Related papers: Generalizations of Mat\'ern's hard-core point proc…

We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…

Proximal point algorithm has found many applications, and it has been playing fundamental roles in the understanding, design, and analysis of many first-order methods. In this paper, we derive the tight convergence rate in subgradient norm…

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is…

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with…

In this study we present a Microcanonical Monte Carlo investigation of one dimensional self-gravitating toy models. We study the effect of hard-core potentials and compare to those results obtained with softening parameters and also the…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading…

Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…

The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…

Consistent factorization theorems in high-energy scattering near the threshold are presented in the framework of the soft-collinear effective theory. Traditional factorization theorem separates the soft and collinear parts successfully, but…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and…

The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…

Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…

While overfitting and, more generally, double descent are ubiquitous in machine learning, increasing the number of parameters of the most widely used tensor network, the matrix product state (MPS), has generally lead to monotonic…

In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine learning literature, where they are used in random forest…

Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a…