Related papers: Euler Integration of Gaussian Random Fields and Pe…

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…

By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.

In this paper, we study some typical arithmetic properties of Euler's totient function of polynomials over finite fields. Especially, we study polynomial analogues of some classical conjectures about Euler's totient function, such as…

Berman's inequality is the key for establishing asymptotic properties of maxima of Gaussian random sequences and supremum of Gaussian random fields. This contribution shows that, asymptotically an extended version of Berman's inequality can…

Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion…

In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.

In this paper, we study modulus of continuity and rate of convergence of series of conditionally sub-Gaussian random fields. This framework includes both classical series representations of Gaussian fields and LePage series representations…

Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…

This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…

The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…

In this short note, we build upon some recent results to present a precise expression for the asymptotic variance of the Euler-Poincar\'e characteristic for the excursion sets of Gaussian eigenfunctions on ${\cal S}^2$.

We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a…

The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…

We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.