Bounds for mixing time of quantum walks on finite graphs

Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples of walks on a cycle, a hypercube and a complete graph, quantum walks provide no speed-up in mixing over the classical counterparts. In addition, non-unitary quantum walks (i.e., walks with decoherence) are considered and a criterion for their convergence to the unique stationary distribution is derived.Comment: This is the journal version (except formatting); it is a significant revision of the previous version, in particular, it contains a new result about the convergence of quantum walks with decoherence; 16 page

ОСОБЕННОСТИ ИНТЕЛЛЕКТУАЛЬНОГО РАЗВИТИЯ МЛАДШИХ ШКОЛЬНИКОВ ПРИ ПЕРЕХОДЕ К ОБУЧЕНИЮ В ОСНОВНОЙ ШКОЛЕ

The article reveals different approaches to the definition of the term «intellectual development», explains the features of intellectual development of younger students. The author presents the data of theoretical analysis of scientific works on the topic, the results of the study, which allows to determine the features of intellectual development of younger students in the transition to secondary school.В статье раскрываются различные подходы к определению термина «интеллектуальное развитие», разъясняются особенности интеллектуального развития младших школьников, его взаимосвязь со школьной успеваемостью. Автором представлены данные теоретического анализа научных трудов по теме, результаты исследования, позволяющего определить особенности интеллектуального развития младших школьников при переходе к обучению в средней школе

Mode-Dependent Loss and Gain: Statistics and Effect on Mode-Division Multiplexing

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information.Comment: 22 pages, 8 figure

Data Vaults: a Database Welcome to Scientific File Repositories

Efficient management and exploration of high-volume scientific file repositories have become pivotal for advancement in science. We propose to demonstrate the Data Vault, an extension of the database system architecture that transparently opens scientific file repositories for efficient in-database processing and exploration. The Data Vault facilitates science data analysis using high-level declarative languages, such as the traditional SQL and the novel array-oriented SciQL. Data of interest are loaded from the attached repository in a just-in-time manner without need for up-front data ingestion. The demo is built around concrete implementations of the Data Vault for two scientific use cases: seismic time series and Earth observation images. The seismic Data Vault uses the queries submitted by the audience to illustrate the internals of Data Vault functioning by revealing the mechanisms of dynamic query plan generation and on-demand external data ingestion. The image Data Vault shows an application view from the perspective of data mining researchers

Study of the radical products of the thermal decomposition of nitrocellulose

The thermal transformations of nitrocellulose are accompanied by the formation of RN02 - radicals and allyl radicals. A mechanism for the formation of these radicals was proposed. © 1990 Plenum Publishing Corporation

Lyapunov exponents for products of complex Gaussian random matrices

The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.Comment: 15 page

Rates of convergence for empirical spectral measures: a soft approach

Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more quantitative, non-asymptotic results. In this paper, we describe a systematic approach to bounding rates of convergence and proving tail inequalities for the empirical spectral measures of a wide variety of random matrix ensembles. We illustrate the approach by proving asymptotically almost sure rates of convergence of the empirical spectral measure in the following ensembles: Wigner matrices, Wishart matrices, Haar-distributed matrices from the compact classical groups, powers of Haar matrices, randomized sums and random compressions of Hermitian matrices, a random matrix model for the Hamiltonians of quantum spin glasses, and finally the complex Ginibre ensemble. Many of the results appeared previously and are being collected and described here as illustrations of the general method; however, some details (particularly in the Wigner and Wishart cases) are new. Our approach makes use of techniques from probability in Banach spaces, in particular concentration of measure and bounds for suprema of stochastic processes, in combination with more classical tools from matrix analysis, approximation theory, and Fourier analysis. It is highly flexible, as evidenced by the broad list of examples. It is moreover based largely on "soft" methods, and involves little hard analysis

Amino-nitrile cleavage in the electrochemical reduction of hydeazones of aromatic aldehydes

1. Factors which determine the possibility of amino-nitrile cleavage of hydrazones on electrochemical reduction (ECR) include the basicity of the anionic product formed in the course of the ECR and the mobility of the aldehyde hydrogen which depends on the character of the electron polarization of the hydrazone fragment and the polarity of the N-N bond. 2. The primary action in amino-nitrile cleavage under conditions of ECR is the deprotonation of the azomethine fragment in the unreduced molecule by electrochemically generated strong base (anion or dianion). © 1988 Plenum Publishing Corporation