Related papers: Entropy dissipation via Information Gamma calculus…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…
We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
This paper establishes an explicit $L^2$-estimate for weak solutions $u$ to linear elliptic equations in divergence form with general coefficients and external source term $f$, stating that the $L^2$-norm of $u$ over $U$ is bounded by a…
A restricted form of Landauer's Principle, independent of computational considerations, is shown to hold for thermal systems by reference to the joint entropy associated with conjugate observables. It is shown that the source of the…
We consider the numerical approximation of a general second order semi--linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media which is fundamental in many…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
We study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $C^*$-algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…
We propose a new semi-discretization scheme to approximate nonlinear Fokker-Planck equations, by exploiting the gradient flow structures with respect to the 2-Wasserstein metric. We discretize the underlying state by a finite graph and…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be…
Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible…