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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The complexity of computing Markov perfect equilibrium in general-sum stochastic games
一般 随机博弈 马尔可夫完美均衡 计算复杂性
2023/5/12
Similar to the role of Markov decision processes in reinforcement learning, Markov games (also known as stochastic games) form the basis for the study of multi-agent reinforcement learning and sequenc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Perfect Matchings in hypergraphs
超图 完美匹配 图论
2023/4/27
Matchings are fundamental objects in the study of graph theory. Unlike in graphs, finding maximum matchings in general hypergraphs is NP-hard -- its decision problem is actually one of the Karp’s 21 N...
Passion makes perfect
Passion makes perfect
2016/7/15
Po-Shen Loh loves math. He doesn't say that outright, but he doesn't have to, either.His first brush with the Math Olympiads was in 1994, when he was a sixth grader. That year, the International Math ...
Frames which are tight might be considered optimally conditioned in the sense of their numerical stability.This leads to the question of perfect preconditioning of frames,i.e., modification of a given...
An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspac...
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the
deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on
top. The in shuffle I leave...
Existence, uniqueness, universality and functoriality of the perfect locality over a Frobenius P-category
Existence functoriality of the perfect locality Frobenius P-category Group Theory
2012/7/9
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
Solving the Odd Perfect Number Problem: Some New Approaches
Odd perfect number Euler factor inequalities OPN components non-injective and non-surjective mapping
2012/6/29
A conjecture predicting an injective and surjective mapping $X = \displaystyle\frac{\sigma(p^k)}{p^k}, Y = \displaystyle\frac{\sigma(m^2)}{m^2}$ between OPNs $N = {p^k}{m^2}$ (with Euler factor $p^k$)...
Abstract: The existence question for tiling of the $n$-dimensional Euclidian space by crosses is well known. A few existence and nonexistence results are known in the literature. Of special interest a...
Edge-Removal and Non-Crossing Perfect Matchings
Edge-Removal Non-Crossing Matchings Combinatorics Probability
2011/9/5
Abstract: We study the following problem - How many arbitrary edges can be removed from a complete geometric graph with 2n vertices such that the resulting graph always contains a perfect non-crossing...
On Rees algebras and invariants for singularities over perfect fields
Rees algebras Integral closure Singularities Commutative Algebra
2011/8/31
Abstract: This purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations i...
Developments in perfect simulation for Gibbs measures
Perfect Simulation Stochastic Order Gibbs Measures
2011/8/30
Abstract: This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are l...
Perfect Sampling of Markov Chains with Piecewise Homogeneous Events
Markov chains perfect sampling queueing systems
2011/3/2
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a nite time without ever computing the distribution.
Exponentially many perfect matchings in cubic graphs
Exponentially many perfect matchings cubic graphs
2011/1/21
We show that every cubic bridgeless graph G has at least 2|V (G)|/3656 perfect matchings.
This confirms an old conjecture of Lov´asz and Plummer.
Julia sets of uniformly quasiregular mappings are uniformly perfect
Julia uniformly quasiregular mappings uniformly perfect
2011/1/19
It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus,with the bound depending only on f. In th...