Related papers: On capacity computation for symmetric polygonal co…
We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary…
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…
The type $A$ Kostant partition function is an important combinatorial object with various applications: it counts integer flows on the complete directed graph, computes Hilbert series of spaces of diagonal harmonics, and can be used to…
We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of condensers $(G,E)$…
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows to use just a single charge point for each component. The…
We study the conformal capacity ${\rm cap}(\Omega,K)$ where $\Omega$ is a bounded domain of $\mathbb{R}^2$ and $K$ is a compact connected set in $\Omega$. Because the exact numerical value of the capacity is known only in a handful of…
The problem of computing $\alpha$-capacity for $\alpha>1$ is equivalent to that of computing the correct decoding exponent. Various algorithms for computing them have been proposed, such as Arimoto and Jitsumatsu--Oohama algorithm. In this…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
The accurate computation of the electrostatic capacity of three dimensional objects is a fascinating benchmark problem with a long and rich history. In particular, the capacity of the unit cube has widely been studied, and recent advances…
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D one-infinity run-length limited constrained channel, but the…
A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a generalization of the method of Calkin and Wilf…
We propose a fast method for high order approximation of potentials of the Helmholtz type operator Delta+kappa^2 over hyper-rectangles in R^n. By using the basis functions introduced in the theory of approximate approximations, the cubature…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
We introduce a deficiency-based representation and approximation framework for values of the Riemann zeta function. The method is based on comparing two nonlinear accumulation mechanisms: global transformation of a base partial sum and…
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…
The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…