Related papers: Analytical Solution of Covariance Evolution for Re…
Integrability of the differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordinary differential equations are obtained in this way, which are…
LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
It is shown that dominant trapping sets of regular LDPC codes, so called absorption sets, undergo a two-phased dynamic behavior in the iterative message-passing decoding algorithm. Using a linear dynamic model for the iteration behavior of…
Evolutionary algorithms have been widely used for a range of stochastic optimization problems in order to address complex real-world optimization problems. We consider the knapsack problem where the profits involve uncertainties. Such a…
In this work we present a scheme for construction of solutions for evolutionary PDEs of some polynomial types q'_t = P(q,q'_x,...), where P is a polynomial in a finite number of variables. This scheme is a generalization of the existing…
Evolutionary computation offers a variety of tools to solve complex real-world optimization problems. However, research often focuses on smaller, simplified problems and optimization algorithms that sometimes miss expectations in real-world…
LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. In this paper, asymptotic methods are used to calculate a lower bound…
We introduce CodeEvolve, an open-source framework that couples large language models with island-based evolutionary search for end-to-end algorithmic discovery. CodeEvolve integrates inspiration-based crossover, meta-prompting, and…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-output pairs with a PDE solver, train the neural network in the…
This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of…
Over the past 30 years many researchers in the field of evolutionary computation have put a lot of effort to introduce various approaches for solving hard problems. Most of these problems have been inspired by major industries so that…
An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is…