IAMR Structure

# Laboratory for Probability Theory and Computer Statistics

**Head**: Dr. (DSc) of Phys. and Math., Professor Pavlov, Yuri L.

Major research trends
Main activity results
Scientific publications
Events
Staff
Contact information

### Major research trends

### Main activity results

The members of Laboratory for Probability Theory and Computer Statistics had obtained results in the following fields:**The theory of random forests**

**Methods for solving problems of combinatorial analysis**

**Configuration Graphs**

**Stochastic Models and Data Analysis**

**Functorial constructions of topology and their applications to the study of probability measures**

**Classes of spaces with a special spectral decomposition**

The theory of random forests

A theory of random forests, the main provisions of which are presented in the book [1] has been created. Critical Galton-Watson forests generated by branching processes with a finite third moment of the offspring distribution were considered. In all main zones where the number of trees and the number of vertices tend to infinity, limit distributions of the maximum tree size, the number of trees of a given size, and the height of a random forest are found. Then it was shown that these results remain valid even if only the variance of the number of particle offspring is finite [2]. In [3, 4], limit theorems for the number of vertices in strata of a random forest and for the terms of the variational series of tree sizes were proved. In addition, conditions are found for the appearance of a giant tree, i.e., a tree whose number of vertices is proportional to the number of all graph vertices tending to infinity, while the sizes of other trees are infinitesimal compared to the size of the maximum tree.

We also considered random forests that are not Galton-Watson forests; they cannot be formed by branching processes. In [5, 6], limit theorems for the sizes of trees of a random recursive forest were proved, and in [7] conditions for the appearance of a giant tree were found.

For random forests described in [1], the dynamics of the number of vertices of a given degree was studied [8], and for a random unrooted unlabeled forest, the asymptotics of the maximum tree size was found [9]. The article [10] was the first to consider the asymptotic properties of Galton-Watson random forests, in which the number of vertices is not known, as it was considered before, but is limited.

Random graph theory is widely used in modeling complex communication networks. One of the most successful models of such networks is the configuration graph. It turned out that to study the structure and dynamics of such graphs, one can successfully use the methods of the theory of Galton-Watson branching processes. Since the set of trajectories of a branching process, together with the probability distribution induced naturally on this set, forms a random forest, the idea of using the results on random forests to study configuration graphs was first proposed in [11]. However, an important feature of modern complex networks is that the number of offsprings of the corresponding branching processes has infinite variance. This means that all the results that were known before about random forests are inapplicable to solving network model problems. Therefore, there was a need for a significant expansion of the theory and the development of new research methods. Limit theorems were proved on the sizes of Galton-Watson random forest trees formed by critical branching processes with an infinite variance of the number of offsprings [11, 12].

Methods for solving problems of combinatorial analysis

The probabilistic approach to solving enumerative problems of combinatorial objects is very efficient. It makes it much easier to obtain the desired results compared to direct calculations, and in some cases even uncontested. The essence of the approach is to define a probabilistic measure on the set of considered objects and to find the probabilities of the appearance of the studied properties. Under the known power of the set of objects, this probability is equal to the fraction of objects that have desired properties.

The book [13] studied random single-valued mappings of a finite set into itself. Such mappings can be represented by a directed graph, in which each arc corresponds to a mapping of one element of the set to another. Each connected component of such a graph contains one cycle, and the cyclic vertices serve as the roots of trees whose arcs are directed towards the roots. If we remove the cyclic vertices, then the remaining subgraph forms a forest, which makes it possible to use the results on random forests to study random mappings. If we consider a one-to-one mapping, which is called a substitution, then the components of the corresponding graph are directed cycles. For equiprobable mappings, the limit distributions of the number of cyclic vertices, the sizes of trees, and the maximum tree size are found. The same problems are solved for mappings with restrictions on the number of cycles. In addition, the asymptotic behavior of the number of cycles of a random substitution is studied.

