*Compressive Sensing
*

Randomization of
Measurements and *l**1*-optimization

*O. N. Granichin*

*St.
Petersburg** State
University*

*Key words: *compressive
sensing, compressive sampling, randomized measurements, *l_**1*-optimization.

At
present, the new coding/decoding paradigm named compressive sensing is being
actively developed for signals having sparse representation in some basis. The
underlying idea is randomization of measurement processes and *l_**1*-optimization technique. The paper describes a new
“acquiring” method of sparse signals and their representation using
considerably less amount of data than in the classical representation with Nyquist rate.

Bibliogr.: 31
refs.

*Randomized
Algorithms*

Non-stationary
Stochastic Optimization with Fixed Gain SPSA-type
Algorithms in the Case of Infinite Variance of Random Uncertainties

*A. T. Vakhitov*

*St.
Petersburg** State
University*

*Key words:*
non-stationary stochastic optimization, dynamic optimization, infinite variance,
stochastic approximation, SPSA

In
this paper, we formulate the problem of non-stationary stochastic optimization
in the case of infinite variance of uncertainties. The three randomized
stochastic approximation-type algorithms with fixed gain are proposed. The
conditions of stabilization of the estimates are given and probabilistic bounds
on the estimation error are presented.

Bibliogr.: 16 refs.

Financial
Market Data Randomized R/S-analysis

*A. A. Gatchkov*

*St.
Petersburg** State
University*

*Key words:* *R/S*-analysis,
financial data analysis, randomization.

At
present, the fractal approach to the financial markets risks definition is
rapidly developing. It proposes to use a fractal dimension of market asset
prices as a measure of risk. The R/S-analysis algorithm is often used during
the calculation of such fractal dimension. The algorithm works quite well for
input data purified from noise. However, when a system is subjected to noise
and deviations that may occur, for example, as a result of the impact of major
market players during the speculative trade, the algorithm exposes a big error.
The proposed randomized *R/S*-analysis
algorithm allows to estimate risks more precisely in
the case of systematic noise.

Bibliogr.: 13 refs.

On
Fast Variants

of the Simulated Annealing Algorithm

*A. S. Tikhomirov*

*Novgorod** State University*

__Tikhomirov.AS@mail.ru, TikhomirovAlesha@gmail.com__

*Key words:* simulated
annealing, random search, stochastic search, global optimization, stochastic
optimization.

Fast
versions of the simulated annealing algorithm are constructed. It is shown that
the asymptotic rate of convergence of the simulated annealing algorithm may be
just marginally worse than the rate of convergence of a standard descent
algorithm (e.g., steepest descent).

Bibliorg.: 23 refs.

Generation
of Stable Polynomials

*P. S. Shcherbakov*

*Institute** of Control Science, RAS, *

*Key words:*
stable polynomials, randomization, random generation methods, parametrization, Matlab-realizations.

In
this paper, various techniques for random generation of stable polynomials in
discrete and continuous time are considered and presented in a unified framework.
An attempt is made to present a “global vision” of the potentials of random
generation techniques for stable polynomials. Moreover, their properties are
discussed and compared, with a particular attention to the Matlab
implementation issues. Possible applications are indicated and illustrative
results of simulations are provided.

Bibliogr.: 34 refs.

*Queuing Systems*

The
Analysis of Some Queue with n Priorities Allocation
Methods

*A. V. Drac, A.
V. Sokolov*

*Petrozavodsk** State University,
IAMR KarSC RAS, *

__adeon88@mail.ru, avs@krc.karelia.ru__

*Key words:* priority
queue, FIFO-queues, Random walk, Markov chains, dynamical data structures.

This
paper considers a representation of queues with n
priorities in single-level memory in the form of array or as n consecutive FIFO queues. Possible operations are “insert
element,” “delete an element with maximum priority,” and “find element.”
Proposed are the algorithms of state enumeration, construction of appropriate
absorbent Markov chains, and finding the optimal memory partition that
maximizes the average time until memory overflow. The results of numerical
experiments are presented.

Bibliorg.: 9 refs.

