Related papers: Shape theory via affine transformation: Some gener…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
Supervised transfer learning has received considerable attention due to its potential to boost the predictive power of machine learning in scenarios where data are scarce. Generally, a given set of source models and a dataset from a target…
We examine the affine Wigner distribution from a quantization perspective with an emphasis on the underlying group structure. One of our main results expresses the scalogram as (affine) convolution of affine Wigner distributions. We strive…
In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
The dependence of the nuclear level density on intrinsic deformation is an important input to dynamical nuclear processes such as fission. Auxiliary-field Monte Carlo (AFMC) method is a powerful method for computing nuclear level densities.…
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional…
Coarse-grained spin density functional theory (SDFT) is a version of SDFT which works with number/spin densities specified to a limited resolution --- averages over cells of a regular spatial partition --- and external potentials constant…
Models for inferring monocular shape of surfaces with diffuse reflection -- shape from shading -- ought to produce distributions of outputs, because there are fundamental mathematical ambiguities of both continuous (e.g., bas-relief) and…
Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…