The central place in the proofs of the results obtained in [1, 13] and in the majority of subsequent works is occupied by the use of the generalized allocation scheme, introduced and studied by V.F. Kolchin. This scheme allows to obtain both explicit enumerative formulas and their asymptotics as the number of objects tends to infinity. The most important advantage of the generalized scheme is the ability to reduce problems on dependent random variables to simpler problems in which the random variables are independent. Therefore, considerable attention has been paid to the development of methods using the allocation scheme. In the process of this work, it was possible to significantly expand the scope of such methods. The main technical difficulty in research is the need to prove integral and local limit theorems for distributions of sums of random variables on convergence to stable laws, including series schemes and large deviations.

In [14], limit distributions were found for the number of pairs of one-color balls in classical urn schemes, the number of chains in a random forest, where a chain is a pair of non-rooted vertices connected by a simple path, and the number of pairs of elements contained in one cycle of random substitution. In [15], the asymptotic behavior of the number of cycles of a given length in a random substitution with a known number of cycles was studied. Classes of isomorphic graphs of a random mapping were studied, for which limit theorems on the sizes of trees were proved [16]. The limit distributions of the number of cyclic vertices in the graph of a random single-valued mapping with a known number of cycles are found [17]. An estimate for the rate of convergence to the limit law for the distribution of the number of cycles of a given length of a random substitution with a known number of cycles was obtained [18]. In [19], the limit distribution of the number of trees of a given size in a graph of a random mapping with a known number of connected components was found, and in [20], the number of vertices of a given degree was found.

In models of modern complex communication networks, it is often assumed that the distributions of vertex degrees depend on slowly varying functions, which are often unknown. Such random graphs are considered in [11, 12]. To obtain results about these graphs, in addition to a generalized allocation scheme, it is proposed to use the properties of regularly varying functions and Tauberian theorems.

Configuration Graphs

Random graphs are widely used as models of complex communication networks, such as the Internet, social networks, transport networks, mobile communication systems, etc. Numerous observations of real networks have shown that the vertex degrees of a graph modeling a network can be considered as independent identically distributed random variables. One of the types of random graphs that meet these conditions is the configuration graph. In such a graph, the degree of any vertex is equal to the number of labeled semi-edges incident to the vertex, i.e., edges for which adjacent vertices have not yet been determined. The graph is constructed by pairwise equiprobable connection of semi-edges with each other to form edges. Since the sum of vertex degrees must be even, an auxiliary vertex of degree one is introduced into the graph, or an additional semi-edge is added to the equiprobably chosen vertex. It is known that these auxiliary elements do not affect the asymptotic behavior of the main numerical characteristics of graphs as the number of vertices tends to infinity. It is clear that loops and multiple edges may appear in such a graph construction. Empirical data show that in real networks the distributions of vertex degrees usually have tails corresponding to a discrete power-law, and the number of vertices with higher degrees is proportional to the total number of graph vertices.

The studies of the models described above began with the simplest configuration graphs, in which all vertex degrees follow the discrete Pareto law, the parameter of which lies in the interval (1, 2), which, as it is well known, corresponds to the majority of network models. This distribution has finite mean but infinite variance. It is also known that a graph with such properties contains a giant connected component. It was shown [21] that the limit distribution of the size of the giant component is the normal law. In [22], conditional configuration graphs were first considered under the condition that the number of edges is known. Such graphs can serve as models of networks in which the number of possible connections can be estimated. In addition, the results on conditional graphs can also be used to study networks without restrictions on the number of links by averaging the corresponding results over the distributions of the number of edges. Such distributions can be found using the methods of proving both integral and local limit theorems for sums of random variables. It is clear that obtaining results about configuration graphs with a known number of edges is technically much easier than in the case when the sum of vertex degrees is random. It was shown in [22, 23] that to study conditional configuration graphs, one can use a generalized allocation scheme, which is a new example of solving applied problems using this scheme. As a result, theorems typical for an allocation scheme were proved for the maximum vertex degree and the number of vertices of a given degree in a configuration graph. The degree structure of conditional configuration graphs, whose vertex distributions do not have not only variance, but also mathematical expectation, was studied in [24]. Limit distributions of the number of loops of a configuration graph without restrictions on the number of edges were found in [25].

