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Highmark Caring Place To Honor Midstate Volunteers
More Than 6,500 Hours Dedicated to Help Grieving Children and Families CAMP HILL, Pa. June 11 /PRNewswire/ -- The Highmark Caring Place will recognize 185 volunteers on Monday, June 15 at the Radisson Penn Harris Convention Center. These individuals have collectively volunteered more than 6,5...An Interactive Health Caring Conversation With SAVE THE PATIENT
CHICAGO, May 13 /PRNewswire-USNewswire/ -- Continuing its efforts to educate, inform, and empower the people of Chicago, SAVE THE PATIENT, a not-for-profit patient-focused organization, is hosting its 25-minute live call-in show, "Community Health," on Chicago Access Network Television (CAN-TV) on...Highmark Caring Place Dedicates New Facility in Warrendale
With one in 20 children experiencing the death of a parent before they graduate high school, new center offers peer support group programs PITTSBURGH, May 8 /PRNewswire/ -- With the Highmark Caring Place, A Center for Grieving Children, Adolescents and Their Families, nearing capacity to ...Health Caring - A Network of Strength
CHICAGO, April 23 /PRNewswire-USNewswire/ -- Continuing its efforts to educate, inform, and empower the people of Chicago, SAVE THE PATIENT, a not-for-profit patient-focused organization, is hosting its 25-minute live call-in show, "Community Health," on Chicago Access Network (CAN-TV) on Monday,...Healthcare Gathering Addresses Increasing Need of Caring for the Nation's Elderly Population
LOS ANGELES, April 20 /PRNewswire/ -- In direct response to America's aging population and the acknowledged gaps in geriatric care, healthcare professionals recently gathered in Los Angeles to find creative approaches to address one of the nation's most pressing healthcare needs - caring for a soc...Compassion fatigue: Impact on healthcare providers of caring for the terminally ill
INDIANAPOLIS Compassion fatigue in nurses, doctors and other front line cancer-care providers significantly impacts how they interact with patients, with patient families, with other healthcare workers, and with their own family, according to analysis by Indiana University School of Medicine and ...Medicare Faces Challenges Caring for Chronically Ill
Initiatives to lower costs, improve service seldom work, study finds TUESDAY, Feb. 10 (HealthDay News) -- Only a fraction of Medicare pilot programs aimed at cutting costs and improving care for people with chronic illness actually did the job, a new study shows. That doesn't necess...Study to explore ethical challenges health professionals face while caring for children with LTNMDs
(Baltimore) The Greenwall Foundation recently awarded two core faculty members of the Johns Hopkins Berman Institute of Bioethics a grant that will allow Drs. Gail Geller and Cynda Hylton Rushton to explore the ethical challenges health professionals face while caring for children and families af...Does Your Senior Need Help at Home? A Holiday Checklist for Anyone Caring for Seniors
The stockings are hung by the chimney with care as your parents and loved ones prepare for your holiday visit. Over the years, your parents have managed to keep most of familiar traditions that helped define your family's holiday celebrations. Yet, this year, when you arrive, you notice that thin...The Gift of Health Caring at End of Life
PATIENT-FOCUSED ORGANIZATION REACHES OUT TO EDUCATE CHICAGOANS CHICAGO, Dec. 2 /PRNewswire-USNewswire/ -- Continuing its efforts to educate, inform, and empower the people of Chicago, SAVE THE PATIENT, a not-for-profit patient-focused organization, is hosting its 25-minute live call-in sh...In sickness and health: Caring for ailing spouse may prolong your life
ANN ARBOR, Mich.---Older people who spent at least 14 hours a week taking care of a disabled spouse lived longer than others. That is the unexpected finding of a University of Michigan study forthcoming in Psychological Science , a journal of the Association for Psychological Science. The stud...People Caring for Aging Parents Can Win $2,000 of Free Housecleaning
AgingCare.com Hosts Contest in Honor of National Family Caregiver Month NAPLES, Fla., Nov. 13 /PRNewswire/ -- In honor of National Family Caregivers Month, AgingCare.com wants to make a deserving caregiver's life a little easier. AgingCare.com is holding a contest. The prize? $2,000 of free ho...Hector Elizondo: Caring for a Loved One with Alzheimer's Dementia
NEW YORK, Nov. 10 /PRNewswire/ -- For Emmy-award winning actor Hector Elizondo, the challenges of caring for a loved one with Alzheimer's dementia are very personal. In the 1960s, Elizondo's mother was afflicted with Alzheimer's dementia, a degenerative disease that alters the brain, causing i...Area Women Gather in Milford on July 10 to Further the Mission of Women's Caring Program
MILFORD, Mich., July 2 /PRNewswire/ -- The legacy of caring begun 29 years ago by a small group of friends has grown to become one of the area's most significant Summer fundraisers, thanks to the enthusiastic support of women who see the value in helping fund childcare for low-income families ...Late-life remarriage: Stepfamilies make caring more complex
"I felt so insulted and so hurt. It was like [their father] had met some gal at a bar and married her the next day, and she wanted all his money. I felt they didn't give me any credit, or any respect, appreciation or anything. It still hurts." --Remarried wife of 12 years, caring for husband with...U.S. Hospitals Vary Widely in Caring for Women
From birth complications to heart disease, top-rated centers a better choice, health study concludes TUESDAY, June 24 (HealthDay News) -- Women who give birth at top-rated hospitals have fewer complications for Caesarean section and fewer complications for vaginal birth, according to ...Experts highlight gaps in knowledge on caring for survivors of teenage and young adult cancers
London, UK: Over 95% of patients with testicular cancer are cured nowadays, but this success has produced a new problem for cancer survivors, the medical profession and national governments, a cancer expert will tell Teenage Cancer Trust's Fifth International Conference on Teenage and Young Adult...Long Term Care Newsletter Helps Preserve Solvency & Sanity While Caring for Loved One
Subscriptions Available Free from LTC Financial Partners KIRKLAND, Wash., Feb. 27 /PRNewswire/ -- If you suddenly have to care for an incapacitated parent or spouse, the impact can be life-changing. Rising care costs can devour your estate or inheritance. And your loved one's daily nee...Highmark Caring Place to Expand Services to New Facility in Cranberry Area
Grieving children from northern Allegheny, Armstrong, Beaver, Butler, Lawrence and Mercer counties to be served at new facility PITTSBURGH, Feb. 25 /PRNewswire/ -- The Highmark Caring Place, A Center for Grieving Children, Adolescents and Their Families, announced today its intention to...Study Finds High Cost of Caring for Aging Parent
Adult day care is affordable option to consider SAVAGE, Minn., Nov. 28 /PRNewswire/ -- Caring for an aging parent or spouse is expensive -- averaging about $5,500 a year -- according to a new national study. The findings, released this week, provide the first detailed look at out...Getting to the Root of Caring for Your Hair at Any Age
Dermatologist Offers Top Tips for Maintaining a Lifetime of Healthy Hair NEW YORK, Nov. 8 /PRNewswire/ -- For most people, and especially women, hair is their crowning glory that defines a significant part of their appearance and personal style. Yet, despite its delicate composition, hair is r...Grandparents' Care Makes Grandchildren More Caring for Them
A new research has found that grandchildren, who were taken care of by their grandparents during childhood, show a greater desire to take care of their grandparents as they age . The University of Haifa study demonstrated that grandchildren, who stayed with their grandparents and received t...World Kidney Day – Caring for the Kidney
March 8th is commemorated as the World Kidney Day every year. In today's world, communicable diseases have paved the way// for non-communicable ailments, like chronic kidney disease, hypertension, diabetes and cardiovascular diseases as leading cause of death and despair. There is an incre...Learning to Prevent Medical Mistakes in Caring for Stroke Patients
Medical errors and adverse events can happen in patients with stroke, and hospital procedures need to be modified to reduce the likelihood// of error and patients getting hurt, according to a study. For the study, researchers analyzed provider-reported adverse events and errors within a volu...Melbourne University Launches Plan To Produce More Caring Doctors
Melbourne University has launched a plan to improve the bedside manners of would-be doctors. For this plan to come into effect, the medical students will be "embedded" with patients suffering from a chronic illness such as diabetes or arthritis for two years. // This program will be compulsor...Kaiser Foundation Health Plan and Hospitals Report Second Quarter 2009 Financial Results
...for members and patients is focused on their total health and guided by their personal physicians, specialists, and team of caregivers. Our expert and caring medical teams are empowered and supported by industry-leading technology advances and tools for health promotion, disease prevention, state-of-the art...School Closures May Not Be Necessary When Swine Flu Strikes
... plan should important personnel, such as school nurses, fall ill. The CDC recommends the use of surgical masks for ill students or staff and those caring for them. The education of students who are ill at home with the flu should be continued, using phone calls, homework packets and Web-based learn...Electronic Health Records Help Cardiac Patients Remain Healthy
... for members and patients is focused on their total health and guided by their personal physicians, specialists and team of caregivers. Our expert and caring medical teams are empowered and supported by industry-leading technology advances and tools for health promotion, disease prevention, state-of-the art...Is it Exam Time for Georgia's School Children Already?
