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Football and fishing.
Those are the prevalent themes of Jimmy Johnson: A Football Life, which premieres tonight on NFL Network.
The latest documentary from NFL Films chronicles Johnson's coaching career, most notably with the University of Miami (Fla.) and Dallas Cowboys. However many of the show's best scenes are gleaned from watching Johnson bask in what's obviously a very satisfying semi-retirement.
He devotes some of his time in South Florida to hosting coaches from various sports and offering pearls of wisdom culled from a career that produced one college national championship and two Lombardi Trophies.
Bill Belichick of the New England Patriots is among those who's made the trip south to visit Johnson, who still draws a paycheck as an NFL analyst for FOX.
As is his wont, Johnson takes Belichick fishing on his boat, Three Rings — incidentally, we learned in a previous episode of A Football Life that Belichick's vessel is dubbed V Rings (three with the Pats, two with the New York Giants) — but laments after the trip, "He's (Belichick) a cooler on fishing. When he's on board, we don't catch any fish."
You will catch plenty of football from the Johnson biopic as well, from his often-stormy years leading the Hurricanes to his frustrating early days in Dallas (he opines his 'Canes might have beaten the '89 Cowboys) to his controversial divorce from Jerry Jones shortly after winning Super Bowl XXVIII following the 1993 NFL season.
MORE: Jerry Jones says there's 'no way' he'd leave as Cowboys GM
That latter chapter still stings for some Cowboys Hall of Famers, if not for Johnson himself.
"It was devastating," says ex-Dallas and Hurricanes wideout Michael Irvin of his coach's departure. "As blessed and as fortunate as we've been, when I'm with Troy (Aikman) — to this day — we still talk about, 'We should have at least five rings.' "
Says Aikman, the three-time champion Cowboys quarterback: "I'm disappointed that we didn't get a chance to really exhaust that relationship and find out how great could it have been. And I don't think Jimmy spends a moment thinking about it, I really don't."
Indeed Johnson doesn't seem caught up in his long-ago battle of egos with Jones the way his former players and many Dallas fans still are.
"Jerry takes a lot of grief for me leaving, and he shouldn't," says Johnson. "I was leaving (regardless). It got to where it wasn't fun for me. I was hard on our team. After winning the first Super Bowl, I was harder. I had to be the bad guy because people get complacent."
Aikman, for one, now has added insight on the outcome, offering: "He's said that a number of times to me that he was tired of being the bad guy. Which I guess that was a little bit of a shock to me — because he was so good at it, you know? It seemed like he really enjoyed being the bad guy. But it's been since I've gotten to know him that (I realized) that's not him."
To learn more about Johnson, catch A Football Life on Wednesday night at 8 p.m. ET (and many subsequent airings) on NFL Network.


text:
Responsive Emails & Newsletters? We got it!
Email professionals say making and testing a custom responsive email takes days. They were totally right... until the release of the unique Responsive Email Designer (aka RED)!
The modern CSS3 controls, custom breakpoints tool, snazzy width slider, and flexible layouts are supported by a unique and powerful email code generator. If you want to create the best possible reader experience across devices and email clients, this is the one app you need.

subset: commoncrawl


text:
If the season ended today, the Southeastern Conference's six-year run of BCS championships would be over as a result of unanimous No.1 Alabama's upset loss to conference newcomer Texas A&M on Saturday.
But it doesn't, so everybody take a deep breath. There's still a lot that can happen on this wild ride we like to call college football.
TOP 25: Complete Coaches Poll
HOMER?: Notre Dame gets lone No. 1 vote from own coach
For now, there are three undefeated teams left vying for the coveted top two spots in the final standings with three weeks to go in the regular season. Oregon moves into the No. 1 position in the USA TODAY Sports Coaches Poll, one of the components of the BCS standings that will be released later Sunday. The Ducks received 44 of 59 first-place votes and were picked second on all the others after improving to 10-0 with a win at California.
Kansas State moved into the No. 2 spot in the coaches poll and figures to be well positioned for a top-two BCS ranking thanks to its standing in the computer formulas. The Wildcats, also 10-0, received 14 of the remaining 15 No. 1 votes and were voted second on all but two of the remaining 45 ballots.
Notre Dame claimed the last No.1 vote and checks in at No.3, but the Fighting Irish probably would be on the outside of the top two unless more upsets occur over the final weeks. Still, it is the first time Notre Dame got a No. 1 vote since September 2006, and the Irish are no lower than No. 5 on any ballot.
The SEC is well represented throughout the rest of the top 10. Georgia moved up to No. 4 after officially securing its spot in the conference title game by blanking Auburn. The Crimson Tide slid to No. 5, their lowest ranking since the end of the 2010 season, but they're still likely to meet the Bulldogs in Atlanta.
