has always been a particular way does not mean it cannot be looked at differently and given a ‘newer’, more empowering interpretation. So here are my newest ways of looking at the world. 1. Old Economy: “Fake it until you make it.” Which loosely translates to living a life that has little or nothing to do with authenticity, tell ‘made up’ stories (not your true stories), simply to brag, impress and make yourself look ‘bigger.’ The irony is of course that in living and doing business this way, you diminish your true value. This is also one of the main reasons people rack up obscene high-debt levels! New Economy: “Focus all your energy on making it, so that you never have to fake it!” This suggests that you channel every resource you have towards your goals. Become one with your goals, and take quantum leaps and create value by solving problems, while sharing your truth and telling your unique story and journey! People can sense, small and feel B.S from a mile, so be yourself, period. It’s also way healthier for your life overall. As the saying goes: “When you tell the truth you do not have to remember anything.” So rather than blindly following the ‘Joneses’, begin to set yourself apart as an original and simply take action towards your purpose. Life is much more fun and less stressful in the ‘REAL’ zone. The ‘FAKE zone, may initially be thrilling, however it ultimately drains, depresses and depletes because the brain simply does not have that strong a firewall to fuel the various incongruent parts! It is healthier to ‘sew your cloth according to your material’ and not according to your size. 2. Old Economy: “Forgive but don’t forget.” In order words, cling on to the myth of your non-existent pain in the present and create a future based on it. Fight the healing power of time and continue to perpetuate your ‘woe me’ story. New Economy: “Forgive AND Forget.” The whole essence of forgiveness is the willingness, courage and acknowledgement of what has happened, the vulnerability to embrace and feel the pain it caused and yet decide to let it go. Forgiveness is total surrendering and acceptance. You forgive and forget both the pain and its perpetrator, rather, focus on what the experience taught you. It is a DECISION to release and free up your heart to love and experience joy fully. True forgiveness does not hold on to the event, rather it filters only the learnings from the event. It also gifts you with the ability to set firmer and clearer boundaries to others. So with the passage of time, re-telling the story of your past pain simply becomes content-free (less focused on the drama), and more focused on preserving and sharing the learnings. This is true empowerment. 3. Old Economy: “It is better to teach a man how to fish than to give him fish.” Sometimes, it is important to know the other person’s model of the world and perhaps even enter it in order to gently, yet firmly guide them to navigate their way to a new understanding and hopefully, embrace healthier options and choices. New Economy: “It is good to give a man fish, it is better to teach him how to fish and it is best to give him some fish while you teach him, lest he quenches before the lessons are finished.” In an empathy-driven economy, we acknowledge that one size never fits all and there’s a need to meet people at their level in order to lift them up to where they really belong or aspire to reach. 4. Old Economy: The law of attraction was based on feeling only ‘positive’ feelings, using your powers of imagination and focus. It was largely based on the notion that ‘You attract whatever you want.’ New Economy: This postulates a revised law of attraction based on feeling ALL your feelings, gaining mastery of your internal representation (state mastery) and the idea that what ever you are, have or do, essentially flows from who you are BEING. Thus, ‘you attract who you are.’ It also focuses a lot on taking congruent and consistent ACTION. The law of Attraction is simply the law of manifestation (of your actions). Thus, the questions you should answer are: ‘Who are you really BEING when you’re DOING what you’re doing? ‘Are you congruent and are your values aligned, in your thoughts, words and action steps, in both your inner and outer lives?’ In the words of Aristotle: We are what we repeatedly do! 4. Old Economy: “When life hands you lemons, you make lemonade.” New Economy: Here, there’s a need to reflectively think about what you do in the wake of any situation. Is your default reaction to see it through the ‘victim lens’ or do you see life through the ‘opportunity lens?’ In the new economy, everything you encounter and everyone you interact with offer you new learning and an opportunity for collaboration, synergy and growth. You must have a deep awareness of who you are and also have the courage to embrace all of you, both your weaknesses and your strengths! Thus, When life hands you Lemons: a) YOU complain and gripe that they are not ripe enough, big enough, sweet enough. OR b) YOU ignore them and waste your time searching for apples, till someday, you get famished and realize the lemons are now rotten and have gone bad. OR c. YOU get angry and become permanently mad at the world. To express your self-justified anger and self-inflicted pain, you throw the lemons at others. Or cut them up and squirt the juice into people’s eyes so that they too can experience your pain and desolation. And then you all hang out and swap stories of your pain, while drinking your bitter tequila/gin/lemon filled cup. OR d) YOU are grateful for your lemons and embrace the challenge and opportunity they hold. And even though you may prefer apples or oranges, you decide to take action, turn them into lemonade and sell it all for profit. Also, you plant the seeds and grow a lemon orchard. You begin to attract like-minded people who embraced their lemons. And you share ideas and joint-venture with them. Then, with the profits from your deals, you buy apples (your preferred fruit) 🙂 and bigger, riper, sweeter lemons which you sell (and give some away) to those in group (a), (b) and (c)! In fact, you become so busy creating different opportunities, and consequently, enriching your inner and outer world. Your lemons suddenly become the keys that unlock your life’s purpose! It all starts with a simple step. Whatever skills, talents, energy, money, time, passions, pains, relationships/networks…be grateful for them and use them passionately, powerfully and purposefully. Everything you have in your life right NOW, whether good or ‘bad’, are your life lemons. the choice of what to do with them is yours. You have the unique talents and skills to co-create your reality and design your destiny. Are you ready to take a chance and bet on YOU? Are you ready to get out of your own damn way? 🙂 The questions then become: Will you continue to sit on the toxic fence and continue telling ‘woe me’ stories of blaming, complaining, condemning and justifying why life handed you ‘bad’ lemons OR will today be the day you decide to take ACTION in the direction of your dreams and goals? Are you ready to hear, see and live your truth by telling ‘wow me’ stories of yourself, taking control of your destiny and owning up to the responsibility and consequences for your actions and results? Your goals are your sacred contracts you hold with yourself. If you are not willing to honour your commitment to yourself, it is near impossible to honour your commitment to others. Conversely, the universe returns to you exactly what you put out. Say your goals exactly how you want them and take congruent actions to fulfil them. BE who you want to become. You can attract only what and who you are. Dream wonderful dreams and co-create your destiny with God! The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]! She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook. Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” | Mid | [
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Reported Severe Hypersensitivity Reactions after Intravenous Iron Administration in the European Economic Area (EEA) Before and After Implementation of Risk Minimization Measures. Severe hypersensitivity reactions (HSRs) such as anaphylaxis are of great clinical concern because of their life-threatening potential. The adverse events attributable to intravenous iron products include HSRs. An investigation by the European Medicines Agency presented in late 2013 resulted in the implementation of risk minimization measures (RMMs). This study evaluated the number of severe HSRs reported for intravenous iron substances related to exposure for the 4-year periods before and after this implementation. This was a retrospective pharmacoepidemiologic study with a case-population design. We obtained information from the safety surveillance database EudraVigilance on spontaneously reported severe HSRs using the Medical Dictionary for Regulatory Activities preferred terms "anaphylactic reaction/shock" and "anaphylactoid reaction/shock". Exposure was estimated using IQVIA MIDAS sales data in European economic area countries. Reporting rates for individual products were heterogenous, and the implementation of RMMs appeared to have no clear impact. Reporting rates remained low for the full study period for iron sucrose (0.03-0.20) and ferric gluconate (0.02-0.14) and were higher at the beginning and lower at the end of the study period for ferric carboxymaltose (1.47-0.18). No clear trend was detected for iron dextran (range 0.22-2.80) and iron (III) isomaltoside 1000 (range 0-7.94). Future research is needed to investigate whether the wide variability in reporting rates for severe HSRs associated with these intravenous iron products are due to potential differences in the safety profiles of these substances. | Mid | [
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# From http://www.liblogging.org/ sha256 338c6174e5c8652eaa34f956be3451f7491a4416ab489aef63151f802b00bf93 liblogging-1.0.6.tar.gz # Hash for license file: sha256 a5626f700d3ee92513673b5f43733af5b651d9e7a9157d4bd81ceb9c89ec04b0 COPYING | Mid | [