...oritization for those administering the vaccine to first immunize children and young adults from six months to 24-years-old, and people living with or caring for children younger than six months of age before administering vaccines to the general population. The message seems to be hitting home beca...Hospice Care Eases the End for Loyal Pets
...be exhausting, especially for elderly owners or those who work full-time. But Kenneth Koch of Modesto, Calif., doesn't regret the three years he spent caring for his cat, Midnight. Adopted by Koch nearly two decades earlier, the black domestic shorthair had chronic renal failure, among other illnesses. I...


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Cab fares around Manhattan can be ridiculous, that's expected. But imagine paying more than $1 million just to own a licensed taxi in New York City. That's the reality now. » 11/19/13 10:44am 11/19/13 10:44am
This brand-spankin'-new yellow New York taxi-ready Ford Crown Victoria fleet I stumbled across yesterday, springing up like a patch of daisies through the cracks of the concrete urban jungle of Hoboken, New Jersey, is both poignant and beautiful. » 6/13/11 12:00pm 6/13/11 12:00pm


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Below are the all-time best Storm poems written by Poets on PoetrySoup. These top poems in list format are the best examples of storm poems written by PoetrySoup members
View ALL Storm Poems
Search for Storm poems, articles about Storm poems, poetry blogs, or anything else Storm poem related using the PoetrySoup search engine at the top of the page.
Definition & Discussion of Storm Poems Read Storm Poems
See also: Best Famous Poems
I saw you yesterday I saw you yesterday, your features grinned, some silken scarf was waving in the blue, I thought of what the rains could not rescind; our images, that in the fields imbue. I saw tempestuous, around me shades, the rain's persistence had engraved your name upon the slate, around she formed cascades, inviting flash amid the drops, and flame. I saw flash yesterday, inside the rain, how beautiful it was, her kiss of dew your words became my sails on trip arcane the clouds, your messengers, 'mid skies to strew. I sensed the crooked line reticulate, the sulfur acrid smell and pale flame's hue, transmuting to abderian road skate, zigzagging on a water copper tube. The flame transformed to runnel flowing laughs; the rustling of droplets on the leaves, combined the bright and shapely drawing graphs with clouds to form above, celestial eaves. I saw flash yesterday, my features grinned, like silken scarf was waving in the blue, I thought of what the rains could not rescind: two images, amidst the fields imbue. © G. V., 10-21-2013, All Rights Reserved (Iambic pentameter)
~ Yolanda--her name ~ Featuring:) Leonora Galinta From a hell storm, A mighty she devil took on its form Like a woman scorn ascending from the sea Haiyan whipped across the central Philippines, A deadly typhoon, maximum winds of around 315 Terrorizing the fragile mind before making landfall Hitting with the center eye off from her hostility A merciless turbulence that came and changed everything Like a Massive Storm She comes in as the wise thief of the day and night, In her notorious gust of rage roars in disguise of thunder, With the company of her own knight of darkness, Raze all in a blast of waves wherever her path crosses, Ruining one of the cities down to a devastation in the land "Pearl of the Orient Seas." A mighty tempest in a woman's name….. Yet, A disgrace with more than an immortal man in strength, Nature devouring nature itself Including her stewards and stewardesses An unmerciful encroachment, robbing, killing adults and children. Yolanda, so cruel in her evil walloping! A gust left smiling, Engraving echoes of tears, from every single mourn Vain, wicked, and colorless -no other air's compare The lives she stole, one heart at a time Pouring down the most nauseating rain, The pain is dissenting with everyone-- everywhere. The bully of wind, invading sands of serenity Unknowingly, far beyond your back---------------------------- Everybody will be summoning up more than your strength- ~A Poet Destroyer Collaboration~
lightning punching down, fast, blinding, loud – blood pain a prayer of tears to all who have suffered violence David Meade
Sometimes, life has no reason unlike the seasons It aimlessly drifts with the wind We find ourselves in places of unfamiliar faces Bathing in the shadows of sin Our souls become lost up in the holocaust That once was a beautiful life Like a ship drifting upon the tide we bang and then we ride The white horse straight into death Into a giant black hole we dive in with our soul Until we have nothing left We then fall prey to our host who spreads butter on our toast Our habits take over our lives Everything we hold dear falls with one last tear Into the darkness of night Tired and defeated all our hope is depleted Because we have nothing left to lose Sometimes the storm passes as slow as molasses Left frozen somewhere in the snow Then our red eyes run dry with no tears left to cry As we admit, I'd rather be dead If you have a desire to live right, please take heed of my plight And know that it's never to late Soon as you give it away find your knees and pray You will find the comfort of home And all of the disgrace will fall off of your face Like the leaves that fall off the tree And just like the bare tree soon you will see Life is reborn in the spring Like a warm days cool breeze, God fills us with his ease And through him we find some peace One day at time the trials all unwind As the jigsaw falls into place As everything gets better we become one with the weather And the seasons suddenly become our friend Our lives suddenly fly past, because we want to make them last Like an ice-cream on a really hot day We are overcome with the obligation to tell of our salvation Remembering all of those left behind Some will find their way, others all we can say Is Lord, we truly did our best Dear Lord we write for your glory, telling our stories That we would rather keep hid on the shelf Our desire is to aspire so we can rise ever higher With the words that flow though our pen Giving of ourselves becomes our greatest wealth As our souls become one with the Son No high could be higher than faith and desire Knowing we have been born again One day we will stand before the gates that shall open to our fate As heaven welcomes us in We will look down on this earth, spirits of a new birth Watching over the seeds that we spread Knowing their lives were made better, because we were able to weather The storm that raged through night Until the day I become shadows and dust I'll forever trust The words that flow through my pen
The gentle music flows from every drop of rain, as it just lightly taps against my window pane. The wind begins to whistle it's own melodious song, while the wind-chimes dance and play along. The soothing sounds cast open the windows and doors. I close my eyes and breathe. The energy surrounds me as my spirit soars. I hold out my hand and feel the raindrops as if they were at play. My breath now quickened with emotion. I taste the rain on my lips as I embrace the glorious day. The curtains blow inward the breeze itself is warm, my mind is so peaceful in the calm before the storm. The sky's voice trembles from above a darkening cloud, as the rolling thunder speaks it's thoughts aloud. The thunder awakens the flash of light. The part of nature that sends some to flight. I chose to embrace the power of nature in the earth and sky. And bask in the wonder that fills my eyes. The rain seems to be letting up as it puddles on the green grass, and the once powerful winds are now calming down at last. The gray clouds are parting and a bright rainbow forms, proving that something beautiful can come from such dangerous storms. My eyes close and I breathe in the scent of the cleansing rain. The brilliant hues of the rainbow dance in my mind where I feel no pain. The sun peaks from behind the clouds just to say hi. I feel the warmth against my face as I view the beauty with a sigh. Written by: Kelly Deschler & Nature Boy For Jared Pickett's contest - "Collaboration"
