arXiv subjects

Charles E. M. Pearce

Publications and source records attributed to Charles E. M. Pearce.

4 recordsLinked to original sources

arXiv2014

A probabilistic approach to quantum Bayesian games of incomplete information

A Bayesian game is a game of incomplete information in which the rules of the game are not fully known to all players. We consider the Bayesian game of Battle of Sexes that has several Bayesian Nash equilibria and investigate its outcome when the underlying probability set is obtained from generalized Einstein-Podolsky-Rosen experiments. We find that this probability set, which may become non-factorizable, results in a unique Bayesian Nash equilibrium of the game.

quant-ph↗

arXiv2008

The duration problem with multiple exchanges

We treat a version of the multiple-choice secretary problem called the multiple-choice duration problem, in which the objective is to maximize the time of possession of relatively best objects. It is shown that, for the $m$--choice duration problem, there exists a sequence (s1,s2,...,sm) of critical numbers such that, whenever there remain k choices yet to be made, then the optimal strategy immediately selects a relatively best object if it appears at or after time $s_k$ ($1\leq k\leq m$). We also exhibit an equivalence between the duration problem and the classical best-choice secretary problem. A simple recursive formula is given for calculating the critical numbers when the number of objects tends to infinity. Extensions are made to models involving an acquisition or replacement cost.

math.PR↗

arXiv2008

A Ring Isomorphism and corresponding Pseudoinverses

This paper studies the set of $n\times n$ matrices for which all row and column sums equal zero. By representing these matrices in a lower dimensional space, it is shown that this set is closed under addition and multiplication, and furthermore is isomorphic to the set of arbitrary $(n-1)\times (n-1)$ matrices. The Moore-Penrose pseudoinverse corresponds with the true inverse, (when it exists), in this lower dimension and an explicit representation of this pseudoinverse in terms of the lower dimensional space is given. This analysis is then extended to non-square matrices with all row or all column sums equal to zero.

math.RA↗

arXiv2004

Point singularities and suprathreshold stochastic resonance in optimal coding

Motivated by recent studies of population coding in theoretical neuroscience, we examine the optimality of a recently described form of stochastic resonance known as suprathreshold stochastic resonance, which occurs in populations of noisy threshold devices such as models of sensory neurons. Using the mutual information measure, it is shown numerically that for a random input signal, the optimal threshold distribution contains singularities. For large enough noise, this distribution consists of a single point and hence the optimal encoding is realized by the suprathreshold stochastic resonance effect. Furthermore, it is shown that a bifurcational pattern appears in the optimal threshold settings as the noise intensity increases. Fisher information is used to examine the behavior of the optimal threshold distribution as the population size approaches infinity.

cond-mat.stat-mech↗