|
|
Fundamental Mathematics and Physics
The necessary and sufficient conditions for
convergence of the distributions of symmetric calibration functions from dependent random
variables to max-stable distributions are obtained in this article. These conditions include
the so-called minimal conditions of the weak dependence.
Keywords: calibration functions of random variables, max-stable distributions, minimal conditions of the weak dependence.
S.V. Belim.
Effect of a Magnetic Field on Phase Transitions in a Semi-Bounded Antiferromagnetic Ising Model.
The article investigated the critical behavior of three-dimensional
semi-infinite antiferromagnetic Ising model in a magnetic field by computer simulation.
The values of the Neel temperature for surface and bulk phase transitions at
different magnetic field values are received. The phase diagram of the system is built.
The position of tricritical point of a special phase transition depending on the strength
of the magnetic fields is determined.
Keywords: antiferromagnetic Ising model, surface phase transition, special phase transition.
I.A. Zubareva.
On Curves with Constant Curvatures in the Pseudo-Euclidean Space.
The author proved all curvatures of a regular curve
in \(n\)-dimensional pseudo-Euclidean space of an arbitrary index, \(n\geq 2\),
are constant if and only if the curve is an orbit of a one-parameter isometry group of the space.
Keywords: curvature, Frenet frame, orbit of a one-parameter isometry group, pseudo-Euclidean space.
R.Yu. Simanchev, P.V. Solov'eva.
\(b\mathcal{H}\)-bases for a Some Class of Facet of a Clique Partitioning Polytope.
Let \(K_n=(V,E)\) be a complete undirected \(n\)-vertex graph without loops and multiple edges.
A spanning subgraph \(H\subset K_n\) is called an \(M\)-graph if each of its connected components (possibly one-vertex) is a clique.
We denote the family of all \(M\)-graphs in \(K_n\) by \(\mathcal{H}\).
This family is the set of feasible solutions of the clique partitioning problem, consisting in finding in the complete edge-weighted graph of an \(M\)-graph of minimal weight [GroWak1990,GroWak1989,SU1].
In the mentioned papers, the polyhedral properties [GroPad1985] of this problem are considered.
The classes of inequalities that generate the faces of the problem polytope are constructed, on the basis of which algorithms for branches and cuts are developed.
In this paper, using the technique proposed in [Sim2017], we prove the facetness of inequalities of a special class with respect to the clique partitioning polytope.
The work was supported by the Russian Foundation for Basic Research (project 18-07-00599).
Keywords: polytope, facet, the clique partitioning problem.
I.V. Urazova.
Heuristics for the Separation Problem of 1-Parachutes in the Graph Approximation Problem.
In work (see [1]) a class of inequalities supporting to the polyhedron of the given problem was proposed. Conditions are found under which the constructed inequalities are faceted. When these inequalities are used in cutting algorithms, the Separation problem becomes an actual problem. In the paper (see [2]) it was shown that the problem of identifying the proposed inequalities is $NP$-hard. In this paper, a local search procedure has been developed to identify clipping. To analysis the effectiveness of the proposed methods, a computer experiment was carried out.
This work was supported by the Russian Foundation for Basic Research (project 18-07-00599).
Keywords: separation problem, plyhedra, facet, approximation problem.
O. Kosheleva, V. Kreinovich.
In the Discrete Case, Averaging Cannot Be Consistent.
When we have two estimates of the same quantity,
it is desirable to combine them into a single more accurate
estimate. In the usual case of continuous quantities, a natural
idea is to take the arithmetic average of the two estimates. If we
have four estimates, then we can divide them into two pairs,
average each pair, and then average the resulting averages.
Arithmetic average is {\em consistent} in the sense that the
result does not depend on how we divide the original four
estimates into two pairs. For discrete quantities - e.g.,
quantities described by integers - the arithmetic average of two
integers is not always an integer. In this case, we need to select
one of the two integers closest to the average. In this paper, we
show that no matter how we select - even if we allow
probabilistic selection - the resulting averaging cannot be
always consistent.
Keywords: averaging, processing estimates, consistency, discrete case
O. Kosheleva, V. Kreinovich.
All Maximally Complex Problems Allow Simplifying Divide-and-Conquer Approach: Intuitive Explanation of a Somewhat Counterintuitive Ladner's Result.