Oh darkness lies entrenched within my heart Fears, like ocean waves flood over my soul Drowning in the abyss of a sea that is all mine These black storms have left me without hope I'm a sinking ship that is listing and all alone So desperate this very moment for a lifeline But in this churning flood there is not a lifeline Only sorrow upon sorrows drowning my heart The rising sea billows have washed over any hope Speechless and unattended I am a mortified soul And though I hear the cries of others I am alone A vanquished life with nothing left that is mine I do remember a time when things were mine There was no thought and no need of a lifeline I sometimes felt lonely but never really alone There wasn't yet a broken and battered heart The future was still unknown to my naive soul Back then my tomorrow's were filled with hope Skies were clear and a bright magnificent hope As if a postcard that said the world was mine The warmth of the sun was peace to my soul The gentle breeze upon my sails a steady lifeline Calm waters brought comfort and gave me heart Too taken to realize I was enjoying this bliss alone Then one day an unexpected storm cloud rose up alone This tempest would only grow overtaking all my hope A fierce head wind pushing against my anchored heart Waves of thunder burst threatening all that is mine An ominous beast and not even a compass for a lifeline Lightning strikes illuminating the hidden dread in my soul The ship that carried me has now abandoned my soul Broken into pieces an orphan castaway that is all alone Longing through tears to be thrown a life saving lifeline Looking for a brilliant lighthouse to point the way home All that I ever dreamed for was a family that was mine To be rescued from this storm and save my dying heart Oh what my sad soul would give for such an abiding hope No longer alone and fully loved by parents that are mine A family is my only lifeline and the sole desire of my heart Contest: Carol's "Best Of 2014" Poet: LyricMan
Drenching rains, no shape nor form Howling winds, skies midnight black Lightning striking, a powerful storm Our little haven, now under attack Plans for our moonlit stroll are dashed No lights, no music, just you and me Squeezing me tighter with every flash Letting our two longing hearts be free Waiting out the storm, we cuddle by the fire Enjoying the crackling embers until it's done Soft touches, slow kisses, both showing desire Two kindred spirits, coming together as one
Lightning flashed, blinded my innocent, trusting eyes. Thunder ravaged my soul, and forced out my cries. Destructive winds threatened, ripped me all apart. Raindrops, the tears that ever flooded my heart. Dark clouds were ever-present, in turbulent air. Yet, no winds could stir the flowers in my hair. No longer waiting for that storm to pass the hill. I left it behind, and walked away by my own will. A rainbow shined beautifully, yet arched into a frown. As every now and then, the rain still comes down. I have stepped right over you, like scattered debris. As the sun's rays now light down a new path for me. For Shanity Rain's contest - "After The Storm"
In an open field of endless, noiseless distance, Rolling clouds cast an impending gloom; A welcomed and promised darkness descends. My eyes shut as I breathe in the aroma, In anticipation of The cleansing that quickly approaches. I cloak myself in the breeze, as it promises a release.. The cool wind, calming, so gently serene... Sweeping over my overheated skin. Finally, the fury is perfectly unleashed down upon me. The winds, gusting in a frenzied rush My hair whipping haphazardly around, Stinging at my face. I smirk toward the sky, as I silently, but eagerly Await the onslaught - This desperate release that I longed for in secret. It sought me out, and found me. I hear the angry sounds The roaring, begging to weep alongside me. When suddenly, the violent tears begin to fall With a sudden, breathtaking destructiveness. The thunder, like me, cries out in pain, With such sadness, angry liquid bathing the parched earth. It saturates my face, my body drenched. As I stand in the midst of the deluge, in awe, Crashing winds attempt to destroy me, But cannot find the strength. Until the tears eventually run dry, The painful clashes and cries become silent.. The skies yield to light, as the great and Terrible sun demands to be seen. I open my tear-stained eyes, And glimpse a different world before me... Cleansed and made new. And I cannot understand, nor Fathom the reality... Of the beautifully, perfect Broken release.
Summer Storm The wind blows – quick, hard, fast – the hot stillness is broken Corn stalks weave wildly as the wind marches through it rows Dust rises to greet this invading storm Large drops of heavy rain hit with a thud Lightening electrifies and paints the blacking sky Hail rips leaves from their home – a hard crack of thunder Clouds tumbling, rolling, forming into a funnel A loud rushing noise – a banshee scream Trees snap, the wind-train thunders by . . . then a deep silence Holding hands they arise from underground Sky clearing, sun peeking through A double rainbow appears – a promise – life . . . love Winter Storm The night is cold and wet, slick over bridges curving edge The rain freezes turning sheets of ice into nature's sculpture Electrical power lines coated thick -- snap, taking heat away from all Nights of darkness with candles are filled with hearts of hope Ice storms that cripple a city and put a halt on activities As beautiful as they are terrifying, they demand a reckoning When January blows out fierce and February is held captive Our human spirit tired and cold but not beaten Prays for warmer days ahead with confidence Nights of hearths and man made fires Fur lined slippers and flannel robes Better off indoors, with close kin . . . warmed with hope and love Written in collaboration with Mystic Rose Beautiful is the friendship of a Mystic Rose . . . sweet and warm
Strange colored skies climb northernly this night Calling our future with wild deamons eyes Abscure as the creatures who answer the call Wild are the answers of the reasons and the faults Certain as the well swept winds Alluring in it's grasp fought negatively through single wins I pray twords the skies and it curdles and swims Thoughts twords the sun and it scorches my rims Carry me far enough I can be within your sights Stash us away and the sun will be bright Motors may break but oceans will be light I will stay on the coast and wait The award I will do is make the evening a minute late Parched is the gulf as the single minute breaks Great is the second docks a seperate mans gate The Earths crust slowly begins to crumble It quivers, then quakes, it slowly opens, the rivers break A star is born somewhere, a beautiful new star Great is the struggle, born from the heavens a small light it makes The new star pulls, it turns, then it feeds and it's fuel it burns Gently it orbits following all things it understands The new star bends it dances it stands Tancing outwardly as creations comprehend A continient wavers as the new star binds its brand It feeds off of our oceans as our tides wash in It goes just as softly forward and back As the rays of its placement barrow up to the sun We watch very carefully because it's damages are already done
early winter storm snowflakes mixed with freezing rain chilling to the bone your killer smile warms me along with some lemon tea
A Rage Against The Storm Alas! against the storm I did bellow, you bloweth upon the wrong fellow My soul you have now so sorely tried fear, your gift has now so surely died! Nature feeds your evil blowing wrath, I curse your daring this upon my path Heaven's powers ignore your wicked deeds you the rot that eats away joy's seeds! Hark! all the destruction you have wrought, fruits of sins that man surely has bought Yet, I defy your right to so hammer me I, the strongest root of my family tree! Rage on , tear out the withered and the old This man defies you with a heart very bold! Robert J. Lindley, 08-27-2014
The lighthouse stands, the lighthouse stands Above the foaming wave, Above the sands. He stands so brave, he stands so brave, As winds against him blow; The ships to save. He sends below, he sends below His fiery, gleaming light, The way to show. All through the night, all through the night He guards the lonely point With torches bright.
