Related papers: Signature Kernel and Schwinger-Dyson Kernel Equati…
Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous…
We study the ridge regression (L2 regularized least squares) problem and its dual, which is also a ridge regression problem. We observe that the optimality conditions describing the primal and dual optimal solutions can be formulated in…
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by…
In this paper the Feynman path integral technique is applied to two-dimensional spaces of non-constant curvature: these spaces are called Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the metric and then analyze the…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. In the aspect of kernelization, an impressive hardness theory has been established [Bodlaender etc. (ICALP 2008,…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that…
Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process…
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory for time series. Its components can be viewed as successive…
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a…
We provide a unique and novel extension of da Costa's calculation of a quantum mechanically constrained particle. This is achieved by analyzing the perturbative back reaction of the quantum confined particle's eigenstates and spectra upon…
We present the Hopf algebra of renormalization and introduce the renormalization group equation in this framework. Some linear Schwinger--Dyson equations are studied, and exact solutions are presented. Then we study the Schwinger--Dyson…
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with…
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…