Related papers: Distances for Weighted Transition Systems: Games a…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…

This study presents a quantitative framework to compare teams in collective sports with respect to their style of play. The style of play is characterized by the team's spatial distribution over a collection of frames. As a first step, we…

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…

In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…

Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies…

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…

We derive distance relay characteristics in terms of incremental quantities. The characteristics are operating-point independent in that they depend on the network structure and types of sources, but not their real-time voltages or current…

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…

More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…

1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…

The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the…

This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…

In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…

A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…