After The Storm, Rebirth Storm has torn the majestic forested scene as ravaged are the shrubs on high hills Surviving birds yet sing and calmly preen unmindful of last night's ripping thrills Trees now broken, toppled at Nature's behest all forested tranquility yet to be restored Nature shook violently and did its very best lakes many boats sunk where they moored From this destruction new life shall reign savage death brings on creation's birth Beauty shall come with all that we see plain earth renews the landscape for all its worth I see with these renewing things a greater plan All teaches life's lessons to the heart of man Robert J. Lindley, 11-17-2014 Inspired by Gry's Christensen's poem , Brewing Sunsets In Teapots that I read early this morn.
Feet not up yet dreaming looking into the deep distant horizon screams need to take turf in remembering howls across oceans mourning dream special wish You would want a good fire tonight for sure ice stormy fierce cold cutting out walking giant waves hitting of the shore thundering pounds lashing clash Today the wind fairly woke me up piercing wide eye opening vision Then when I got home just felt ten years younger alive again one storm Now that's a good omen laughing to myself carries one to the high Heavens Must be the salted spray love mixed with sea mist smashes you to the ground love New therapy go out to the sea front as gales howling with angry force break news blowing giant waves crashing heavy of cliffs thundering roars echoes inside sad Wind spitting sea salt sand peppering the face in your hardened heart hate remains your driving engine unforgiving hung up on the past
Could You Tell Me! Could you tell me again, your heart needs mine could you do it again with your smile so fine softly speak those secret words you use to melt my heart and soul while sharing all you felt! Will you speak of past love encounters please set my heart a singing and put my soul at ease gently running your sweet fingers in my hair as you whisper, love you, my darling so fair! Can you stir my ardor more than it's ever been even higher and greater than on our first spin that saw us naked and hot under the midnight moon with daybreak so cruelly daring to appear too soon! Could you heat my soul into a passionate storm with us naked and locked into each other's arms! Robert J. Lindley, 06-24-2014
Secrets sail on the whirling winds, along with the dark and driven clouds. Carried aloft with litter and leaves are invisible, partly submerged longings: to hitch a ride on the primal rawness, to abandon all things set and tethered, to project oneself toward the unknown, while thriving through the natural chaos.
Sharp, rocky, dangerous promontories, dark crashing violence maleficent down below. Weathering belligerent waves, sailors agonize increasingly, eyes straining, constantly calculating. Light streaming, searchingly intelligent- the lighthouse, beautiful revelation- comes into exhausted perspective. September 19, 2014 Faye Lanham Gibson The Lighthouse Contest Nette Onclaud, sponsor
White Devil Call it what you want! I call it, his favorite season hunt... Two hoofs imprinted near the riverfront. Echoes calling my soul with a loud, ferocious grunt. I smell it in the air, lost upon the white golden stair. A deep frost dwelling all over his lair. Tangled by the frozen grip of my hair. A decision, I declare to give what he won't spare. This man has no red suit.. Lurking in the white to recruit. A midnight suicide clouding me with pollute. I pause my tongue on mute, lost in a white castle chute. Headed straight into a shivering blazing star path. The land of snow covered like a bubble bath. Breaking icicles like crystal glass, suck3d by the milky-way mass. Multiplying bruises like a cascade, enjoying the aftermath. Finding a way to slit the pain in my domain. I grab a coat and lace my name to Mary-Jane. Inserting the finest line to ease the drain in my brain. I drink the icy scotch, and drop a silver nickel into the devils cocaine. Fallen in to his bait, its too late, I got 7 lines on my dinner plate. I'm covered up in snow, enjoying the amazing way to suffocate. Eight beats to every minute is my new heart rate. I'm reaching for the white golden gate, where the white devil waits. Drowning like liquor in a frappe mixing the winter's high tide. Death to my soul is where I hide under this white blanket neutral side. Too heavy to uplift this storm lost in the devil's cold custard suicide guide. Waking up in a coma, in a world where white collides with the rage of suicide. by;p.d. (( Trapped in a snowy blizzard))
Amid the woods and snow he saw her form, predestined oracle he sensed this was, her recollected glance, was lone in storm, outside the chapel she became first cause . Lit were the chandelier's ocher chandelles, his heartbeat thrummed an airy rhythmic spell, the forest snowstorm reeled - shaped ghostly belles invited him beneath the ringing knell. Their Angel's bliss, his soul received in flames, adept and kind the whisper of her voice, "- Forgiveness calms those who indulge in blames; devoutness is the prelude of free choice." Outside he stepped beneath the Abbey's knell: His voice dispersed above the snow and mass, in cold embraced the iron wrought of bells, - as waxen light passed through the chapel's glass. His mind and woods enjoined in forceful prayer, spells sacrosanct and numinous instilled, in abstinence the sanctified abbe, abandoned Convent life to years and thrills. Escaped then he, to meet the woods in dark, amidst their sovereign heights he was her groom, continuum of time and space to arc, his childhood's wraith became in mists and tomb. © G. V. 01-04-2012 All rights reserved (Iambic Pentameter)
My weeping eyes behold the changing sky O'erspread with clouds of grey where once was blue With gaze upturned, I heave a burdened sigh At all the world now changed to leaden hue Yet still they onward, ever onward fly And more appear to change the sky anew And now, as troubled hearts their sorrows spill These maudlin clouds the heavy rain distill The sun obscured in shame, he hides his face And lightning lights instead the cheerless gloom While thunder follows swift in furious chase As if to herald thoughts of coming doom And still, the rain descends at hurried pace As if the earth in water to entomb It seems belike this storm would rage for aye And all the earth would never chance to dry But lo! The setting sun that once was veiled! Draws nigh to show his grandeur forth below He shines his beams abroad the clouds to gild And sparks the drops as diamonds all aglow Mid pools of sapphire blue the sky is filled With vibrant coloured shades of heaven's bow What eye could see and not revive its fire? Nor mind behold and not its thoughts inspire?
