2022 № 3(56)

CONTENTS

Britvin A.V., Nikitenko N. S., Poller A.B., Poller В. V., Shakhov N. V. Characteristics of trends in the radiation dynamics of polymer planar waveguide structures with phosphors for ultraviolet information systems during long-term held tests
Bobrov E.A. Algorithm for predicting human age based on a convolutional neural network using only anonymized images of eye corners
Scherbakova N. G. Modeling group interactions of complex systems. Review
Belyaev N.A. Automated construction of highly-efficient parallel programs for sparse linear algebra in LuNA system
Vlasenko A. Yu, Michurov M.A., Mustafin D. E. Automating debugging and load balancing in fragmented programs
Gerb A.R., Omarova G. A. Fpplication of graph theory in algebraic multigrid methods for solving sparse SLAES

A.V. Britvin*, N.S. Nikitenko*, A.B. Poller*, B.V. Poller*’**, N. V. Shakhov *’**

* Institute of Laser Physics SB RAS, 630090, Novosibirsk, Russia

**Novosibirsk State Technical University, 630087, Novosibirsk, Russia

CHARACTERISTICS OF TRENDS IN THE RADIATION DYNAMICS OF POLYMER PLANAR WAVEGUIDE

STRUCTURES WITH PHOSPHORS FOR ULTRAVIOLET INFORMATION SYSTEMS DURING LONG-TERM FIELD TESTS

DOI: 10.24412/2073-0667-2022-3-5-13

EDN: IZOMFV

Polymer film and fiber phosphor converters — luminescent antennas — offer significant prospects for the construction of UV information sensor and telecommunication systems. Unlike lens and reflex optical elements, they have a large area and light weight, have large angles of field of view. Due to the complete internal reflection of UV radiation from phosphors in the film or fiber, the signal is concentrated at the output ends, which can be connected to photodetectors or optical cables.

Key words: ultraviolet, atmospheric optical communication lines, communication without direct visibility.

References

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Bibliographic reference: Britvin A.V., Nikitenko N. S., Poller A.B., Poller В. V., Shakhov N. V. Characteristics of trends in the radiation dynamics of polymer planar waveguide structures with phosphors for ultraviolet information systems during long-term held tests //journal “Problems of informatics”. 2022, № 3. P.5-13. DOI:10.24412/2073-0667-2022-3- 5-13. EDN: IZOMFV

E. A. Bobrov

M. V. Lomonosov Moscow State University

ALGORITHM FOR PREDICTING HUMAN AGE BASED ON ACONVOLUTIONAL NEURAL NETWORK USING ONLY ANONYMIZED IMAGES OF EYE CORNERS

DOI: 10.24412/2073-0667-2022-3-14-23

EDN: KVNXKW

Age-related biomarkers are qualitative and quantitative indicators of the human body’s aging processes. An organism’s biological age is critical in defining its physiological state. Machine learning has resulted in the development of a wide range of age predictors that differ in importance, simplicity of use, cost, applicability, and interpretability. The current work presents and investigates a noninvasive class of visual photographic markers of aging. This research describes a simple and reliable age indicator based on deep neural networks that uses just anonymised images of a person’s eye corners. In a large age range of a specific human population, the trained neural network has an average absolute error of less than three years.

Key words: Age Prediction, Biomedical Imaging, Computer Vision, Deep Learning, Photographic Aging Biomarker.