No. 6 Florida State and No. 7 Florida held their spots with narrow wins. LSU jumped past Clemson into No. 8 after beating then-No. 23 Mississippi State. Texas A&M vaulted to No. 10 with its historic win in Tuscaloosa, leapfrogging No. 11 South Carolina and No. 12 Oklahoma. Stanford, which travels to Eugene to face the top-ranked Ducks this week, checks in at No. 13.
Michigan moves back into the poll at No. 23 after staging a rally to beat Northwestern in overtime, knocking the Wildcats out of the top 25 in the process. No.24 Oklahoma State and No.25 Texas Tech also climbed back into the poll after only a one-week absence. Mississippi State and Toledo were the week's other dropouts.


text:
Blaine T. Phillips Distinguished Professor of Environmental Law
Hunton & Williams Professor of Law
Director, Environmental and Land Use Law Program
J.D., University of Pennsylvania Law School, 1974
B.A., Williams College, 1967
Jonathan Cannon, director of the Law School's Environmental and Land Use Law Program, joined the Law School faculty in 1998 from the Environmental Protection Agency, where he served as general counsel (1995-98) and assistant administrator for administration and resources management (1992-95). Prior to his work with the EPA, Cannon was in the private practice of environmental law; served as an adjunct professor at Washington and Lee Law School, where he taught environmental law; and was a lecturer at the Law School.
Cannon is the author of the new book, "Environment in the Balance: The Green Movement and the Supreme Court."
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Homemade Gifts From the Kitchen
- - Per Person
What You Will Learn
Is there a more tangible way to express your care than to prepare and give carefully crafted and delicious food from your own kitchen? We'll create sweet and savory recipes that are sure to please most palates. Then discuss creative and artful ways to beautifully package your edible gifts for memorable giving.
Maegan McPhee


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Invention Marketing Scams
Home Invention Marketing Scams
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InventNet is a web-based inventor organization similar to an inventor club ( inventors forum ) and is suitable for people that want to be an inventor, have an invention or need patent help and learn how to patent an invention or a simple idea. We provide a social network for inventors with integrated features like find a patent attorney or patent agent, invention for sale listing directory, inventor forum, real time chat, etc. American inventors or www inventors can ask questions about how to invent, how to sell an invention, about patent application, prototype, patent search, non-disclosure agreement and other intellectual property law questions. Questions like: I have many simple inventions will any invention sale ? You can use the Community Wall, the Forum and real time Chat to discuss and network with others interested in inventing or patenting ideas.


text:
Hands-on with Leaked Builds of Windows Blue 8.1
With several leaked builds for Windows Blue hitting the web in rapid succession, it seems as though Microsoft is as leaky as a sieve these days. A leak for build 9364 made its way to the internet last March, and two more leaked builds (9369 & 9374) have hit the Internet in the weeks since.
...Well, there's no sign of a Start Button on the builds we've tried out.
Full article,
Click HERE


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I purchased my SS V2 Stepped Header and CPI Euro200 from Jack at Custom Performance. Jack is an amazing guy, very knowledgable, and offers amazing products and prices on all your exhaust needs! Upon the installation of the perfectly fitting SS V2 Stepped Header and CPI Euro200, I could feel the drastic difference in power from stock. There was just much more power everywhere throughout the power band. All the typical flat spots in the power band were now gone and the car just pulled nice and smooth to redline. You could almost tangibly feel the car breathing better. When I got my SS V2 Stepped Headers, I chose to go with the CPI Euro200 to meet emissions requirements here in IL, along with decreasing the smell and rasp. The Section 1 utilizes two Magnaflow Metallic Race Cats that are 200cpsi. Overall, I was extremely pleased with the money spent and performance gain.
Fast forward many many months to Black Friday 2011. Jared at Supersprint NA announced an incredible sale on the SS V1 Stepped Header and V1 SPipe. In all honesty, this was the header for many years that I truly wanted. At the time that I committed to purchasing headers, my budget just didn't allow me to swing for these bad boys. Thanks to Supersprint's generosity and willingness to please our community, I had to take advantage of their great sale. Honestly, I was not really expecting any gains from making the switch. Everyone has told me that there really is not much to be gained from moving to catless and the bigger headers. Due to my stubbornness, I persisted and bit the bullet.
Supersprint V2 Stepped Headers
Well crafted collector. Notice how seamless everything is merged together.
~1.5" Primaries that step up to ~2" before meeting at the collector
Close up of collector and EGT bung. Notice the beautiful TIG welding.