Models of communication networks, expressed as a configuration graph, can be used to evaluate the resilience of networks to destructive influences. Two types of destruction were considered - "random breakout" and a targeted "terrorist act". In the first case, equiprobably chosen vertices together with the edges incident to them were removed one by one from the graph, and in the second case, the vertex with the maximum degree was removed at each step. For graphs containing a giant connected component, a destruction criterion was proposed based on a comparison of the sizes of the giant and the second largest component. This made it possible to evaluate the robustness of networks by counting the number of steps required for the network to be considered destroyed. It also turned out that configuration graphs can be used not only to model complex communication networks, but also such phenomena as banking crises and forest fires. In the latter case, the vertices of the graph can be interpreted as trees growing in a certain area, and the edges as possible fire transitions from tree to tree (for example, through dry grass in the case of a ground fire or through the air under the influence of wind in a crown fire). Another parameter of the model is the probability of fire transfer along the edge. It is assumed that this probability is estimated by forestry specialists, taking into account the terrain, wind rose, type of fire, etc. As in the case of the network destruction, two types of fire were considered - an accidental ignition (“lightning strike”), in which the fire spreads from an equiprobably chosen vertex, and purposeful arson, starting from the vertex with the maximum degree. Such models are proposed to be used to assess the consequences of a fire. In the case of forest plantation planning, the model makes it possible to find the optimal arrangement of trees, which, on the one hand, provides a sufficient amount of wood for the forest industry, and, on the other hand, minimizes losses in case of fire. In [26], models were considered that describe both the destruction of networks and forest fires. The dependences of the sizes of the connected components on the type of destructive action, the parameters of the vertex degree distributions and the initial graph size are constructed, and for a forest fire, the dependences of the proportion of vertices surviving after a fire on the type of fire, the initial graph size, the parameters of the vertex degree distributions and the probabilities of fire transition along the edges are found. It turned out that the considered configuration graphs are very resistant to random destructive influences, but rather vulnerable to targeted attacks. This means that to protect networks, it is necessary to focus efforts on critical nodes, and not evenly distribute available funds. The main method for studying stability problems on graphs was simulation.

In [27, 28], graphs with two vertex degree distributions, power-law and Poisson, were considered and compared. It was assumed that ignition occurs in a random environment, where the probabilities of fire transition along the edges are random variables uniformly distributed on the interval [0, 1]. Another version of the random environment was discussed in [29], where the distribution of the degree of each vertex was chosen from a family of power-law distributions with a random parameter. When choosing the distribution parameter in accordance with empirical data, preference was given to the truncated gamma distribution. The model in a random environment is compared with a similar model with the averaged parameter of the degree distribution. Conditions are found under which the study of stability in a random environment can be reduced to studying the evolution of graphs in an ordinary environment, which is much simpler [30].

In [31], for the first time, conditional configuration graphs were considered under the condition that the number of edges is unknown, but limited. In [32], limit distributions of the maximum vertex degree were found for a changing parameter of the power-law vertex degree distribution, the values of which approach the phase transition points, at which the structure of the graph changes dramatically.

For the first time, the dynamics of the degree structure of configuration graphs with a known or limited number of edges and with a degree distribution, about which only weak restrictions on the asymptotic behavior of probabilities of large values of degrees are known, was studied [33, 34]. Limit distributions of the number of vertices of a given degree in a graph with a uniformly distributed parameter of the power-law degree distribution on a finite interval and with a limited number of edges are obtained [35]. A theorem on the asymptotic behavior of the cluster coefficient of a configuration graph with an unknown vertex degree distribution was proved [36]. Conditions are found under which the probability of connectivity of a configuration graph converges to one with the number of vertices tending to infinity, and an estimate is given for the rate of such convergence [37, 38].

Stochastic Models and Data Analysis

An original model of the "parasite-host" relationship has been proposed and studied. It is known that the number of parasites on a host usually has a negative binomial distribution, and this regularity is observed almost independently of host and parasite species. The well-known representation of the negative binomial law in the form of a compound Poisson distribution was used, the parameter of which is random and has a gamma distribution. It is shown that in such a model, Poisson's law characterizes the occurrence of parasites by the host, and the gamma distribution is associated with the individual characteristics (including genetic ones) of the host organisms. Observations of hosts and parasites in nature and in laboratory conditions have shown the adequacy of the proposed model. It makes it possible to describe the interactions between parasites and hosts and to predict the ongoing processes in various populations [39–43].

