The use of the symbolic software package GeM for Maple is illustrated with examples of computation of nonlocal symmetries and nonlocal conservation laws of nonlinear partial differential equations. In the considered examples, the nonlocal symmetries and conservation laws arise as local symmetries and conservation laws of potential systems. FullMaple codewith detailed comments is presented. Exam...

Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal d...

We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions...

Additional nonlocal symmetries of diffusion-convection equations and the Burgers equation are obtained. It is shown that these equations are connected via a generalized hodograph transformation and appropriate nonlocal symmetries arise from additional Lie symmetries of intermediate equations. Two entirely different techniques are used to search nonlocal symmetry of a given equation: the first i...

The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric ...

We introduce a paradigm for nonlocal sparsity reinforced deep convolutional neural network denoising. It is a combination of a local multiscale denoising by a convolutional neural network (CNN) based denoiser and a nonlocal denoising based on a nonlocal filter (NLF) exploiting the mutual similarities between groups of patches. CNN models are leveraged with noise levels that progressively decrea...

Quantum mechanics permits nonlocality—both nonlocal correlations and nonlocal equations of motion—while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: “superquantum” correlations, and nonlocal “jamming” of correlations. These models are consistent with so...

Quantum mechanics permits nonlocality—both nonlocal correlations and nonlocal equations of motion—while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: “superquantum” correlations, and nonlocal “jamming” of correlations. These models are consistent with so...

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valued Lp-spaces of these problems are given. By using these results, the maximal regularit...

Spin-dependent properties of single-layer graphene (SLG) have been studied by nonlocal spin valve measurements at room temperature. Gate voltage dependence shows that the nonlocal magnetoresistance (MR) is proportional to the conductivity of the SLG, which is the predicted behavior for transparent ferromagnetic-nonmagnetic contacts. While the electron and hole bands in SLG are symmetric, gate v...