DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Methionine sulfoxide reductase B from Corynebacterium diphtheriae catalyzes sulfoxide reduction via an intramolecular disulfide cascade

Corynebacterium diphtheriae is a human pathogen that causes diphtheria. In response to immune system–induced oxidative stress, C. diphtheriae expresses antioxidant enzymes, among which are methionine sulfoxide reductase (Msr) enzymes, which are critical for bacterial survival in the face of oxidative stress. Although some aspects of the catalytic mechanism of the Msr enzymes have been reported, several details still await full elucidation. Here, we solved the solution structure of C. diphtheriae MsrB (Cd-MsrB) and unraveled its catalytic and oxidation-protection mechanisms. Cd-MsrB catalyzes methionine sulfoxide reduction involving three redox-active cysteines. Using NMR heteronuclear single-quantum coherence (HSQC) spectra, kinetics, biochemical assays, and MS analyses, we show that the conserved nucleophilic residue Cys122 is S-sulfenylated after substrate reduction, which is then resolved by a conserved cysteine, Cys66, or by the non-conserved residue Cys127. We noted that the overall structural changes during the disulfide cascade expose the Cys122–Cys66 disulfide to recycling through thioredoxin (Trx). In the presence of hydrogen peroxide, Cd-MsrB formed reversible intra- and intermolecular disulfides without losing its Cys-coordinated Zn2+, and only the non-conserved Cys127 reacted with the low-molecular-weight (LMW) thiol mycothiol, protecting it from overoxidation. In summary, our structure–function analyses reveal critical details of the Cd-MsrB catalytic mechanism, including a major structural rearrangement that primes the Cys122–Cys66 disulfide for Trx reduction and a reversible protection against excessive oxidation of the catalytic cysteines in Cd-MsrB through intra- and intermolecular disulfide formation and S-mycothiolation

Microstructure and Structural Defects in MgB2 Superconductor

We report a detailed study of the microstructure and defects in sintered polycrystalline MgB2. Both TEM and x-ray data reveal that MgO is the major second-phase in our bulk samples. Although MgB2 and MgO have different crystal symmetries, being P6/mmm and Fm-3m, respectively, their stacking sequence of Mg and B (or O) and lattice spacings in certain crystallographic orientations are very similar. The size of MgO varies from 10~500nm, and its mismatch with the MgB2 matrix can be a source for dislocations. Dislocations in MgB2 often have a Burgers vector of . 1/3 and 1/3 partial dislocations and their associated stacking faults were also observed. Since both dislocations and stacking faults are located in the (001) basal plane, flux pinning anisotropy is expected. Diffuse scattering analysis suggests that the correlation length along the c-axis for defect-free basal planes is about 50nm. (001) twist grain-boundaries, formed by rotations along the c-axis, are major grain boundaries in MgB2 as a result of the out-of-plane weak bonding between Mg and B atoms. An excess of Mg was observed in some grain boundaries. High-resolution nano-probe EELS reveals that there is a difference in near edge structure of the boron K-edge acquired from grain boundaries and grain interiors. The change at the edge threshold may be suggestive of variation of the hole concentration that would significantly alter boundary superconductivity.Comment: 20 pages and 12 figure

Развитие перспективных сетевых тренажерных комплексов на воздушном транспорте с применением нечетких моделей и помехоустойчивого кодирования

The article analyzes foreign experience and concludes that one of the ways to improve the efficiency of aviation security in the Russian Federation is to use modern network training complexes. A new approach to the assessment of the competence of the aviation security screeners was proposed and tested, that allows to take into account the parameters of the oculomotor activity and heart rate variability of the aviation security screeners being tested, different from the existing approaches using fuzzy classification models. The eye-tracking technology and the device of psychophysiological testing UPFT-1/30 "Psychophysiologist" were used as instruments of psychophysiological monitoring. The basics of automatic generation of fuzzy models such as Sugeno and Mamdani from experimental data are presented. Experimental studies were conducted on the basis of the Ulyanovsk Civil Aviation Institute. The results of the comparison of the generated models showed that the Sugeno model trained with the use of ANFIS-algorithm is more accurate than the Mamdani model and the linear regression model identifies the dependence being studied, according to the competence of aviation security screeners. As a criterion of quality of models on training and test data the average square error is used. The actual problem of choosing an effective concept of noise-resistant coding in the telecommunication component of advanced training complexes is substantiated. The ways of solving the important problem of increasing the reliability of actual digital data in network training complexes based on the use of noise-resistant coding are described. A model of permutation decoder of non-binary redundant code based on lexicographic cognitive map is presented. This model of redundant code decoder uses methods of cognitive data processing in the implementation of the procedure of permutation decoding to effectively protect remote control commands from the influence of destructive factors on the control process.В данной работе проведен анализ зарубежного опыта и сделан вывод, что один из путей повышения эффективности обеспечения авиационной безопасности в Российской Федерации заключается в применении современных сетевых тренажерных комплексов. Предложен и апробирован новый подход к оценке уровня компетентности операторов досмотра, позволяющий учитывать параметры глазодвигательной деятельности и вариабельности сердечного ритма испытуемых операторов, отличающийся от существующих подходов применением нечетких моделей классификации. В качестве аппаратурных средств психофизиологического мониторинга использованы технология Eye tracking и устройство психофизиологического тестирования УПФТ-1/30 «Психофизиолог». Представлены основы автоматической генерации нечетких моделей типа Сугено и Мамдани из экспериментальных данных. Проведены экспериментальные исследования на базе ФГБОУ ВО УИ ГА. Результаты сравнения сгенерированных моделей показали, что модель Сугено, обученная с применением ANFIS-алгоритма, точнее, чем модель Мамдани и модель линейной регрессии, идентифицирует исследуемую зависимость по оценке компетентности операторов досмотра. В качестве критерия качества моделей на обучающих и тестовых данных использована средняя квадратическая ошибка. Обоснована актуальная задача выбора эффективной концепции помехоустойчивого кодирования в телекоммуникационной составляющей перспективных тренажерных комплексов. Описаны пути решения важной задачи повышения достоверности актуальных цифровых данных в сетевых тренажерных комплексах на основе применения средств помехоустойчивого кодирования. Представлена модель перестановочного декодера недвоичного избыточного кода на базе лексикографической когнитивной карты. Данная модель декодера избыточного кода использует методы когнитивной обработки данных при реализации процедуры перестановочного декодирования для эффективной защиты команд дистанционного управления от влияния деструктивных факторов на процесс управления

Search for Axionlike and Scalar Particles with the NA64 Experiment

We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a(s) would penetrate the downstream HCAL module, serving as shielding, and would be observed either through their $a(s)\to\gamma \gamma$ decay in the rest of the HCAL detector or as events with large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing the a(s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to $2.84\times10^{11}$ electrons on target allowing to set new limits on the $a(s)\gamma\gamma$-coupling strength for a(s) masses below 55 MeV.Comment: This publication is dedicated to the memory of our colleague Danila Tlisov. 7 pages, 5 figures, revised version accepted for publication in Phys. Rev. Let

Isotopic Scaling in Nuclear Reactions

A three parameter scaling relationship between isotopic distributions for elements with Z$\leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed iso-scaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.Comment: 10 Pages, 2 Figure

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page