We consider the eigenvalues of a fixed, non-normal matrix subject to small additive perturbation. In particular, we case when fixed is banded Toeplitz matrix, where bandwidth allowed grow slowly with dimension, and perturbation drawn from one several different random ensembles. establish number non-asymptotic results for this model, including local law rate convergence in Wasserstein distance e...

Additive Randomization has been a primary tool to hide sensitive private information during privacy preserving data mining. The previous work based on Spectral Filtering empirically showed that individual data can be separated from the perturbed one and as a result privacy can be seriously compromised. Our previous work initiated the theoretical study on how the estimation error varies with the...

The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently devel...

Necessary and sufficient conditions are given for the existence of a countably additive extension of a given finite measure in the case of any finite or disjoint countable perturbation of its -algebra. It provides a complete description of all countably additive extensions of finite measures in such cases. In particular, simple characterizations are obtained for the existence of some extremal c...

We study the problem of maximizing the overlap of two convex polytopes under translation in R for some constant d ≥ 3. Let n be the number of bounding hyperplanes of the polytopes. We present an algorithm that, for any ε > 0, finds an overlap at least the optimum minus ε and reports the translation realizing it. The running time is O(n d/2 +1 log n) with probability at least 1 − n−O(1), which c...

This paper investigates an application of Neural Networks (NNs) to the decentralized guaranteed H∞ performance for a class of large-scale uncertain nonlinear systems. In order to guarantee the adequate H∞ performance level for the nonlinear systems, nonlinear linear matrix inequality (NLMI) condition is derived. The linear matrix inequality (LMI) approach instead of the NLMI is used to construc...

In this paper, we model complex signals by approximating the phase and the logarithm of the time-varying amplitude of the signal as a finite-order polynomial. We refer to a signal that has this form as an exponential polynomial signal (EPS). We derive an iterative maximum-likelihood (ML) estimation algorithm to estimate the unknown parameters of the EPS model. The initialization of the ML algor...

A semiclassical perturbation expansion is developed for the ground state energy of three identical particles interacting via pair and three-body potentials. The result is applied for the ground state energy of three neon atoms, where the non-pair-additive terms make a small contribution, and for three beryllium atoms where such terms make a large contribution. Models are constructed for the pai...

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...