Related papers: A discrete trace theory for non-conforming polytop…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
We have derived an analytical trace formula for the level density of the H\'enon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has…
In the trace reconstruction problem our goal is to learn an unknown string $x\in \{0,1\}^n$ given independent traces of $x$. A trace is obtained by independently deleting each bit of $x$ with some probability $\delta$ and concatenating the…
We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings…
In this paper we prove a complete panel of consistency results for the discrete de Rham (DDR) complex introduced in the companion paper [D. A. Di Pietro and J. Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes. Part…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…
In this note we focus on the discrete fractional integrals as a natural continuation of our previous work about nonlocal fractional derivatives, discrete and continuous. We define the discrete fractional integrals by using the semigroup…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
In this work, we prove some trace theorems for function spaces with a nonlocal character that contain the classical $W^{s,p}$ space as a subspace. The result we obtain generalizes well known trace theorems for $W^{s,p}(\Omega)$ functions…
Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that…
Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to…
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…
Incomplete data are common in real-world tabular applications, where numerical, categorical, and discrete attributes coexist within a single dataset. This heterogeneous structure presents significant challenges for existing diffusion-based…
In this paper, we present a novel cross-consistency based semi-supervised approach for semantic segmentation. Consistency training has proven to be a powerful semi-supervised learning framework for leveraging unlabeled data under the…
The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…
Let $S$ be a seminorm on an infinite-dimensional real or complex vector space $X$. Our purpose in this note is to study the continuity and discontinuity properties of $S$ with respect to certain norm-topologies on $X$.
We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We demonstrate that in a model of public goods provision, multidimensional…
We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…