Related papers: Mathematical properties of the SimpleX algorithm
The binary radix expansion of a real number can be used to code the outcome of any series of coin tosses, a fact that provides an intriguing link between number theory, measure theory and statistical physics. Inspired by this fact, a…
Linear representation learning is widely studied due to its conceptual simplicity and empirical utility in tasks such as compression, classification, and feature extraction. Given a set of points $[\mathbf{x}_1, \mathbf{x}_2, \ldots,…
This paper presents an attempt to come to a natural field model of individual photons considered as finite entities and propagating along some distinguished direction in space in a consistent translational-rotational manner. The starting…
The fundamental notions of radiative transfer, e.g., Lambert's cosine rule, are studied from the point of view of flux and stress theory of continuum mechanics. For the classical case, where the radiance is distributed regularly over the…
We consider the complexity of Delaunay triangulations of sets of points in R^3 under certain practical geometric constraints. The spread of a set of points is the ratio between the longest and shortest pairwise distances. We show that in…
The transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first…
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
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…
Resonance lines encode rich information about astrophysical sources and their environments, yet fully analytic treatments of multi-line radiative transfer remain almost entirely unexplored. We present exact, closed-form solutions for…
In this paper, we study information transport in multiplex networks comprised of two coupled subnetworks. The upper subnetwork, called the logical layer, employs the shortest paths protocol to determine the logical paths for packets…
The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance…
The problem of solution transfer between meshes arises frequently in computational physics, e.g. in Lagrangian methods where remeshing occurs. The interpolation process must be conservative, i.e. it must conserve physical properties, such…
We discuss an algorithm to compute transport maps that couple the uniform measure on $[0,1]^d$ with a specified target distribution $\pi$ on $[0,1]^d$. The primary objectives are either to sample from or to compute expectations w.r.t.…
Diffusion models learn to reverse the progressive noising of a data distribution to create a generative model. However, the desired continuous nature of the noising process can be at odds with discrete data. To deal with this tension…
This is the second in the series of papers on transport phenomena along random rough surfaces. We apply our simple general approach\cite{r1} to transport in very narrow channels, when the particles wavelength is comparable to the width of…
The transmissions as functions of energy are central for electron or phonon transport in the Landauer transport picture. We suggest a simple and computationally "cheap" post-processing scheme to interpolate transmission functions over…
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation…
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…