On the possibility of a thermal spectrum of particles produced by an electric field

The exponentially damped electric field is shown to produce particles with a thermal spectrum from vacuum if the residual action of the field on the particles produced may be neglected.     

On the shape–from–moments problem and recovering edges from noisy Radon data

We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from–moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near–optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data.Mathematics Subject Classification (2000):62C20, 62G20, 94A12     

Random Gradient-Free Minimization of Convex Functions

In this paper, we prove new complexity bounds for methods of convex optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most n times more iterations than the standard gradient methods, where n is the dimension of the space of variables. This conclusion is true for both nonsmooth and smooth problems. For the latter class, we present also an accelerated scheme with the expected rate of convergence \(O\Big ({n^2 \over k^2}\Big )\), where k is the iteration counter. For stochastic optimization, we propose a zero-order scheme and justify its expected rate of convergence \(O\Big ({n \over k^{1/2}}\Big )\). We give also some bounds for the rate of convergence of the random gradient-free methods to stationary points of nonconvex functions, for both smooth and nonsmooth cases. Our theoretical results are supported by preliminary computational experiments.     

Sharp deviation bounds for quadratic forms

This paper presents sharp inequalities for deviation probability of a general quadratic form of a random vector ξ with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The results are stated under general conditions and do not suppose any special structure of the vector ξ. The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.     

Interacting quantum fields in a nonsingular cosmological model

The density of massless vector bosons created in a conformally flat nonsingular cosmological model is calculated.     

Portfolio value at risk based on independent component analysis

Risk management technology applied to high-dimensional portfolios needs simple and fast methods for calculation of value at risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy-tailed distributional properties that are observed in data. A principle component-based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here, we propose and analyze a technology that is based on independent component analysis (ICA). We study the proposed ICVaR methodology in an extensive simulation study and apply it to a high-dimensional portfolio situation. Our analysis yields very accurate VaRs.     

Nonasymptotic Estimates for the Closeness of Gaussian Measures on Balls

Upper bounds for the closeness of two centered Gaussian measures in the class of balls in a separable Hilbert space are obtained. The bounds are optimal with respect to the dependence on the spectra of the covariance operators of the Gaussian measures. The inequalities cannot be improved in the general case.     

Particle production in a slowly alternating electric field

The spectral density of particles produced in a slowly alternating electric field E(t) is calculated. At m²/|eE|?1 the field can be considered as constant, provided |?/E| ? m(|eE|/m²)^{$\text{3}\text{2}$}.     

The effect of the electromagnetic fields on the evolution of homogeneous cosmological models near the singularity

Homogeneous cosmological models of all Bianchi types with a general (nondiagonal) metric are considered near the singularity. The spaces are filled with an arbitrary sourceless six-component electromagnetic field (EMF) and a perfect fluid at rest. It is shown that in the general case the models of types VI₀, VII₀, VIII, and IX have an oscillatory regime. The models of all the other types have Kasner asymptotics. The main result of the present paper is the derivation of the law of rotation of the Kasner axes.