| 1. |
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| 2. |
- 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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| 3. |
- Abola, Benard, et al.
(författare)
-
Nonlinearly Perturbed Markov Chains and Information Networks
- 2019
-
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
-
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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| 4. |
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| 5. |
- Abola, Benard
(författare)
-
Perturbed Markov Chains with Damping Component and Information Networks
- 2020
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis brings together three thematic topics, PageRank of evolving tree graphs, stopping criteria for ranks and perturbed Markov chains with damping component. The commonality in these topics is their focus on ranking problems in information networks. In the fields of science and engineering, information networks are interesting from both practical and theoretical perspectives. The fascinating property of networks is their applicability in analysing broad spectrum of problems and well established mathematical objects. One of the most common algorithms in networks' analysis is PageRank. It was developed for web pages’ ranking and now serves as a tool for identifying important vertices as well as studying characteristics of real-world systems in several areas of applications. Despite numerous successes of the algorithm in real life, the analysis of information networks is still challenging. Specifically, when the system experiences changes in vertices /edges or it is not strongly connected or when a damping stochastic matrix and a damping factor are added to an information matrix. For these reasons, extending existing or developing methods to understand such complex networks is necessary.Chapter 2 of this thesis focuses on information networks with no bidirectional interaction. They are commonly encountered in ecological systems, number theory and security systems. We consider certain specific changes in a network and describe how the corresponding information matrix can be updated as well as PageRank scores. Specifically, we consider the graph partitioned into levels of vertices and describe how PageRank is updated as the network evolves.In Chapter 3, we review different stopping criteria used in solving a linear system of equations and investigate each stopping criterion against some classical iterative methods. Also, we explore whether clustering algorithms may be used as stopping criteria.Chapter 4 focuses on perturbed Markov chains commonly used for the description of information networks. In such models, the transition matrix of an information Markov chain is usually regularised and approximated by a stochastic (Google type) matrix. Stationary distribution of the stochastic matrix is equivalent to PageRank, which is very important for ranking of vertices in information networks. Determining stationary probabilities and related characteristics of singularly perturbed Markov chains is complicated; leave alone the choice of regularisation parameter. We use the procedure of artificial regeneration for the perturbed Markov chain with the matrix of transition probabilities and coupling methods. We obtain ergodic theorems, in the form of asymptotic relations. We also derive explicit upper bounds for the rate of convergence in ergodic relations. Finally, we illustrate these results with numerical examples.
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| 6. |
- Seleka Biganda, Pitos, 1981-
(författare)
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Analytical and Iterative Methods of Computing PageRank of Networks
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is about variants of PageRank, methods of PageRank computation and perturbation analysis of a PageRank vector as a stationary distribution of a kind of perturbed Markov chain model. Chapter 2 of this thesis gives closed form formulae for ordinary and lazy PageRanks for some specific simple line graphs. Different cases of changes made to the simple line graph are considered and for each case, a corresponding formula for each of the two variants of PageRank is provided.Chapter 3 is dedicated to the exploration of relationships that exist between three known variants of PageRank: ordinary PageRank, lazy PageRank and random walk with backstep PageRank in terms of their convergence and consistency in rank scores for different graph structures with reference to PageRank parameters, the damping factor c and backstep parameter β. In Chapter 4, we discuss numerical methods used in solving the PageRank problem as a linear system and evaluate some stopping criteria that can be employed in such methods. Finally, in Chapter 5, we address the PageRank problem as a first order perturbed Markov chain problem and study the perturbation analysis for stationary distributions of Markov chains with damping component. We illustrate our results on asymptotic perturbation analysis by using different computational examples.
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| 7. |
- Silvestrov, D., et al.
(författare)
-
Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 37-66
-
Bokkapitel (refereegranskat)abstract
- In Chapter 3, we introduce a model of perturbed semi-Markov processes, formulate basic perturbation conditions, describe a one-step time-space screening procedure of phase space reduction for perturbed semi-Markov processes, introduce hitting times, and prove an invariant property of them with respect to the procedure of phase space reduction. We, also, present algorithms for re-calculation of asymptotic expansions for transition characteristics of nonlinearly perturbed semi-Markov processes with reduced phase spaces and algorithms for sequential reduction of phase space for semi-Markov processes and construction of Laurent asymptotic expansions, without and with explicit upper bounds for remainders, for power moment of hitting times. © 2017, The Author(s).
