Teen Titans (season 1)
The first season of the animated television series Teen Titans, based on the DC comics series created by Bob Haney and Bruno Premiani aired on Cartoon Network in the United States. Developed by television writer David Slack, the series was produced by DC Entertainment and Warner Bros. Animation, it stars Scott Menville, Hynden Walch, Khary Payton, Tara Strong, Greg Cipes as the voices of the main characters. The series revolves around a team of crime-fighting teenaged superheroes – Robin, the team's fearless leader; the show focuses on the Titans adventures in protecting the city. The first season features an overarching storyline focused on the Titans' main villain Slade, a mysterious mastermind who takes an interest in Robin. Teen Titans debuted on Cartoon Network on July 19, 2003 and concluded its first season on November 11, 2003; the season aired on the Kids' WB from November 1, 2003 to February 28, 2004. The season premiered to strong ratings for Cartoon Network while displaying a moderate showing on the Kids' WB.
While initial reaction to the series was mixed to negative, the season as a whole received positive reviews with many critics highlighting the series' storytelling and dialogue. The first season of Teen Titans aired on Cartoon Network; the season aired on Kids' WB Saturday mornings at 8:30 A. M. EST, beginning on November 1, 2003; the series was first greenlit in late September 2002, with Japanese-American animator Glen Murakami signed on. The series' creation was inspired based on DC Comics characters. However, as opposed to Justice League and other DC animated television series, the intention behind Teen Titans was to create the series for a younger audience. Series producer and animator Glen Murakami noted that the series is "lighter and has humor" while staying true to the "intent of the characters." Murakami noted that the process of transforming material from the comics into material suitable for the target audience was similar to what was done with both Batman: The Animated Series and Batman Beyond: "We kind of have to take into consideration that were not making this cartoon just for fans of the comic book, the ones who know all the backstory and know all the continuity.
We have to tell the Starfire story in half an hour! I think we took all those things into consideration, but there's just some things you can't do for children's programming." The series' mixes American style animation with Japanese anime. According to Murakami, the incorporating of anime came noting that he and Tim were anime fans and the increased presence of anime at the time; the first season employs a cast of five main voice actors. Scott Menville provided the voice of the Titans' leader and martial arts expert. Greg Cipes voiced a green-skinned shapeshifter who can change into any animal. Cyborg, the half-robot half-human technological genius of the Titans, was portrayed by Khary Payton. Tara Strong played Raven, a sorceress from Azarath whose powers are triggered and controlled by her emotions. Starfire, a Tamaranian princess who still struggles to acclimate to Earth customs, was voiced by Hynden Walch. Walch provided the voice for Blackfire, Starfire's older sister, in the episode "Sisters" while Menville played Robin's alter-ego Red X in the episode "Masks".
In addition to the main cast, the season employs several guest voice actors. Actor Dee Bradley Baker provided the voice effects for Cinderblock, a humanoid concrete monster, appearing in two episodes of the season. Baker provided the voice of Plasmus in the episode "Divide and Conquer." Veteran actor Ron Perlman played the season's main villain, appearing in six episodes. The episode "Final Exam" featured the vocal talents of Lauren Tom, who voiced H. I. V. E. Members Jinx and Gizmo, Kevin Michael Richardson, who provided the voice of Mammoth. Tom voiced Gizmo in the episode "Car Trouble." In the episode "Forces of Nature", Stuart Scott Bullock, better known as S. Scott Bullock, provided the voice of Thunder and Quinton Flynn provided the voice for Lightning. Thunder and Lightning are supernatural brothers who use their powers to cause mischief-they would become allies of the Titans in Season 5. In the episode "The Sum of His Parts", Tom Kenny, the voice of SpongeBob SquarePants in the Nickelodeon series, provided the voices of Mumbo Jumbo and robot hermit Fixit, the episode's main villains.
Recurring villain Dr. Light, voiced by character actor Roger Bumpass, debuted in the episode "Nevermore." Keith Szarabajka filled the voice of Trigon. He returns in Season 4 as the season's main villain, important to that season's story arc. Tracey Walter lent his voice to the main villain of the episode "Switched", Puppet King; the episode "Deep Six" featured the vocal talents of Clancy Brown, veteran actor and comedian Dave Coulier, actor and writer Wil Wheaton. The episode "Mad Mod" featured English actor Malcolm McDowell providing the voice of the titular character. Actor and singer James Arnold Taylor provided the voices for Cash and Sammy in the episode "Car Trouble." Teen Titans debuted on Cartoon Network on July 19, 2003 with the highest ratings among boy 6–11 for the network. Ratings for the following two episodes showed growth across the target demographics, including a 78 percent rise in viewers age 6–11 and an 87% rise in boy viewers age 6–11. Season one completed its run on the network as the network'
Divide-and-conquer eigenvalue algorithm
Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the divide-and-conquer approach from computer science. An eigenvalue problem is divided into two problems of half the size, each of these are solved recursively, the eigenvalues of the original problem are computed from the results of these smaller problems. Here we present the simplest version of a divide-and-conquer algorithm, similar to the one proposed by Cuppen in 1981. Many details that lie outside the scope of this article will be omitted; as with most eigenvalue algorithms for Hermitian matrices, divide-and-conquer begins with a reduction to tridiagonal form. For an m × m matrix, the standard method for this, via Householder reflections, takes 4 3 m 3 flops, or 8 3 m 3 if eigenvectors are needed as well.
