相关论文: Homomesy via Toggleability Statistics

We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot's morphology, frequently observed in animal biology and robotics, which stem from the…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. The question is how to introduce the connective implication in such a logic. We show that this is possible when the orthomodular poset in question is of…

The co-adaptation of robots has been a long-standing research endeavour with the goal of adapting both body and behaviour of a system for a given task, inspired by the natural evolution of animals. Co-adaptation has the potential to…

We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies…

Predicting the macroscopic mechanical behavior of polymeric materials from the micro-structural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to…

We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…

We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm approximating zeros of differences of maximally monotone…

Given a monocular video of a soccer match, this paper presents a computational model to estimate the most feasible pass at any given time. The method leverages offensive player's orientation (plus their location) and opponents' spatial…

The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…

An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…

Given a bounded operator $Q$ on a Hilbert space $\mathcal{H}$, a pair of bounded operators $(T_1, T_2)$ on $\mathcal{H}$ is said to be $Q$-commuting if one of the following holds: \[ T_1T_2=QT_2T_1 \text{ or }T_1T_2=T_2QT_1 \text{ or…

In this paper we study the problem of estimating innercyclic time intervals within repetitive motion sequences of top-class swimmers in a swimming channel. Interval limits are given by temporal occurrences of key-poses, i.e. distinctive…

We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

We extend the existing idea of "cellular poset", introduce a collection of "cellular methods" for the computation of homology of intersection lattice of a complicated subspace arrangement, and for the computation of multiplicative structure…

We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…

Fej\'er monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fej\'er* monotonicity, which was initially proposed in [SIAM…

Within convex analysis, a rich theory with various applications has been evolving since the proximal average of convex functions was first introduced over a decade ago. When one considers the subdifferential of the proximal average, a…