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Fundamental mathematics and physics
N.A. Gaydamakin
Measures of Similarity among Finite Sequences
This article presents a measure of similarity among finite sequences of
arbitrary nature elements. The measure uses number and quality of matches between
elements at the same positions as similarity criteria with priority to quality of the
match. Quality of the match is treated as maximization of matches between adjacent
elements. Examples of similarity measure calculations are adduced for a number
of match significance weight coefficients in m-adjacent
element positions (m-grams matches).
Keywords: measure of similarity, finite sequences, m-grams, variations.
A.G. Grin’
On the Moments of Symmetric Functions of Dependent Random Variables
Estimates for the moments and uniform integrability of a certain class of
functions of random variables with uniformly strong mixing is obtained in this article.
Keywords: symmetric functions of random variables, uniformly strong mixing condition,
uniform integrability.
A.V. Levichev,
A.Yu. Palyanov
U(1,1)-Based Analysis in Space-Time Bundles: The Tables
of the Infinitesimal SU(2,2)-Action
Segal’s Chronometric Theory is based on the space-time D which can
be represented by a Lie group with a causal structure determined by an invariant
Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is represented
by a Lie group with a causal structure determined by an invariant Lorentzian form on
the Lie algebra u(1, 1). The Lie groups G, GF are introduced as two representations
of SU(2, 2) which are conjugate via particular matrix W from Gl(4). Linear-fractional
G-action on D is global and conformal; it is instrumental in the analysis of space-time
bundles which is based on the parallelizing group U(2). The latter analysis was carried
out by Paneitz and Segal in 1980s. Linear-fractional GF-action on F (introduced by
Levichev in 2000s) is also conformal. Despite singularities of the latter action, the
group U(1, 1) can be chosen as the parallelizing one. In the paper we obtain tables
(similar to the ”Paneitz-Segal tables”) which are necessary in order to perform the
analysis of space-time bundles based on the parallelizing group U(1, 1).
Keywords: parallelizations of space-time bundles, Segal’s cosmos, conformal group
SU(2, 2) actions on U(2) and on U(1, 1), DLF-theory.
O. Kosheleva, V. Kreinovich
Why Locating Local Optima Is Sometimes More Complicated Than Locating Global Ones
In most applications, practitioners are interested in locating
global optima. In such applications, local optima that result from
some optimization algorithms are an unnecessary side effect. In
other words, in such applications, locating global optima is a
much more computationally complex problem than locating local
optima. In several practical applications, however, local optima
themselves are of interest. Somewhat surprisingly, it turned out
that in many such applications, locating all local optima is a
much more computationally complex problem than locating all global
optima. In this paper, we provide a theoretical explanation for
this surprising empirical phenomenon.
Keywords:
O. Kosheleva, V. Kreinovich
Bell-Shaped Curve for Productivity Growth: An Explanation
A recent analysis of the productivity growth data
shows, somewhat surprisingly, that the dependence of the
20-century productivity growth on time can be reasonably well
described by a Gaussian formula. In this paper, we provide a
possible theoretical
explanation for this observation.
Keywords:
A.M. Pownuk, P. Barragan Olague, V. Kreinovich
Why Compaction Meter Value (CMV) Is a Good Measure of Pavement Stiffness: Towards a Possible Theoretical Explanation
To measure stiffness of the compacted pavement,
practitioners use the Compaction Meter Value (CMV); a ratio
between the amplitude for the first harmonic of the compactor's
acceleration and the amplitude corresponding to the vibration
frequency. Numerous experiments show that CMV is highly correlated
with the pavement stiffness, but as of now, there is no convincing
theoretical explanation for this correlation. In this paper, we
provide a possible theoretical explanation for the empirical
correlation. This explanation also explains why, the stiffer the
material, the more higher-order harmonics we observe.
Keywords:
V. Kreinovich
Why 3-D Space? Why 10-D Space? A Possible Simple Geometric Explanation
In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact,
without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is known that for some physical quantities, the 3-D space model with point-wise particles leads to meaningless infinities. To avoid these infinities, physicists have
proposed that particles are more adequately described not as 0-D points, but rather as 1-D strings or, more generally, as multi-D ``M-branes''. In the corresponding M-theory, proper space is 10-dimensional. We provide a possible geometric explanation for the 10-D character of the corresponding space.
Keywords:
Applied Mathematics and Modeling
B.K. Nartov
Method of Return and Implementation of Dynamic Limits in the Optimal Control Problem
Presented in the paper method, designed to directionally optimize the initial
conditions in problems of dynamic systems management, — a method of return — was
originally designed to optimize the vector of initial coordinates in a particular model
of moving objects conflict whose characteristics deteriorated as a result of interaction
with the objects of the opponent and aging. The model was binding characteristics (state
vector) and coordinates (control vector) of objects by Lanchester-type differential
equations. Then the specific problems of optimal control of the movements of a group of
objects, opposing another group of objects with the specified paths in the control
interval (by the criterion of minimizing a function of the final states of objects), were
set and solved. The problem of the construction of an acceptable on time and accuracy
algorithm to optimize the initial control vector, i.e. the initial placement of the group
of managed objects, was much more complicated. The found approach has been very general
and allows us to directionally optimize the initial control vector, at least in the
class of managed smooth systems with continuously differentiable quality functional. In
the most general form the idea of the method is that for optimization, in terms of
selected quality functional, of the initial conditions of the original optimal control
problem the supporting dual problem is written and the iterative process is implemented,
which steps alternate original and dual problems, and as part of the initial conditions
of the next iteration the part of the final values of the previous iteration is using.
Keywords: dynamic systems, optimization of the initial conditions, the inverse problem,
the dynamic limits.
