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• 1.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A Variant of Updating Page Rank in Evolving Tree graphs2019Ingår i: 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, s. 31-49Konferensbidrag (Refereegranskat)

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.

• 2.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank in evolving tree graphs2018Ingår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 375-390Kapitel i bok, del av antologi (Refereegranskat)

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.

• 3.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Evaluation of Stopping Criteria for Ranks in Solving Linear Systems2019Ingår i: Data Analysis and Applications 1: Clustering and Regression, Modeling‐estimating, Forecasting and Data Mining, Volume 2 / [ed] Christos H. Skiadas, James R. Bozeman, John Wiley & Sons, 2019, Chapter 10, s. 137-152Kapitel i bok, del av antologi (Refereegranskat)

Bioinformatics, internet search engines (web pages) and social networks are some of the examples with large and high sparsity matrices. For some of these systems, only the actual ranks of the solution vector is interesting rather than the vector itself. In this case, it is desirable that the stopping criterion reflects the error in ranks rather than the residual vector that might have a lower convergence. This chapter evaluates stopping criteria on Jacobi, successive over relaxation (SOR) and power series iterative schemes. Numerical experiments were performed and results show that Kendall's correlation coefficient gives good stopping criterion of ranks for linear system of equations. The chapter focuses on the termination criterion as means of obtaining good ranks. It outlines some studies carried out on stopping criteria in solving the linear system.

• 4.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola. Mälardalens högskola.
Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model2019Ingår i: 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, s. 81-90Konferensbidrag (Refereegranskat)

The double-mean-reverting model by Gatheral [1] is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the- money. Using the method by Pagliarani and Pascucci [6], we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

• 5.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A comparison of graph centrality measures based on random walks and their computation2019Ingår i: 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, s. 121-135Konferensbidrag (Refereegranskat)

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.

• 6.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Traditional and lazy pageranks for a line of nodes connected with complete graphs2018Ingår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 391-412Kapitel i bok, del av antologi (Refereegranskat)

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.

• 7.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank and perturbed Markov chains2019Ingår i: 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, s. 233-247Konferensbidrag (Refereegranskat)

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.

• 8.
CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. LIM&BIO UFR SMBH Universit´e Paris 13, France. CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms2013Ingår i: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885 / [ed] Niels Peek, Roque Marín Morales, Mor Peleg, Berlin Heidelberg: Springer, 2013, s. 58-67Kapitel i bok, del av antologi (Refereegranskat)

In different applications (i.e., information retrieval, filteringor analysis), it is useful to detect similar terms and to provide the possibilityto use them jointly. Clustering of terms is one of the methods whichcan be exploited for this. In our study, we propose to test three methodsdedicated to the clustering of terms (hierarchical ascendant classification,Radius and maximum), to combine them with the semantic distance algorithmsand to compare them through the results they provide whenapplied to terms from the pharmacovigilance area. The comparison indicatesthat the non disjoint clustering (Radius and maximum) outperformthe disjoint clusters by 10 to up to 20 points in all the experiments.

• 9.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank in Evolving Networks and Applications of Graphs in Natural Language Processing and Biology2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

This thesis is dedicated to the use of graph based methods applied to ranking problems on the Web-graph and applications in natural language processing and biology.

Chapter 2-4 of this thesis is about PageRank and its use in the ranking of home pages on the Internet for use in search engines. PageRank is based on the assumption that a web page should be high ranked if it is linked to by many other pages and/or by other important pages. This is modelled as the stationary distribution of a random walk on the Web-graph.

Due to the large size and quick growth of the Internet it is important to be able to calculate this ranking very efficiently. One of the main topics of this thesis is how this can be made more efficiently, mainly by considering specific types of subgraphs and how PageRank can be calculated or updated for those type of graph structures. In particular we will consider the graph partitioned into strongly connected components and how this partitioning can be utilized.

