| 1. |
- Abdallah, N., et al.
(författare)
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Hilbert Functions and Jordan Type of Perazzo Artinian Algebras
- 2024
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Ingår i: Springer INdAM Series. - : Springer-Verlag Italia s.r.l.. ; , s. 59-80
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smallest possible Hilbert function, we give a description of the possible Jordan types for multiplication by any linear form.
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| 2. |
- Abelli, Björn
(författare)
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Directing and Enacting the Information System
- 2007
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Ingår i: Advances in Information Systems Development - New Methods and Practice for the Networked Society.. - Boston, MA : Springer US. - 9780387708010 ; , s. 13-23
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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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, 1971-, et al.
(författare)
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Evaluation of Stopping Criteria for Ranks in Solving Linear Systems
- 2019. - Chapter 10
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Ingår i: Data Analysis and Applications 1: Clustering and Regression, Modeling‐estimating, Forecasting and Data Mining, Volume 2. - Hoboken, NJ, USA : John Wiley & Sons. - 9781119597568 - 9781786303820 ; , s. 137-152
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Bokkapitel (refereegranskat)abstract
- 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.
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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. |
- 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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| 8. |
- Abrahamsson, Gun, 1977-, et al.
(författare)
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Ekonomiska ansvarsenheter
- 2013. - 1
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Ingår i: Perspektiv på ekonomistyrning. - Stockholm : Liber. - 9789147096947 ; , s. 14-35
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Abut, Hüseyin, et al.
(författare)
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Real-World Data Collection with UYANIK
- 2009
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Ingår i: In-Vehicle Corpus and Signal Processing for Driver Behavior. - Boston, MA : Springer. - 9780387795812 - 9780387795829 ; , s. 23-44
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 10. |
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