相关论文: Acceleration-Induced Nonlocality: Uniqueness of th…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
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…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings.…
We study the asymptotic behavior for nonlocal diffusion equations $\partial_tu=\mathcal{J}u-\chi_0u$ in $\mathbb{R}^n\times(0,\infty)$ and obtain a sufficient condition so that solutions of the Cauchy problem decay in time at the rate of a…
The existence of a fundamental scale is expected to be a key feature of quantum gravity. Many approaches take this property as a starting assumption. Here, instead, we take a less conventional viewpoint based on a critical inspection of…
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…
In this paper, we investigate the quantum correlations and coherence of two accelerating Unruh-deWitt detectors coupled to a scalar field in 3 + 1 Minkowski space-time. We show that the entanglement is completely destroyed in the limit of…
Entanglement is the basic building block of quantum technologies whose property is in the unique quantum feature of nonlocal realism. However, such a nonlocal quantum property is known as just a weird phenomenon that cannot be obtained by…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel which is not Lipschitz continuous, thus preventing the…
We prove optimal H\"older boundary regularity for a non-local operator with a singular, symmetric kernel that depends on the distance to the boundary of the underlying domain. Additionally, we prove higher boundary regularity of solutions.
In computer vision, 2D convolution is arguably the most important operation performed by a ConvNet. Unsurprisingly, it has been the focus of intense software and hardware optimization and enjoys highly efficient implementations. In this…
A phenomenological formalism is presented in which the apparent acceleration of the universe is generated by cosmic structure formation, without resort to Dark Energy, modifications to gravity, or a local void. The observed acceleration…
We study the analyticity properties of amplitudes in theories with nonlocal vertices of the type occurring in string field theory and a wide class of nonlocal field theory models. Such vertices are given in momentum space by entire…
Quantum entanglement is the quintessential characteristic of quantum mechanics and the basis for quantum information processing. When one of two maximally entangled particles is measured, without measurement the state of another one is…
"action at a distance" is a weird concept in quantum theory which people always avoid mentioning in most occasions. In this work, without involving any concept about "action at a distance", we naturally construct a physical structure that…