Chapter 5-7 is dedicated to graph based methods and their application to problems in Natural language processing. Specifically given a collection of texts (corpus) we will compare different clustering methods applied to Pharmacovigilance terms (5), graph based models for the identification of semantic relations between biomedical words (6) and modifications of CValue for the annotation of terms in a corpus.

In Chapter 8-9 we look at biological networks and the application of graph centrality measures for the identification of cancer genes. Specifically in (8) we give a review over different centrality measures and their application to finding cancer genes in biological networks and in (9) we look at how well the centrality of vertices in the true network is preserved in networks generated from experimental data.

• 10.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A componentwise PageRank algorithm2015Ingår i: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, s. 185-198Konferensbidrag (Refereegranskat)

In this article we will take a look at a variant of the PageRank algorithminitially used by S. Brinn and L. Page to rank homepages on the Internet. The aim ofthe article is to see how we can use the topological structure of the graph to speed upcalculations of PageRank without doing any additional approximations. We will seethat by considering a non-normalized version of PageRank it is easy to see how wecan handle dierent types of vertices or strongly connected components in the graphmore eciently. Using this we propose two PageRank algorithms, one similar to theLumping algorithm proposed by Qing et al which handles certain types of verticesfaster and last another PageRank algorithm which can handle more types of verticesas well as strongly connected components more eectively. In the last sections we willlook at some specic types of components as well as verifying the time complexity ofthe algorithm.

• 11.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
An evaluation of centrality measures used in cluster analysis2014Ingår i: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2014, s. 313-320Konferensbidrag (Refereegranskat)

Clustering of data into groups of similar objects plays an important part when analysing many types of data especially when the datasets are large as they often are in for example bioinformatics social networks and computational linguistics. Many clustering algorithms such as K-means and some types of hierarchical clustering need a number of centroids representing the 'center' of the clusters. The choice of centroids for the initial clusters often plays an important role in the quality of the clusters. Since a data point with a high centrality supposedly lies close to the 'center' of some cluster this can be used to assign centroids rather than through some other method such as picking them at random. Some work have been done to evaluate the use of centrality measures such as degree betweenness and eigenvector centrality in clustering algorithms. The aim of this article is to compare and evaluate the usefulness of a number of common centrality measures such as the above mentioned and others such as PageRank and related measures.

• 12.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Calculating PageRank in a changing network with added or removed edges2017Ingår i: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020052-1-020052-8, artikel-id 020052Konferensbidrag (Refereegranskat)

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

• 13.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Generalisation of the Damping Factor in PageRank for Weighted Networks2014Ingår i: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, s. 313-333Kapitel i bok, del av antologi (Refereegranskat)

In this article we will look at the PageRank algorithm used to rank nodes in a network. While the method was originally used by Brin and Page to rank home pages in order of “importance”, since then many similar methods have been used for other networks such as financial or P2P networks. We will work with a non-normalised version of the usual PageRank definition which we will then generalise to enable better options, such as adapting the method or allowing more types of data. We will show what kind of effects the new options creates using examples as well as giving some thoughts on what it can be used for. We will also take a brief look at how adding new connections between otherwise unconnected networks can change the ranking.

• 14.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Graph partitioning and a component wise PageRank algorithmManuskript (preprint) (Övrigt vetenskapligt)

In this article we will present a graph partitioning algorithm which partitions a graphinto two different types of components: the well known ‘strongly connected components’ as well as another type of components we call ‘connected acyclic component’. We will give analgorithm based on Tarjan’s algorithm for finding strongly connected components used to find such a partitioning. We will also show that the partitioning given by the algorithm is unique and that the underlying graph can be represented as a directed acyclic graph (similar to a pure strongly connected component partitioning). In the second part we will show how such an partitioning of a graph can be used to calculate PageRank of a graph effectively by calculating PageRank for different componentson the same ‘level’ in parallel as well as allowing for the use of different types of PageRankalgorithms for different types of components. To evaluate the method we have calculated PageRank on four large example graphs and compared it with a basic approach, as well as our algorithm in a serial as well as parallel implementation.