A young girl who believed in rainbows all those colors were just so cool You grew up, life's storms battered you these last few years have been so cruel Hard to remember dreams from long ago a beautiful Princess you wanted to be Floods of tears blinding future's hope a single mom with a child your reality But this morning a rainbow greeted you all those colors were still cool to see Young girl's dream to chase that rainbow this time you did and it led right to me You finally found the end of a rainbow indeed there was a pot of pure gold Not the kind found in rocks or rivers But a man with many secrets untold And he longed to share them with you called you Princess and took your hand My first secret when I was a young boy was to grow up and become your man! Contest: SKAT's "One Word Title" Date: 6-12-14
The trail was long and very dusty great clouds churned up by hooves of the vast herd being wrangled on 300 more miles of eating their dust Bandana's tightly wrapped round faces cries of "get up there" ringing out bawling calves separated from mothers hiss of hot branding irons scorching A rumbling constantly moving mass stretching back as far as eyes can see horses reeling back and forth, pushing always pushing them on, 200 miles to go Storm is approaching as they settle down tightly bunched up wranglers keeping watch hard as nails falls the rain, lashing down cattle milling round and round as flashes Of lightning light up the sky causing restless beasts to try to break and flee away tumultuous thunder now joining in causing panic "Keep them circling, don't let them break out" Came the cries of the foreman as they tried to hold chuck wagon knocked over as through camp they run woe to anyone on foot or even a thrown rider "keep them going south, They will stop at the river" Gradually the storm quietens and dies down first light shows how scattered they are some needing to be shot where they lay mangled the rest pushed through the river to the plains Here they can be regrouped, lush grasses to eat no urgency now 10 miles or so a day we push them letting them gain some more weight, 50 miles to go the foreman sends two men on to warn the yards At last they see the rail tracks, only 15 miles away "one last big push lads and we will have them there tonight we will wet our whistles and eat like kings" hot tubs to soak in, washing away dirt that is caked We push them into the waiting pens as they bawl and churn settled now with fresh hay and water the plaintive calls of mothers looking for their calves, the wranglers push them together keeping the bulls apart, they will ship first Now work is done, 800 miles or so we have driven them it is time to relax and let our hair down, find ladies of the night with which to dally for awhile, some poker played, several fights break out over who gets which one As dawn breaks low rumbles from the pens as the cattle stir the town but for a few still fast asleep, until the train spitting steam and smoke arrives, and buyers now alight many offers are made and rejected out of hand, these cows Are already sold to keep our armies fed as they war against the Maverick Indians, that are plundering the homesteads 30,000 at first of drove, now reduced to 27,000 or so loaded up on the train our job is done we are homeward bound written 09/17/2013 contest Epic Only
Wind so cold. Blowing. Fondles my face. Tickling. The tears from heaven. Pouring. Tapping. Dancing. Unrelenting. I wonder if i wish to stop them From numbness, to waking, then sensing. The little voice in me says, Wait, don't go. Stay a little longer. I plead. Sing for me today, rain. With the gliding rhythm on my piano, I'll play. Chilly Wind, caress my bare skin with the pure coldness that you bring. Unusual, like it's my first time in the snow. Somehow, the fire tree never fades in the picture. The yellow sunkissed leaves, too. What is it about Summer and Fall that I can't forget? Memories. Sweet imaginations. The chilly rain. The misty wind. You are here. Freeze me with the sharp coldness you give. Calm me. Maybe, comfort me. And, if you leave Will you visit me when summertime comes? Before it gets too late And again I fold.


text:
- Conference date: 30 July-2 August 2003
- Location: Konigstein (Germany)
The atomic orientation generated by polarized‐electron impact excitation of Hg (6s 2) 1S0 → (6s6p) 3P1 is discussed with regard to the so‐called 'orientation propensity rules'. Experimental results for the orientation parameter as well as existing theoretical predictions employing a five‐state semi‐relativistic R‐matrix (close‐coupling) description and the relativistic distorted‐wave approximation show that the orientation propensity rules are apparently violated if the electron spin is initially down with respect to the scattering plane. The applicability of the propensity rules to electron‐impact excitation of heavy atoms is analyzed within a non‐relativistic description. The observed apparent violation can be attributed to a quantum mechanical interference caused by 'intermediate coupling' within the excited state. A re‐evaluation of the data supports the validity of the propensity rules and yields a consistency check of the non‐relativistic approach.
Key Topics
- Relativistic scattering theory
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- Electron scattering
- 1.0
- Excited states
- 1.0
- Mercury (element)
- 1.0
- Scattering theory
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This article describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches accommodate signals of different strengths contaminated by a colored Gaussian background, and perform detection without reconstructing the underlying signals from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets coming from a known dictionary. The anomaly detector is designed to control the number of false discoveries. The proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the distance preservation property of the measurement matrix. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.
Target detection; Anomaly detection; False discovery rate; ip-value; Incoherent projections; Compressive sensingIntroduction
The theory of compressive sensing (CS) has shown that it is possible to accurately
reconstruct a sparse signal from few (relative to the signal dimension) projection measurements
[1,2]. Though such a reconstruction is crucial to visually inspect the signal, there are
many instances where one is solely interested in identifying whether the underlying
signal is one of several possible signals of interest. In such situations, a complete
reconstruction is computationally expensive and does not optimize the correct performance
metric. Recently, CS ideas have been exploited in
[3-5] to perform target detection and classification from projection measurements, without
reconstructing the underlying signal of interest. In
[3,5], the authors propose nearest-neighbor based methods to classify a signal
For example, recent advances in CS have led to the development of new spectral imaging platforms which attempt to address challenges in conventional imaging platforms related to system size, resolution, and noise by acquiring fewer compressive measurements than spatiospectral voxels [16-21]. However, these system designs have a number of degrees of freedom which influence subsequent data analysis. For instance, the single-shot compressive spectral imager discussed in [18] collects one coded projection of each spectrum in the scene. One projection per spectrum is sufficient for reconstructing spatially homogeneous spectral images, since projections of neighboring locations can be combined to infer each spectrum. Significantly more projections are required for detecting targets of unknown strengths without the benefit of spatial homogeneity. We are interested in investigating how several such systems can be used in parallel to reliably detect spectral targets and anomalies from different coded projections.
In general, we consider a broadly applicable framework that allows us to account for background and sensor noise, and perform target detection directly from projection measurements of signals obtained at different spatial or temporal locations. The precise problem formulation is provided below.
Problem formulation
Let us assume access to a dictionary of possible targets of interest
• i∈{1,…,M} indexes the spatial or temporal locations at which data are collected;
• αi≥0 is a measure of the signal-to-noise ratio at location i, which is either known or estimated from observations;
For example, in the case of spectral imaging
(1) Dictionary signal detection (DSD): Here we assume that each
(2) Anomalous signal detection (ASD): Here, our task is to detect all signals which
are not members of our dictionary, i.e., detect
Our goal is to accurately perform DSD or ASD without reconstructing the spectral input
In this article, we develop detection performance bounds which show how performance
scales with the number of detectors in a compressive setting as a function of SNR,
the similarity between potential targets in a known dictionary, and their prior probabilities.
Our bounds are based on a detection strategy which operates directly on the collected
data as opposed to first reconstructing each
Performance metric
To assess the performance of our detection strategies, we consider the false discovery rate (FDR) metric and related quantities developed for multiple hypothesis testing problems [29]. Since we collect M independent observations of potentially different signals, we are simultaneously conducting M hypothesis tests when we search for targets. Unlike the probability of false alarm, which measures the probability of falsely declaring a target for a single test, the FDR measures the fraction of declared targets that are false alarms, that is, it provides information about the entire set of M hypotheses instead of just one. More formally, the FDR is given by,
where V is the number of falsely rejected null hypotheses, and R is the total number of rejected null hypotheses. Controlling the FDR in a multiple hypothesis testing framework is akin to designing a constant false alarm rate (CFAR) detector in spectral target detection applications that keeps the false alarm rate at a desired level irrespective of the background interference and sensor noise statistics [22].
