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Engström, Christopherorcid.org/0000-0002-1624-5147
##### Publications (10 of 21) 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
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
Abola, B., Biganda, P., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2018). PageRank in evolving tree graphs. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789 (pp. 375-390). Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789. Springer, 271
Open this publication in new window or tab >>PageRank in evolving tree graphs
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 375-390Chapter in book (Refereed)
##### Abstract [en]

In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

Springer, 2018
##### Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
##### Keywords
Breadth-first search, Forward edge, PageRank, Random walk, Tree, Forestry, Graph theory, Iterative methods, Random processes, Stochastic systems, Trees (mathematics)
##### National Category
Computational Mathematics Probability Theory and Statistics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-41833 (URN)10.1007/978-3-030-02825-1_16 (DOI)2-s2.0-85058567338 (Scopus ID)978-3-030-02824-4 (ISBN)
##### Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Biganda, P., Abola, B., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2018). Traditional and lazy pageranks for a line of nodes connected with complete graphs. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789 (pp. 391-412). Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789. Springer, 271
Open this publication in new window or tab >>Traditional and lazy pageranks for a line of nodes connected with complete graphs
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 391-412Chapter in book (Refereed)
##### Abstract [en]

PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Due to existence of diverse methods of random walk on the graph, variants of PageRank now exists. They include traditional (or normal) PageRank due to normal random walk and Lazy PageRank due to lazy random walk on a graph. In this article, we establish how the two variants of PageRank changes when complete graphs are connected to a line of nodes whose links between the nodes are in one direction. Explicit formulae for the two variants of PageRank are presented. We have noted that the ranks on a line graph are the same except their numerical values which differ. Further, we have observed that both normal random walk and lazy random walk on complete graphs spend almost the same time at each node.

Springer, 2018
##### Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009
##### Keywords
Graph, Lazy PageRank, PageRank, Random walk, Random processes, Stochastic systems, Websites, Complete graphs, Diverse methods, Explicit formula, Line graph, Numerical values, Graph theory
Mathematics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-41835 (URN)10.1007/978-3-030-02825-1_17 (DOI)2-s2.0-85058552957 (Scopus ID)978-3-030-02824-4 (ISBN)
##### Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Engström, C. & Silvestrov, S. (2017). Calculating PageRank in a changing network with added or removed edges. In: Seenith Sivasundaram (Ed.), AIP Conference Proceedings, Volume 1798: . Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016; University of La RochelleLa Rochelle; France; 4 July 2016 through 8 July 2016 (pp. 020052-1-020052-8). American Institute of Physics (AIP), 1798, Article ID 020052.
Open this publication in new window or tab >>Calculating PageRank in a changing network with added or removed edges
2017 (English)In: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020052-1-020052-8, article id 020052Conference paper, Published paper (Refereed)
##### Abstract [en]

PageRank was initially developed by S. Brinn and L. Page in 1998 to rank homepages on the Internet using the stationary distribution of a Markov chain created using the web graph. Due to the large size of the web graph and many other real worldnetworks fast methods to calculate PageRank is needed and even if the original way of calculating PageRank using a Power iterations is rather fast, many other approaches have been made to improve the speed further. In this paper we will consider the problem of recalculating PageRank of a changing network where the PageRank of a previous version of the network is known. In particular we will consider the special case of adding or removing edges to a single vertex in the graph or graph component

##### Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017
##### Keywords
PageRank, Random walk, graph
##### National Category
Computational Mathematics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-33457 (URN)10.1063/1.4972644 (DOI)000399203000052 ()2-s2.0-85013661500 (Scopus ID)9780735414648 (ISBN)
##### Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016; University of La RochelleLa Rochelle; France; 4 July 2016 through 8 July 2016
Available from: 2016-10-24 Created: 2016-10-24 Last updated: 2017-09-03Bibliographically approved
Weishaupt, H., Čančer, M., Engström, C., Silvestrov, S. & Swartling, F. J. (2017). Comparing the landcapes of common retroviral insertion sites across tumor models. In: Seenith Sivasundaram (Ed.), AIP Conference Proceedings, Volume 1798: . Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016 (pp. 020173-1-020173-9). American Institute of Physics (AIP), 1798, Article ID 020173.
Open this publication in new window or tab >>Comparing the landcapes of common retroviral insertion sites across tumor models
2017 (English)In: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020173-1-020173-9, article id 020173Conference paper, Published paper (Refereed)
##### Abstract [en]

Retroviral tagging represents an important technique, which allows researchers to screen for candidate cancer genes. The technique is based on the integration of retroviral sequences into the genome of a host organism, which might then lead to the artificial inhibition or expression of proximal genetic elements. The identification of potential cancer genes in this framework involves the detection of genomic regions (common insertion sites; CIS) which contain a number of such viral integration sites that is greater than expected by chance. During the last two decades, a number of different methods have been discussed for the identification of such loci and the respective techniques have been applied to a variety of different retroviruses and/or tumor models. We have previously established a retrovirus driven brain tumor model and reported the CISs which were found based on a Monte Carlo statistics derived detection paradigm. In this study, we consider a recently proposed alternative graph theory based method for identifying CISs and compare the resulting CIS landscape in our brain tumor dataset to those obtained when using the Monte Carlo approach. Finally, we also employ the graph-based method to compare the CIS landscape in our brain tumor model with those of other published retroviral tumor models.

##### Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017
##### National Category
Mathematics Probability Theory and Statistics Bioinformatics and Systems Biology
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-35006 (URN)10.1063/1.4972765 (DOI)000399203000172 ()2-s2.0-85013659805 (Scopus ID)9780735414648 (ISBN)
##### Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016
Available from: 2017-03-09 Created: 2017-03-09 Last updated: 2019-10-14Bibliographically approved
Weishaupt, H., Johansson, P., Engström, C., Nelander, S., Silvestrov, S. & Swartling, F. (2017). Loss of Conservation of Graph Centralities in Reverse-engineered Transcriptional Regulatory Networks. Paper presented at 15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015. Methodology and Computing in Applied Probability, 19(4), 1095-1105
Open this publication in new window or tab >>Loss of Conservation of Graph Centralities in Reverse-engineered Transcriptional Regulatory Networks
2017 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, ISSN 1387-5841, Vol. 19, no 4, p. 1095-1105Article in journal (Refereed) Published
##### Abstract [en]

Graph centralities are commonly used to identify and prioritize disease genes in transcriptional regulatory networks. Studies on small networks of experimentally validated protein-protein interactions underpin the general validity of this approach and extensions of such findings have recently been proposed for networks inferred from gene expression data. However, it is largely unknown how well gene centralities are preserved between the underlying biological interactions and the networks inferred from gene expression data. Specifically, while previous studies have evaluated the performance of inference methods on synthetic gene expression, it has not been established how the choice of inference method affects individual centralities in the network. Here, we compare two gene centrality measures between reference networks and networks inferred from corresponding simulated gene expression data, using a number of commonly used network inference methods. The results indicate that the centrality of genes is only moderately conserved for all of the inference methods used. In conclusion, caution should be exercised when inspecting centralities in reverse-engineered networks and further work will be required to establish the use of such networks for prioritizing disease genes.

Springer, 2017
##### Keywords
Transcriptional regulatory network inference,  Simulated gene expression,  Graph centrality
##### National Category
Probability Theory and Statistics Bioinformatics and Systems Biology Bioinformatics (Computational Biology)
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-36593 (URN)10.1007/s11009-017-9554-7 (DOI)000413792200006 ()2-s2.0-85016734266 (Scopus ID)
##### Conference
15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015
##### Funder
Swedish Childhood Cancer Foundation Available from: 2017-09-30 Created: 2017-10-01 Last updated: 2019-02-06Bibliographically approved
Engström, C. & Silvestrov, S. (2017). PageRank for networks, graphs and Markov chains. Theory of Probability and Mathematical Statistics, 96, 61-83
Open this publication in new window or tab >>PageRank for networks, graphs and Markov chains
2017 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, p. 61-83Article in journal (Refereed) Published
##### Abstract [en]

In this work it is described how a partitioning of a graph into components can be used to calculate PageRank in a large network and how such a partitioning can be used to re-calculate PageRank as the network changes. Although considered problem is that of calculating PageRank, it is worth to note that the same partitioning method could be used when working with Markov chains in general or solving linear systems as long as the method used for solving a single component is chosen appropriately. An algorithm for calculating PageRank using a modified partitioning of the graph into strongly connected components is described. Moreover, the paper focuses also on the calculation of PageRank in a changing graph from two different perspectives, by considering specific types of changes in the graph and calculating the difference in rank before and after certain types of edge additions or removals between components. Moreover, some common specific types of graphs for which it is possible to find analytic expressions for PageRank are considered, and in particular the complete bipartite graph and how PageRank can be calculated for such a graph. Finally, several open directions and problems are described.

##### Keywords
PageRank, random walk, Markov chain, graph, strongly connected component
##### National Category
Probability Theory and Statistics Computational Mathematics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-36589 (URN)10.1090/tpms/1034 (DOI)000412769200006 ()2-s2.0-85055703888 (Scopus ID)
Available from: 2017-09-30 Created: 2017-09-30 Last updated: 2019-06-25Bibliographically approved
Weishaupt, H., Johansson, P., Engström, C., Nelander, S., Silvestrov, S. & Swartling, F. J. (2016). Prediction of high centrality nodes from reverse-engineered transcriptional regulator networks. In: Christos H Skiadas (Ed.), Proocedings of the 4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop: . Paper presented at 4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop (pp. 517-531).
Open this publication in new window or tab >>Prediction of high centrality nodes from reverse-engineered transcriptional regulator networks
2016 (English)In: Proocedings of the 4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop / [ed] Christos H Skiadas, 2016, p. 517-531Conference paper, Published paper (Refereed)
##### Abstract [en]

The prioritization of genes based on their centrality in biological networkshas emerged as a promising technique for the prediction of phenotype related genes.A number of methods have been developed to derive one such type of network, i.e.transcriptional regulatory networks, from expression data. In order to reliably prioritizegenes from such networks, it is crucial to investigate how well the inferencemethods reconstruct the centralities that exist in the true biological system. We haverecently reported that the correlation of centrality rankings between reference andinferred networks is only modest when using an unbiased inference approach. In thisstudy we extend on these results and demonstrate that the correlation remains modestalso when using a biased inference utilizing a priori information about transcriptionfactors. However, we show further that despite this lack of a strong correlation, theinferred networks still allow a signicant prediction of genes with high centralities inthe reference networks.

##### Keywords
Transcriptional network inference, network inference, graph centrality, degree, betweenness.
##### National Category
Bioinformatics (Computational Biology) Probability Theory and Statistics
##### Research subject
Mathematics/Applied Mathematics
##### Identifiers
urn:nbn:se:mdh:diva-36583 (URN)
##### Conference
4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop
Available from: 2017-09-30 Created: 2017-09-30 Last updated: 2019-10-14Bibliographically approved
##### Identifiers
ORCID iD: orcid.org/0000-0002-1624-5147

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