Related papers: The gradient flow of the polarization measure. Wit…
Political polarization can be beneficial to competing political parties. I study how electoral competition itself generates incentives to polarize voters, even when parties are ex ante identical and motivated purely by political power,…
The form of political polarization where citizens develop strongly negative attitudes towards out-party policies and members has become increasingly prominent across many democracies. Economic hardship and social inequality, as well as…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…
We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Polarization and unexpected correlations between opinions on diverse topics (including in politics, culture and consumer choices) are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…
Partial polarization is the manifestation of the correlation between two mutually orthogonal transverse field components associated with a light beam. We show both theoretically and experimentally that the origin of this correlation can be…
We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number $k$ that expresses its level of agreement…
A complete description is given of the class of probability measures on the group ${\mathbb Z}_2^3$, which are uniquely determined by the modulus of their characteristic function up to a shift.
Measuring the alignment of polarized radio sources requires comparing vectors at different locations on the sky, i.e. on a sphere. A test of alignment is derived herein. While both large scale and coordinate independent, the test avoids the…
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…
This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…
We present experimental results on a method to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two level systems. The setup has no moving parts…
This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, ${g}_{ij}({\bf x})$, which we…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…