Related papers: Superposition principle and schemes for Measure Di…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
Gradient schemes is a framework which enables the unified convergence analysis of many different methods -- such as finite elements (conforming, non-conforming and mixed) and finite volumes methods -- for $2^{\rm nd}$ order diffusion…
In this paper we will argue that the superposition of waves can be calculated and taught in a simple way. We show, using the Gauss's method to sum an arithmetic sequence, how we can construct the superposition of waves - with different…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
We consider stochastic particle dynamics on hypersurfaces represented in Monge gauge parametrization. Starting from the underlying Langevin system, we derive the surface Dean-Kawasaki (DK) equation and formulate it in the martingale sense.…
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…
In this paper, we study large and moderate deviation principles for stochastic partial differential equations (SPDEs) on metric graphs and their associated multiscale models via the weak convergence approach, providing a refined…
While in most cases the absolute accuracy, resolution, and noise floor are the only relevant specifications for the dynamic range of a photodetector, there are experiments for which the linearity plays a more important role than the former…
We describe the notion of a \emph{weighting} along a submanifold $N\subset M$, and explore its differential-geometric implications. This includes a detailed discussion of weighted normal bundles, weighted deformation spaces, and weighted…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued -- strong uniqueness principle. This means that they coincide with a strong solution…
We investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…
Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition,…