Related papers: The gradient flow of the polarization measure. Wit…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
Politically divided societies are also often divided emotionally: people like and trust those with similar political views (in-group favoritism) while disliking and distrusting those with different views (out-group animosity). This…
A class of distance measures on probabilities -- the integral probability metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in more…
Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters…
We introduce a simple, geometric model of opinion polarization. It is a model of political persuasion, as well as marketing and advertising, utilizing social values. It focuses on the interplay between different topics and persuasion…
We propose a new concept of codivergence, which quantifies the similarity between two probability measures $P_1, P_2$ relative to a reference probability measure $P_0$. In the neighborhood of the reference measure $P_0$, a codivergence…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
Comparing the top $k$ elements between two or more ranked results is a common task in many contexts and settings. A few measures have been proposed to compare top $k$ lists with attractive mathematical properties, but they face a number of…
Polarization phenomena are essential for the understanding of elementary processes, and are typically large in the threshold region. The selection rules with respect to P-parity, angular momentum, isotopic spin and the Pauli principle allow…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
We derive an expression for the local transverse polarization of a boost-invariant expanding system of massive particles, which involves a set of dynamical spin moments. Starting from spin kinetic theory, we obtain a closed set of equations…
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to…
Clustering is the technique to partition data according to their characteristics. Data that are similar in nature belong to the same cluster [1]. There are two types of evaluation methods to evaluate clustering quality. One is an external…
Pulsar radio emission is modelled as a sum of two completely polarized non-orthogonal modes with the randomly varying Stokes parameters and intensity ratio. The modes are the result of polarization evolution of the original natural waves in…
Conley indices and Morse decompositions of flows can be found by using algorithms which rigorously analyze discrete dynamical systems. This usually involves integrating a time discretization of the flow using interval arithmetic. We compare…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…