There are other algorithms, such as the Arnoldi iteration, which may do better for certain classes of matrices. In certain cases, it is possible to deflate an eigenvalue problem into smaller problems. Consider a block diagonal matrix T =; the eigenvalues and eigenvectors of T are those of T 1 and T 2, it will always be faster to solve these two smaller problems than to solve the original problem all at once. This technique can be used to improve the efficiency of many eigenvalue algorithms, but it has special significance to divide-and-conquer. For the rest of this article, we will assume the input to the divide-and-conquer algorithm is an m × m real symmetric tridiagonal matrix T. Although the algorithm can be modified for Hermitian matrices, we do not give the details here; the divide part of the divide-and-conquer algorithm comes from the realization that a tridiagonal matrix is "almost" block diagonal. The size of submatrix T 1 we will call n × n, T 2 is ×. Note that the remark about T being block diagonal is true regardless of how n is chosen.
However, it makes sense, from an efficiency standpoint, to choose n ≈ m / 2. We write T as a block diagonal matrix, plus a rank-1 correction: The only difference between T 1 and T ^ 1 is that the lower right entry t n n in T ^ 1 has been replaced with t n n − β and in T ^ 2 the top left entry t n + 1, n + 1 has been replaced with t n + 1, n + 1 − β; the remainder of the divide step is to solve for the eigenvalues of T ^ 1 and T ^ 2, to find the diagonalizations T ^ 1 = Q 1 D 1 Q 1 T and T ^ 2 = Q 2 D 2 Q 2 T. This can be accomplished with recursive calls to the divide-and-conquer algorithm, although practical implementations switch to the QR algorithm for small enough submatrices; the conquer part of the algorithm is the unintuitive part. Given the diagonalizations of the submatrices, calculated above, how do we find the diagonalization of the original matrix? First, define z T =, where
Divide and choose
Divide and choose is a procedure for envy-free cake-cutting between two partners. It involves a heterogeneous good or resource and two partners which have different preferences over parts of the cake; the protocol proceeds as follows: one person cuts the cake into two pieces. Divide-and-choose is mentioned in the Book of Genesis; when Abraham and Lot come to the land of Canaan, Abraham suggests. Abraham, coming from the south, divides the land to a "left" part and a "right" part, lets Lot choose. Lot chooses the eastern part which contains Sodom and Gomorrah, Abraham is left with the western part which contains Beer Sheva, Beit El and Shechem. Divide-and-choose is envy-free in the following sense: each of the two partners can act in a way that guarantees that, according to their own subjective taste, their allocated share is at least as valuable as the other share, regardless of what the other partner does. Here is how each partner can act: The cutter can cut the cake to two pieces that they consider equal.
Regardless of what the chooser does, they are left with a piece, as valuable as the other piece. The chooser can select the piece. If the cutter divided the cake to pieces that are unequal, the chooser still has no reason to complain because they chose the piece, more valuable in their own eyes. To an external viewer, the division might seem unfair, but to the two involved partners, the division is fair - no partner envies the other. If the value functions of the partners are additive functions divide-and-choose is proportional in the following sense: each partner can act in a way that guarantees that their allocated share has a value of at least 1/2 of the total cake value; this is because, with additive valuations, every envy-free division is proportional. The protocol works both for dividing an undesirable resource. Divide and choose assumes the parties have equal entitlements and wish to decide the division themselves or use mediation rather than arbitration; the goods are assumed to be divisible in any way.
The cutter has an incentive to divide as as possible: for if they do not, they will receive an undesirable portion. This rule is a concrete application of the veil of ignorance concept; the divide and choose method does not guarantee each person gets half the cake by their own valuations, so is not an exact division. There is no finite procedure for exact division but it can be done using two moving knives. Divide-and-choose might produce inefficient allocations. One used example is a cake, half vanilla and half chocolate. Suppose Bob likes only chocolate, Carol only vanilla. If Bob is the cutter and he is unaware of Carol's preference, his safe strategy is to divide the cake so that each half contains an equal amount of chocolate, but regardless of Carol's choice, Bob gets only half the chocolate and the allocation is not Pareto efficient. It is possible that Bob, in his ignorance, would put all the vanilla in one larger portion, so Carol gets everything she wants while he would receive less than what he could have gotten by negotiating.