Both Pre and Post Cat O2 Bungs and 2.36" outlet piping.
More Pre and Post Cat O2 Bungs
More fancy stepped goodness
Perfect flanges
Etched Supersprint shameless plug
Custom Performance Innovations Euro200
TIG welded flanges
MIG welded cats and O2 bungs
MIG welded cats and O2 bungs
SS V2 Stepped + CPI Euro200
Supersprint V1 Stepped Headers
Primaries with incredibly TIG welds
~1.5" stepped up to ~2"
Sexy collector and welds
Full 2.5" outlet flange!!
Internal portion of Post Cat O2 sensor
SS V1 Stepped vs SS V2 Stepped
2.36" vs 2.5"
Notice the different pathways
2.36" vs 2.5"
Slip On vs OEM style
Massive full 2.5" piping for SS V1 SPipe
Post Cat O2 Sensor
As I noted before, I was not really expecting to feel an incredible difference between the two. The Magnaflow cats flow very well, the V2 Stepped is already a great design, and the V1 Stepped has been said to provide minimal gains over the V2 Stepped.
Upon installation, I noticed that smell of exhaust fumes has increased, but it wasn't as bad as people said. Maybe my sense of smell isn't as sensitive, but I really don't notice it in the car with the windows up and in traffic. It is definitely noticeable on cold start in the garage first thing in the winter morning though.
Sound wise, not too much different either. I was expecting a ton of more rasp. Nope, didn't notice much of a difference. The tone was slightly different, almost a crisper more refined type of rasp with the V1 Stepped Headers. Personally, I actually enjoy it more with it being catless. The volume is no louder either, no more drone than stock. Overall, I am very happy with the sound of the car. It's soft, quiet, and not terribly raspy.
Driving impressions, there is a tangible difference between the two for sure. The biggest difference that I could feel was just how hard it pulls to redline. I really kept telling myself that it must be adrenaline or the placebo effect. So I just kept driving it and driving it and driving it and I still noticed the difference. It pulls great at the very end and doesn't seem to run out of steam.
Overall, I am very pleased with the upgrade to the SS V1 Stepped Header and V1 SPipe. It was worth the annoying removal and installation of all headers. It was worth waiting months for them and shipping out my prior setup. I am very happy I came full circle and ended up with the headers that I originally wanted.
I will be the firs to admit that this is not a true apples to apples comparison. Primarily because my dynos with the SS V2 Stepped Headers included the CPI Euro200. Whether the Euro200 robs power or increases low end power/torque...I don't know. In addition, the dyno runs were done on two different days weeks apart. Weather conditions were ever so slightly different, mainly the drastic drop in humidity. I truthfully don't know if that will effect power or not. So please take this review and dyno results with a grain of salt. All I can guarantee is that either setup is well worth the money to me. The car pulls so hard down low and screams all the way to the top of redline.
Dynojet 248X at Dean's Peformance, St. Charles, IL
4th Gear | 93 OCT | Hood Open
SPEED (depicts that same gear was used)
Overall, I was a bit surprised to see these results. The dyno graphs clearly depict the drastic power gained, pretty much throughout the whole power band! The whole purpose of the stepped design was to provide strong low-end torque and monstrous top end. Looking at the substantial gain in area-under-the-curve is clearly seen! That data collection is very tangible on the street. There is no doubt in my mind that the larger 2.5" piping and removing of the cats is helping a lot.
Looking back in hindsight, I can't really pinpoint where all the gains are coming from. Are they mostly from removing the cats despite everyone saying that it doesn't rob that much power? Is it really coming from the difference in piping design and flow characteristics?
Who knows...
All I know is that Supersprint currently makes the best headers on the market for the S54B32. Perfect fitment. Superior build quality. Welds that look like art.
Stay tuned for more. I have been doing all these dynos in the past to get consistent baselines before I dyno my Evolve Carbon Fiber Airbox and AlphaN Tune.
Hans at Dean's Performance for the dyno time and great patience.
Jared at Supersprint NA for providing an amazing opportunity to acquire the SS V1 Stepped Headers and V1 S Pipe.
Jack at Custom Performance Innovations for getting me hooked on the power mod craze and the SS V2 Stepped Header along with your incredible CPI Euro200.
My buddies at iND Distribution for installing removing the prior exhaust setup and throwing in my power sapping OEM headers.
My buddies at VS Motorsports for installing the SS V1 Stepped Headers and SPipe. Thanks for letting me borrow the sick E28 528e! That thing had more electronics in the car than my E46 and E90 have.
