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Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…
A new class of linear sequence generators based on cellular automata is here introduced in order to model several nonlinear keystream generators with practical applications in symmetric cryptography. The output sequences are written as…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of…
The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches,…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
Over the last decade, both the neural network and kernel adaptive filter have successfully been used for nonlinear signal processing. However, they suffer from high computational cost caused by their complex/growing network structures. In…
The Parks-McClellan algorithm provides an efficient method for designing a linear phase FIR filter with a pre-specified weight function on the approximation error. For the given filter order and the specified weight function, the filter…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…