Related papers: The gradient flow of the polarization measure. Wit…
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as…
We consider the problem of sampling from a probability distribution $\pi$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions…
The orientation of a polarization vector on the Poincare sphere is defined by its position angle (PA) and ellipticity angle (EA). The radio emission from pulsars, magnetars, and fast radio bursts can be elliptically polarized, and…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…
We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the…
We report on the experimental implementation of a polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-1/2 quantum systems, and the alignment procedure for this polarimeter is…
Motivated by a recent method for approximate solution of Fredholm equations of the first kind, we develop a corresponding method for a class of Fredholm equations of the \emph{second kind}. In particular, we consider the class of equations…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
We discuss two research areas dealing respectively with (1) a class of multivariate medians and (2) a symmetrization algorithm for probability measures.
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between…
Visibility $V$ and distinguishability $D$ quantify wave-ray duality: $V^2 + D^2 \le 1$. We join them to polarization $P$ via the Polarization Coherence Theorem, a tight equality: $P^2 = V^2 + D^2$.
We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
In undergraduate optics courses, diffraction gratings are studied extensively, generally within the scalar approximation. When the vector nature of light is taken into account, so-called polarization diffraction gratings have been proposed,…
The degree of elliptical polarization of intense short laser pulses is shown to be related to the timing of strong-field non-sequential double ionization. Higher ellipticity is predicted to force the initiation of double ionization into a…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
We measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of…
We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…
A statistical model is used to determine how stochastic fluctuations in the intensities of orthogonal polarization modes contribute to the modulation and depolarization of pulsar radio emission. General expressions for the distributions of…