Related papers: Recent Progress in Optimization of Multiband Elect…
We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings.
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…
We provide a writeup of a resolution of Erd\H{o}s Problem #728; this is the first Erd\H{o}s problem (a problem proposed by Paul Erd\H{o}s which has been collected in the Erd\H{o}s Problems website) regarded as fully resolved autonomously by…
We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings. We identify those cases where optimal nonlinear approximation is better than optimal linear approximation.
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable…
The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…
Predicting fading channels is a classical problem with a vast array of applications, including as an enabler of artificial intelligence (AI)-based proactive resource allocation for cellular networks. Under the assumption that the fading…
In the transmission of digital data at a relatively high rate over a particular band limited channel, it is normally necessary to employ an equalizer at the receiver in order to correct the signal distortion introduced by the channel .ISI…
The design of both FIR and IIR digital filters is a multi-variable optimization problem, where traditional algorithms fail to obtain optimal solutions. A modified Shuffled Frog Leaping Algorithm (SFLA) is here proposed for the design of FIR…
We study existence problem for semilinear equations with Borel measure data and operator generated by a symmetric Markov semigroup. We assume merely that the nonlinear part satisfies the so-called sign condition. Using the method of sub and…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…
Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for entropy solutions of nonlinear scalar conservations laws . In this short paper we will restrict our attention to the simpler one-dimensional case. First,…
In the settings of Euclidean Jordan algebras, normal decomposition systems (or Eaton triples), and structures induced by complete isometric hyperbolic polynomials, we consider the problem of optimizing a certain combination (such as the…
We consider the problem of estimating an input signal from noisy measurements in both parallel scalar Gaussian channels and linear mixing systems. The performance of the estimation process is quantified by the $\ell_\infty$ norm error…
In the \emph{incremental cycle detection} problem arcs are added to a directed acyclic graph and the algorithm has to report if the new arc closes a cycle. One seeks to minimize the total time to process the entire sequence of arc…
Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent…
It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining it with a non-standard variant of the Central…
The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of any…