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Rothenberg: Who Is Least Likely to Lose the Virginia Gubernatorial Race? McAuliffe, above, is expected to face Cuccinelli in Virginia’s gubernatorial race this year. While most political attention these days is focused on the nation’s capital and President Barack Obama’s second term, across the river in Virginia, politicians from both parties are preparing for what seems to be the oddest gubernatorial race the state has seen in years. Each party is poised to nominate a deeply flawed candidate for the state’s top post, with the winner replacing the popular current governor, Republican Bob McDonnell. GOP Attorney General Ken Cuccinelli is widely regarded as the sort of politician who never met a Democrat he didn’t want to fight — an ideologue for whom burning bridges is the preferred option. Allies of the attorney general prefer to emphasize the positive aspects of his agenda and style, arguing that he is principled, honest and straightforward. “There is never any doubt where he stands on an issue,” one ally said. “He has a spine of steel rooted in principle, but he is engaging, friendly and has a good sense of humor,” said another admirer of the attorney general, adding, “And he is wicked smart.” Supporters argue that the picture painted of the attorney general by the media is as unfair as it is unflattering. They point to his years trying to educate people about and mobilize action against sexual assault, going all the way back to his days as an undergraduate at the University of Virginia, and they promise that by the time November rolls around, voters will have a better idea of who Cuccinelli really is. But while criticism of Cuccinelli coming from liberals and Democrats is predictable and therefore less convincing, it is criticism of him from conservatives and Republicans that raises the most questions about the attorney general’s appeal and viability in a general election. “Cuccinelli’s biggest problem isn’t his ideology,” said one Republican who generally agrees with him on most issues. “It’s his attitudes toward voters and his fellow Republicans that it’s ‘my way or the highway.’ When he’s attacked, he’ll almost always double down. He sees backing off as compromising on principle.” Republicans note that Cuccinelli and McDonnell don’t disagree on many issues but have much different campaign styles. The governor ran and has governed as a smiling, likable, consensus-building conservative. During his 2009 campaign, he stayed focused on economic issues, steering away from social issues even when critics tried to make the election about his master’s thesis for Regent University two decades earlier. While allies of Cuccinelli say the engineer-turned-attorney can be just as disciplined as McDonnell, other Republicans are skeptical. They believe that too often he sounds confrontational and inflexible, and they doubt that he will be able to ignore criticism. | Low | [
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/* * Copyright 2018 Meituan Dianping. All rights reserved. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package com.meituan.dorado.transport.http.netty; import com.meituan.dorado.common.util.NetUtil; import com.meituan.dorado.rpc.handler.http.DefaultHttpResponse; import com.meituan.dorado.rpc.handler.http.HttpHandler; import io.netty.buffer.ByteBuf; import io.netty.channel.ChannelHandlerContext; import io.netty.channel.ChannelInboundHandlerAdapter; import io.netty.handler.codec.http.HttpContent; import io.netty.handler.codec.http.HttpHeaders; import io.netty.handler.codec.http.HttpRequest; import io.netty.handler.codec.http.LastHttpContent; import org.slf4j.Logger; import org.slf4j.LoggerFactory; import java.net.InetSocketAddress; import java.util.HashMap; import java.util.Iterator; import java.util.Map; public class NettyHttpServerHandler extends ChannelInboundHandlerAdapter { private static final Logger logger = LoggerFactory.getLogger(NettyHttpServerHandler.class); private HttpRequest request; private HttpHandler httpHandler; private NettyHttpServer server; private byte[] frontBuff; public NettyHttpServerHandler(HttpHandler httpHandler, NettyHttpServer server) { this.httpHandler = httpHandler; this.server = server; } @Override public void channelRead(ChannelHandlerContext ctx, Object msg) throws Exception { if (msg instanceof HttpRequest) { request = (HttpRequest) msg; } if (msg instanceof HttpContent) { if ("/favicon.ico".equals(request.uri())) { return; } if (msg instanceof LastHttpContent) { HttpContent content = (HttpContent) msg; ByteBuf buf = content.content(); byte[] buffer = new byte[buf.readableBytes()]; buf.readBytes(buffer); buf.release(); byte[] fullBuff; if (frontBuff != null) { fullBuff = new byte[frontBuff.length + buffer.length]; System.arraycopy(frontBuff, 0, fullBuff, 0, frontBuff.length); System.arraycopy(buffer, 