相关论文: Saigo Space-Time Fractional Poisson Process via Ad…

We show among other things how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on time variable with the…

Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs which are liable to anomalous…

The extraction of natural gas from the earth has been shown to be governed by differential equations concerning flow through a porous material. Recently, models such as fractional differential equations have been developed to model this…

Based on the Denoising Diffusion Probabilistic Model (DDPM), medical image segmentation can be described as a conditional image generation task, which allows to compute pixel-wise uncertainty maps of the segmentation and allows an implicit…

We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit…

Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…

We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…

The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto in \cite{sfpp}, is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional…

We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…

In order to perform quantum Hamiltonian dynamics minimizing localization effects, we introduce a quasi-one dimensional tight-binding model whose mean free path is smaller than the size of the sample. This one, in turn, is smaller than the…

We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson…

Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the…

In this article we introduce an analytical method, namely Homotopy Analysis Transform Method (HATM) which is a combination of Homotopy Analysis Method (HAM) and Laplace Decomposition Method (LDM).This scheme is simple to apply linear and…

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…