If Bob knew Carol's preference and liked her, he could cut the cake into an all-chocolate piece, an all-vanilla piece, Carol would choose the vanilla piece, Bob would get all the chocolate. On the other hand, if he doesn't like Carol he can cut the cake into more than half vanilla in one portion and the rest of the vanilla and all the chocolate in the other. Carol might be motivated to take the portion with the chocolate to spite Bob. There is a procedure to solve this but it is unstable in the face of a small error in judgement. More practical solutions that can't guarantee optimality but are much better than divide and choose have been devised by Steven Brams and Alan Taylor, in particular the adjusted winner procedure. In 2006 Steven J. Brams, Michael A. Jones, Christian Klamler detailed a new way to cut a cake called the surplus procedure that satisfies equitability and so solves the above problem. Both people's subjective valuation of their piece as a proportion of the whole is the same.
Martin Gardner popularized the problem of designing a fair procedure for larger groups, in his "Mathematical Games" column in Scientific American. One procedure begins with one person cutting. Anyone can trim it down to be smaller, but whoever is the last person to trim it, has to take it. A newer method is reported in, it was developed by Mackenzie. While faster in principle than the earlier method, it is still very slow: O, where n is the number of divisions desired. Fair division Resource allocation Market maker, players in financial markets who offer to either buy or sell at a given price
Divide and Conquer (film)
Divide and Conquer is the third film of Frank Capra's Why We Fight propaganda film series, dealing with the Nazi conquest of Western Europe in 1940. The film begins after the fall of Poland. Of the two major Western Allies of 1940, the United Kingdom is first to be mentioned; the role of the Royal Navy in blockading Germany is highlighted, in that it means that Germany must overcome British resistance in order to clear the way for its world conquest. Hitler's treachery towards the small neutral countries of Europe is exposed - to Denmark: "We have concluded a non-aggression pact with Denmark" - to Norway: "Germany never had any quarrel with the Northern States and has none today" - to the Netherlands: "The new Reich has always endeavored to maintain the traditional friendship with Holland" - and to Belgium: "The Reich has put forth no claim which may in any way be regarded as a threat to Belgium"; these quotes are repeated. The first targets of the Nazis in 1940 were Norway. Nazi interest in Norway is described in terms of Germany's desire to use Norway's fjords as U-boat bases, to use airfields in Norway for a bomber attack on the British naval base at Scapa Flow.
After Hitler's surprise invasion of Denmark is mentioned, the film accuses the Nazis of using Trojan Horse ships - designed to look like merchant ships but concealing troops and artillery guns - as a way of seizing control of all of Norway's ports. The role of Norwegian traitors such as Vidkun Quisling in aiding the Nazi conquest of Norway is emphasized. At the end of the section on Norway, Hitler is likened to gangster John Dillinger and Nazi-occupied Norway is portrayed as the northern claw of a giant pincer movement aimed against Britain; the conquest of France would provide the southern claw. The film's story of France begins in 1914 at the Battle of the Marne; the offensive-minded spirit of French general Ferdinand Foch is emphasized: "My right is driven in, my center is giving way, the situation is excellent, I attack!". The film goes on to describe the defensive orientation of 1930s France, exemplified by the Maginot Line; this is explained as being due to the 6 million casualties which France suffered in World War I, but due to factors including Nazi fifth column activities, political corruption and greedy vested interests.
Possible routes for a German invasion of France are discussed: the 1870 attack through Alsace-Lorraine and the 1914 attack through Belgium. The French, believing the Maginot Line impregnable, expect the German attack to come through Belgium, as in 1914; the French order of battle in 1940 is described: 78 divisions along the border with Belgium, 15 in the Maginot Line, 10 divisions facing Benito Mussolini's forces in Italy and 3½ divisions as a safeguard against Spain. The British Expeditionary Force contributed an additional 10 divisions; the important role of paratroopers in the conquest of the Netherlands is covered, as is the fact that the Germans defeated Belgian resistance at Fort Eben-Emael knowing the best method of attack after extensive practice on an exact copy of the fortress built in occupied Czechoslovakia. Special attention is paid to Nazi atrocities, such as the Rotterdam Blitz after the surrender of the city and Nazi attacks on villages and small towns, it is mentioned that the Nazis' attack on Belgium and the Netherlands was a feint to distract from the main attack through the Ardennes, where the Allies least expected it.
A U. S. military officer shows an animation which demonstrates the German blitzkrieg technique - tanks form the front spearhead, while infantry spill off from the sides to form solid walls, thus protecting the center of the column through which trucks pass to supply all forces involved. List of films in the public domain in the United States Propaganda in the United States Divide and Conquer is available for free download at the Internet Archive Divide and Conquer on IMDb