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Silvestrov, Sergei, Professororcid.org/0000-0003-4554-6528
##### Publications (10 of 172) Show all publications
Anguzu, C., Engström, C. & Silvestrov, S. (2019). A comparison of graph centrality measures based on random walks and their computation. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 121-135). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>A comparison of graph centrality measures based on random walks and their computation
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 121-135Conference paper, Published paper (Refereed)
##### Abstract [en]

When working with a network it is often of interest to locate the "most important" nodes in the network. A common way to do this is using some graph centrality measures. Since what constitutes an important node is different between different networks or even applications on the same network there is a large amount of different centrality measures proposed in the literature. Due to the large amount of different centrality measures proposed in different fields, there is also a large amount very similar or equivalent centrality measures in the sense that they give the same ranks. In this paper we will focus on centrality measures based on powers of the adjacency matrix or similar matrices and those based on random walk in order to show how some of these are related and can be calculated efficiently using the same or slightly altered algorithms.

##### Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
##### Keywords
Graph, Graph centrality, Lazy walk, Adjacency matrix, Power series
##### National Category
Probability Theory and Statistics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-47085 (URN)978-618-5180-33-1 (ISBN)
##### Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
##### Funder
Sida - Swedish International Development Cooperation Agency Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
Abola, B., Biganda, P., Engström, C., Anguzu, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2019). A Variant of Updating Page Rank in Evolving Tree graphs. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 31-49). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>A Variant of Updating Page Rank in Evolving Tree graphs
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 31-49Conference paper, Published paper (Refereed)
##### Abstract [en]

PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.

##### Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
##### Keywords
PageRank, randomwalk, graph, networks.
##### National Category
Probability Theory and Statistics Computational Mathematics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-47083 (URN)978-618-5180-33-1 (ISBN)
##### Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
##### Funder
Sida - Swedish International Development Cooperation Agency Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
Silvestrov, D. & Silvestrov, S. (2019). Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1. Methodology and Computing in Applied Probability, 21(3), 945-964
Open this publication in new window or tab >>Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1
2019 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 945-964Article in journal (Refereed) Published
##### Abstract [en]

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders.

SPRINGER, 2019
##### Keywords
Markov chain, Semi-Markov process, Nonlinear perturbation, Stationary distribution, Expected hitting time, Laurent asymptotic expansion
##### National Category
Probability Theory and Statistics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-45309 (URN)10.1007/s11009-017-9605-0 (DOI)000484932800019 ()2-s2.0-85034254377 (Scopus ID)
Available from: 2019-12-10 Created: 2019-12-10 Last updated: 2019-12-14Bibliographically approved
Silvestrov, D. & Silvestrov, S. (2019). Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2. Methodology and Computing in Applied Probability, 21(3), 965-984
Open this publication in new window or tab >>Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2
2019 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 21, no 3, p. 965-984Article in journal (Refereed) Published
##### Abstract [en]

Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces.

Springer, 2019
##### Keywords
Markov chain, Semi-Markov process, Nonlinear perturbation, Stationary distribution, Expected hitting time, Laurent asymptotic expansion
##### National Category
Probability Theory and Statistics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-46334 (URN)10.1007/s11009-017-9607-y (DOI)000484932800020 ()2-s2.0-85034227153 (Scopus ID)
Available from: 2019-12-13 Created: 2019-12-13 Last updated: 2019-12-17Bibliographically approved
Ongong'A, E., Richter, J. & Silvestrov, S. (2019). Classification of 3-dimensional Hom-Lie algebras. In: Journal of Physics: Conference Series. Paper presented at 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018, 9 July 2018 through 13 July 2018. Institute of Physics Publishing, 1194(1), Article ID 012084.
Open this publication in new window or tab >>Classification of 3-dimensional Hom-Lie algebras
2019 (English)In: Journal of Physics: Conference Series, Institute of Physics Publishing , 2019, Vol. 1194, no 1, article id 012084Conference paper, Published paper (Refereed)
##### Abstract [en]

For any n-dimensional Hom-Lie algebra, a system of polynomial equations is obtained from the Hom-Jacobi identity, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. The equations are linear in the constants representing the endomorphism and non-linear in the structure constants. The space of possible endomorphisms has minimum dimension 6, and we describe the possible endomorphisms in that case. We further give families of 3-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphism constructed upto isomorphism.

##### Place, publisher, year, edition, pages
Institute of Physics Publishing, 2019
##### Keywords
Polynomials, 3-dimensional, Bilinear map, Lie Algebra, Nilpotent, Non linear, Skew-symmetric, Structure constants, System of polynomial equations, Group theory
##### National Category
Algebra and Logic
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-43500 (URN)10.1088/1742-6596/1194/1/012084 (DOI)2-s2.0-85065590036 (Scopus ID)
##### Conference
32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018, 9 July 2018 through 13 July 2018
##### Note

Conference code: 147785; Export Date: 24 May 2019; Conference Paper

Available from: 2019-06-11 Created: 2019-06-11 Last updated: 2019-12-14Bibliographically approved
Lundengård, K., Rancic, M., Javor, V. & Silvestrov, S. (2019). Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design. Facta Universitatis Series: Electronics and Energetics, 32(1), 25-49
Open this publication in new window or tab >>Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design
2019 (English)In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, Vol. 32, no 1, p. 25-49Article in journal (Refereed) Published
##### Abstract [en]

In this paper the Analytically Extended Function (AEF) with p peaks is used for representation of the electrostatic discharge (ESD) currents and lightning discharge currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. The method is illustrated using several examples of currents taken from standards and measurements.

