相关论文: Bounding Game Temperature Using Confusion Interval…
Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs).…
The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature -- the thermal entrance length -- is a consequence of diffusion…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
The game coloring number gcol($G$) of a graph $G$ is a two player competitive variant of the coloring number. We introduce the preordered game coloring number to study the consequences of either player skipping any number of turns. In…
A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…
In numerically simulated vibrated beds of powder, we measure temperature under convection by the generalized Einstein's relation. The spatial temperature distribution turns out to be quite uniform except for the boundary layers. In addition…
We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…
We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such…
In this paper we discuss whether thermodynamical concepts and in particular the notion of temperature could be relevant for the dynamics of granular systems. We briefly review how a temperature-like quantity can be defined and measured in…
Motivated by applications to 3D printing, this paper presents two algorithms for calculating an ensemble of solutions to heat conduction problems. The ensemble average is the most likely temperature distribution and its variance gives an…
Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property…
We study the statistical properties of a gas of interacting bosons trapped in a box potential in two and three dimensions. Our primary focus is the characteristic temperature $\tchar$, i.e. the temperature at which the fluctuations of the…
Consider the scenario where an infinite number of players (i.e., the \textit{thermodynamic} limit) find themselves in a Prisoner's dilemma type situation, in a \textit{repeated} setting. Is it reasonable to anticipate that, in these…
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…
We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…
A thermodynamic model of a plasma boundary layer, characterized by enhanced temperature contrasts is proposed. The theory is constructed to determine the inner boundary temperature $T_1$ for a specified outer (colder) boundary temperature…
In statistical physics, the efficiency of tempering approaches strongly depends on ingredients such as the number of replicas $R$, reliable determination of weight factors and the set of used temperatures, ${\mathcal T}_R = \{T_1, T_2,…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
A combinatorial game is a two-player game without hidden information or chance elements. The disjunctive sum $G + H$ of games $G$ and $H$ is the game in which $G$ and $H$ are played in parallel, and a player makes a move on exactly one of…
We derive a simple system of equations to describe the magnetization relaxation of a molecular spin in weak interaction with a thermal bath for the whole temperature domain. Using this for the intermediate temperature domain where the…