To test hypotheses about the vertex degree distribution of a conditional configuration graph, chi-square type statistics was proposed and its limit distribution was found [44].

The analysis of medical data obtained in the course of blood tests of patients with arthrosis was carried out and conclusions were drawn about the diagnostic value of some indicators [45, 46].

Some tasks related to the problem of parametric identifiability of factor analysis models were solved, including the case of dependent factors and the presence of latent variables [47, 48, 49].

One of the most popular and widely used modern methods of applied statistics is the method of random forests. Issues related to the consistency of the method and the features of its use in solving problems of classification, regression, etc. were considered. A review of the literature and software was published in [50].

A graph model of communication networks was built, through which the products of the Neolithic workshops of the coast of Lake Onega were distributed, a statistical method was proposed for comparing the stages of production of stone tools from different workshop sites. The method is based on a comparison of the fractal dimensions of the distribution of finished product flakes [51, 52].

By order of the Kizhi Museum-Reserve by means of dispersion and correlation analyzes, the criteria were found, according to which the selection of wood for the construction of religious buildings in the Republic of Karelia was carried out [53].

The methods of cluster and factor analysis were used to obtain estimates of atmospheric precipitation on the territory of Finland and Karelia in order to identify sources of pollution and search for methods for controlling anthropogenic impact on the environment [54].

Functorial constructions of topology and their applications to the study of probability measures

For any seminormal metrizable functor, the notion of the dimension of a finite approximation of elements of spaces that arise under the action of a functor on metric compacta was introduced. Examples of this concept are the box dimension (which plays an important role in the theory of dynamical systems) and the quantization dimension of probability measures, defined in the framework of probability theory. The functorial approach makes it possible to identify general patterns, which provides a basis for constructing similar theories in other areas. Along this path, the quantization dimension of idempotent measures was defined and studied in [55], which are increasingly being used in applied fields. For all indicated dimensions, intermediate values theorems were proved [55], [56]. The proposed methods make it possible to define and study the notion of a uniform distribution on a metric compactum, which generalizes the classical notion of a uniform distribution on subsets of a Euclidean space [57].

Classes of spaces with a special spectral decomposition

The problem of S. Watson on belonging the Helly space to the class of F-compact spaces is solved [58]. A theorem on the antimultiplicativity of the class of F-compact spaces was proved [59]. The notion of a quasi-F-compact space was defined and studied [60]. It was proved that for an F-compact space of spectral height 3 there exists a LUR-norm on the space C(X) [61].

References

1. Pavlov Yu.L. Random forests. Utrecht, VSP, 2000, 122 p. Doi: 10.1515/9783110941975

2. Kazimirov N.I., Pavlov Yu.L. A remark on Galton-Watson forests. Discrete Math. Appl., 10(1), 2000, 49-62. Doi: 10.1515/dma.2000.10.1.49

3. Cheplyukova I.A. Emergence of the giant tree in a random forest. Discrete Math. Appl., 8(1), 1998, 17-33. Doi: 10.1515/dma.1998.8.1.17

4. Pavlov Yu. L., Cheplyukova I.A. Limit distributions of the number of vertices in strata of simply generated forests. Discrete Math. Appl., 9(2), 1999, 137-154. Doi: 10.1515/dma.1999.9.2.137

5. Pavlov Yu.L., Loseva E.A. Limit distributions of the maximum size of a tree in a random recursive forest. Discrete Math. Appl., 12(1), 2002, 45-60. Doi: 10.1515/dma-2002-0105

6. Pavlov Yu.L. Limit theorems for sizes of trees in the unlabelled random forest. Discrete Math. Appl., 15(2), 2005, 153-170. Doi: 10.1515/1569392053971424

7. Khvorostyanskaya E.V. On conditions for emergence of a giant tree in a random unlabeled forest. Discrete Math. Appl., 17(5), 2007, 439-454. Doi: 10.1515/dma.2007.035