0, fullBuff, frontBuff.length, buffer.length); frontBuff = null; } else { fullBuff = buffer; } NettyHttpSender httpSender = new NettyHttpSender(ctx.channel(), request); try { Map<String, String> headers = getRequestHeaders(request.headers()); httpHandler.handle(httpSender, request.uri(), fullBuff, headers); } catch (Throwable e) { logger.warn("Handle http request({}) exception,", request.uri(), e); String errorMsg = e.getMessage(); errorMsg = errorMsg == null ? e.getClass().getName() : errorMsg; DefaultHttpResponse httpResponse = new DefaultHttpResponse(); httpResponse.generateFailContent(errorMsg); httpSender.send(httpResponse); } } else { HttpContent content = (HttpContent) msg; ByteBuf buf = content.content(); byte[] buffer = new byte[buf.readableBytes()]; buf.readBytes(buffer); buf.release(); if (frontBuff == null) { frontBuff = buffer; } else { byte[] newBuff = new byte[frontBuff.length + buffer.length]; System.arraycopy(frontBuff, 0, newBuff, 0, frontBuff.length); System.arraycopy(buffer, 0, newBuff, frontBuff.length, buffer.length); frontBuff = newBuff; } } } } @Override public void channelActive(ChannelHandlerContext ctx) throws Exception { server.getChannels().put(NetUtil.toIpPort((InetSocketAddress) ctx.channel().remoteAddress()), ctx.channel()); } @Override public void channelInactive(ChannelHandlerContext ctx) throws Exception { server.getChannels().remove(NetUtil.toIpPort((InetSocketAddress) ctx.channel().remoteAddress())); } @Override public void exceptionCaught(ChannelHandlerContext ctx, Throwable cause) throws Exception { logger.error("Netty http request fail", cause); ctx.close(); } private Map<String, String> getRequestHeaders(HttpHeaders headers) { Map<String, String> headerMap = new HashMap<String, String>(); Iterator<Map.Entry<String, String>> iterator = headers.iterator(); while (iterator.hasNext()) { Map.Entry<String, String> entry = iterator.next(); headerMap.put(entry.getKey(), entry.getValue()); } return headerMap; } } | Mid | [
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Arizona Man Gasps and Snorts During Lethal Injection Execution That Took Nearly Two Hours After a high-profile legal battle over the drugs used in the lethal injection cocktail, the execution of convicted murder, Joseph Wood, finally went ahead in Arizona on Wednesday. The execution was carried out, but how it took place will surely add fuel to the growing controversy over lethal injections in America. According to the AP, Wood “was put to death in an apparently flawed procedure that took too long to conclude. An hour into the execution, his lawyers [filed] an emergency [Supreme Court] appeal, saying he'd been ‘gasping’ and ‘snorting’ for an hour… Word that Justice Anthony Kennedy denied the appeal came about a half hour after Wood's death.” The AP reporter on the scene witnessed Wood gasp more than 600 times before he died from a procedure that experts say should have taken 10 minutes. The execution of Joseph Wood — which Arizona carried out with a lethal-injection it had never before tried — is certain to fan the debate over how U.S. states carry out the death penalty. Midway through the execution, defense attorneys asked a judge to stop the execution of Joseph Wood and order prison officials to try to resuscitate him. But before the court acted, he was pronounced dead. "The execution commenced at 1:52 p.m. at the Arizona State Prison Complex (ASPC) - Florence. He was pronounced dead at 3:49 p.m," a statement Arizona Attorney General Tom Horne said. The statement did not say what problems the execution team had encountered, but Wood's lawyers painted a macabre picture. Wood was given the death penalty for the double murder of his girlfriend and her father in 1989. On Tuesday a federal appeals court sided with Wood’s lawyers who in seeking to delay the execution, the Associated Press reports, “used a new legal tactic in which defense attorneys claim their clients' First Amendment rights are being violated by the government's refusal to reveal details about lethal injection drugs.” The legal team was seeking information on the drug combination used by the state of Arizona. The Supreme Court, however, overruled the stay, allowing the execution to be carried out. | Low | [
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Job Description Should you be passionate about teaching, hold an M.Cur degree or are looking to complete your Masters’ degree, and seek to grow within a large hospital group, we have the right position for you! The successful incumbent must be registered with the SANC as a Professional Nurse and have prior experience as a Clinical Facilitator or Educator within the private healthcare sector. Candidates with practical knowledge of specific disciplines such as Theatre, ICU, Neonatal, etc. will take preference. Candidates are required to have good understanding and application of the nursing scope of practice and knowledge of patient care, and can demonstrate professional ethics and reliability. Should you meet the requirements for this position, please email your CV to [email protected] or fax to 0866 023 398. You can alternatively contact Rebecca on 0211 804 047. Please note that correspondence will only be conducted with short listed candidates within 3 days of application received Job Tools Like This Job for R2000! Like or Share this job and if one of your Facebook friends gets this job, we pay you R2 000 if you were the 1st of his/her friends to like it!If you are a registered Mass Staffing Projects Member on our website we will pay you R2 500! T&C’s apply. | Mid | [