Previous investigations
Much of the classical target detection literature
[30-34] assume that each target lies in a P-dimensional subspace of
Recently, several methods for target or anomaly detection that rely on recovering
the full spatiospectral data from projection measurements
[36,37] have been proposed. However, they are computationally intensive and the detection
performance associated with these reconstructions is unknown. Other researchers have
exploited CS to perform target detection and classification without reconstructing
the underlying signal
[3-5]. Duarte et al.
[4] propose a matching pursuit based algorithm, called the incoherent detection and estimation
algorithm (IDEA), to detect the presence of a signal of interest against a strong
interfering signal from noisy projection measurements. The algorithm is shown to perform
well on experimental data sets under some strong assumptions on the sparsity of the
signal of interest and the interfering signal. Davenport et al.
[3] develop a classification algorithm called the smashed filter to classify an image
The authors of a more recent work [38] extend the classical RX anomaly detector [39] to directly detect anomalies from random, orthonormal projection measurements without an intermediate reconstruction step. They numerically show how the detection probability improves as a function of the signal-to-noise ratio when the number of measurements changes. Though probability of detection is a good performance measure, in many applications controlling the false discoveries below a desired level is more crucial. As a result, in our work, we propose an anomaly detection method that controls the FDR below a desired level.
This article makes the following contributions to the above literature:
• A compressive target detection approach, which (a) is computationally efficient, (b) allows for the signal strengths of the targets to vary with spatial location, (c) allows for backgrounds mixed with potential targets, (d) considers targets with different a priori probabilities, and (e) yields theoretical guarantees on detector performance. This article unifies preliminary work by the authors [40,41], presents previously unpublished aspects of the proofs, and contains updated experimental results.
• A computationally efficient anomaly detection method that detects anomalies of different strengths from projection measurements and also controls the FDR at a desired level.
• A whitening filter approach to compressive measurements of signals with background contamination, and associated analysis leading to bounds on the amount of background to which our detection procedure is robust.
The above theoretical results, which are the main focus of this article, are supported with simulation studies in Section "Experimental results". Classical detection methods described in [22,26,27,30-35,39,42-45] do not establish performance bounds as a function of signal resolution or target dictionary properties and rely on relatively direct observation models which we show to be suboptimal when the detector size is limited. The methods in [3,4] do not contain performance analysis, and our analysis builds upon the analysis in [5] to account for several specific aspects of the compressive target detection problem.
Whitening compressive observations
Before we present our detection methods for DSD and ASD problems, respectively, we briefly discuss a whitening step that is common to both our problems of interest.
Let us suppose that there are enough background training data available to estimate
the background mean μb and covariance matrix Σb. We can assume without loss of generality that μb=0since Φμb can be subtracted from y. Given the knowledge of the background statistics, we can transform the background
and sensor noise model
We can now choose Φ so that the corresponding Ahas certain desirable properties as detailed in Sections "Dictionary signal detection" and "Anomalous signal detection".
For a given A, the following theorem provides a construction of Φthat satisfies (3) and a bound on the maximum tolerable background contamination:
Theorem 1
Let B=I−AΣbAT. If the largest eigenvalue of Σb satisfies
where ∥A∥ is the spectral norm of A, then B is positive definite and Φ=σB−1/2Ais a sensing matrix, which can be used in conjunction with a whitening filter to produce observations modeled in (2).
The proof of this theorem is provided in Appendix 1. This theorem draws an interesting relationship between the maximum background perturbation that the system can tolerate and the spectral norm of the measurement matrix, which in turn varies with K and N. Hardware designs such as those in [17,19] use spatial light modulators and digital micro mirrors, which allow the measurement matrix Φ to be adjusted easily in response to changing background statistics and other operating conditions.
In the sections that follow, we consider collecting measurements of the form
Dictionary signal detection
Suppose that the end user wants to test for the presence of one known target versus
the rest, but it is not known a priori which target from
Decision rule
We define our decision rule corresponding to target
The decision rule can be formally expressed in terms of the significance regions as follows:
We analyze this detector by extending the positive FDR (pFDR) error measure introduced by Storey to characterize the errors encountered in performing multiple, independent and nonidentical hypothesis tests simultaneously [48]. The pFDR, discussed formally below, is the fraction of falsely rejected null hypotheses among the total number of rejected null hypotheses, subject to the positivity condition that one rejects at least one null hypothesis. The pFDR is similar to the FDR except that the positivity condition is enforced here. In our context, the positivity condition means that we declare at least one signal to be a nontarget, which in turn implies that the scene of interest is composed of more than one object in the case of spectral imaging, or that the scene is not static in the case of video imaging.
Consider a collection of significance regions
is the number of falsely rejected null hypotheses,
is the total number of rejected null hypotheses, and
Theorem 2
Given observations of the form (2), if one performs multiple, independent, nonidentical hypothesis tests of the form (5) and decides according to (7), then the worst-case pFDR given by pFDRmax=maxj∈{1,…,m}pFDR(j)(Γ), satisfies the following bound:
The proof of this theorem is detailed in Appendix 2. A key element of our proof is the adaptation of the techniques from [48] to nonidentical independent hypothesis tests.
An achievable bound on the worst-case pFDR
Theorem 2 in the preceding section shows that, for a given A, the worst-case pFDR is bounded from above by a function of the worst-case misclassification
probability. In this section, we use this theorem to establish an achievable bound
on the worst-case pFDR that explicitly depends on the number of observations K, signal
Let us first define the quantities
Then we have the following theorem, whose proof is given in Appendix 3:
Theorem 3
Let λmax denote the largest eigenvalue of Σb. For a given 0 < ε < 1−pmax, assume that K and N are sufficiently large so that the following conditions hold:
Then there exists a K×N sensing matrix Athat satisfies the condition of Theorem 1, and for which
This result has the following implications and consequences:
(1) For a given N, the upper bound (13b) on λmaxincreases as K increases, which implies that the system can tolerate more background perturbation if we collect more measurements.
(2) The pFDR bound (14) decays with the increase in the values of K, dminand αmin, and increases as pmindecreases. For a fixed pmax, pmin, αminand dmin, the bound in (14) enables one to choose a value of K to guarantee a desired pFDR value.
(3) The dominant part of the bound (14) is independent of N, and is only a function
of K, pmax, pmin, αmin, and dmin. The lack of dependence on N is not unexpected. Indeed, when we are interested in
preserving pairwise distances among the members of a fixed dictionary of size m, the
Johnson–Lindenstrauss lemma
[49] says that, with high probability,
(4) The bound on K given in (13c) increases logarithmically with the increase in the
difference between pmax and pmin. This is to be expected since one would need more measurements to detect a less probable
target as our decision rule weights each target by its a priori probability. If all
targets are equally likely, then pmax=pmin=1/m, and
(where the first inequality holds since K < N). In addition, the lower bound on K
also illustrates the interplay between the signal strength of the targets, the similarity
among different targets in
Inspection of the proof shows that if Ais generated according to a Gaussian distribution, then the conditions of Theorem 3 will be met with high probability.