8. Myllari T., Pavlov Yu. Limit distributions of the number of vertices of a given out-degree in a random forest. Journal of mathematical sciences, 138(1), 2006, 5424-5433. Doi: 10.1007/s10958-006-0309-1

9. Bernikovich E.S., Pavlov Yu.L. On the maximum size of a tree in a random unlabeled unrooted forest. Discrete Math. Appl., 21(1), 2011, 1-21. Doi: 10.1515/dma.2011.001

10. Pavlov Yu.L., Khvorostyanskaya E.V. On the maximum size of a tree in the Galton-Watson forest with a bounded number of vertices. Discrete Math. Appl., 24(6), 2014, 363-371. Doi: 10.1515/dma-2014-0032

11. Pavlov Yu.L. The maximum tree of a random forest in the configuration graph. Sbornik: Mathematics, 212(9), 2021, 1329-1346. Doi: 10.1070/SM9481

12. Pavlov Yu. L., Cheplyukova I.A. Tree sizes of random forest and configuration graphs. Proceedings of the Steklov Institute of Mathematics, 316, 2022.

13. Pavlov Yu.L. Random forests. Petrozavodsk, KRC RAS, 1996, 258 p.

14. Pavlov Yu.L., Cherepanova E.V. Limit distribution of the number of pairs in generalized allocation scheme. Discrete Math. Appl., 13(5), 2002, 421-423. Doi: 10.1515/dma-2002-0410

15. Cherepanova E.V. Limit distributions of the number of cycles of given length in a random permutation with given number of cycles. Discrete Math. Appl., 13(5), 2003, 507-522. Doi: 10.1515/156939203322694772

16. Pavlov Yu.L. Limit theorems for sizes of trees in the unlabelled graph of a random mapping. Discrete Math. Appl., 14(4), 2004, 329-312. Doi: 10.1515/1569392041938767

17. Cheplyukova I.A. The limit distribution of the number of cyclic vertices in random mapping in a special case. Discrete Math. Appl., 14(4), 2004, 343-352. Doi: 10.1515/1569392041938785

18. Cherepanova E. A. On the rate of convergence of the distribution of the number of cycles of given length in a random permutation with known number of cycles to the limit distributions. Discrete Math. Appl., 16(4), 2006, 385-400.

19. Cheplyukova I. A. On one characteristic of a random mappings with given number of cycles. Discrete Math. Appl., 16(5), 2006, 479-497. Doi: 10.1515/156939206779238454

20. Pavlov Yu. L., Myllari T.B. Limit distributions of the number of vertices of given degree in the forest of a random mapping with a given number of cycles. Discrete Math. Appl., 22(2), 2012, 225-234. Doi: 10.1515/dma-2012-016

21. Pavlov Yu. L. The limit distribution of the size of a giant component in an Internet-type random graph. Discrete Math. Appl., 17(5), 2007, 425-437. Doi: 10.1515/dma.2007.034

22. Pavlov Yu. L., Cheplyukova I. A. Random graphs of Internet type and the generalized allocation scheme. Discrete Math. Appl., 18(5), 2008, 447-463. Doi: 10.1515/DMA.2008.033

23. Pavlov Yu. L. On the limit distributions of the vertex degree of conditional Internet graphs. Discrete Math. Appl., 19(4), 2009, 349-359. Doi: 10.1515/DMA.2009.023

24. Pavlov Yu. L. On conditional Internet graphs whose vertex degrees have no mathematical expectation. Discrete Math. Appl., 20(5-6), 2010, 509-524. Doi: 10.1515/dma.2010.031

25. Pavlov Yu. L., Stepanov M. M. Limit distributions of the number of loops in a random configuration graph. Proceedings of the Steklov Institute of Mathematics, 282(1), 2013, 202-219. Doi: 10.1134/S0081543813060175

26. Leri M. M., Pavlov Yu. L. Power-law random graph’s robustness: link saving and forest fire model. Austrian journal of statistics, 43(4), 2014, 229-236. Doi: 10.17713/ajs.v43i4.34

27. Leri M. M. Forest fire on a configuration graph with random fire propagation. Informatics and Applications, 9(3), 2015, 65-71. Doi: 10.14357/19922264150307

