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In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.

Buildings (Group theory) --- Moufang loops --- Automorphisms --- Affine algebraic groups --- Moufang loops. --- Automorphisms. --- Affine algebraic groups. --- Algebraic groups, Affine --- Loops, Moufang --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Group schemes (Mathematics) --- Group theory --- Symmetry (Mathematics) --- Loops (Group theory) --- Linear algebraic groups --- Buildings (Group theory). --- Addition. --- Additive group. --- Additive inverse. --- Algebraic group. --- Algebraic structure. --- Ambient space. --- Associative property. --- Automorphism. --- Big O notation. --- Bijection. --- Bilinear form. --- Bounded set (topological vector space). --- Bounded set. --- Calculation. --- Cardinality. --- Cauchy sequence. --- Commutative property. --- Complete graph. --- Complete metric space. --- Composition algebra. --- Connected component (graph theory). --- Consistency. --- Continuous function. --- Coordinate system. --- Corollary. --- Coxeter group. --- Coxeter–Dynkin diagram. --- Diagram (category theory). --- Diameter. --- Dimension. --- Discrete valuation. --- Division algebra. --- Dot product. --- Dynkin diagram. --- E6 (mathematics). --- E7 (mathematics). --- E8 (mathematics). --- Empty set. --- Equipollence (geometry). --- Equivalence class. --- Equivalence relation. --- Euclidean geometry. --- Euclidean space. --- Existential quantification. --- Free monoid. --- Fundamental domain. --- Hyperplane. --- Infimum and supremum. --- Jacques Tits. --- K0. --- Linear combination. --- Mathematical induction. --- Metric space. --- Multiple edges. --- Multiplicative inverse. --- Number theory. --- Octonion. --- Parameter. --- Permutation group. --- Permutation. --- Pointwise. --- Polygon. --- Projective line. --- Quadratic form. --- Quaternion. --- Remainder. --- Root datum. --- Root system. --- Scientific notation. --- Sphere. --- Subgroup. --- Subring. --- Subset. --- Substructure. --- Theorem. --- Topology of uniform convergence. --- Topology. --- Torus. --- Tree (data structure). --- Tree structure. --- Two-dimensional space. --- Uniform continuity. --- Valuation (algebra). --- Vector space. --- Without loss of generality.

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Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to "the game" solve the original design problem? Using the fundamentals of game theory, Hespanha explores these issues and more.The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria-such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, Hespanha examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty-the unforgiving variable that can wreck engineering designs. Hespanha looks at such standard topics as zero-sum, non-zero-sum, and dynamics games and includes a MATLAB guide to coding.Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications.An introduction to game theory applications for students of engineering and computer science Materials presented sequentially and in an easy-to-understand fashionTopics explore zero-sum, non-zero-sum, and dynamics gamesMATLAB commands are included

Noncooperative games (Mathematics) --- Game theory --- Cooperative games (Mathematics) --- MATLAB. --- Minimax Theorem. --- N-player game. --- Nash equilibrium. --- Separating Hyperplane Theorem. --- Sudoku puzzle. --- action space. --- action. --- admissible Nash equilibrium. --- advertising campaign. --- alternate play. --- average security level. --- battle of the sexes. --- behavioral policy. --- behavioral saddle-point equilibrium. --- best-response equivalent games. --- bilateral symmetric game. --- bimatrix game. --- bimatrix potential. --- chicken game. --- circuit design. --- completely mixed Nash equilibrium. --- computational complexity. --- computer science. --- congestion game. --- continuous time cost-to-go. --- continuous time differential. --- continuous time dynamic programming. --- continuous time dynamic. --- convex analysis. --- convex hull. --- decoupled game. --- design methodology. --- differential game. --- discrete time cost-to-go. --- discrete time dynamic programming. --- discrete time dynamic. --- distributed resource allocation. --- dummy game. --- dynamic game. --- engineering. --- extensive form game representation. --- feedback game. --- fictitious play. --- finite one-player. --- game theory. --- graphical method. --- hyperplane. --- identical interests. --- information structure. --- linear program. --- linear quadratic dynamic. --- minimum. --- mixed Nash equilibrium. --- mixed action space. --- mixed policy. --- mixed saddle-point equilibrium. --- mixed security policy. --- multi-stage game. --- network routing. --- non-feedback game. --- non-zero-sum. --- noncooperative game theory. --- open-loop policy. --- open-loop. --- optimization-based design. --- order interchangeability property. --- policy. --- potential game. --- probability distribution. --- pure N-player game. --- pure policy. --- recursive computation. --- regret. --- robust design. --- rock-paper-scissors. --- rope-pulling. --- saddle-point equilibrium. --- security level. --- security policy. --- simultaneous play. --- single-stage game. --- state feedback information structure. --- state-feedback policy. --- stochastic policy. --- strictly dominating policy. --- symmetry game. --- tic-tac-toe. --- tree structure. --- uncertainty. --- variable termination time. --- war of attrition. --- weakly dominating policy. --- zebra in the lake. --- zero sum dynamic. --- zero-sum matrix. --- zero-sum two-person. --- zero-sum. --- MATLAB. --- Minimax Theorem. --- N-player game. --- Nash equilibrium. --- Separating Hyperplane Theorem. --- Sudoku puzzle. --- action space. --- action. --- admissible Nash equilibrium. --- advertising campaign. --- alternate play. --- average security level. --- battle of the sexes. --- behavioral policy. --- behavioral saddle-point equilibrium. --- best-response equivalent games. --- bilateral symmetric game. --- bimatrix game. --- bimatrix potential. --- chicken game. --- circuit design. --- completely mixed Nash equilibrium. --- computational complexity. --- computer science. --- congestion game. --- continuous time cost-to-go. --- continuous time differential. --- continuous time dynamic programming. --- continuous time dynamic. --- convex analysis. --- convex hull. --- decoupled game. --- design methodology. --- differential game. --- discrete time cost-to-go. --- discrete time dynamic programming. --- discrete time dynamic. --- distributed resource allocation. --- dummy game. --- dynamic game. --- engineering. --- extensive form game representation. --- feedback game. --- fictitious play. --- finite one-player. --- game theory. --- graphical method. --- hyperplane. --- identical interests. --- information structure. --- linear program. --- linear quadratic dynamic. --- minimum. --- mixed Nash equilibrium. --- mixed action space. --- mixed policy. --- mixed saddle-point equilibrium. --- mixed security policy. --- multi-stage game. --- network routing. --- non-feedback game. --- non-zero-sum. --- noncooperative game theory. --- open-loop policy. --- open-loop. --- optimization-based design. --- order interchangeability property. --- policy. --- potential game. --- probability distribution. --- pure N-player game. --- pure policy. --- recursive computation. --- regret. --- robust design. --- rock-paper-scissors. --- rope-pulling. --- saddle-point equilibrium. --- security level. --- security policy. --- simultaneous play. --- single-stage game. --- state feedback information structure. --- state-feedback policy. --- stochastic policy. --- strictly dominating policy. --- symmetry game. --- tic-tac-toe. --- tree structure. --- uncertainty. --- variable termination time. --- war of attrition. --- weakly dominating policy. --- zebra in the lake. --- zero sum dynamic. --- zero-sum matrix. --- zero-sum two-person. --- zero-sum.