Extension to a manifold-based target detection framework
The DSD problem formulation in Section "ASD problem formulation" is accurate if the
signals in the dictionary are faithful representations of the target signals that
we observe. In reality, however, the target signals will differ from the dictionary
signals owing to the differences in the experimental conditions under which they are
collected. For instance, in spectral imaging applications, the observed spectrum of
any material will not match the reference spectrum of the same material observed in
a laboratory because of the differences in atmospheric and illumination conditions.
To overcome this problem, one could form a large dictionary to account for such uncertainties
in the target signals and perform target detection according to the approaches discussed
in Sections "Whitening compressive observations" and "Dictionary signal detection".
A potential drawback with this approach is that our theoretical performance bound
increases with the size of
Let us consider a dictionary of manifolds
(1) Given {yi}, form a data-dependent dictionary
for ℓ∈{1,…,m} and i=1,…,M.
(2) Given
and declare that the ith observed spectrum corresponds to class j if
This two-step procedure is studied in
[3] for the case
Anomalous signal detection
The target detection approach discussed above assumes that the target signal of interest resides in a dictionary that is available to the user. However, in some applications (such as military applications and surveillance), one might be interested in detecting objects not in the dictionary. In other words, the target signals of interest are anomalous and are not available to the user. In this section, we show how the target detection methods discussed above can be extended to anomaly detection. In particular, we exploit the distance preservation property of the sensing matrix A to detect anomalous targets from projection measurements.
ASD problem formulation
Given observations of the form in (2), we are interested in detecting whether
Note that the definition of the hypotheses given in (15a) and (15b) matches the definition in (5) for the special case where the dictionary contains just one signal. In this special case, the signal input f∗ is in the dictionary under the null hypothesis in both DSD and ASD problem formulations.b
Anomaly detection approach
Our anomaly detection approach and the associated theoretical analysis are based on a "distance preservation" property of A, which is stated formally in (18). We propose an anomaly detection method that controls the FDR below a desired level δ for different background and sensor noise statistics. In other words, we control the expected ratio of falsely declared anomalies to the total number of signals declared to be anomalous. Note that here we work with the FDR as opposed to the pFDR, since it is possible for a scene to not contain any anomalies at all. We let V/R=0 for R=V=0 since one does not declare any signal to be anomalous in this case. In [29], Benjamini and Hochberg discuss a p-value based procedure, "BH procedure", that controls the FDR of M independent hypothesis tests below a desired level. Let,
be the test statistic at the ith location. The p-value can be defined in terms of our test statistic as follows:
To apply this procedure in our setting, we need to find a tractable expression for
the p-value at every location. This can be accomplished when A satisfies the distance-preservation condition stated below. Let
The existence of such projection operators is guaranteed by the celebrated Johnson
and Lindenstrauss (JL) lemma
[49], which says that there exists random constructions of A for which (18) holds with probability at least 1−2|V|2e−Kc(ε)provided
We now state our main theorem that gives a tight upper bound on the p-value at every
location when {αi} are unknown and are estimated from the observations. Let
for i=1,…,M where ζ∈[0,1] is a measure of the accuracy of the estimation procedure.
Theorem 4
If the ith hypothesis test is defined according to (15a) and (15b), the projection
matrix A satisfies (18) for a given ε∈(0,1), and the estimates
holds for all i=1,…,M where
The proof of this theorem is given in Appendix 4. We find the p-value upper bounds
at every location and use the BH procedure to perform anomaly detection. The performance
of this procedure depends on the values of K, {αi}, τ and ε. The parameter ε is a measure of the accuracy with which the projection
matrix A preserves the distances between any two vectors in
One can easily estimate {αi} from {yi} for some choices of A. For instance, if the entries of the projection matrix Aare drawn from
In practice, we use
for some absolute constants C,c > 0. This result shows that with high probability,
The experimental results discussed in Section "Experimental results" demonstrate the performance of this detector as a function of K, {αi} and τ when {αi} are known and as a function of K, τ and ζ when {αi} are estimated.
Experimental results
In the experiments that follow, the entries of Aare drawn from
Dictionary signal detection
To test the effectiveness of our approach, we formed a dictionary
We evaluate the performance of our detector (7) on the transformed observations, relative
to the number of measurements K, by comparing the detection results to the ground
truth. Our MAP detector returns a label
where m is the number of signals in
Figure 1. Compressive target detection results under the AK ({α} known) and AU ({αi} unknown) cases respectively as a function of K.(a) Comparison of the worst-case empirical pFDR curves with the theoretical bounds when SNR is high. (b) Comparison of the results obtained by the proposed method using projection measurements using Φdesigned according to (24), Φchosen at random, and the ones using downsampled measurements (DM) when the SNR is low.
In the experiment that follows, we let
For an input spectrum
Anomaly detection
In this section, we evaluate the performance of our anomaly detection method on (a) a simulated dataset and provide a comparison of the results obtained using the proposed projection measurements and the ones obtained using downsampled measurements, and (b) real AVIRIS (Airborne Visible InfraRed Imaging Spectrometer) dataset.
Experiments on simulated data
We simulate a spectral image f∗composed of 8100 spectra, where each of them is either drawn from a dictionary
For a fixed τ=0.1 and ε=0.1, we evaluate the performance of the detector as the number of measurements K increases under the AK and AU cases respectively, by comparing the pseudo-ROC (receiver operating characteristic) curves obtained by plotting the empirical FDR against 1−FNR, where FNR is the false nondiscovery rate. Note that 1−FNR is the expected ratio of the number of null hypotheses that are correctly rejected to the number of declared null hypotheses. The empirical FDR and FNR are computed according to
where ptis the p-value threshold such that the BH procedure rejects all null hypotheses for which
pi≤pt, and the ground truth label
We compare the performance of our method to a generalized likelihood ratio test (GLRT)-based
procedure operating on downsampled data, where we collect measurements of the form
in (23) and
for i=1,…,M, where η is a user-specified threshold [26]. While our anomaly detection method is designed to control the FDR below a user-specified threshold, the GLRT-based method is designed to increase the probability of detection while keeping the probability of false alarm as low as possible. To facilitate a fair evaluation of these methods, we compare the pseudo-ROC curves (FDR versus 1−FNR) and the actual ROC curves (probability of false alarm pfversus probability of detection pd) corresponding to these methods obtained by averaging the empirical FDR, FNR, pd and pf over 1,000 different noise and sensing matrix realizations for different values of K. We also compare the performance of the proposed method when Φis chosen according to (24) and when it is chosen at random, as discussed in the previous section. Figure 2a,e show the pseudo-ROC plots and the conventional ROC plots obtained using the GLRT-based method operating on downsampled data when {αi} are known. Figure 2b,f show the results obtained by using a random Gaussian Φ instead of the Φ in (24). Figure 2c,g show the pseudo-ROC plots and the conventional ROC plots obtained using our method when {αi} are known. These plots show that performing anomaly detection from our designed projection measurements yields better results than performing anomaly detection on downsampled measurements and on measurements obtained using a random Gaussian Φ. This is largely due to the fact that carefully chosen projection measurements preserve distances (up to a constant factor) among pairs of vectors in a finite collection, where as the downsampled measurements fail to preserve distances among vectors that are very similar to each other. Similarly, a random projection matrix Φ is not necessarily distance-preserving post-whitening transformation, which leads to poor performance as illustrated in Figure 2b,f. Figure 2d,h shows the pseudo-ROC plots and the conventional ROC plots obtained using our method when {αi} are unknown, and are estimated from the measurements. Note that the value of ζ decreases as K increases since the estimation accuracy of {αi} increases with increase in K. These plots show that the performance improves as we collect more observations, and that, as expected, the performance under the AK case is better than the performance under the AU case.