28. Leri M., Pavlov Yu. Forest fire models on configuration random graph. Fundamenta Informaticae, 145(3), 2016, 313-322. Doi: 10.3233/FI-2016-1362

29. Leri M. M., Pavlov Yu. L. Random graphs’ robustness in random environment. Austrian journal of statistics, 46(3-4), 2017, 89-98. Doi: 10.17713/ajs.v46i3-4

30. Leri M. M., Pavlov Yu. L. On the robustness of configuration graphs in a random environment. Informatics and Applications, 12(2), 2018, 2-10. Doi: 10.14357/19922264180201

31. Pavlov Yu. L., Khvorostyanskaya E. V. On the limit distributions of the degree of vertices in configuration graphs with a bounded number of edges. Sbornik: Mathematics, 207(3), 2016, 400-417. Doi: 10.1070/SM8512

32. Pavlov Yu. L. Feklistova E. V. On limit behavior of maximum vertex degree in a conditional configuration graph near critical points. Discrete Math. Appl., 27(4), 2017, 213-222. Doi: 10.1515/dma-2017-0023

33. Pavlov Yu. L. Conditional configuration graphs with discrete power-law distribution of vertex degrees. Sbornik: Mathematics, 209(2), 2018, 258-275. Doi: 10.1070/SM8832

34. Pavlov Yu. L., Cheplyukova I. A. Limit distributions of the number of vertices of a given degree in a configuration graph with bounded number of edges. Theory Probab. Appl., 66(3), 2021, 376-390. Doi: 10.1137/S0040585X97T990460

35. Pavlov Yu.L., Cheplyukova I. A. On the asymptotics of degree structure of configuration graphs with bounded number of edges. Discrete Math. Appl., 29(4), 2019, 219-232. Doi: 10.1515/dma-2019-0020

36. Pavlov Yu.L. On the asymptotics of clustering coefficient in a configuration graph with unknown distribution of vertex degrees. Informatics and Applications, 13(3), 2019, 9-13. Doi: 10.14357/19922264190302

37. Pavlov Yu. L. On the connectivity of configuration graphs. Discrete Math. Appl., 30(1), 2021, 43-49. Doi: 10.1515/dma-2021-0004

38. Pavlov Yu. L. Connectivity of configuration graphs in complex network models. Informatics and Applications, 15(1), 2021, 18-22. Doi: 10.14357/19922264210103

39. IeshkoE. P., Pavlov Yu. L. Parasite population distribution model. Reports of the Academy of Sciences of the USSR, 289(3), 1986, 746-748.

40. IeshkoE. P., BarskayaYu. Yu., PavlovYu. L. etal. Population dynamics of glochidia of the freshwater pearl mussel margaritifera margaritifera L., parasitizing on juvenile salmonidae fishers in norten water reservoirs. Biology bulletin, 36(6), 2009, 624-629. Doi: 10.1134/S1062359009060120

41. Ieshko E.P., Bugmyrin S.V., Anikanova V.S., Pavlov Ju.L. Patterns in the dynamics and distribution of parasite abundance in small mammals. Proceedings of the Zoological Institute of the Russian Academy of Sciences, 313(3), 2009, 319-328.

42. Pavlov Yu. L. A biological problem and generalized allocation scheme. Discrete Math. Appl., 24(2), 2014, 83-94. Doi: 10.1515/dma-2014-0009

43. Ieshko E. P., Matveeva E. M., Pavlov Yu. L. et.al. Parasitic nematode abundance aggregation as a mechanism of the adaptive response of the host plant to temperature variation. Biology bulletin, 45(4), 2018, 345-350. Doi: 10.1134/S1062359018040076

44. Cheplyukova I. A., Pavlov Yu. L. Local limit theorem for shi-square type statistics in Internet graphs. Computer data analysis and modeling. Proceedings of the ninth International conference, vol. 2, Minsk, Publishing center of BSU, 2010, 10-13.

45. Svetlova M. S., Vezikova N. I., Pavlov Yu. L., Cheplyukova I. A. et.al. Cartilage ol-igomeric matrix protein, a possible marker of synovitis in early knee joint osteoarthrosis. Clinical Medicine (Russian Journal), 86(11), 2008, 65-68.