Ladner's 1975 result says that any NP-complete
problem - i.e., in effect, any maximally complex problem - can
be reduced to solving two easier problems. This result sounds
counterintuitive: if a problem is maximally complex, how can it
be reduced to simpler ones? In this paper, we provide an intuitive
explanation for this result. Our main argument is that since
complexity and easiness-to-divide are not perfectly correlated, it
is natural to expect that a maximally complex problem is not
maximally difficult to divide. Our related argument is that - as
this result shows - NP-completeness is a sufficient but not a
necessary condition for a problem to be maximally complex; how to
come up with a more adequate notion of complexity is still an open
problem.
Keywords: NP-complete, divide-and-conquer approach, Ladner's result, maximally complex problems.
Applied Mathematics and Modeling
S.A. Terentyev, A.K. Guts.
Investigations of the Spectral Density of the Electromagnetic Field in a Vertically Inhomogeneous Conductive Medium.
The electromagnetic field in electrical exploration
problems is often represented as integrals with a fast-oscillating
nucleus. When calculating these integrals on a computer, it is
necessary to deform the contour of integration into the plane of
the complex variable. The article studies the allowable
deformation region of the integration contour in the case of a
non-uniform medium. The source of the field is a vertical dipole.
A similar problem was solved for a horizontally layered medium
with a horizontal harmonious dipole as a source.
Keywords: Electrical exploration, electromagnetic field of
vertical electric dipole, fast-oscillating integrals, deformation
contour, complex plane, absence of singular points, deformation
domain.
V.A. Shovin.
Factor Analysis Based on the \(k\)-means Method.
Actual problems and research methods are analysis and search
for hidden dependencies in experimental data. The definition of such
dependencies allows them to construct a model of phenomenon or object that would best
fit the experimental data and at the same time have a minimally complex version. Known
mathematical and software tools for the automatic construction of such models is a
factor analysis. Various generalizations and modernizations of the methods of factor
analysis are in demand. The article proposes a new approach to factor analysis based
on the \(k\)-means data clustering method and subsequent factor rotation. Factor analysis
identifies from a set of initial indicators \(k\) main components or factors -
with the greatest accuracy approximating the scatter and distribution of the initial
data. These main components form the factorial structure of the source data. Various
characteristic points of the original data structure can be used as the directions and
aspects of the main components. In this paper, we propose to use centers of
raw data clusters. There is a large number of clustering methods for dividing data
points into classes. The most popular is the \(k\)-means method. As a result, the \(k\)-means
method allows finding the factor structure in the original multidimensional data
space from the positions of the \(k\) centers of the selected clusters. The subsequent
factor rotation according to the original criterion of interpretability allows us
to find a simple factor structure. Conducting numerical experiments showed good
agreement with the results of this method of factor analysis with previously known
methods. The proposed method of factor analysis has good and superior efficiency
compared with other methods of factor analysis. It has limited capabilities and
resources needed to determine the factor structure.
Keywords: k-means method, factor analysis, factor rotation.
Computer Science
D.N. Lavrov, M.A. Kharlamova, E.A. Kostushina.
Representation of the Corpus of Medium Irtysh Folk Dialect.
The article discusses ways of representing dialect entries in the regional corpus.
The focus is on models for the presentation of thematic, structural and partly
phonetic markings. Particular attention is paid to the presentation model of extralinguistic data.
The proposed solutions are based on the representation of relational databases and XML format.
The reported study was funded by RFBR according to the research project № 18-012-00519.
Keywords: thematic markup, metatext markup, XML format, regional dialect body.
Information Security
N.F. Bogachenko.
On the Complexity of Access Control Subsystems of Large-Scale Complex IT Systems.
Signs of large-scale systems are described.
Possible metric characteristics of these signs are defined.
Large-scale complex IT systems and their access control subsystems are considered.
Belonging of such access control subsystems to a class of larged-scale systems is proved.
The automation need of the management processes by the access control subsystem in the large-scale complex IT system is explained.
Keywords: larged-scale systems, access control, management, automation.
A.V. Bazhenov, A.K. Guts.
Software for Modeling of Network and Simulation of Computer Network Attacks.
The article presents a software application that simulates different computer networks and attacks on these networks.
Keywords: software application, modeling, network attack, smurfing.
S.V. Belim, D.E. Vilkhovskiy.
Koch-Zhao Algorithm Steganalysis.