Special
Optimization Procedures for Periodically Nonstationary
Stochastic Automata

*A. Yu. Ponomareva,
R. M. Stroilov, M. K. Tchirkov
*

*St.* *Petersburg** State University*

*Key words:* periodically
nonstationary stochastic automata, optimization of
stochastic automata, inaccessible states, restricted initial conditions.

The paper
deals with solution of some special optimization problems for nonstationary stochastic automaton with periodically
variable structure. These problems are related to theoretical justification
and development of certain procedures which optimize the number of states of
such automata in various structural cycles with constrained initial conditions.

Bibliogr.: 6 refs.

The
Rank-Model and Its Investigations

*A. V. Timonina*

*Moscow Institute of Physics and Technology*

*Key words:*
rank, stochastic matrix, eigenvector, PageRank,
power method.

This
paper presents analysis of a large-dimensional network exemplified by the
Internet. The goal of the study is to develop an algorithm that correctly finds
the PageRank of a web-page. The test model of the
Internet is constructed that demonstrates the existence of a
significant discrepancies between the exact value of the page-weight and
the Page-Rank.

Bibliorg.: 8 refs.

*Learning and
Adaptation*

Adaptive
Control of Autonomous Group of Unmanned Aerial Vehicles

*K. S Amelin.,K. I. Antal, V. I. Vasiliev, N. O. Granichina*

*St.
Petersburg** State
University*

__konstantinamelin@mail.ru, cathrineantal@gmail.com,
gnome@bk.ru,__

*Key words:* multiagent systems, unmanned aerial vehicles,
adaptive control, autonomous group of unmanned aerial vehicles.

In
this paper, we discuss possible use of a multiagent
system for adaptive control of a group of unmanned aerial vehicles (UAV). The system is based on independent dialogue of the
agents through a radio signal. Adaptability will facilitate efficient on-line
decision-making in changing the scenario of the goal attainment.

Bibliogr.: 6 refs.

A Randomized
Algorithm of Cluster Stability

*N. O. Granichina, D. S. Shalymov*

*St.*
*Petersburg** State University*

*Key words:*
clustering, cluster stability, randomized algorithms, randomized
algorithms of cluster stability.

Clustering
is the subject of active research in several fields such as statistics, pattern
recognition, machine learning. etc. In this paper, the
notion of clustering and cluster stability is introduced,
the urgency and the basic problems of clustering are described. A new
randomized algorithm of cluster stability is formulated and its convergence
properties are proved.

Bibliogr.: 42 refs.

An
Unsupervised Learning and Statistical Approach for Vietnamese Word Recognition
and Segmentation

*Le Trung Hieu*

*St.
Petersburg** State
University*

*Key words:* Vietnamese
word recognition, segmentation Vietnamese documents, unsupervised learning, statistical methods.

There
are two main topics considered in this paper: (i) Vietnamese words are
recognized and sentences are segmented into words by using probabilistic
models; (ii) the optimum probabilistic model is constructed by an unsupervised
learning iteration. For each probabilistic model, new words are recognized and
their syllables are linked together. They are new syllables in a new
probabilistic model. The syllable-linking process increases the accuracy of
statistical functions resulting in a better recognition of the new words. This
ensures the convergence of the probabilistic model to the optimal one.

Our
experimented corpus is generated from about 250.034 online news articles, which
consist of about 15 000 000 sentences. The accuracy
of the segmented algorithm is over 90%. Our Vietnamese word and phrase
dictionary contains more than 100 000 words and word combinations.

Bibliogr.: 15 refs.

*Electric Power
Systems*

Iterative
Steady-state Stability Criterion of Power System Described by Algebro-differential Equations

*M. Sh. Misrikhanov,
V. N. Ryabchenko,*

*Main electricity transmission company
“Center”, Moskow*

__(mms, rvn)@mes-centra.ru__

*Key words:* power
system, algebro-differential form, steady-state
stability, generalized matrix sign function, iterative algorithm.

A new
iterative steady-state stability criterion of power system given by the algebro-differential equations is described. The core of
the criterion is an iterative algorithm for computing the generalized matrix
sign function. The problem of steady-state stability of UPS of Center model,
described in the Cauchy form and by algebro-differential
equations is solved.

Bibliogr.: 14 refs.