References

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Bibliographic reference: Bobrov E.A. Algorithm for predicting human age based on a convolutional neural network using only anonymized images of eye corners //journal “Problems of informatics”. 2022, № 3. P.14-23. DOI:10.24412/2073-0667-2022-3- 14-23. EDN: KVNXKW

N. G.Scherbakova

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

MODELING GROUP INTERACTIONS OF COMPLEX SYSTEMS. REVIEW

DOI: 10.24412/2073-0667-2022-3-24-45

EDN: MHBGVI

Many important properties of complex systems can be described using networks. The analysis of such complex networks is based on graph theory Diestel (2005) and statistical mechanics Albert, Barabasi (2002), which provide universal tools for studying the structural and dynamic properties of the system and its components. The study of complex networks made it possible to reveal such important properties inherent in many real systems as the power law of the distribution of degrees of nodes, belonging to a small world, the presence of a giant component, evolution models. Many methods have been developed to identify important network actors and the presence of communities of actors. Reviews of research methods for complex networks can be found in publications Albert, Barabasi (2002), Newman (2010).

In many cases the use of complex networks does not provide complete information about the investigated systems. The real-life systems have many heterogeneous parts with complicated subsystem dependencies that can’t be derived from a simple graph. The concept of “higher-order networks” refers to three main lines of research designed to overcome the limitations associated with traditional models that capture only pairwise connections Battiston etal. (2020), Lambiotte etal. (2019). The first line is based on the assumption that multiple link types can be described in terms of multilayer networks, reviews of the approach can be found in Boccalctti et al. (2014), Bianconi (2018). The second has introduced non-Markovian model of nodes interactions, taking into account the correlation and temporal characteristics to identify the implicit influence of components on each other Holme (2015). The third line generalizes pairwise interactions to arbitrary node sets, these are “networks beyond pairwise interactions” Battiston etal. (2020). This direction is the scope of our short review.

To analyze complex data, a number of techniques have been developed that use various mathematical structures to represent “multiple” relationships. Hire we examine three methods of explicit encoding higher order interactions in terms of a social system that includes a certain set of individuals. Any attribute or a number of attributes that can be associated with the individuals of the system can provide a basis for forming a collection of subsets of individuals, where the subset corresponds to the individuals that have the given property. Thus, the structural framework imposed on the set of individuals by such set of subsets is considered.

R. H. Atkin in Atkin (1972, 1974, 1976) uses an algebraic approach in which the basis for the study is the concept of a simplex, a geometric figure that is an n-dimensional generalization of a triangle. Analytical methodology is based on the algebraic topology, which uses algebraic methods for studying topological spaces (see, for example, Hatcher (2002). This work was carried out under state contract with ICMMG SB RAS (0251-2021-0005).

The simplicial complex is the set of simplices closed under the inclusion of all faces of all simplices. Q-analysis is a mathematical framework for describing and analyzing simplicial complexes.

In Seidman (1981), a collection of subsets is considered as the backcloth of a set of individuals. To the subset the term “event” (or group), which contributes to the formation of the subset, is applied. The analysis of structures imposed on a set by a collection of subsets is based on the concept of a hypergraph

S. B. Seidman noted that while the hypergraph focuses on the incidence relationships between vertices and edges (individuals and events), structures representing relationships between individuals (or between events) can be derived from the hypergraph. As an example of using the hypergraph representation, the problem of searching for “anomalies” in the original basic structure is considered.

In Wilson (1982), a research method is based on treating data as a bipartite graph. A graph is bipartite if the vertices may be partitioned into exactly two mutually exclusive sets, so that every edge has its ends in different sets: vertices of the same set cannot be adjacent Diestel (2005). In this case the two sets are the set of actors and the set of events. Such an approach, as shown in Wilson (1982), makes it possible, for example, to reveal the division of a set into groups that do not have common individuals and at the same time cover the entire set of individuals or to find sets of groups that allow activity only within the selected set of groups, forming a collective. The methods of visualizing and analyzing higher order interactions can rely on traditional network analytic technique.

Despite different approaches, the relationship between individuals and events can be represented by an incidence matrix, in which 1 in the intersection of the ith row and jth column indicates that the individual i belongs to the group j: However, simplicial complexes, hypergraphs and bipartite graphs are different structural formations. In Ouvrard (2020), comments are formulated regarding the fact that instead of studying hypergraphs, one can restrict oneself to bipartite graphs. In Torres etal. (2021), the relationships between simplicial complexes and hypergraphs were explored and showed that some information can be lost when moving from one to another.