The good friends at Evolve Automotive for educating me on how to analyze data and to strive for only the best products out there! Time get this bad boy tuned along with the CF Airbox


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User:Michiexile/MATH198/Lecture 1
From HaskellWiki
This page now includes additional information based on the notes taken in class. Hopefully this will make the notes reasonably complete for everybody.
1 Welcome, administratrivia
I'm Mikael Vejdemo-Johansson. I can be reached in my office 383-BB, especially during my office hours; or by email to email@example.com.
I encourage, strongly, student interactions.
I will be out of town September 24 - 29. I will monitor forum and email closely, and recommend electronic ways of getting in touch with me during this week. I will be back again in time for the office hours on the 30th.
2 Introduction
2.1 Why this course?
An introduction to Haskell will usually come with pointers toward Category Theory as a useful tool, though not with much more than the mention of the subject. This course is intended to fill that gap, and provide an introduction to Category Theory that ties into Haskell and functional programming as a source of examples and applications.
2.2 What will we cover?
The definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases of these, adjunctions, freeness and presentations as categorical constructs, monads and Kleisli arrows, recursion with categorical constructs.
Maybe, just maybe, if we have enough time, we'll finish with looking at the definition of a topos, and how this encodes logic internal to a category. Applications to fuzzy sets.
2.3 What do we require?
Our examples will be drawn from discrete mathematics, logic, Haskell programming and linear algebra. I expect the following concepts to be at least vaguely familiar to anyone taking this course:
- Sets
- Functions
- Permutations
- Groups
- Partially ordered sets
- Vector spaces
- Linear maps
- Matrices
- Homomorphisms
2.4 Good references
On reserve in the mathematics/CS library are:
- Mac Lane: Categories for the working mathematician
- This book is technical, written for a mathematical audience, and puts in more work than is strictly necessary in many of the definitions. When Awodey and Mac Lane deviate, we will give Awodey priority.
- Awodey: Category Theory
- This book is also available as an ebook, accessible from the Stanford campus network. The coursework webpage has links to the ebook under Materials.
2.5 Monoids
In order to settle notation and ensure everybody's seen a definition before:Definition A monoid is a set M equipped with a binary associative operation * (in Haskell:
A semigroup is a monoid without the requirement for an identity element.
A function is a monoid homomorphism if the following conditions hold:
- f(m * m') = f(m) * f(m')
- Any group is a monoid. Thus, specifically, the integers with addition is a monoid.
- The natural numbers, with addition.
- Strings L * in an alphabet L is a monoid with string concatenation forming the operation and the empty string the identity.
- Non-empty strings form a semigroup.
For more information, see the Wikipedia page on Monoids. [[1]].
Awodey: p. 10.
2.6 Partially ordered set
Definition A partially ordered set, or a partial order, or a poset is a set P equipped with a binary relation which is:
- Reflexive: for all
- Anti-symmetric: and implies x = y for all .
- Transitive: and implies for all .
If or , we call x,y comparable. Otherwise we call them incomparable. A poset where all elements are mutually comparable is called a totally ordered set or a total order.
If we drop the requirement for anti-symmetry, we get a pre-ordered set or a pre-order.
If we have several posets, we may indicate which poset we're comparing in byindicating the poset as a subscript to the relation symbol.
A monotonic map of posets is a function such that implies .
- The reals, natural numbers, integers all are posets with the usual comparison relation. A poset in which all elements are comparable.
- The natural numbers, excluding 0, form a poset with if a | b.
- Any family of subsets of a given set form a poset with the order given by inclusion.
For more information, see the Wikipedia page on Partially ordered set. [[2]]
Awodey: p. 6. Preorders are defined on page 8-9.
3 Category
Awodey has a slightly different exposition. Relevant pages in Awodey for this lecture are: sections 1.1-1.4 (except Def. 1.2), 1.6-1.8.
3.1 Graphs
We recall the definition of a (directed) graph. A graph G is a collection of edges (arrows) and vertices (nodes). Each edge is assigned a source node and a target node.
Given a graph G, we denote the collection of nodes by G0 and the collection of arrows by G1. These two collections are connected, and the graph given its structure, by two functions: the source function and the target function .
We shall not, in general, require either of the collections to be a set, but will happily accept larger collections; dealing with set-theoretical paradoxes as and when we have to. A graph where both nodes and arrows are sets shall be called small. A graph where either is a class shall be called large. 0 If both G0 and G1 are finite, the graph is called finite too.
The empty graph has .
A discrete graph has .
A complete graph has .
A simple graph has at most one arrow between each pair of nodes. Any relation on a set can be interpreted as a simple graph.
- Show some examples.
