Empirical Analysis of Fictitious Play for Nash Equilibrium Computation
in Multiplayer Games
January 29, 2020
Computer Science
Economics
Computer Science and Game Theory
Artificial Intelligence
Multiagent Systems
Theoretical Economics
While fictitious play is guaranteed to converge to Nash equilibrium in
certain game classes, such as two-player zero-sum games, it is not guaranteed
to converge in non-zero-sum and multiplayer games. We show that fictitious play
in fact lea...
The Ramanujan-Petersson and Selberg conjectures for Maass forms
January 29, 2020
Mathematics
Group Theory
Number Theory
We prove the Ramanujan-Petersson conjecture for Maass forms of the group
SL(2,Z), with the help of automorphic distribution theory: this is an
alternative to classical automorphic function theory, in which the plane takes
the place usuall...
The geometry of C1,α flat isometric immersions
January 29, 2020
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Mathematics
Analysis of PDEs
Differential Geometry
We show that any isometric immersion of a flat plane domain into R3 is developable provided it enjoys the little H\"older regulairty
c1,2/3. In particular, isometric immersions of local C1,α
regularity with $\alpha...
Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and
its Application to the High-Order Strong Numerical Methods for Ito Stochastic
Differential Equations
January 28, 2020
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Mathematics
Probability
Probability
The problem of the Taylor-Ito and Taylor-Stratonovich expansions of the Ito
stochastic processes in a neighborhood of a fixed moment of time is considered.
The classical forms of the Taylor-Ito and Taylor-Stratonovich expansions are
transfo...
Understanding North Atlantic Climate Instabilities and Complex
Interactions using Data Science
January 28, 2020
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Statistics
Applications
Applications
The North Atlantic Oscillation (NAO) index, a measure of sea-level
atmospheric pressure variability, holds significant influence over weather
patterns in North America and Northern Europe. A negative (positive) NAO value
signifies increased...
On the dual positive cones and the algebraicity of a compact K\"ahler
manifold
January 28, 2020
Mathematics
Complex Variables
Algebraic Geometry
We investigate the algebraicity of compact K\"ahler manifolds admitting a
positive rational Hodge class of bidimension (1,1). We prove that if the dual
K\"ahler cone of a compact K\"ahler manifold X contains a rational class as
an inter...
Holographic entanglement negativity for disjoint subsystems in
AdSd+1/CFTd
January 28, 2020
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Physics
High Energy Physics - Theory
We propose a construction to compute the holographic entanglement negativity
for bipartite mixed state configurations of two disjoint subsystems in higher
dimensional conformal field theories (CFTds) dual to bulk AdSd+1
geometries. ...
Newton non-degenerate μ-constant deformations admit simultaneous
embedded resolutions
January 28, 2020
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Mathematics
Algebraic Geometry
Let Con+1 denote the germ of Cn+1 at the origin.
Let V be a hypersurface germ in Con+1 and W a deformation of
V over Com. Under the hypothesis that W is a Newton
non-degen...
Invariants of links and 3-manifolds from graph configurations
January 27, 2020
Mathematics
Physics
Geometric Topology
Mathematical Physics
Differential Geometry
Mathematical Physics
In this self-contained book, following Edward Witten, Maxim Kontsevich, Greg
Kuperberg and Dylan Thurston, we define an invariant Z of framed links in
rational homology 3-spheres, and we study its properties. The invariant Z,
which is often...
On the Unruh effect and the Thermofield Double State
January 27, 2020
Physics
High Energy Physics - Theory
The purpose of this review is to provide a pedagogical development of the
Unruh effect and the thermofield double state. In Section 2, we construct
Rindler spacetime and analyze the perspective of an observer undergoing
constant acceleratio...