As many applications of high-order models arose from systems initially modeled with graphs, many analysis methods imitate those originally used for graphs. This is a study of the underlying structure based on the distribution of degrees and clustering coefficients Malefic et al. (2008), Estrada, Rodriguez-Velazquez (2005) as well as identifying important actors based on measures of centrality Estrada, Ross (2018), Borgatti, Everett (1997), Faust (1997). But the definitions of classical centrality measures require generalization and clarification, since it is desirable that they reflect the relationship between the centralities of groups and the centralities of the actors that belong to the groups.

Conclusion. There is no universal complex system framework. As noted in Johnson (2013), the simplest structure can be used in any situation, but it should be choosed a framework that best fits the data and gives the necessary representational power.

Key words: complex system, hypernetwork, bipartite graph, hypergraph, simplicial complex, centrality measures.

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Bibliographic reference: Scherbakova N. G. Modeling group interactions of complex systems. Review //journal “Problems of informatics”. 2022, № 3. P.24-45. DOI:10.24412/2073-0667-2022-3- 24-45. EDN: MHBGVI

N. Belyaev

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

AUTOMATED CONSTRUCTION OF HIGHLY-EFFICIENT PARALLEL PROGRAMS FOR SPARSE LINEAR ALGEBRA IN LUNA SYSTEM

DOI: 10.24412/2073-0667-2022-3-46-60

EDN: MTTVTE

Automatic construction of efficient scientific parallel programs for supercomputers is in general a complex problem of system parallel programming. Therefore, various specialized system algorithms for automated parallel programs construction are of use. Of interest are algorithms for automated parallel program construction from a given numerical algorithm description. These algorithms can either be general purpose or specialized. The specialized parallel program construction algorithms are of particular interest. Despite the fact that such specialized system algorithms are applicable only for restricted classes of input numerical algorithms, such specialized algorithms have a significant advantage. These algorithms allow parallel program generators to employ parallel programming techniques which are widely used in manual parallel programming to construct highly efficient parallel programs. LuNA system for automatic construction of distributed parallel programs provides a basis for accumulation of such specialized system algorithms to provide high-quality parallel programs construction in particular subject domains. This system allows automated construction of parallel programs for a distributed memory parallel computer from a given numerical algorithm description written with high-level LuNA language. In this paper, a novel specialized algorithm of parallel programs construction for sparse linear algebra domain is presented. It is applicable for a class of sparse linear algebra algorithms which includes widely used preconditioner algorithms for sparse systems of linear equations. This fact makes the developed specialized system algorithm of practical interest. The presented specialized automated parallel program construction algorithm has been implemented as a specialized run-time system which has been integrated into the LuNA system and the module which has been integrated into the LuNA compiler. In order to integrate the implementation of the developed specialized system algorithm into the LuNA system the following approach is used. The LuNA compiler detects if the input numerical algorithm description written with LuNA language belongs to a class of numerical algorithms for which the LuNA system has a specialized support. In this case the corresponding specialized system algorithms are used to construct the so-called intermediate parallel program. Otherwise the previously developed general purpose parallel program construction algorithms are used. The control program constructs an executable representation of the input numerical algorithm at run-time. The executable representation of the input algorithm is a directed acyclic graph of single assignment variables and operations. This representation is then executed by the specialized run-time system. The specialized run-time system employs parallel programming techniques which are widely used in manual development of parallel preconditioners for sparse matrices. In order to assess the performance of parallel programs constructed using the developed specialized system algorithms, a test parallel program was automatically constructed from the description of sparse-vector multiply algorithm. The performance of the automatically constructed parallel program was compared to the

performance of implementation of the same algorithm from Intel MKL and Parallel Sparse BLAS libraries. Experimental results demonstrate that the performance of the automatically generated parallel program is comparable with the performance of the corresponding implementation from Intel MKL (the performance of the automatically constructed parallel program is only 15 % less than the performance of the matrix-vector multiply implementation from Intel MKL) . Also the constructed parallel program outperforms the implementation for Parallel Sparse BLAS library by approximately 10 %. These facts show that the LuNA system is practically applicable for automated construction of high performance distributed parallel programs for supercomputers in the sparse linear algebra field.