A homomorphism of graphs is a pair of functions and such that sources map to sources and targets map to targets, or in other words:
- s(f1(e)) = f0(s(e))
- t(f1(e)) = f0(t(e))
By a path in a graph G from the node x to the node y of length k, we mean a sequence of edges such that:
- s(f1) = x
- t(fk) = y
- s(fi) = t(fi − 1) for all other i.
Paths with start and end point identical are called closed. For any node x, there is a unique closed path () starting and ending in x of length 0.
For any edge f, there is a unique path from s(f) to t(f) of length 1: (f).
We denote by Gk the set of paths in G of length k.
3.2 Categories
We now are ready to define a category. A category is a graph G equipped with an associative composition operation , and an identity element for composition 1x for each node x of the graph.
Note that G2 can be viewed as a subset of , the set of all pairs of arrows. It is intentional that we define the composition operator on only a subset of the set of all pairs of arrows - the composable pairs. Whenever you'd want to compose two arrows that don't line up to a path, you'll get nonsense, and so any statement about the composition operator has an implicit "whenever defined" attached to it.
The definition is not quite done yet - this composition operator, and the identity arrows both have a few rules to fulfill, and before I state these rules, there are some notation we need to cover.
3.2.1 Backwards!
If we have a path given by the arrows (f,g) in G2, we expect and to compose to something that goes . The origin of all these ideas lies in geometry and algebra, and so the abstract arrows in a category are supposed to behave like functions under function composition, even though we don't say it explicitly.Now, we are used to writing function application as f(x) - and possibly, from Haskell, as
On the other hand, the way we write our paths, we'd read f then g. This juxtaposition makes one of the two ways we write things seem backwards. We can resolve it either by making our paths in the category go backwards, or by reversing how we write function application.
In the latter case, we'd write x.f, say, for the application of f to x, and then write x.f.g for the composition. It all ends up looking a lot like Reverse Polish Notation, and has its strengths, but feels unnatural to most. It does, however, have the benefit that we can write out function composition as and have everything still make sense in all notations.
In the former case, which is the most common in the field, we accept that paths as we read along the arrows and compositions look backwards, and so, if and , we write , remembering that elements are introduced from the right, and the functions have to consume the elements in the right order.
The existence of the identity map can be captured in a function language as well: it is the existence of a function .
Now for the remaining rules for composition. Whenever defined, we expect associativity - so that . Furthermore, we expect:
- Composition respects sources and targets, so that:
- s(u(x)) = t(u(x)) = x
In a category, arrows are also called morphisms, and nodes are also called objects. This ties in with the algebraic roots of the field.
We denote by HomC(A,B), or if C is obvious from context, just Hom(A,B), the set of all arrows from A to B. This is the hom-set or set of morphisms, and may also be denoted C(A,B).
If a category is large or small or finite as a graph, it is called a large/small/finite category.
A category with objects a collection of sets and morphisms a selection from all possible set-valued functions such that the identity morphism for each object is a morphism, and composition in the category is just composition of functions is called concrete. Concrete categories form a very rich source of examples, though far from all categories are concrete.
Again, the Wikipedia page on Category (mathematics) [[3]] is a good starting point for many things we will be looking at throughout this course.
3.3 New Categories from old
As with most other algebraic objects, one essential part of our tool box is to take known objects and form new examples from them. This allows us generate a wealth of examples from the ones that shape our intuition.
Typical things to do here would be to talk about subobjects, products and coproducts, sometimes obvious variations on the structure, and what a typical object looks like. Remember from linear algebra how subspaces, cartesian products (which for finite-dimensional vectorspaces covers both products and coproducts) and dual spaces show up early, as well as the theorems giving dimension as a complete descriptor of a vectorspace.
We'll go through the same sequence here; with some significant small variations.
A category D is a subcategory of the category C if:
- D1 contains 1X for all
- sources and targets of all the arrows in D1 are all in D0
- the composition in D is the restriction of the composition in C.
Written this way, it does look somewhat obnoxious. It does become easier though, with the realization - studied closer in homework exercise 2 - that the really important part of a category is the collection of arrows. Thus, a subcategory is a subcollection of the collection of arrows - with identities for all objects present, and with at least all objects that the existing arrows imply.
A subcategory is full if D(A,B) = C(A,B) for all objects A,B of D. In other words, a full subcategory is completely determined by the selection of objects in the subcategory.
A subcategory is wide if the collection of objects is the same in both categories. Hence, a wide subcategory picks out a subcollection of the morphisms.
The dual of a category is to a large extent inspired by vector space duals. In the dual C * of a category C, we have the same objects, and the morphisms are given by the equality C * (A,B) = C(B,A) - every morphism from C is present, but it goes in the wrong direction. Dualizing has a tendency to add the prefix co- when it happens, so for instance coproducts are the dual notion to products. We'll return to this construction many times in the course.
Given two categories C,D, we can combine them in several ways:
- We can form the category that has as objects the disjoint union of all the objects of C and D, and that sets whenever A,B come from different original categories. If A,B come from the same original category, we simply take over the homset from that category. This yields a categorical coproduct, and we denote the result by C + D. Composition is inherited from the original categories.
- We can also form the category with objects for every pair of objects . A morphism in is simply a pair . Composition is defined componentwise. This category is the categorical correspondent to the cartesian product, and we denot it by .
In these three constructions - the dual, the product and the coproduct - the arrows in the categories are formal constructions, not functions; even if the original category was given by functions, the result is no longer given by a function.
Given a category C and an object A of that category, we can form the slice category C / A. Objects in the slice category are arrows for some object B in C, and an arrow is an arrow such that . Composites of arrows are just the composites in the base category.
Notice that the same arrow φ in the base category C represents potentially many different arrows in C / A: it represents one arrow for each choice of source and target compatible with it.
There is a dual notion: the coslice category , where the objects are paired with maps .
Slice categories can be used, among other things, to specify the idea of parametrization. The slice category C / A gives a sense to the idea of objects from C labeled by elements of A.We get this characterization by interpreting the arrow representing an object as representing its source and a type function. Hence, in a way, the
Alternatively, we can phrase the importance of the arrow in a slice categories of, say, Set, by looking at preimages of the slice functions. That way, an object gives us a family of (disjoint) subsets of B indexed by the elements of A.
Finally, any graph yields a category by just filling in the arrows that are missing. The result is called the free category generated by the graph, and is a concept we will return to in some depth. Free objects have a strict categorical definition, and they serve to give a model of thought for the things they are free objects for. Thus, categories are essentially graphs, possibly with restrictions or relations imposed; and monoids are essentially strings in some alphabet, with restrictions or relations.
3.4 Examples
- The empty category.
- No objects, no morphisms.
- The one object/one arrow category 1.
- A single object and its identity arrow.
- The categories 2 and 1 + 1.
- Two objects, A,B with identity arrows and a unique arrow .
- The category Set of sets.
- Sets for objects, functions for arrows.
- The catgeory FSet of finite sets.
- Finite sets for objects, functions for arrows.
- The category PFn of sets and partial functions.
- Sets for objects. Arrows are pairs .
- PFn(A,B) is a partially ordered set. precisely if and .
- The exposition at Wikipedia uses the construction here: [[4]].
- There is an alternative way to define a category of partial functions: For objects, we take sets, and for morphisms , we take subsets such that each element in S occurs in at most one pair in the subset. Composition is by an interpretation of these subsets corresponding to the previous description. We'll call this category PFn'.
- Every partial order is a category. Each hom-set has at most one element.
- Objects are the elements of the poset. Arrows are unique, with precisely if .
- Every monoid is a category. Only one object. The elements of the monoid correspond to the endo-arrows of the one object.
- The category of Sets and injective functions.
- Objects are sets. Morphisms are injective functions between the sets.
- The category of Sets and surjective functions.
- Objects are sets. Morphisms are surjective functions between the sets.
- The category of k-vector spaces and linear maps.
- The category with objects the natural numbers and Hom(m,n) the set of -matrices.
- Composition is given by matrix multiplication.
- The category of Data Types with Computable Functions.
- Our ideal programming language has:
- Primitive data types.
- Constants of each primitive type.
- Operations, given as functions between types.
- Constructors, producing elements from data types, and producing derived data types and operations.
- We will assume that the language is equipped with
- A do-nothing operation for each data type. Haskell has .id
- An empty type 1, with the property that each type has exactly one function to this type. Haskell has . We will use this to define the constants of type t as functions . Thus, constants end up being 0-ary functions.()
- A composition constructor, taking an operator and another operator and producing an operator . Haskell has .(.)
- A do-nothing operation for each data type. Haskell has
- This allows us to model a functional programming language with a category.
- Our ideal programming language has:
- The category with objects logical propositions and arrows proofs.
- The category Rel has objects finite sets and morphisms being subsets of . Composition is by if there is some such that . Identity morphism is the diagonal .
3.5 Homework
For a passing mark, a written, acceptable solution to at least 3 of the 6 questions should be given no later than midnight before the next lecture.
For each lecture, there will be a few exercises marked with the symbol *. These will be more difficult than the other exercises given, will require significant time and independent study, and will aim to complement the course with material not covered in lectures, but nevertheless interesting for the general philosophy of the lecture course.
- Prove the general associative law: that for any path, and any bracketing of that path, the same composition results.
