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Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
We derive the asymptotic behavior of the transition probability density of the Bessel-like diffusions for "dimension" $\rho = 0$.
Due to its efficiency and reasonable accuracy, density functional theory is one of the most widely used electronic structure theories in condensed matter physics, materials physics, and quantum chemistry. The accuracy and efficiency of a…
Given a symmetric matrix $M$ and a vector $\lambda$, we present new bounds on the Frobenius-distance utility of the Gaussian mechanism for approximating $M$ by a matrix whose spectrum is $\lambda$, under $(\varepsilon,\delta)$-differential…
By introducing Q^2-dependence in resonance-reggeon "soft" dual models with nonlinear trajectories, they are extended to "hard" processes, sharing the property of parton-hadron duality. The resulting object is a two-component complex…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…
With $M(t):=\sup_{s\in[0,t]}A(s)-s$ denoting the running maximum of a fractional Brownian motion $A(\cdot)$ with negative drift, this paper studies the rate of convergence of $\mathbb {P}(M(t)>x)$ to $\mathbb{P}(M>x)$. We define two metrics…
In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions…
Let $F$ be a discrete Morse function on a simplicial complex $L$. We construct a discrete Morse function $\Delta(F)$ on the barycentric subdivision $\Delta(L)$. The constructed function $\Delta(F)$ "behaves the same way" as $F$, i. e. has…
Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations…
Within the field of hierarchical modelling, little attention is paid to micro-macro models: those in which group-level outcomes are dependent on covariates measured at the level of individuals within groups. Although such models are perhaps…
Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures…
In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…