UNIV NIS, 2019
##### Keywords
Analytically extended function, electrostatic discharge (ESD) current, lightning discharge current, D-optimal design
##### National Category
Computational Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-42695 (URN)10.2298/FUEE1901025L (DOI)000457549900002 ()
Available from: 2019-02-15 Created: 2019-02-15 Last updated: 2019-08-13Bibliographically approved
Armakan, A., Silvestrov, S. & Farhangdoost, M. R. (2019). Enveloping algebras of color hom-Lie algebras. Turkish Journal of Mathematics, 43(1), 316-339
Open this publication in new window or tab >>Enveloping algebras of color hom-Lie algebras
2019 (English)In: Turkish Journal of Mathematics, ISSN 1300-0098, E-ISSN 1303-6149, Vol. 43, no 1, p. 316-339Article in journal (Refereed) Published
##### Abstract [en]

In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincare- Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

##### Place, publisher, year, edition, pages
SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2019
##### Keywords
Color hom-Lie algebra, enveloping algebra
##### National Category
Algebra and Logic
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-42608 (URN)10.3906/mat-1808-96 (DOI)000456188000026 ()2-s2.0-85061657637 (Scopus ID)
Available from: 2019-02-07 Created: 2019-02-07 Last updated: 2019-02-28Bibliographically approved
Ongong'a, E., Richter, J. & Silvestrov, S. (2019). Hom-Lie structures on 3-dimensional skew symmetric algebras. Journal of Physics, Conference Series, 1416(1), 1-8, Article ID 012025.
Open this publication in new window or tab >>Hom-Lie structures on 3-dimensional skew symmetric algebras
2019 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1416, no 1, p. 1-8, article id 012025Article in journal (Refereed) Published
##### Abstract [en]

We describe the dimension of the space of possible linear endomorphisms that turn skew-symmetric three-dimensional algebras into Hom-Lie algebras. We find a correspondence between the rank of a matrix containing the structure constants of the bilinear product and the dimension of the space of Hom-Lie structures. Examples from classical complex Lie algebras are given to demonstrate this correspondence.

##### Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2019
##### National Category
Algebra and Logic
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-46714 (URN)10.1088/1742-6596/1416/1/012025 (DOI)2-s2.0-85078279927 (Scopus ID)
##### Funder
Sida - Swedish International Development Cooperation Agency Available from: 2020-01-15 Created: 2020-01-15 Last updated: 2020-02-20Bibliographically approved
Dutkay, D. E., Picioroaga, G. & Silvestrov, S. (2019). On Generalized Walsh Bases. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 163(1), 73-90
Open this publication in new window or tab >>On Generalized Walsh Bases
2019 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 163, no 1, p. 73-90Article in journal (Refereed) Published
##### Abstract [en]

This paper continues the study of orthonormal bases (ONB) of L2[0, 1] introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128-1139, 2014) by means of Cuntz algebra ON representations on L2[0, 1]. For N = 2, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery.

Springer, 2019
##### Keywords
Cuntz algebras, Walsh basis, Hadamard matrix, Uncertainty principle
##### National Category
Mathematics Mathematical Analysis
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-46333 (URN)10.1007/s10440-018-0214-x (DOI)000487033800004 ()2-s2.0-85053700909 (Scopus ID)
Available from: 2019-12-13 Created: 2019-12-13 Last updated: 2019-12-17Bibliographically approved
Biganda, P., Abola, B., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2019). PageRank and perturbed Markov chains. In: Christos H. Skiadas (Ed.), Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019: . Paper presented at ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference (pp. 233-247). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>PageRank and perturbed Markov chains
2019 (English)In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 233-247Conference paper, Published paper (Refereed)
##### Abstract [en]

PageRank is a widely-used hyperlink-based algorithm to estimate the relative importance of nodes in networks [11]. Since many real world networks are large sparse networks, this makes efficient calculation of PageRank complicated. Moreover, one needs to escape from dangling effects in some cases as well as slow convergence of the transition matrix. Primitivity adjustment with a damping (perturbation) parameter ε$\in$(0,ε0] (for fixed ε$\simeq$0.15) is one of the essential procedure that is known to ensure convergence of the transition matrix [24]. If ε is large, the transition matrix looses information due to shift of information to teleportation matrix [27]. In this paper, we formulate PageRank problem as the first and second order Markov chains perturbation problem. Using numerical experiments, we compare convergence rates for the two problems for different values of ε on different graph structures and investigate the difference in ranks for the two problems.

##### Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2019
##### Keywords
PageRank, Markov chains, Perturbation problem
##### National Category
Probability Theory and Statistics Computational Mathematics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-47086 (URN)978-618-5180-33-1 (ISBN)
##### Conference
ASMDA2019, 18th Applied Stochastic Models and Data Analysis International Conference
##### Funder
Sida - Swedish International Development Cooperation Agency Available from: 2020-02-20 Created: 2020-02-20 Last updated: 2020-02-24Bibliographically approved
##### Identifiers
ORCID iD: orcid.org/0000-0003-4554-6528
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