Related papers: Directed Paths in Random Media
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…
This paper explores an eclectic range of path-planning methodologies engineered for rolling surfaces. Our focus is on the kinematic intricacies of rolling contact systems, which are investigated through a motion planning lens. Beyond…
Based only on the information gathered in a snapshot of a directed network, we present a formal way of checking if the proposed model is correct for the empirical growing network under study. In particular, we show how to estimate the…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in…
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
Exact calculations of transmission and reflection coefficients in surface randomly corrugated optical waveguides are presented. As the length of the corrugated part of the waveguide increases, there is a strong preference to forward…
As a newly emerging advance in deep generative models, diffusion models have achieved state-of-the-art results in many fields, including computer vision, natural language processing, and molecule design. The remote sensing (RS) community…
Diffusion models (DMs) have been investigated in various domains due to their ability to generate high-quality data, thereby attracting significant attention. However, similar to traditional deep learning systems, there also exist potential…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's $r$-pdf (Type II) governs the distribution of the internal energy of a…
We consider a directed percolation process on an ${\cal M}$ x ${\cal N}$ rectangular lattice whose vertical edges are directed upward with an occupation probability y and horizontal edges directed toward the right with occupation…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several…
Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two…
The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this…