The analysis of the Koch-Zhao steganographic algorithm was carried out. The
possibility of an attack on the detection of messages is considered. An algorithm for
calculating the boundaries of the embedded message based on the analysis of the discrete
cosine transform coefficients is proposed. A computer experiment is conducted. Embedding
parameters that allow the attack are defined.
Keywords: steganography, steganalysis, Koch-Zhao algorithm, discrete cosine transform.
S.V. Belim, P.G. Cherepanov.
Selection of Blocks in a Video Stream for Embedding Digital Watermarks
The article proposes a method for selecting blocks for embedding digital
watermarks in video files. The video stream is represented as a three-dimensional object.
For embedding digital watermarks, the Koch-Zhao method is used, which is generalized to
the three-dimensional case. The main goal of the proposed method is to reduce visible
distortions from embedding data. For the selection of blocks, their statistical analysis
is performed. The variance of the color intensity of individual pixels is chosen as the
main parameter. A computer experiment is conducted. To assess the level of visibility,
the ratio of noise to the main signal is calculated. The threshold value of the variance
above which the embedding is the least noticeable is experimentally determined.
Keywords: digital watermarks, video steganography, discrete cosine transform.
S.V. Usov.
On the Representation of Role-Based Access Control Models by Object-Oriented HRU Model.
In this paper the possibility of representing of some types of role-based access control models by object-oriented discretionary access control model is considered. The role-based security model without hierarchy and the role-based security model with hierarchy with inheritance "from above" are considered. The permissions of the role-based access control model are represented as a set of pairs of object and access right. A hierarchy of classes of the object-oriented HRU model based on the role-based access control policy is constructed. Commands of the object-oriented HRU model corresponding to the reassignment of roles in the original role-based model are described.
Keywords: role-based access control model, object-oriented discretionary access control model, role hierarchy.
D.N. Lavrov.
Principles of Building a Protocol for Guaranteed Message Delivery.
As a rule, in computer networks information security is considered from the point of view of
three properties: confidentiality, integrity and availability.
Currently, it is important to consider such property of information as anonymity.
To ensure the latter, a tool such as TOR is used. The TOR network gives us the
illusion of anonymity on the Internet and lulls the vigilance of the end user. But
at the output node of the TOR network, the traffic is decrypted and its contents may
become known to the owner of this output node. If the owner of a node or
a series of nodes is an authoritarian government, or a foreign agent, then he can not
only know the contents of the message being transmitted, but also try to modify it or
completely interrupt the communication channel. Confidentiality of the message can be
protected by encryption, but one can only hope that it is secure. Accessibility and
integrity remain at risk. Here, availability means a guarantee of delivering a complete
message to a destination. The article discusses the principles that should be the basis
of the data transfer protocol with guaranteed delivery. The idea of the protocol is based
on the existence in the network of several independent delivery routes and the use of cryptographic \((k, n)\)-threshold secret
separation schemes in the \(n\) network flows of different routes. This will allow not
only to further anonymize traffic, but also in the case of control by the authoritarian
government of the output nodes (lower than \(k\) threshold) will provide additional
protection for the confidentiality of traffic.
This research was done as part of a research project NIOKTR number 01-06/683.
Keywords: secret sharing, routed network, anonymity, availability.
Y.S. Rakitskiy.
Import and Export of Role-Based Security Policies in Oracle DBMS.
The article discusses the role-based security policy implemented in the Oracle DBMS. The role model in a DBMS can be quite complex, contain a large number of roles and authorities. This information is stored in a large number of related tables. A mechanism has been implemented to extract data mapped to role-based security policies in an Oracle DBMS and to present this information in GraphML format. It also implemented the ability to import role-based security policy, presented in GraphML format, in Oracle DBMS.
Keywords: role-based model, DBMS, graph representation language.
S.V. Belim, Y.S. Rakitskiy.
Chaotic Masking Scheme for Messages Based on Orthogonal Functions.
The method of chaotic masking of a discrete signal is proposed in the
article. The proposed approach does not require the synchronization of chaotic generators and is resistant to noise in the communication channel. These properties remove the main problem of chaotic masking associated with the desynchronization of control parameters. The basic idea is to use message coding using orthogonal functions. Next, a simple summation of a hidden message with a chaotic signal is applied. The extraction of the message can be performed on the basis of the orthogonality property without subtraction of the chaotic component.
Keywords: orthogonal functions, signal, masking.