A.K. Guts
Quantum Approach to Description of Social Statics and Social
Dynamics of Auguste Comte
A quantum approach to description of the Auguste Comte’s ideas on social
statics and social dynamics is given. We use the apparatus of quantum cosmology,
which allows us to describe the social physics.
Keywords: Auguste Comte, social statics, social dynamics, social physics.
S.N. Chukanov,
D.B. Abramov,
S.O. Baranov,
S.V. Lejhter
Application of Diffeomorphic Transform of Curves for Solving Pattern Recognition Problems
The problem of estimating the norm of the distance between the two closed
smooth curves for pattern recognition is considered. Diffeomorphic transformations of
curves based on the model of large deformations are described. For estimating of
the norm of the distance between two closed curves the functional, corresponding
normalized distance between the two curves, and the equation of diffeomorphic
transformations evolution are formed. An algorithm for solving the equation of
diffeomorphic transformation is proposed, built on the basis of PSO which can
significantly reduce the number of computing operations compared with gradient methods
for solving. The developed algorithms can be used in bioinformatics and biometrics
systems, classification of images and objects, machine vision systems, for pattern
recognition and object tracking systems.
Keywords: pattern recognition, invariance, diffeomorphic transformation, biometrics,
PSO method.
V.A. Shovin
Structural, Entropy Modeling and Correlation Analysis of Hypertension
Estimates of the parameters of expert structural model of normal hemodynamics
was implemented by numerical methods for nonlinear optimization with conditions. Slight
increased agreement between experimental data after physiotherapy and structural model of
normal hemodynamic showed lack of physiotherapy efficiency for the normalization of blood
pressure regulation. Entropy modeling also showed no reduction in entropy of
self-organization and growth of the total entropy of the system after treatment. Detailed
analysis revealed a disorganization of correlation between the parameters of normal
functional status of the hemodynamics.
Keywords: hypertension, structural equations, entropy modeling, correlation analysis.
A.N. Mironenko
This paper examines the possibility of applying the analytic hierarchy
process, known in mathematics, in conjunction with the FOREL clustering algorithm
to classify different subjects. By term “conjunction” we mean a process when the
analytic hierarchy process (namely decision making under certainty) is used for
preparation of data for further work with them, and the clustering algorithm (taxonomy)
is used for direct processing of the data. The proposed approach can be divided
into two stages: the training stage and the work stage. We carried out a computer
simulation which verifies validity of the proposed approach
Computer Science V.A. Shovin
The program of the virtual person or chatbot based on an external API,
algorithm of search of responses in the knowledge base of expanded markup AIML,
as well as the recurrent neural network are developed. The algorithm allows us to find
answers to relevant questions from the knowledge base. The procedure of relevant
responses sorting includes regular expression search, search by category, search by
history and search for the best match of words in questions. The recurrent neural
network is defined on the set of words of Q & A knowledge base.
S.V. Guss
This paper is about private wireless mesh networks. There are definitions
and comments for main features of ad hoc networks, survey of public mesh networks
and proprietary technologies, routing, modeling and prototyping.
T.A. Pogromskaya
The article describes the experience of the development and transition
to a new information system for reception of entrants to higher education in Omsk
State University n.a. F.M. Dostoevskiy. The system is based on the same program,
introduced in four Russian universities, it uses old data structure and logic, but has
a new web interface.
S.V. Belim,
I.B. Larionov,
Y.S. Rakitskiy
The article presents one of the possible approaches of formation of electronic
educational environment. The problems of educational resources, as well as
operational information about the learning process, are considered. Special attention is
paid to issues of access control and authentication when requesting access to resources.
I.A. Balezin,
D.N. Lavrov,
M.A. Harlamova
The architecture is presented and the mobile client-server application is
developed for access from iPhone to the dictionary of the constants of folk speech of the
Middle Irtysh area with the necessary set of options.
Information Security I.D. Siganov
In the article we overview how to implement zero knowledge proof authentication
protocol in the web. The proposed system consists of two parts: a server side
and Android application. Despite the classical password-based approach, users have to
install special application and use it as authentication manager. We use QR-codes
to send necessary data from the server to the application, so login experience is
just scanning this code. Finally, because of zero knowledge proof features the system
is resistant to interception, secret-cracking and fishing, so supposed even to use on
insecure public devices.
The article deals with object-oriented Harrison-Ruzzo-Ullman access control
model and subject-object model with mandatory access control. It is shown
that the Bell-LaPadula model and classic mandatory model can be implemented with
object-oriented HRU model.
Applying the Analytic Hierarchy Process in Conjunction with Clustering Algorithm to Classify Different Subjects
Keywords: analytic hierarchy process, AHP, clustering, taxonomy.
Chatbot Program - Chatbot or Virtual Companion
Keywords: chatbot, virtual companion, AIML, recurrent neural network.
Private Wireless Mesh Networks
Keywords: mesh networks, ad hoc networks, 802.11s, WMN.
Development in OmSU of the New Information System for Admission to University
Keywords: information system, development, reception of entrants, applicant, web
interface.
The Development of Electronic Educational Environment of High School
Keywords: e-learning environment, education, educational process, teaching materials,
library, electronic educational resources.
The Architecture of the Mobile Client for iOS to Access Web-Dictionary of Folk Speech of the Middle Irtysh
Keywords: application architecture, iOS, mobile app, dictionary of folk speech.
Zero Knowledge Proof Authentication on Web Applications
Keywords: zero knowledge proof, Web authentication, passwordless.
Keywords: access control, discretionary security models, mandatory security models, HRU, Bell-LaPadula model.