Related papers: Interface Identification constrained by Local-to-N…

Information sources used for communication purposes usually are assumed to be i.i.d. type, especially as far as entanglement or nonlocality properties are concerned. Here we proposed simple scheme for detection of nonlocality of non i.i.d.…

Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural…

In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…

We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.

Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and…

For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…

Nonlocality and its connections to entanglement are fundamental features of quantum mechanics that have found numerous applications in quantum information science. A set of correlations is said to be nonlocal if it cannot be reproduced by…

Despite providing similar functionality, multiple network services may require the use of different interfaces to access the functionality, and this problem will only get worse with the widespread deployment of ubiquitous computing…

Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…

Controlling the spread of correlations in quantum many-body systems is a key challenge at the heart of quantum science and technology. Correlations are usually destroyed by dissipation arising from coupling between a system and its…

Current best local descriptors are learned on a large dataset of matching and non-matching keypoint pairs. However, data of this kind is not always available since detailed keypoint correspondences can be hard to establish. On the other…

Topological defects in low-dimensional non-linear systems feature a sliding-to-pinning transition of relevance for a variety of research fields, ranging from biophysics to nano- and solid-state physics. We find that the dynamics after a…

Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…

We propose a method to couple local and nonlocal diffusion models. By inheriting desirable properties such as patch tests, asymptotic compatibility and unintrusiveness from related splice and optimization-based coupling schemes, it enables…

We study the problem of recovering the relative positions of objects moving along the real line based only on pairwise collision data. While interaction-based sensing systems arise naturally in a variety of practical settings, a systematic…

In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…

We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal…

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…

In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of…

We consider three cosmological models with linear interaction between the dark components and obtain restrictions on the coupling constant in terms of the cosmographic parameters. It enables us to find constraints on the coupling constant…