Related papers: Analytical Solution of Covariance Evolution for Re…
We discuss precision Monte Carlo (MC) calculations for solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo algorithms, which provide rigorous solutions of the above…
We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner…
Diversification in a set of solutions has become a hot research topic in the evolutionary computation community. It has been proven beneficial for optimisation problems in several ways, such as computing a diverse set of high-quality…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
We study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long--wavelength instability. We show that the main bifurcation branch can be derived from a variational…
The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while Covariance Matrix Adaptation Evolution Strategy is one of the most efficient algorithms…
Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low-density parity-check (LDPC) codes can detect and correct transmission errors if one encodes the original…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
This paper proposes a method for designing error correction codes by combining a known coding scheme with an autoencoder. Specifically, we integrate an LDPC code with a trained autoencoder to develop an error correction code for intractable…
Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…
Covariance selection seeks to estimate a covariance matrix by maximum likelihood while restricting the number of nonzero inverse covariance matrix coefficients. A single penalty parameter usually controls the tradeoff between log likelihood…
Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We…
In this note, we announce a systematic analysis of continuous dependence on the data in classical spaces for the initial-boundary-value problem of the diffusion equation on the half-line, with data that are not necessarily compatible at the…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the…