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Minimal N=1/2 supersymmetric extension of bosonic Polyakov's string is constructed. This model is natural generalization of Di Vecchia-Ravndal superparticle. The classical sector of the model is investigated, Noether currents and Virosoro…
We consider the problem of computing the q-gram profile of a string \str of size $N$ compressed by a context-free grammar with $n$ production rules. We present an algorithm that runs in $O(N-\alpha)$ expected time and uses $O(n+q+\kq)$…
We study small perturbations around the exactly marginal time-dependent string configuration of [1], and demonstrate the lack of the appropriate linearization. This implies that this configuration is an isolated fixed point of the…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
The aim of the paper is to reduce one spectral optimization problem, which involves the minimization of the decay rate $|\mathrm{Im} \, k |$ of a resonance $k$, to a collection of optimal control problems on the Riemann sphere…
We study the problem of finding the nearest $\Omega$-stable matrix to a certain matrix $A$, i.e., the nearest matrix with all its eigenvalues in a prescribed closed set $\Omega$. Distances are measured in the Frobenius norm. An important…
New exact solutions of Einstein equations which describe black hole with radial cosmic strings are constructed in the paper. The case of infinitely thin strings and the case of delocalized strings are considered. The case of delocalized…
We construct an adaptive asymptotically optimal in the classical norm of the space L(2,\Omega) of square integrable random variables the Energy estimation of a signal (function) observed in some points (plan of experiment) on the background…
Tuning the regularization hyperparameter $\alpha$ in inverse problems has been a longstanding problem. This is particularly true in the case of fetal brain magnetic resonance imaging, where an isotropic high-resolution volume is…
We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to…
This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…
Regularities in strings are often related to periods and covers, which have extensively been studied, and algorithms for their efficient computation have broad application. In this paper we concentrate on computing cyclic regularities of…
Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem,…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
The talk is about the power corrections in QCD. Renormalons, both infrared and ultraviolet, provide with a kind of a kinematical framework to fix exponents of the leading power corrections to various observables. Any viable dynamical…
In this paper we give an unified approach to some questions arising in different fields of nonlinear analysis, namely: (a) the study of the structure of the Fu\v{c}\'\i k spectrum and (b) possible variants and extensions of the monotonicity…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…
For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…
In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under…