| 1. |
- Muhumuza, Asaph Keikara, et al.
(författare)
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Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomial
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 791-818
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Bokkapitel (refereegranskat)abstract
- The problem of optimising the Vandermonde determinant on a few different surfaces defined by univariate polynomials is discussed. The coordinates of the extreme points are given as roots of polynomials. Applications in curve fitting and electrostatics are also briefly discussed.
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| 2. |
- Abola, Benard, et al.
(författare)
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A Variant of Updating Page Rank in Evolving Tree graphs
- 2019
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Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 31-49
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 3. |
- Abola, Benard, et al.
(författare)
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A Variant of Updating PageRank in Evolving Tree Graphs
- 2021
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Ingår i: Applied Modeling Techniques and Data Analysis 1. - : John Wiley & Sons, Inc. Hoboken, NJ, USA. - 9781786306739 - 9781119821564 ; , s. 3-22
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Bokkapitel (refereegranskat)abstract
- A PageRank update refers to the process of computing new PageRank valuesafter a change(s) (addition or removal of links/vertices) has occurred in real-lifenetworks. The purpose of updating is to avoid re-calculating the values from scratch.To efficiently carry out the update, we consider PageRank to be the expected numberof visits to a target vertex if multiple random walks are performed, starting at eachvertex once and weighing each of these walks by a weight value. Hence, it mightbe looked at as updating a non-normalized PageRank. We focus on networks of treegraphs and propose an approach to sequentially update a scaled adjacency matrix afterevery change, as well as the levels of the vertices. In this way, we can update thePageRank of affected vertices by their corresponding levels.
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| 4. |
- Abola, Benard, et al.
(författare)
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Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks
- 2021
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Ingår i: Applied Modeling Techniques and Data Analysis 1. - Hoboken, NJ : John Wiley & Sons. - 9781786306739 - 9781119821564 ; , s. 23-55
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Bokkapitel (refereegranskat)abstract
- This chapter is devoted to studies of perturbed Markov chains, commonly used for the description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularized by adding aspecial damping matrix, multiplied by a small damping (perturbation) parameter ε. In this chapter, we present the results of detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.
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| 5. |
- Abola, Benard, et al.
(författare)
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Nonlinearly Perturbed Markov Chains and Information Networks
- 2019
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Ingår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180331 ; , s. 51-79
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Konferensbidrag (refereegranskat)abstract
- The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. In this paper, we present results of the detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.
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| 6. |
- Abola, Benard, 1971-, et al.
(författare)
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PageRank in evolving tree graphs
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 375-390
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Bokkapitel (refereegranskat)abstract
- 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.
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| 7. |
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| 8. |
- Abola, Benard, 1971-, et al.
(författare)
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Updating of PageRank in Evolving Tree graphs
- 2020
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Ingår i: Data Analysis and Applications 3. - : John Wiley & Sons. - 9781786305343 - 9781119721871 ; , s. 35-51
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Bokkapitel (refereegranskat)abstract
- Summary Updating PageRank refers to a process of computing new PageRank values after changes have occurred in a graph. The main goal of the updating is to avoid recalculating the values from scratch. This chapter focuses on updating PageRank of an evolving tree graph when a vertex and an edge are added sequentially. It describes how to maintain level structures when a cycle is created and investigates the practical and theoretical efficiency to update PageRanks for an evolving graph with many cycles. The chapter discusses the convergence of the power method applied to stochastic complement of Google matrix when a feedback vertex set is used. It also demonstrates that the partition by feedback vertex set improves asymptotic convergence of power method in updating PageRank in a network with cyclic components.
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| 9. |
- Anguzu, Collins, et al.
(författare)
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Algorithms for recalculating alpha and eigenvector centrality measures using graph partitioning techniques
- 2022
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Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer Nature. - 9783031178191 ; , s. 541-562
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Konferensbidrag (refereegranskat)abstract
- In graph theory, centrality measures are very crucial in ranking vertices of the graph in order of their importance. Alpha and eigenvector centralities are some of the highly placed centrality measures applied especially in social network analysis, disease diffusion networks and mechanical infrastructural developments. In this study we focus on recalculating alpha and eigenvector centralities using graph partitioning techniques. We write an algorithm for partitioning, sorting and efficiently computing these centralities for a graph. We then numerically demonstrate the technique on some sample small-sized networks to recalculate the two centrality measures
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| 10. |
- Biganda, Pitos, 1981-, et al.
(författare)
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Exploring The Relationship Between Ordinary PageRank, Lazy PageRank and Random Walk with Backstep PageRank for Different Graph Structures
- 2020
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Ingår i: Data Analysis and Applications 3. - : John Wiley & Sons, Ltd. - 9781786305343 - 9781119721871 ; , s. 53-73
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Bokkapitel (refereegranskat)abstract
- PageRank is an algorithm for ranking web pages. It is the first and best known webgraph-based algorithm in the Google search engine. The algorithm is simple, robust and reliable to measure the importance of web pages. This chapter presents a comparative review of three variants of PageRank, namely ordinary PageRank (introduced by Brin and Page as a measure of importance of a web page), lazy PageRank and random walk with backstep PageRank. It compares the variants in terms of their convergence and consistency in rank scores for different graph structures with reference to PageRank’s parameters, damping factor and backstep parameter. The chapter also shows that ordinary PageRank can be formulated from the other two variants by some proportionality relationships.
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