- Which of the following form categories? Proof and disproof for each:
- Objects are finite sets, morphisms are functions such that for all morphisms f, objects B and elements b.
- Objects are finite sets, morphisms are functions such that for all morphisms f, objects B and elements b.
- Objects are finite sets, morphisms are functions such that for all morphisms f, objects B and elements b.
- Recall that .
- Suppose in some category C.
- If for all in the category, then u = 1A.
- If for all in the category, then u = 1A.
- These two results characterize the objects in a category by the properties of their corresponding identity arrows completely. Specifically, there is a way to rephrase the definition of a category such that everything is stated in terms of arrows.
- For as many of the examples given as you can, prove that they really do form a category. Passing mark is at least 60% of the given examples.
- Which of the categories are subcategories of which other categories? Which of these are wide? Which are full?
- For this question, all parts are required:
- For which sets is the free monoid on that set commutative.
- Prove that for any category C, the set Hom(A,A) is a monoid under composition for every object A.
- For details on the construction of a free monoid, see the Wikipedia pages on the Free Monoid [[5]] and on the Kleene star [[6]].
- * Read up on ω-complete partial orders. Suppose S is some set and is the set of partial functions - in other words, an element of is some pair with . We give this set a poset structure by precisely if and .
- Show that is a strict ω-CPO.
- An element x of S is a fixpoint of if f(x) = x. Let be the ω-CPO of partially defined functions on the natural numbers. We define a function by sending some to a function k defined by
- k(0) = 1
- k(n) is defined only if h(n − 1) is defined, and then by k(n) = n * h(n − 1).
- Describe and . Show that φ is continuous. Find a fixpoint (S0,f) of φ such that any other fixpoint of the same function is larger than this one.
- Find a continuous endofunction on some ω-CPO that has the fibonacci function F(0) = 0,F(1) = 1,F(n) = F(n − 1) + F(n − 2) as the least fixed point.
- Implement a Haskell function that finds fixed points in an ω-CPO. Implement the two fixed points above as Haskell functions - using the ω-CPO fixed point approach in the implementation. It may well be worth looking at to provide a Haskell context for a partial function for this part of the task.Data.Map


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Over the last years, I have come to really appreciate Greek wines. There are many grape varieties that exist only in Greece and I have the good fortune of being able to try them all. I wish to share my enthusiasm with wine lovers around the world, who often limit themselves to maybe four red and four white grape varieties for most of their life.
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My Aussie - American - Russian friend, Marina V:):)
[pIX COURTESY OF STAN SCHUTZE]
redrabid wrote:Hi, I am back.
The digital world was against me the last few months.
First Facebook denied me, then I was forbidden entry onto this forum, then came Google+, that made my communication almost impossible. The first and the last problem stiil exist, but my problems with this forum somehow disappeared.
Psychy, listen to a new UK band called London Grammar. Their singer Hannah Reid is to me a very pleasant surprise: Voice and looks, what more could you ask for?.
Come on Psychy, you may not like Lady Gaga, you may even despise her, but to say that she has no talent at all under that commercial veil, well, that discredits your judgement.
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How does this transmission differ from the old one? Well, it does not have a torque converter. It uses a compact wet clutch setup with multiple clutches hence the name MCT (multi-clutch technology). It is a dual clutch transmission but not a true dual clutch. Confusing, yes, but really it is the automatic we all know with the torque converter replaced by wet clutch packs. This allows faster shifts of about 100 milliseconds.
This transmission is available already in the SL63 and E63 AMG. It is also used with the new twin turbo V8 motors and is featured in the CLS63 AMG which makes us think it can handle a bit of torque. It is also lighter than the previous automatic transmission weighing in at 80 kilograms.
There are multiple modes the user can choose to use with the transmission. There are four shifting modes the driver can choose from. There is also a completely manual function which will not up-shift automatically for the driver which is a huge plus and mitigates some of the driver interaction advantage BMW has had for some time. Additionally, a "race start" mode is features which is a fancy way of saying launch control.
Overall, this is a great development for the C63 as Mercedes continues to improve the model and make it far more of a drivers car. Mercedes continues to raise the bar and we applaud their efforts. What we are left wondering is if tuners will be able to crack the transmission software on this trans and just how much torque it can handle. Time will tell, but this makes things very interesting in the sport sedan segment as it appears Mercedes has surpassed the M3 by continually upgrading the C63 while the M3 has stayed stagnant.


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I took down the Sunday Big Ticket Poker Tourney the other day, $21.3K
Before that I had 2 withdrawels pending for $2,500 each. I'm planning to cashout 2,500 twice a day until I get down to 3k to play with. Never cashed out of here before.... Hopefully I get paid! I will keep you updated.
