相关论文: Ergodic Optimization and Ground States: a brief In…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
Using a simple, annealed model, some of the key features of the recently introduced extremal optimization heuristic are demonstrated. In particular, it is shown that the dynamics of local search possesses a generic critical point under the…
This is a textbook, in Spanish, for an introductory short course that focusses on the ergodic properties of topological and statistical attractors. It is directed to graduate students in Mathematics and related Science, in particular to the…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
Fields offer a versatile approach for describing complex systems composed of interacting and dynamic components. In particular, some of these dynamical and stochastic systems may exhibit goal-directed behaviors aimed at achieving specific…
We study some ergodicity property of zero-sum stochastic games with a finite state space and possibly unbounded payoffs. We formulate this property in operator-theoretical terms, involving the solvability of an optimality equation for the…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a version of Hofbauer's Markov diagram, (ii) the…
This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to…
To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper, we investigate threshold-type…
In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of…
Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…