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Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the…
In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to…
Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard, belief propagation (BP) combined with…
The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…
The group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving…
Evolutionary algorithms are well suited for solving the knapsack problem. Some empirical studies claim that evolutionary algorithms can produce good solutions to the 0-1 knapsack problem. Nonetheless, few rigorous investigations address the…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of…
We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…
Continuous-variable quantum key distribution utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. One of the challenges is thereby the requirement of capacity approaching error…
In this paper, we study the density evolution analysis of spatially coupled low-density parity-check (SC-LDPC) codes over binary input additive white Gaussian noise (BIAWGN) channels under the belief propagation (BP) decoding algorithm.…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
This paper applies error-exponent and dispersion-style analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The…
Equations are presented which efficiently update or downdate the covariance matrix of a large number of $m$-dimensional observations. Updates and downdates to the covariance matrix, as well as mixed updates/downdates, are shown to be…