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Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105…
The representation of quark distribution and fragmentation functions in terms of non-local operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct…
We present the unpolarized and helicity parton distribution functions calculated within lattice QCD simulations using physical values of the light quark mass. Non-perturbative renormalization is employed and the lattice data are converted…
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
Clinical prediction models are increasingly used to support patient care, yet many deep learning-based approaches remain unstable, as their predictions can vary substantially when trained on different samples from the same population. Such…
We investigate theoretically how the stress propagation characteristics of granular materials evolve as they are subjected to increasing pressures, comparing the results of a two-dimensional scalar lattice model to those of a molecular…
We explore the application of a two-component model of proton structure functions in the analysis of deep-inelastic scattering (DIS) data at low $Q^2$ and small $x$. This model incorporates both vector meson dominance and the correct…
We present an approach to the design of distribution functions that depend on the phase-space coordinates through the action integrals. The approach makes it easy to construct a dynamical model of a given stellar component. We illustrate…
The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in…
Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…
Standard zeta function regularisation enforces a scale-independent prescription for spectral aggregation, effectively fixing the relative weight of spectral contributions. We relax this constraint by replacing the derivative at $s=0$ with a…
In random systems consisting of grains with size distributions the transport properties are difficult to explore by network models. However, the concentration dependence of effective conductivity and its critical properties can be…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The static pair correlation (distribution) function and the structure factor of particle distributions in three-dimensional homogeneous isotropic systems are explicitly restored from two-dimensional data observed in a thin slab sliced out…
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper arXiv:1810.05616. We argue that this framework is…
We present a new theory for the hierarchical clustering of dark matter (DM) halos based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach);…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…