Related papers: P-adic numbers and kernels
Let $1/2\leq\beta<1$, $p$ be a generic prime number and $f_\beta$ be a random multiplicative function supported on the squarefree integers such that $(f_\beta(p))_{p}$ is an i.i.d. sequence of random variables with distribution…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
The form of the kernel that controls the dynamics of the Bethe-Salpeter equations is essential for obtaining quantitatively accurate predictions for the observable properties of hadrons. In the present work we briefly review the basic…
Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…
Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…
For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra $A(k)$ at critical level in terms of Dunkl type operators. Under this representation the center of $A(k)$ produces…
We study generalised prime systems $\mathcal{P}$ $(1<p_1\leq p_2\leq...,$ with $p_j\in\R$ tending to infinity) and the associated Beurling zeta function $\zeta_{\mathcal{P}}(s) =\prod_{j=1}^{\infty} (1-p_j^{-s})^{-1}$. Under appropriate…
In this paper, a model is proposed for the kernel in the generalized mixing rule recently formulated by Anderssen and Mead (1998). In order to derive such a model, it is necessary to take account of the rheological significance of the…
The spectral zeta functions have been found many application in several branches of modern physics, including the quantum field theory, the string theory and the cosmology. In this paper, we shall consider the spectral zeta functions and…
A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
In this paper, we study Catalan numbers which can be represented by the p-adic integral on Zp and we investigate some properties and formulae related to Catalan numbers and special numbers.
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of…
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
We prove a p'-version of a classical theorem of Broline and Garrison. As a consequence, we obtain results on p-parts of character codegrees.
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescoping energy residuals" in particular. We prove new results…
We introduce a layered random spin model, equivalent to the Generalized Random Energy Model (GREM). In analogy with diluted spin systems, a diluted GREM (DGREM) is introduced.It can be applied to calculate approximately thermodynamic…
We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…