46. Svetlova M. S., Vezikova N. I., Pavlov Yu. L., Cheplyukova I. A. et.al. Content of C-reactive protein, interleukin-1, interleukin-6 and interleukin-1 receptor antagonist in the blood of patients with early osteoarthrosis of the knee joints. Terapevticheskiy arkhiv, 81(6), 2009, 52-55.

47. Stafeev S. On the method for finding invariants of factor analysis models. Computer data analysis and modeling. Proceedings of the ninth International conference, vol. 1, Minsk, Publishing center of BSU, 2010, 211-214.

48. Stafeev S. V. On global identifiability conditions of factor analysis models. Trans. KarRC RAS, 2011. No. 5, 111-114.

Identifiability of structural equation models with latent variables

49. Stafeev S. V. Identifiability of structural equation models with latent variables. Trans. KarRC RAS, 2019. No. 7, 53-57. Doi: 10.17076/mat1086

50. Chistyakov S. P. Random forests: an overview. Trans. KarRC RAS, 2013. No. 1, 117-136.

51. Tarasov A., Stafeev S. Estimating the scale of stone axe production: a case study from Onega lake, Russian Karelia. Journal of lithic studies, 1(1), 2014, 239-261. Doi: 10.2218/JLS.V11.757

52. Tarasov A., Zobkov M., Stafeev S. The role of debitage size in assessing the spatial organization of lithic production. The case of lake Onega axe and adze workshops. Lithic technology, 45(7), 2020, 140-153. Doi: 10.1080/01977261.2020.1738766

53. Kisternaya M., Kozlov V., Leri M. et. al. Tree rings as criteria for selection of timber for building of chapels in the Republic of Russia. Dendrochronologia, 40, 2016, 143-150. Doi: 10.1016/j.dendro2016.10.002

54. Feoktistov V. M., Leri M. M. Assessment of atmospheric precipitation composition in the territory of Finland and Karelia Republic using multivariate analysis methods. Bulletin of the Tomsk Polytechnic University. Geo Àssets Engineering. 322(1), 2021, 193-203. Doi: 10.18799/24/31830/2021/1/3012

55. Ivanov A. V. On quantization dimensions of idempotent probability measures. Topology and its Applications, 306, 2022, 107931. Doi: 10.1016/j.topol.2021.107931

56. Ivanov A. V. On the functor of probability measures and quantization dimensions. Tomsk State University Journal of Mathematics and Mechanics, 63, 2020, 15-26. Doi: 10.17223/19988621/63/2

57. Ivanov A. V. On uniform distribution on metric compacta. Siberian Mathematical Journal, 61(6), 2020, 1075-1086. Doi: 10.1134/S003744662006087

58. Ivanov A. V. On products of F-compact spaces. Siberian Mathematical Journal, 59(2), 2018, 270-275. Doi: 10.1134/S003744661802009X

59. Ivanov A. V. The class of Fedorchuk compact is antimultiplicative. Topology and its Applications, 235, 2018, 485-491. Doi: 10.1016/j.topol.2017.12.026

60. Ivanov A. V. On products of quasi-F-compacta. Topology and its Applications, 275, 2020, 106998. Doi: 10.1016/j.topol.2019.106999

61. Gulko S. P., Ivanov A. V., Shulikina M. S. et. al. Locally uniformly rotund renormings of the space of continuous functions on Fedorchuk compacts. Topology and its Applications, 271, 2020, 107211. Doi: 10.1016/j.topol.2020.107211

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### Staff

Senior Researcher, Cand. (PhD) Phys. and Math., Assistant Professor

Leading Researcher, Dr. (DSc) of Phys. and Math., Professor

Senior Researcher, Cand. (PhD) Phys. and Math.

Researcher, Cand. (PhD) of Techn.

Junior Researcher, Cand. (PhD) Phys. and Math.

### Contact information

**Official title**: Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences

**Address**: IAMR KarRC RAS

11, Pushkinskaya str.

Petrozavodsk

Karelia

185910, Russia

**Contact phone(s)**: +7 (8142) 78-12-18

**Fax**: +7 (8142) 76-33-70