FYI: Never played the sportsbook.. just poker.
1/8 $2,500 Pending Check Processed 2/8, received 2/11
1/9 $2,500 Pending Check
1/13 $2,500 Pending Check
1/14 $2,500 Pending Check
Got my first check today via Fedex! Cashed out 1/8, processed on 2/8, got the check via fedex on 2/12. took exactly 5 weeks from cashout to receive the check. I'll update the other pending checks as they change.
Originally Posted by diggler05: has anyone had problems with checks (bounced checks or banks not accepting checks) they received from sportsbook?
I deposited a check for $2,500 on 2/13 and it must have cleared just fine as I still have the money in my account. It was actually available in my account after 2 days. I'm still waiting on several cashouts. I have 8 more check for $2,500 that are pending.
1/8 $2,500 Pending Check Processed 2/8, received 2/11
1/9 $2,500 Pending Check
1/15 $2,500 Pending Check
1/15 $2,500 Pending Check
2/1 $2,500 Pending Check
2/12 $2,500 Pending Check
1/8 $2,500 Pending Check, Processed 2/8, received 2/11
1/9 $2,500 Pending Check, Processed 2/28, Received TBD
Just got an email on Thursday 2/28 indicating my second check has been processed. Last time Fedex was at my door the following Monday with the check. I'll update once I recieve the check.
hey man congrats on cashing in on the Sunday Big Ticket. I was in that tourney this past week. I didnt fare so well. got sucked out on the river. lol
Got my 2nd check today. Took the full 8 weeks. Again, I'll update the checks as I receive them so all of you will know how long it takes and that they are paying people. Checks come from Canada and they look legit. Nice little note provided with it "For the refund of services or purchased products from an affliated company" I've never had a banker ask where/why or WTF when cashing the checks and the first one cleared quickly (2 days). If the banker would've asked.. it would've been a new 3d TV i returned
1/9 $2,500 Pending Check Processed 2/28, received 3/7
1/13 $2,500 Pending Check Processed 3/12, received TBD
Got another withdrawel processed today! Cashed out 1/13, processed 3/12.
1/13 $2,500 Pending Check
Another one went through last friday.
1/13 $2,500 Pending Check Processed 3/12, Recieved 3/20
1/13 $2,500 Pending Check Processed 3/22, Recieved TBD
2/1 $2,500 Pending Check
FoFun: You should get an email this week indicating you have a message in relation to your withdrawal. Most of the checks I have gotten so far took the full 8 weeks (Look at my posts above). It is really annoying that it takes so long but I can tell you first hand the excuses they use are real. Every check I have gotten has came from a different bank. They are constantly changing who they use to process payments to avoid legal problems. It seems like I always get emails Monday evening (5PM) telling the checks have been sent but they have already been shipped the previous Friday and I usually get the them on Wednesday or Thrusday. I guess bottom line is they are paying out - i have recieved 10K from them the last couple months and have another 10 coming. Since they can only process one check a week for 2500 i've been getting checks every week for a while. I'll post again when my next check is processed. Hang in there, you'll get paid.
1/13 $2,500 Pending Check Processed 3/22, Recieved 3/28 Bounced 4/4! FML!
Well some bad news. The last check I deposited bounced yesterday from my bank acccount. $2500 I thought i had in there.. nope. So far Sportsbook.ag has cooperated with me to get this resolved quickly but they haven't fixed anything yet. I'm pissed to say the least. I'll update this post when i find out what they're going to do. The processor they used this time is probably to blame I had three checks go through fine.. and then this one damnit.
Thank you for contacting us.
This is a quick email to inform you that unfortunately, we are experiencing a small delay with the withdrawal process.
However; we have checked with our processors and we have been informed that you should receive your check anytime soon.
Our apologies for any inconvenience caused by this situation. We appreciate your patience and understanding.
We are always here to help you. Please feel free to reply to this email if you have any additional questions in relation to this or any other matter. Your reference ID for this email is please quote this number in any further communication on this subject.
Kind regards,
Obviously Sportsbook.ag is not the book. Look elsewhere
This sportsbook.com is the same outfit as Hollywood. They both
take two months to pay off.
That is exactly why they take so long to pay off. They want you
to fire that money lose it back. Plus every time you fire it they
probably move the cash out date back two months. This way
they get to book with no money.


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Consideration of reports submitted by States parties under article 44 of the Convention : Convention on the Rights of the Child : concluding observations : Republic of Serbia
20 June 2008 | Publisher: UN Committee on the Rights of the Child (CRC) | Document type: Concluding Observations