Primitive digraphs with large exponents and slowly synchronizing automata

We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. All these automata are tightly related to primitive digraphs with large exponent.Comment: 23 pages, 11 figures, 3 tables. This is a translation (with a slightly updated bibliography) of the authors' paper published in Russian in: Zapiski Nauchnyh Seminarov POMI [Kombinatorika i Teorija Grafov. IV], Vol. 402, 9-39 (2012), see ftp://ftp.pdmi.ras.ru/pub/publicat/znsl/v402/p009.pdf Version 2: a few typos are correcte

Interplay between spin-relaxation and Andreev reflection in ferromagnetic wires with superconducting contacts

We analyze the change in the resistance of a junction between a diffusive ferromagnetic (F) wire and normal metal electrode, due to the onset of superconductivity (S) in the latter and a double Andreev scattering process leading to a complete internal reflection of a large fraction of the spin-polarized electrons back into the ferromagnet. The superconducting transition results in an additional contact resistance arising from the necessity to match spin-polarized current in F-wire to spin-less current in S-reservoir, which is comparable to the resistance of a piece of a F-wire with the length equal to the spin-relaxation length.Comment: 4 pages, 2 fig

On the interplay between Babai and Cerny's conjectures

Motivated by the Babai conjecture and the Cerny conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with $n$ states in this class, we prove that the reset thresholds are upper-bounded by $2n^2-6n+5$ and can attain the value $\tfrac{n(n-1)}{2}$. In addition, we study diameters of the pair digraphs of permutation automata and construct $n$-state permutation automata with diameter $\tfrac{n^2}{4} + o(n^2)$.Comment: 21 pages version with full proof

Theoretical investigation of controlled generation of a dense attosecond relativistic electron bunch from the interaction of an ultrashort laser pulse with a nanofilm

For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we propose using a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge. With two-dimensional (2D) particle-in-cell (PIC) simulations, we show that, in spite of Coulomb forces, all of the electrons in the laser spot can be accelerated synchronously, and the REM keeps its surface charge density during evolution. We also developed a self-consistent 1D theory, which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory allows us to predict the REM parameters and shows a good agreement with the 2D PIC simulations.open524

Boson stars from a gauge condensate

The boson star filled with two interacting scalar fields is investigated. The scalar fields can be considered as a gauge condensate formed by SU(3) gauge field quantized in a non-perturbative manner. The corresponding solution is regular everywhere, has a finite energy and can be considered as a quantum SU(3) version of the Bartnik - McKinnon particle-like solution.Comment: errors are corrected, one reference is adde

MANAGEMENT ACTIVITIES EFFECTIVENESS IN MODERN RUSSIAN INSTITUTION IN THE CONTEXT OF HEAD WORKPLACE MODELING

Purpose: The scientific approach to the organization of labor and the workplace of the institution head involves the search for the most optimal model or technique acceptable to the Russian conditions within the current management culture, traditional views on the nature of managerial work, the scale and effectiveness of management activities. Methodology: Methodological guidelines for the study of workplaces’ organization of credit and financial institutions’ heads are based on the provisions of modern ergonomics and the principles of a system-based approach, allowing justifying as a significant one the environment-oriented approach. Result: The obtained results served as the basis for the development of appropriate recommendations to optimize the current situation in the context of eliminating existing gaps and problems in the credit and financial sector of the Russian economy from the standpoint of optimizing the process of organizing working places for managers of institutions in this profile. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of the Management Activities Effectiveness in Modern Russian Institution in the context of Head Workplace Modeling is presented in a comprehensive and complete manner

Computational Complexity of Synchronization under Regular Constraints

Many variations of synchronization of finite automata have been studied in the previous decades. Here, we suggest studying the question if synchronizing words exist that belong to some fixed constraint language, given by some partial finite automaton called constraint automaton. We show that this synchronization problem becomes PSPACE-complete even for some constraint automata with two states and a ternary alphabet. In addition, we characterize constraint automata with arbitrarily many states for which the constrained synchronization problem is polynomial-time solvable. We classify the complexity of the constrained synchronization problem for constraint automata with two states and two or three letters completely and lift those results to larger classes of finite automata

Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). It defines an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. The free energy of the model is exactly calculated in the thermodynamic limit. The model describes quantum fluctuations of circle patterns and the associated discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In particular, in the quasi-classical limit the model precisely describe the geometry of integrable circle patterns with prescribed intersection angles.Comment: 26 pages, 18 color figures, minor correction