We consider the problem of correcting the posterior marginal approximations computed by expectation propagation and Laplace approximation in latent Gaussian models and propose correction methods that are similar in spirit to the Laplace approximation of Tierney and Kadane (1986). We show that in the case of sparse Gaussian models, the computational complexity of expectation propagation can be m...

This article is an introduction to the Petersson trace formula and Kuznetsov trace formula, both of which are now important, standard techniques in analytic number theory. To illustrate their applications to modular forms, we will explain their role in a proof of subconvexity bounds for Rankin-Selberg L-functions L(s, f ⊗ g) on the critical line σ = 1/2, where here and throughout, we write s = ...

We review some recent results on asymptotic properties of polynomials of large degree, of general holomorphic sections of high powers of positive line bundles over Kahler manifolds, and of Laplace eigenfunctions of large eigenvalue on compact Riemannian manifolds. We describe statistical patterns in the zeros, critical points and L norms of random polynomials and holomorphic sections, and the i...

We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of them, with possible discontinuities at the endpoints. Even more surprising is the fact that functions preserving moments of three point masses must preserve...

Abstract. We prove Poincaré and Plancherel–Polya inequalities for weighted p-spaces on weighted graphs in which the constants are explicitly expressed in terms of some geometric characteristics of a graph. We use a Poincaré-type inequality to obtain some new relations between geometric and spectral properties of the combinatorial Laplace operator. Several well-known graphs are considered to dem...

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial diffe...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity i...

The Laplace transform approach of [GY] is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a nancial perspective. In this paper, we discuss two observations regarding the nancial relevance of its results. First, we show that the [GY] Laplace transform is not that of an Asian option price, as reported in [GY] and other papers. We nonetheles...

We solve the problem of best approximation closed operators by linear bounded in Hilbert spaces under assumption that operator transforms orthogonal basis space into an system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple is established. also demonstrate application these results concrete situations: powers Laplace-Beltrami on classes functions defined Ri...