Related papers: On nonlocal perturbations of integral kernels

We put forward a strategy to achieve synthetic nonlinearities where local and nonlocal contributions compete on similar footing, thus yielding intermediate tunable responses ranging from fully local to strongly nonlocal. The physical…

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…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric…

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…

In this paper we consider a large class of fully nonlinear integro-differential equations. The class of our nonlocal operators we consider is not spatial homogeneous and we put mild assumptions on its kernel near zero. We prove the H\"older…

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…

In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…

An alternative description imbedding nonlocality in a relativistic chronology is proposed. It is argued that vindication of Quantum Mechanics in forthcoming experiments with moving beam-splitters would mean that there is no real time…

We study nonlocal convolution-type operators with singular, possibly anisotropic kernels. Our main objective is to establish and quantify their nonlocal-to-local convergence to a local differential operator with natural boundary conditions,…

We reconsider the problem of the compatibility of quantum nonlocality and the requests for a relativistically invariant theoretical scheme. We begin by discussing a recent important paper by T. Norsen [arXiv:0808.2178] on this problem and…

A new nonlocality experiment with moving beam-splitters is proposed. The experiment is analysed according to conventional quantum mechanics, and to an alternative nonlocal description in which superposition depends not only on…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

We consider the problem of uniqueness of the kernel in the nonlocal theory of accelerated observers. In a recent work, we showed that the convolution kernel is ruled out as it can lead to divergences for nonuniform accelerated motion. Here…

Our main result shows that if a lower-semicontinuous kernel K satisfies some mild additional hypotheses, then asympotitically polarization optimal configurations are precisely those that are asymptotically distributed according to the…

Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations with degenerate potential is shown. The nonlocality is described by means of a symmetric singular kernel not falling within the framework of any previous existence…

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions…

Quantum nonlocality is a counterintuitive phenomenon that lies beyond the purview of causal influences. Recently, Bell inequalities have been generalized to the case of quantum inputs, leading to a powerful family of semi-quantum Bell…

We study the conditions for two-photon classical interference with coherent pulses. We find that the temporal overlap between optical pulses is not required for interference However, coherence within the same inputs is found to be essential…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…