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Methodologies for analyzing equilibria in wireless games
- IEEE Signal Processing Magazine, Special issue on Game Theory for Signal Processing
, 2009
"... Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure s ..."
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Cited by 48 (25 self)
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Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide non-exhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection and efficiency.
THE LEFSCHETZ-HOPF THEOREM AND AXIOMS FOR THE LEFSCHETZ NUMBER
, 2004
"... Abstract. The reduced Lefschetz number, that is, L(·) − 1 where L(·) denotes the Lefschetz number, is proved to be the unique integer-valued function λ on selfmaps of compact polyhedra which is constant on homotopy classes such that (1) λ(fg) = λ(gf), for f: X → Y and g: Y → X; (2) if (f1, f2, f3) ..."
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Cited by 9 (1 self)
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Abstract. The reduced Lefschetz number, that is, L(·) − 1 where L(·) denotes the Lefschetz number, is proved to be the unique integer-valued function λ on selfmaps of compact polyhedra which is constant on homotopy classes such that (1) λ(fg) = λ(gf), for f: X → Y and g: Y → X; (2) if (f1, f2, f3) is a map of a cofiber sequence into itself, then λ(f1) = λ(f1)+λ(f3); (3) λ(f) = −(deg(p1fe1)+···+deg(pkfek)), where f is a selfmap of a wedge of k circles, er is the inclusion of a circle into the rth summand and pr is the projection onto the rth summand. If f: X → X is a selfmap of a polyhedron and I(f) is the fixed point index of f on all of X, then we show that I(·) − 1 satisfies the above axioms. This gives a new proof of the Normalization Theorem: If f: X → X is a selfmap of a polyhedron, then I(f) equals the Lefschetz number L(f) of f. This result is equivalent to the Lefschetz-Hopf Theorem: If f: X → X is a selfmap of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of f is the sum of the indices of all the fixed points of f. 1. Introduction.
Olga Taussky-Todd/s Influence on Matrix Theory and Matrix Theorists -- A Discursive Personal Tribute
, 1977
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Unipotent Jacobian matrices and univalent maps
- Contemp. Math
"... Abstract. The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for C 1 maps is explored here. Some results known in the polynomial case are extended to the C 1 context, and some special c ..."
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Cited by 3 (0 self)
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Abstract. The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for C 1 maps is explored here. Some results known in the polynomial case are extended to the C 1 context, and some special cases are resolved. 1.
EMMY NOETHER’S “SET THEORETIC ” TOPOLOGY: FROM DEDEKIND TO THE FIRST FUNCTORS
"... Abstract. Emmy Noether’s “set theoretic foundations ” for alge-bra were not what we usually call set theory. They were a program to disregard the elements and operations in algebraic structures in favor of selected subsets, linked to homomorphisms between struc-tures by the homomorphism and isomorph ..."
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Abstract. Emmy Noether’s “set theoretic foundations ” for alge-bra were not what we usually call set theory. They were a program to disregard the elements and operations in algebraic structures in favor of selected subsets, linked to homomorphisms between struc-tures by the homomorphism and isomorphism theorems. We con-sider how this conception drew on, and differed from, Dedekind’s. In 1926-27 Noether persuaded young topologists in Laren Holland visiting L. E. J. Brouwer to extend this viewpoint to topology, notably Paul Alexandroff and Leopold Vietoris. It was a natural match as Brouwer’s topology had always emphasized maps as much as spaces. So algebraic topology began using Noether’s conception of algebra to correlate maps between spaces with homomorphisms between homology groups. This became the model for functors in category theory, while the homomorphism and isomorphism theo-rems in particular led to the Abelian category axioms.
Nielsen numbers of n-valued fiber maps
- Journal of Fixed Point Theory and Applications
, 2008
"... The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to ..."
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Cited by 2 (2 self)
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The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of single-valued maps. If the fibration is orientable, the product formula for single-valued fiber maps fails to generalize, but a “semi-product formula ” is obtained. In this way, the class of n-valued multimaps for which the Nielsen number can be computed is substantially enlarged. Subject Classification 55M20, 54C60 1
Fix-Finite Approximation Property in Normed Vector Spaces
"... Let D and A be two nonempty subsets in a metric space. We say that the pair (D,A) satisfies the fix-finite approximation property (in short F.F.A.P.) for a family F of maps (or multifunctions) from D to A, if for every f ∈ F and all ε> 0 there exists g ∈ F which is ε-near to f and has only a fini ..."
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Cited by 1 (1 self)
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Let D and A be two nonempty subsets in a metric space. We say that the pair (D,A) satisfies the fix-finite approximation property (in short F.F.A.P.) for a family F of maps (or multifunctions) from D to A, if for every f ∈ F and all ε> 0 there exists g ∈ F which is ε-near to f and has only a finite
Methodologies for Analyzing Equilibria
, 2009
"... nder certain assumptions in terms of informa-tion and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where rational enti-ties interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which ..."
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nder certain assumptions in terms of informa-tion and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where rational enti-ties interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide non-exhaustive methodologies for characterizing equilibria in wireless games in terms of exis-tence, uniqueness, selection, and efficiency. The major works by Von Neumann, Morgenstern, and Nash are recognized as real catalyzers for the theory of games, which originates from the works by
