Related papers: Revisiting Feller Diffusion: Derivation and Simula…
Optical turbulence modelling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of…
We study time-dependent density segregation of granular mixtures flowing over an inclined plane. Discrete Element Method (DEM) simulations in a periodic box are performed for granular mixtures of same size and different density particles…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…
The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that…
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of…
The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…
We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity…
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and…