Key words: DAG, parallel preconditioner, parallel program synthesis, fragmented programming, task based parallelism, parallel run-time system, parallel programming system.

References

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Bibliographic reference: Belyaev N.A. Automated construction of highly-efficient parallel programs for sparse linear algebra in LuNA system //journal “Problems of informatics”. 2022, № 3. P.46-60. DOI:10.24412/2073-0667-2022-3- 46-60. EDN: MTTVTE

A. Vlasenko, M. Michurov*, D. Mustafin*

Institute of Computational Mathematics and Mathematical Geophysics of SB RAS, 630090, Novosibirsk, Russia

*Novosibirsk State University, 630090, Novosibirsk, Russia

AUTOMATING DEBUGGING AND LOAD BALANCING IN FRAGMENTED PROGRAMS

DOI: 10.24412/2073-0667-2022-3-61-76

EDN: NBFMPU

The LuNA (Language for Numerical Algorithms) fragmented programming system is a high-level tool for creating parallel applications. Programs created using the LuNA can be run on computing systems with shared or distributed memory. The users create their program using a language resembling the standard imperative programming languages (C/C++, Fortran, Pascal, etc.), but does not specify any constructions regarding parallelism. Each operator of the LuNA language causes the generation of a new calculation fragment (CF) at runtime, which accepts objects called data fragments (DF) as its input and output. The totality of CFs makes up a fragmented program at the execution stage. Thus, the algorithm of a fragmented program is represented as a bipartite oriented graph with vertices of types CF and DF. The paper explains the important properties of fragmented programs: the non- deterministic order of operators execution in procedures, the uniqueness of assigning DF values and the absence of arrays in the programmer’s usual understanding.

The most typical logical errors for fragmented programs are described, which include an attempt to use uninitialized data, repeated initialization of the same data and a mismatch of data types during initialization and during use. In the case of running a fragmented program on a distributed memory computing system, the processes share the work of executing fragments of calculations. During this work, a situation of computational load imbalance may occur. The paper substantiates the importance of solving this problem.

Since LuNA is a high-level parallel programming tool, it is very difficult for the user to solve debugging and load balancing problems. In this regard, the authors of paper develop an automated debugging module based on the ,,post-mortem“ analysis method and an automatic centralized load balancing module for the system.

The automated debugging module collects trace files in JSON format during the execution of a fragmented program on each process. These files record information about the processed CFs, as well as their input and output DFs. After the normal or emergency shutdown of the program, the user can call a special software tool (luna_trace) that analyzes the collected traces. The result of its work is the output of detailed information about the detected errors, including a verbal description of the problem, a program statement indicating the string and file name of the source code, a stack of procedure calls and the names of the DFs with which the error is associated. In addition, information specific to a particular error is displayed, for example, for uninitialized DFs - the places of their possible initialization.

Another important part of this module functionality is the automatic detection of program hangs. The implementation of hang detection is based on a modification of the distributed Dijkstra-Scholten

algorithm. A hang-up situation occurs when one or more errors from frequently occurring classes are made in the LuNA program. In this regard, in the environment of a supercomputer center, where the user loses the ability to interact with the program after queuing the task, this functionality becomes particularly important.

