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Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
We provide an exact expressions for the 1-Wasserstein distance between independent location-scale distributions. The expressions are represented using location and scale parameters and special functions such as the standard Gaussian CDF or…
Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random…
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…
Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two…
We first extend the result of Ali and Silvey [Journal of the Royal Statistical Society: Series B, 28.1 (1966), 131-142] who first reported that any $f$-divergence between two isotropic multivariate Gaussian distributions amounts to a…
We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
Let $A_{\varphi}$ denote the matrix of rotation with angle $\varphi$ of the Euclidean plane, FLOOR the function, which rounds a real point to the nearest lattice point down on the left and ROUND the function for rounding off a vector to the…
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection…
The analysis of animal movement has gained attention recently. New continuous-time models and statistical methods have been developed to estimate some sets related to their movements, such as the home-range and the core-area among others,…
We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice,…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
In this paper, we propose a novel distributed formation control strategy, which is based on the measurements of relative position of neighbors, with global orientation estimation in 3-dimensional space. Since agents do not share a common…
In this paper we derive a Tully Fisher relation from measured I band photometry and H$\alpha$ rotation curves of a large survey of southern sky spiral galaxies, obtained in Persic \& Salucci (1995) by deprojecting and folding the raw…
The longest increasing subsequence (LIS) of a sequence of correlated random variables is a basic quantity with potential applications that has started to receive proper attention only recently. Here we investigate the behavior of the length…