• 15.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Non-normalized PageRank and random walks on N-partite graphs2014Ingår i: SMTDA 2014 Proceedings / [ed] H. Skiadas (Ed), 2014, s. 193-202Konferensbidrag (Refereegranskat)

In this article we will look at a variation of the PageRank algorithmoriginally used by L. Page and S. Brin to rank home pages on the Web. Wewill look at a non-normalized variation of PageRank and show how this version ofPageRank relates to a random walk on a graph. The article has its main focus inunderstanding the behavior of the ranking depending on the structure of the graphand how the ranking changes as the graph change. More specic we will look atN-partite graphs and see that by considering a random walk on the graph we cannd explicit formulas for PageRank of the vertices in the graph. Both the case withuniform and non-uniform personalization vector are considered.

• 16.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 223-247Kapitel i bok, del av antologi (Refereegranskat)

• 17.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank, Connecting a Line of Nodes with a Complete Graph2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)

The focus of this article is the PageRank algorithm originally defined by S. Brin and L. Page as the stationary distribution of a certain random walk on a graph used to rank homepages on the Internet. We will attempt to get a better understanding of how PageRank changes after you make some changes to the graph such as adding or removing edge between otherwise disjoint subgraphs. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others and different ways to combine the two. Both the ordinary normalized version of PageRank as well as a non-normalized version of PageRank found by solving corresponding linear system will be considered. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.

• 18.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank for networks, graphs and Markov chains2017Ingår i: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, s. 61-83Artikel i tidskrift (Refereegranskat)

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.

• 19.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Using graph partitioning to calculate PageRank in a changing networkManuskript (preprint) (Övrigt vetenskapligt)

PageRank was first defined by S. Brinn and L. Page in 1998 in order to rank homepages on the Internet by ranking pages according to the stationary distribution of a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly different but equally important problem, namely how to improve the calculation of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between different strongly connected components in the network.

• 20.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Using graph partitioning to calculate PageRank in a changing network2016Ingår i: Proceedings of the 4th Stochastic Modeling Techniques and DataAnalysis International Conference with Demographics Workshop (SMTDA2016) / [ed] Christos H Skiadas, 2016, s. 155-164Konferensbidrag (Refereegranskat)

PageRank was first defined by S. Brinn and L. Page in 1998 in order to rank homepages on the Internet for use in search engines using a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly dierent but equally important problem, namely how to improve the calculation speed of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between dierent strongly connected components in the network.

• 21.
LIM&BIO (EA3969), Université Paris 13, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Université Paris 13, France. Universiteá Lille, Villeneuve d'Ascq, France. Universiteá Lille, Villeneuve d'Ascq, France. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Combining Compositionality and Pagerank for the Identification of Semantic Relations between Biomedical Words2012Ingår i: BioNLP: Proceedings of the 2012 Workshop on Biomedical Natural Language Processing, 2012, s. 109-117Konferensbidrag (Refereegranskat)

The acquisition of semantic resources and relations is an important task for several applications, such as query expansion, information retrieval and extraction, machine translation. However, their validity should also be computed and indicated, especially for automatic systems and applications. We exploit the compositionality based methods for the acquisition of synonymy relations and of indicators of these synonyms. We then apply pagerank-derived algorithm to the obtained semantic graph in order to filter out the acquired synonyms. Evaluation performed with two independent experts indicates that the quality of synonyms is systematically improved by 10 to 15% after their filtering.