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| 8. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Asymptotic expansions for stationary and quasi-stationary distributions of perturbed semi-Markov processes
- 2016
-
Ingår i: ICNPAA 2016 World Congress. - New York : American Institute of Physics (AIP). - 0094-243X. - 9780735414648 ; , s. 1-9
-
Konferensbidrag (refereegranskat)abstract
- New algorithms for computing asymptotic expansions, without and with explicit upper bounds for remainders, for stationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to models with an arbitrary asymptotic communicative structure of phase spaces.
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| 9. |
- Silvestrov, D., et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 67-79
-
Bokkapitel (refereegranskat)abstract
- In Chapter 4, new algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on the technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders. © 2017, The Author(s).
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| 10. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1
- 2019
-
Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; 21:3, s. 945-964
-
Tidskriftsartikel (refereegranskat)abstract
- New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders.
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| 11. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2
- 2019
-
Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; 21:3, s. 965-984
-
Tidskriftsartikel (refereegranskat)abstract
- Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of sequen- tial phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces.
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| 12. |
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| 13. |
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| 14. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
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Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
- 2016
-
Ingår i: Engineering Mathematics II. - Cham : Springer. - 9783319421049 - 9783319421056 ; , s. 151-222
-
Bokkapitel (refereegranskat)abstract
- New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.
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| 15. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Coupling and Ergodic Theorems for Markov Chains with Damping Component
- 2019
-
Ingår i: Theory of Probability and Mathematical Statistics. - 0094-9000. ; 101, s. 212-231
-
Tidskriftsartikel (refereegranskat)abstract
- 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 [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 and ε0, 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.
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| 16. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Coupling and ergodic theorems for Markov chains with damping component
- 2020
-
Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society. - 0094-9000 .- 1547-7363. ; 101, s. 243-264
-
Tidskriftsartikel (refereegranskat)abstract
- Perturbed Markov chains are popular models for description of information networks. In such models, the transition matrix P0 of an information Markov chain is usually approximated by matrix Pε = (1 − ε)P0 + εD, where D is a so-called damping stochastic matrix with identical rows and all positive elements, while ε ∈ [0, 1] is a damping (perturbation) parameter. Using procedure of artificial 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 → ∞ and ε → 0, and explicit upper bounds for the rates of convergence in such theorems. In particular, the most difficult case of the model with singular perturbations, where the phase space of the unperturbed Markov chain η0,n split in several closed classes of communicative states and possibly a class of transient states, is investigated.
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| 17. |
- Silvestrov, D., et al.
(författare)
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Examples and Survey of Applied Perturbed Stochastic Models
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 107-121
-
Bokkapitel (refereegranskat)abstract
- In Chapter 6, we present a background for construction of numerical examples for asymptotic results presented in Chapters 2 – 5, some numerical examples as well as a summary survey of applied perturbed stochastic systems. © 2017, The Author(s).
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| 18. |
- Silvestrov, D., et al.
(författare)
-
Introduction
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 1-15
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This book is devoted to the study of asymptotic expansions for moment of hitting times, stationary and conditional quasi-stationary distributions, and other functionals, for nonlinearly perturbed semi-Markov processes. The introduction intends to present in informal form the main problems, methods, and algorithms that constitute the content of the book. © 2017, The Author(s).
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| 19. |
- Silvestrov, D., et al.
(författare)
-
Laurent Asymptotic Expansions
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 17-35
-
Bokkapitel (refereegranskat)abstract
- In Chapter 2, we present operational rules for Laurent asymptotic expansions given in two forms, with remainders given in the standard form o(⋅ ) and with explicit power-type upper bounds for remainders. In the former case, such rules should be possibly considered as generally known, while, in the latter case, asymptotic expansions have some novelty aspects. © 2017, The Author(s).
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| 20. |
- Silvestrov, D., et al.
(författare)
-
Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 81-106
-
Bokkapitel (refereegranskat)abstract
- In Chapter 5, we present asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov processes, which play an important role in many applications. In this case, the corresponding expansions can be given in a more explicit form. © 2017, The Author(s).
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| 21. |
- Silvestrov, Dimitrii, 1947-, et al.
(författare)
-
Nonlinearly Perturbed Semi-Markov Processes
- 2017
-
Bok (refereegranskat)abstract
- The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.
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| 22. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Perturbation analysis for stationary distributions of markov chains with damping component
- 2020
-
Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 903-933
-
Bokkapitel (refereegranskat)abstract
- Perturbed Markov chains are popular models for description of information networks. In such models, the transition matrix P0 of an information Markov chain is usually approximated by matrix Pε = (1 - ε) P0 + ε D, where D is a so-called damping stochastic matrix with identical rows and all positive elements, while ε is a damping (perturbation) parameter. We perform a detailed perturbation analysis for stationary distributions of such Markov chains, in particular get effective explicit series representations for the corresponding stationary distributions πε, upper bounds for the deviation |πε- π0 |, and asymptotic expansions for πε with respect to the perturbation parameter ε.
