Related papers: Universal truncation error upper bounds in irregul…
The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with…
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
Fault-tolerant quantum computation requires non-destructive quantum measurements with classical feed-forward. Many experimental groups are actively working towards implementing such capabilities and so they need to be accurately evaluated.…
We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We…
In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…
We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate global…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
Importance sampling (IS) is a technique that enables statistical estimation of output performance at multiple input distributions from a single nominal input distribution. IS is commonly used in Monte Carlo simulation for variance reduction…
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…
In this paper we analyze the approximation of multivariate integrals over the Euclidean plane for functions which are analytic. We show explicit upper bounds which attain the exponential rate of convergence. We use an infinite grid with…
It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
Discrete random probability measures are central to Bayesian inference, particularly as priors for mixture modeling and clustering. A broad and unifying class is that of proper species sampling processes (SSPs), encompassing many Bayesian…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…