• 22.
LIMSI-CNRS, Orsay, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Term Ranking Adaptation to the Domain: Genetic Algorithm-Based Optimisation of the C-Value2014Ingår i: Advances in Natural Language Processing: 9th International Conference on NLP, PolTAL 2014, Warsaw, Poland, September 17-19, 2014. Proceedings, Springer International Publishing , 2014, Vol. 8686, s. 71-83Konferensbidrag (Refereegranskat)

Term extraction methods based on linguistic rules have been proposed to help the terminology building from corpora. As they face the difficulty of identifying the relevant terms among the noun phrases extracted, statistical measures have been proposed. However, the term selection results may depend on corpus and strong assumptions reflecting specific terminological practice. We tackle this problem by proposing a parametrised C-Value which optimally considers the length and the syntactic roles of the nested terms thanks to a genetic algorithm. We compare its impact on the ranking of terms extracted from three corpora. Results show average precision increased by 9% above the frequency-based ranking and by 12% above the C-Value-based ranking.

• 23.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för ekonomi, samhälle och teknik, Framtidens energi.
Building-type classification based on measurements of energy consumption data2015Ingår i: New Trends in Stochastic Modeling and Data Analysis / [ed] Raimondo Manca, Sally McClean, Christos H SkiadasISAST 2015, ISAST: International Society for the Advancement of Science and Technology , 2015, s. 287-298Kapitel i bok, del av antologi (Refereegranskat)

In this paper we apply data-mining techniques to a classication problemon actual electricity consumption data from 350 Swedish households. Morespecically we use measurements of hourly electricity consumption during one monthand t classication models to the given data. The goal is to classify and later predict whether the building type of a specic household is an apartmentor a detached house. This classication/prediction problem becomes important ifone has a consumption time series for a household with unknown building type. Tocharacterise each household, we compute from the data some selected statistical attributesand also the load prole throughout the day for that household. The most important task here is to select a good representative set of feature variables, whichis solved by ranking the variable importance using technique of random forest. Wethen classify the data using classication tree method and linear discriminant analysis.The predictive power of the chosen classication models is plausible.

• 24.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för ekonomi, samhälle och teknik, Framtidens energi.
Investigating the added values of high frequency energy consumption data using data mining techniques2014Ingår i: AIP Conference Proceedings 1637 (2014): Volume number: 1637; Published: 10 december 2014 / [ed] Seenith Sivasundaram, AIP Publishing , 2014, s. 734-743Konferensbidrag (Refereegranskat)

In this paper we apply data-mining techniques to customer classification and clustering tasks on actual electricity consumption data from 350 Swedish households. For the classification task we classify households into different categories based on some statistical attributes of their energy consumption measurements. For the clustering task, we use average daily load diagrams to partition electricity-consuming households into distinct groups. The data contains electricity consumption measurements on each 10-minute time interval for each light source and electrical appliance. We perform the classification and clustering tasks using four variants of processeddata sets corresponding to the 10-minute total electricity consumption aggregated from all electrical sources, the hourly total consumption aggregated over all 10-minute intervals during that clock hour, the total consumption over each four-hour intervals and finally the daily total consumption. The goal is to see if there are any differences in using data sets of various frequency levels. We present the comparison results and investigate the added value of the high-frequency measurements, for example 10-minute measurements, in terms of its influence on customer clustering and classification.

• 25.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Coupling and Ergodic Theorems for Markov Chains with Damping Component2019Ingår i: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 101, s. 212-231Artikel i tidskrift (Refereegranskat)

Perturbed Markov chains are popular models for description of information networks. Insuch models, the transition matrix P0 of an information Markov chain is usually approximated bymatrix Pε = (1-ε)P0+εD, where D is a so-called damping stochastic matrix with identical rowsand all positive elements, while ε$\in$ [0; 1] is a damping (perturbation) parameter. Using procedure ofarticial regeneration for the perturbed Markov chain ηε,n with the matrix of transition probabilities Pε , and coupling methods, we get ergodic theorems, in the form of asymptotic relations for Pε,ij (n) =Pi {ηε,n =j}, as n $\rightarrow$$\infty$ and ε$\rightarrow$0, and explicit upper bounds for the rates of convergence in such theorems. In particular, the most dicult case of the model with singular perturbations, wherethe phase space of the unperturbed Markov chain η0,n split in several closed classes of communicativestates and possibly a class of transient states, is investigated.