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Q: C# Nested Class I have a class Animal. Within the class Animal I have a list of another class called Dogs. class Animal { List<Dog> Dogs; int CountNeutedDogs; class Dog { // some properties boolean neuted; } } It's possible that the list can contain about 500 dogs at any one time. I want to have an event so that if the value of neuted property in a dog changes the CountNeutedDogs is informed and updated. How do I do this? Edit I should explain the list Dogs is bound to a datagrid. The user can change the neuted property from false to true and vice versa. I have a get & set for the property. So the neuted value can change and I need to update the CountNeutedDogs value which is why I was thinking of using an event but not sure how to do it. A: If you make CountNeutedDogs a property like so, it will always be correct without events updating: int CountNeutedDogs { get { return this.Dogs.Where(d => d.neuted).Count(); } } A: This is a follow-up on the Comments: I made an example, (not tested!!) how you can solve this by implementing the ObservableCollection and INotifyPropertyChanged public class Dog : INotifyPropertyChanged { private bool _isNeutered; public bool IsNeutered { get { return _isNeutered; } set { if (_isNeutered != value) { _isNeutered = value; if (PropertyChanged != null) PropertyChanged(this, new PropertyChangedEventArgs("IsNeutered")); } } } public event PropertyChangedEventHandler PropertyChanged; } public class Animals : INotifyPropertyChanged { private ObservableCollection<Dog> _dogs = new ObservableCollection<Dog>(); public Animals() { _dogs.CollectionChanged += Dogs_CollectionChanged; } // NOTE, I haven't checked this!! But I think it should be something like this: private void Dogs_CollectionChanged(object sender, System.Collections.Specialized.NotifyCollectionChangedEventArgs e) { switch (e.Action) { case NotifyCollectionChangedAction.Add: foreach (INotifyPropertyChanged item in e.NewItems.OfType<INotifyPropertyChanged>()) item.PropertyChanged += Item_PropertyChanged; break; case NotifyCollectionChangedAction.Reset: case NotifyCollectionChangedAction.Remove: foreach (INotifyPropertyChanged item in e.OldItems.OfType<INotifyPropertyChanged>()) item.PropertyChanged -= Item_PropertyChanged; break; } if (PropertyChanged != null) PropertyChanged(this, new PropertyChangedEventArgs("NeuteredDogsCount")); } private void Item_PropertyChanged(object sender, PropertyChangedEventArgs e) { if (PropertyChanged != null) PropertyChanged(this, new PropertyChangedEventArgs("NeuteredDogsCount")); } public IEnumerable<Dog> Dogs { get { return _dogs; } } public int NeuteredDogsCount { get { return Dogs.Where(dog => dog.IsNeutered).Count(); } } public event PropertyChangedEventHandler PropertyChanged; } So when the collection changes, the notify of the NeuteredDogsCount property is sent. This way the bounded controls will re-evaluate the NeuteredDogsCount property. Instead of 'normal' properties, the IsNeutered can be changed to a DependencyProperty. | Mid | [
0.6401137980085341,
28.125,
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Q: Regex character class inside character range failing intellij's jsLint inspection What is the easiest way to rectify my failing inspection? There is no option in intellij (that I can find) to allow character classes inside a character range. A: If you want to allow a literal hyphen - in a character class, you need to put it immediately after the opening [ (Refer "Character Classes" section at http://www.regular-expressions.info/reference.html) or immediately prior to the closing ] (I've found works in some languages at least), else it's deemed to signify a range. And note also this comment by @IanMackinnon on this SO question (although I couldn't find an authoritative source for this after a very brief search): "explicitly escaping hyphens in character classes is another JSLint recommendation." - this was written in the context of literal hyphens. Regardless of if jsLint needs this or not to pass inspection, it's probably good practice to do this in order to future-proof the literal hyphen in case a future developer accidentally turns the class into a range by putting something between the (un-escaped) hyphen and the opening (or closing) bracket. I therefore think the section of your regex that currently reads as [\w-+\s] should be re-written as [\-\w+\s]). And the subsequent [\w-+] as [\-\w+], etc... | Mid | [