The paper explains the fundamental difference between dynamic and static load balancing approaches and outlines the applicability of both approaches for different cases. The importance of developing a dynamic load balancing module in the LuNA system is explained. There are 2 methods of organizing dynamic balancing: based on centralized and distributed algorithms. The module being created implements the first method. The centralized load balancing module launches a service load balancer process along with the „worker processes“ that execute CFs. The role of this service process is to collect information from worker processes about executed and ready-to-execute CFs in order to redistribute them and minimize the imbalance. By collecting this information, the load balancer monitors the relative value of the imbalance between the most and the least loaded processes. When this imbalance reaches the threshold value (this threshold is setting by the parameter), the load balancer generates a „balancing plan“ deciding which CFs should be transferred from one process to another. The balancing plan is based on the fragment’s „weights“. The execution time of the fragment is taken as the weight. At the same time, if a fragment is transferred from one process to another, then its weight increases by the time of transferring.

The paper shows the results of modules testing on the computing cluster of Novosibirsk State University (NSU). Tests were performed on the problem of block matrix multiplication. The presented results demonstrate the effectiveness of the centralized load balancing module and acceptable overhead costs of the automated debugging module.

Further development plans regarding the functionality of the modules are given at the end.

Key words: fragmented programming, LuNA system, automated debugging, dynamic load balancing.

References

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3. Akhmed-Zaki, D., Lebedev, D., Malyshkin, V., Perepelkin, V. Automated Construction of High Performance Distibuted Programs in LuNA System // Malyshkin, V. (ed.) 15th International Conference, PaCT 2019, Almaty, Kazakhstan. August 19-23, 2019. P. 3-9.

4. Malyshkin, V. E. Tehnologiya fragmentirovannogo programmirovaniya // Vestnik YUrGU. Seriya: Vichislitelnaya matematika i informatika. 2012. N 46 305. S. 45-55.

5. Mustafin, D. E. Modul centralizovannoy dinamicheskoy balancirovki nagruzki LuNA-programm // Innovaciyi. Nauka. Obrazovanie. 2021. N 40. S. 365-373.

6. Protze, J., Hilbrich, T., Schulz, M., de Supinski, B. R. MPI Runtime Error Detection with MUST: A Scalable and Crash-Safe Approach // 43rd Intern. Conf, on Parallel Processing Workshops. Minneapolis, MN, USA. 2014. P. 206-215.

7. Michurov, M. A. Sredstvo analiza prichin zavisaniy fragmentirovannih programm v sisteme LuNA // Innovaciyi. Nauka. Obrazovanie. 2021. N 40. S. 354-364.

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Bibliographic reference: Vlasenko A. Yu, Michurov M.A., Mustafin D. E. Automating debugging and load balancing in fragmented programs //journal “Problems of informatics”. 2022, № 3. P.61-76. DOI:10.24412/2073-0667-2022-3- 61-76. EDN: NBFMPU

A. Gerb, G. Omarova*

Novosibirsk State University, 630090, Novosibirsk, Russia

*Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

APPLICATION OF GRAPH THEORY IN ALGEBRAIC MULTIGRID METHODS FOR SOLVING SPARSE SLAES

DOI: 10.24412/2073-0667-2022-3-77-89

EDN: NJDXUZ

In this paper, we discuss geometric and algebraic multigrid methods, graph coarsening algorithms, and metrics used to construct vertex aggregations. A coarsening method based on A. Napov and Y. Notcy’s criteria is implemented. Gustavson’s algorithms for efficient multiplication and transposition of matrices in CSR format are used for computation time optimization, which allowed to process graphs with more than one million vertices. The purpose of the presented work is to develop a data structure and computational environment components for high-performance solution of a wide class of SLAEs.

Key words: graph coarsening, grid graph, metric, sparse matrices, data structures.

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Bibliographic reference: Gerb A.R., Omarova G. A. Fpplication of graph theory in algebraic multigrid methods for solving sparse SLAES //journal “Problems of informatics”. 2022, № 3. P.77-89. DOI:10.24412/2073-0667-2022-3- 77-89. EDN: NJDXUZ

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