• 26.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Using Graph Partitioning to Calculate PageRank in a Changing Network2019Ingår i: Data Analysis and Applications 2: Utilization of Results in Europe and Other Topics / [ed] Christos H. Skiadas, James R. Bozeman, London, UK: John Wiley & Sons, 2019, s. 179-191Kapitel i bok, del av antologi (Refereegranskat)

PageRank was first defined by S. Brin and L. Page in 1998 in order to rank home pages on the Internet by ranking pages according to the stationary distribution of a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly different but equally important problem, namely how to improve the calculation of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular, we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between different strongly connected components in the network.

• 27.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University.
Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University.
Loss of conservation of graph centralities in reverse-engineered transcriptional regulatory networks2015Ingår i: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International ConferenceWith 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, s. 1077-1091Konferensbidrag (Refereegranskat)

Graph centralities are often used to prioritize disease genes in transcrip-tional regulatory networks. Studies on small networks of experimentally validatedinteractions emphasize the general validity of this approach and extensions of suchndings have recently also been proposed for networks inferred from expression data.However, due to the noise inherent to expression data, it is largely unknown howwell centralities are preserved in such networks. Specically, while previous stud-ies have evaluated the performance of inference methods on synthetic expression, ithas yet to be established how the choice of method can aect individual centralitiesin the network. Here we compare two centralities between reference networks andnetworks inferred from corresponding simulated expression data using a number ofrelated methods. The results indicate that there exists only a modest conservationof centrality measures for the used inference methods. In conclusion, caution shouldbe exercised when inspecting centralities in reverse-engineered networks and furtherwork will be required to establish the use of such networks for prioritizing genes.

• 28.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden.
Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Sweden.
Graph Centrality Based Prediction of Cancer Genes2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 275-311Kapitel i bok, del av antologi (Refereegranskat)

Current cancer therapies including surgery, radiotherapy and chemotherapy are often plagued by high failure rates. Designing more targeted and personalized treatment strategies requires a detailed understanding of druggable tumor drivergenes. As a consequence, the detection of cancer driver genes has evolved to a critical scientific field integrating both high-through put experimental screens as well as computational and statistical strategies. Among such approaches, network based prediction tools have recently been accentuated and received major focus due to their potential to model various aspects of the role of cancer genes in a biological system. In this chapter, we focus on how graph centralities obtained from biological networks have been used to predict cancer genes. Specifically, we start by discussing the current problems in cancer therapy and the reasoning behind using network based cancer gene prediction, followed by an outline of biological networks, their generation and properties. Finally, we review major concepts, recent results as well as future challenges regarding the use of graph centralities in cancer gene prediction.

• 29.
Uppsala University, Sweden.
Uppsala University, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Uppsala University, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Uppsala University, Sweden.
Loss of Conservation of Graph Centralities in Reverse-engineered Transcriptional Regulatory Networks2017Ingår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, ISSN 1387-5841, Vol. 19, nr 4, s. 1095-1105Artikel i tidskrift (Refereegranskat)

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.

• 30.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Uppsala University, Sweden.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Prediction of high centrality nodes from reverse-engineered transcriptional regulator networks2016Ingår i: Proocedings of the 4th Stochastic Modeling Techniques and Data Analysis International Conference with Demographics Workshop / [ed] Christos H Skiadas, 2016, s. 517-531Konferensbidrag (Refereegranskat)

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.

• 31.
Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Prioritization of candidate cancer genes on chromosome 17q through reverse engineered transcriptional regulatory networks in medulloblastoma groups 3 and 4Manuskript (preprint) (Övrigt vetenskapligt)
• 32.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University.
Uppsala University, Sweden. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Uppsala University, Sweden.
Comparing the landcapes of common retroviral insertion sites across tumor models2017Ingår i: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020173-1-020173-9, artikel-id 020173Konferensbidrag (Refereegranskat)

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.

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