0.5574229691876751,
24.875,
19.75
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Vanish introduces a revolution in stain removal. Both are so powerful they remove some stains in just 30 seconds! For maximum speed and power pre treat or soak to see results in 30 seconds. Safe to use both on colours and whites. Vanish Oxi Action Pre-treat Spray. If you're having a difficult time removing stains from your clothes, Vanish Oxi Action Pre-Treat Spray can help. To take immediate action against stains, use Vanish Oxi Action Spray to pre-treat the stain directly. It's a powerful formula which penetrates deep into the fibres to break down even the toughest stains like the grime and grease you get on collars and cuffs. It is suitable for both coloured and white clothes. Vanish Power Shot Gel Capsules. Are you having a tough time removing a stain from your clothes? Vanish Powershots Gel Caps can help you remove any stain as they contain 50% extra power per drop compared to the regular Vanish Oxi Action Gel. Vanish Powershots Gel Caps are very convenient to use and suitable for all clothing. I knew straight away what they would be perfect for.....Ellie wears white polo shirts for school and over the last couple of months she hasn't been wearing a jumper with them as the weather has been so warm....She has picked up a whole host of stains from school......Pen, food, grass, paint.....I had slipped on the washing so there was a weeks worth of polo shirts to wash....Eek! The products were easy enough to use.....It doesn't take a rocket scientist to use them.....I sprayed the Vanish Oxi Action Pre-treat Spray on the stains and left them a few minutes before putting them into the washer.....I put one of the Vanish Power Shot Gel Capsules in with the shirts and I added a little of the Powder & Vanish Gold Oxi Action Gel into the tray in the washing machine for a little extra clean.... I let the washer do it's work and was dying to see the end result..... Out on the line the shirts looked whiter than white....Even Becky said they looked so clean.... I couldn't tell which top was stained with what as there was no stains left to show apart from one.....I have marked it out above. It looks like black marker pen but I know it has been there for months.....I was impressed that it removed the blue paint from one of the shirts because that has been there a few weeks and the top has been through the washer a couple of times previously without removing it.... (I only edited the photos by covering my girls school logo with a badge & pointing out the remaining stain) I would absolutely recommend these products....They have removed stains which have been there for weeks so imagine what they can do when there is a fresh stain!! Vanish products are available in most supermarkets....I have just looked on the Tesco grocery website where I get my shopping and each item costs between four and five pounds.....It is good to know they sell them in Tesco because I will be buying them again.... I was sent a these Vanish products for the purpose of this post....This is my honest review! All thoughts and opinions are my own.... Both my teenager girls are messy (I thought they would grow out of being messy - but I'm still waiting!) I have tried the spray and the add in powder but not together, I will certainly now give this a go as your review has demonstrated these products do work. I used to use Vanish years ago but found it wasn't that good. I switched to another brand which I liked but then it stopped being made! On holiday last there was an incident involving young children and rental bed linen so my husband rushed out to buy some stain remover and brought back Vanish. I wasn't very pleased at first because I thought it wouldn't work but it did so I think they must have changed the formula. This could save me a fortune, I dont know how my kids get so dirty at school!!! I have had so many of those white school t shirts that I have had to throw out as I just couldnt get paint or marker pen out of them A very comprehensive report,well written and you'd obviously tried the products.I'm more inclined to listen to another mum than pay attention to a TV ad'.My only negative thing is my pet hate,different coloured pegs on the washing.!!Only kidding,it's one of my odd things that I do x Wow that is pretty good! I always end up soaking a huge pile of stained shirts in buckets of washing powder and then boiling them and they still never come out clean. I would love to try these stain removers and see if I can save some of the school shirts for next year! I remember what it was like trying to get school polo shirts clean. I'm going to try the gel capsules in with my towels. Some of them are going yellow in the middle for some reason. Have tried the spray before on various stains and have found it to be good | Mid | [
0.6370370370370371,
32.25,
18.375
] |
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