Related papers: Distributions and Integration in superspace
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
In this paper we study $g$-fractional diffusion on bounded domains in $\mathbb{R}^d$ with absorbing boundary conditions. We show the explicit representation of the solution and then we study the first passage time distribution, showing the…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific $q$-hypergeometric integrals whose key building block is the…
We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
Applying the distributional formalism to study the dynamics of thin shells in general relativity, we regain the junction equations for matching of two spherically symmetric spacetimes separated by a singular hypersurface. In particular, we…
Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
There has been much recent attention on $h$-functions, so named since they describe the distribution of harmonic measure for a given multiply connected domain with respect to some basepoint. In this paper, we focus on a closely related…
Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
Hyperspectral Image (HSI) classification is an important issue in remote sensing field with extensive applications in earth science. In recent years, a large number of deep learning-based HSI classification methods have been proposed.…
Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…
Non-Gaussian distributions are commonly observed in collisionless space plasmas. Generating samples from non-Gaussian distributions is critical for the initialization of particle-in-cell simulations that investigate their driven and…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability…
Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…