Figure 2. Comparison of the performances of the proposed anomaly detector using a random Φ, the proposed anomaly detector using the designed Φin (24) and the GLRT-based method operating on downsampled data for different values of
Experiments on real AVIRIS data
To test the performance of our anomaly detector on a real dataset, we consider the
unlabeled AVIRIS Jasper Ridge dataset
Figure 3. Anomaly detection results corresponding to real AVIRIS data for a fixed FDR control of 0.01.
We generate measurements of the form
This work presents computationally efficient approaches for detecting known targets and anomalies of different strengths from projection measurements without performing a complete reconstruction of the underlying signals, and offers theoretical bounds on the worst-case target detector performance. This article treats each signal as independent of its spatial or temporal neighbors. This assumption is reasonable in many contexts, especially when the spatial or temporal resolution is low relative to the spatial homogeneity of the environment or the pace with which a scene changes. However, emerging technologies in computational optical systems continue to improve the resolution of spectral imagers. In our future work we will build upon the methods that we have discussed here to exploit the spatial or temporal correlations in the data.
Appendix 1: Proof of Theorem 1
Using linear algebra and matrix theory, it is possible to show that if B=I−AΣbAT is positive definite, then
satisfies (3).c In particular, we can substitute (24) in (3) to verify that the proposed construction of Φ satisfies (3). Observe that CΦ=(ΦΣbΦT + σ2I)−1/2 can be written in terms of (24) as follows:
where the third-to-last equation follows from the definition of B and (25) follows from the fact that B is symmetric and positive definite. If B is positive definite, then B−1 is positive definite as well and can be decomposed as B−1=(B−1/2)TB−1/2, where the matrix square root B−1/2is symmetric and positive definite. By substituting (25) and (24) in (3), we have CΦΦ=σ−1B1/2σB−1/2A=A. A sufficient condition for Bto be positive definite can be derived as follows.
To ensure positive definiteness of B, we must have
for any nonzero
since ∥A∥=∥AT∥ and ∥Σb∥=λmax, where λmax is the largest eigenvalue of Σb. To ensure ∥AΣbAT∥ < 1, ∥A∥2λmax has to be < 1, which leads to the result of Theorem 1.
Appendix 2: Proof of Theorem 2
The proof of Theorem 2 adapts the proof techniques from [48] to nonidentical independent hypothesis tests. We begin by expanding the pFDR definition in (8) as follows:
Observe that R(Γ)=k implies that there exists some subset Sk={u1,…,uk}⊆{1,…,M} of size k such that
By plugging in the definition of V({Γi}) from (9), we have
for all uℓ∈Sk since the tests are independent of each other given A. The posterior probability
The denominator term in (29) can be expanded as follows:
Observe that
Substituting (30) and (31) in (29),
By substituting (32) in (27) and (28) we have:
where pmax=maxℓ∈{1,…,m}p(ℓ).
Appendix 3: Proof of Theorem 3
The proof is via a random selection technique, similar to random coding arguments common in information theory. Specifically, we will draw a K×N sensing matrix A at random from a particular distribution and then show that, for ε, N, and K satisfying the conditions of the theorem, the probability that the conclusions of the theorem will fail to hold for this randomly chosen Ais strictly smaller than unity. This will imply that the conclusions of the theorem must be true for at least one (deterministic) realization of A.
We begin by specifying all the relevant random variables:
• Gis a random K×Nmatrix with i.i.d.
We assume that
where α1,…,αM > 0 are the given signal strengths.
We first consider the case when α1=⋯=αM=α. Given ε, N, and K, we define the following two error events:
where, for each i∈{1,…,M},
We will now prove that
The union bound gives
Next, we bound
Lemma 1 (Compressive classification error)
Consider the problem of classifying a signal of interest
where the probability is taken with respect to the distributions underlying f∗, A, and n.
Using the above lemma, we have
Combining (36) and (37), we get (35).
Because of (13a), the right-hand side of (35) is less than 1−ε−pmax, which is strictly positive by hypothesis. Thus, from the fact that
and from (34), it follows that there exists at least one deterministic choice of the K×N sensing matrix A∗, such that:
where, for a given choice of A, (Pe)max(A) denotes the maximum probability of error defined in Theorem 2.
Next, from (38a) and (13b) it follows that A∗satisfies the conditions of Theorem 1. Finally, we use (11) to bound the worst-case
pFDR achievable with A∗. First of all, we note that the function
Let us choose
Then from (13a) we have x + h≤1−ε−pmax < 1−pmax, and from (13c) we have x + h≥0. Hence, using (39) and simplifying, we obtain the bound
This proves the theorem for the case α1=⋯=αM=α.
To handle the case when the αi's are distinct, we simply let
and replace the definition of the error event
which follows from the following argument. First of all, we can replace the observation model with the equivalent model
Appendix 4: Proof of Theorem 4
We first prove this theorem assuming that {αi} are known and later extend to the case where
Note that
with high probability. Thus,
When {αi} are estimated from the observations such that
where (42) is due to the distance preservation property of A given in (18). Observe that
where third-to-last equation is due to the triangle inequality, second-to-last equation
comes from the assumption that
a Note that τ cannot exceed
Competing interest
The authors declare that they have no competing interests.
This work was supported by the NSF Award No. DMS-08-11062, DARPA Grant No. HR0011-09-1-0036, and AFRL Grant No. FA8650-07-D-1221.
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Well, what have we here? It appears as though someone has captured an image showing that the HTC Incredible has been ordered by Verizon and the shipments are on their way to the warehouse locations. Over at Android Forums someone with Verizon insight appears say that these 156,709 units are actually sitting in the warehouse, just unable to be sold at this point. This information falls in line with the two-week shipping timeframe we previously heard, now it's just a matter of time until these show up in the stores. [Android Forums via Engadget]
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East Carolina vs Florida Atlantic Wrap - Florida Atlantic Wins 78-67
East Carolina vs Florida Atlantic Wrap - Florida Atlantic Wins 78-67 | |
Florida Atlantic got 23 points from Jackson Trapp en route to a 78-67 victory over East Carolina on Thursday at FAU Arena. Florida Atlantic was a favorite by 1.5 points and came through with an ATS victory for bettors. Marquan Botley had 17 points for Florida Atlantic and Pablo Bertone chipped in with 12 points. D'Andre Johnson had 6 assists for them, while Justin Raffington was the team's top rebounder, grabbing 14 boards. East Carolina got 20 points from Akeem Richmond in a losing cause and another 14 points from Michael Zangari. Antonio Robinson contributed 3 assists for them, while Michael Zangari had 11 rebounds. First-half bettors who backed East Carolina were victorious, as the score was 33-30 at the break. East Carolina had a 41-35 advantage in the rebounding department as they won the battle in the paint. |


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Estos románticos aretes pequeños de gemas tienen granates rojos en forma de corazón engarzados en plata de ley.
Consulte nuestra sección de educación para obtener datos sobre nuestras joyas con gemas.
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