We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recog…

We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion cen…

For the spin models with continuous symmetry on regular lattices and finite range of interactions the lower critical dimension is d=2. In two dimensi…

Using the tri-hamiltonian splitting method, the authors of [Anco and Mobasheramini, Physica D, 355:1--23, 2017] derived two $U(1)$-invariant nonlinea…

Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Erudi…

The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA…

We have performed a Monte Carlo study of the classical XY-model on two-dimensional Sierpinski gaskets of several cluster sizes. From the dependence o…

We study the fermionic boundary modes (Andreev bound states) in a time-reversal invariant one-dimensional superconductor. In the presence of a substr…

We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of ite…

In general the method of group foliation reduction using a separation ansatz as illustrated in this paper is able to yield exact solutions to nonlinear 2nd order PDEs with power nonlinearities.

A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in mu…

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Given H it is easy to com…

In this section, we discuss the extent to which the conclusions of Theorem 2.1 extend beyond πd being an i.i.d. product density upon the d-dimensional hypercube and Xd0∼πd. First we present two extensions of Theorem 2.1. The second extension, Theore…

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuou…

Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Solutio Theorematum Ab illustri Viro in Actis hujus Anni Mens…

Effects of disorder on superconducting properties of noncentrosymmetric compounds are discussed. Elastic impurity scattering, even for scalar impurit…

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous…

We study association between macroeconomic news and stock market returns using the statistical theory of copulas, and a new comprehensive measure of …

We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting…

We have performed a Monte Carlo study of the classical XY-model on a Menger sponge with the Wolff cluster algorithm (U. Wolff, 1989). The Menger spon…

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of …

A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity…

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