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Independent Component Analysis (ICA) is a statistical tool that decomposes an observed random vector into components that are as statistically independent as possible. ICA over finite fields is a special case of ICA, in which both the…
We study the multi-agent Smoothed Online Convex Optimization (SOCO) problem, where $N$ agents interact through a communication graph. In each round, each agent $i$ receives a strongly convex hitting cost function $f^i_t$ in an online…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial "guess" for the…
The quantum approximate optimization algorithm (QAOA) is a near-term quantum algorithm aimed at solving combinatorial optimization problems. Since its introduction, various generalizations have emerged, spanning modifications to the initial…
We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces. Our methods require only…
Point-SAGA is a randomized algorithm for minimizing a sum of convex functions using their proximity operators (proxs), proposed by Defazio (2016). At every iteration, the prox of only one randomly chosen function is called. We generalize…
Factor analysis (FA) or principal component analysis (PCA) models the covariance matrix of the observed data as R = SS' + {\Sigma}, where SS' is the low-rank covariance matrix of the factors (aka latent variables) and {\Sigma} is the…
In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method…
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any…
Rouch\'e's Theorem is among the most useful results in complex analysis for counting zeros of analytic functions. Rouch\'e's Theorem also admits a harmonic analogue for counting zeros of complex harmonic functions. Previously, this analogue…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of…
In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…
We propose a new modularity optimization method, Mod-CSA, based on stochastic global optimization algorithm, conformational space annealing (CSA). Our method outperforms simulated annealing in terms of both efficiency and accuracy, finding…
The problem of aggregation is considerable importance in many disciplines. In this paper, a new type of operator called visibility graph averaging (VGA) aggregation operator is proposed. This proposed operator is based on the visibility…
Statistical uncertainties are rarely incorporated in machine learning algorithms, especially for anomaly detection. Here we present the Bayesian Anomaly Detection And Classification (BADAC) formalism, which provides a unified statistical…
The conditional gradient algorithm (also known as the Frank-Wolfe algorithm) has recently regained popularity in the machine learning community due to its projection-free property to solve constrained problems. Although many variants of the…
We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept…
We present the details of the numerical realization of the recently advanced algorithm developed to identify the fragmentation in heavy ion reactions. This new algorithm is based on the Simulated Annealing method and is dubbed as Simulated…