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| 23. |
- Silvestrov, Dmitrii, 1947-, et al.
(författare)
-
Perturbed Markov Chains with Damping Component
- 2021
-
Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1387-5841 .- 1573-7713. ; :1, s. 369-397
-
Tidskriftsartikel (refereegranskat)abstract
- The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter epsilon. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems forn-step transition probabilities, as well as ergodic theorems in triangular array mode.
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| 24. |
- Silvestrov, D., et al.
(författare)
-
Preface
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - : Springer Nature. - 9783319609881 ; , s. v-vii
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 25. |
- Silvestrov, Dmitrii S., et al.
(författare)
-
Asymptotic Expansions for Power-Exponential Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
- 2017
-
Ingår i: Theory of Probability and Mathematical Statistics. - Stockholm : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 97, s. 171-187
-
Tidskriftsartikel (refereegranskat)abstract
- New algorithms for construction of asymptotic expansions for exponential and power-exponential moments of hitting times for nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and the systematical use of operational calculus for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of a phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.
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| 26. |
- Silvestrov, Dmitrii S., et al.
(författare)
-
Asymptotic expansions for stationary distributions of perturbed semi-markov processes
- 2016
-
Ingår i: Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016. - New York, USA : IEEE Computer Society. - 9781467399418 ; , s. 41-46
-
Konferensbidrag (refereegranskat)abstract
- New algorithms for computing asymptotic expansionsfor power moments of hitting times and stationary andquasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are basedon special techniques of sequential phase space reduction, which can be applied to models with an arbitrary asymptoticcommunicative structure of phase spaces.
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| 27. |
- Abola, Benard, et al.
(författare)
-
A Variant of Updating Page Rank in Evolving Tree graphs
- 2019
-
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
-
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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| 28. |
- Abola, Benard, et al.
(författare)
-
A Variant of Updating PageRank in Evolving Tree Graphs
- 2021
-
Ingår i: Applied Modeling Techniques and Data Analysis 1. - : John Wiley & Sons, Inc. Hoboken, NJ, USA. - 9781786306739 - 9781119821564 ; , s. 3-22
-
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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| 29. |
- Abola, Benard, 1971-, et al.
(författare)
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Evaluation of Stopping Criteria for Ranks in Solving Linear Systems
- 2019. - Chapter 10
-
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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| 30. |
- Abola, Benard, 1971-, et al.
(författare)
-
PageRank in evolving tree graphs
- 2018
-
Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 ; , s. 375-390
-
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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| 31. |
- Abola, Benard, 1971-, et al.
(författare)
-
Updating of PageRank in Evolving Tree graphs
- 2020
-
Ingår i: Data Analysis and Applications 3. - : John Wiley & Sons. - 9781786305343 - 9781119721871 ; , s. 35-51
-
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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| 32. |
- Abramov, Viktor, et al.
(författare)
-
3-Hom-Lie Algebras Based on σ-Derivation and Involution
- 2020
-
Ingår i: Advances in Applied Clifford Algebras. - : Springer. - 0188-7009 .- 1661-4909. ; 30:3
-
Tidskriftsartikel (refereegranskat)abstract
- We show that, having a Hom-Lie algebra and an element of its dual vector space that satisfies certain conditions, one can construct a ternary totally skew-symmetric bracket and prove that this ternary bracket satisfies the Hom-Filippov-Jacobi identity, i.e. this ternary bracket determines the structure of 3-Hom-Lie algebra on the vector space of a Hom-Lie algebra. Then we apply this construction to two Hom-Lie algebras constructed on an associative, commutative algebra using σ-derivation and involution, and we obtain two 3-Hom-Lie algebras.
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| 33. |
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| 34. |
- Al-Shujary, Ahmed, 1980-
(författare)
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Kähler-Poisson Algebras
- 2020
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we introduce Kähler-Poisson algebras and study their basic properties. The motivation comes from differential geometry, where one can show that the Riemannian geometry of an almost Kähler manifold can be formulated in terms of the Poisson algebra of smooth functions on the manifold. It turns out that one can identify an algebraic condition in the Poisson algebra (together with a metric) implying that most geometric objects can be given a purely algebraic formulation. This leads to the definition of a Kähler-Poisson algebra, which consists of a Poisson algebra and a metric fulfilling an algebraic condition. We show that every Kähler- Poisson algebra admits a unique Levi-Civita connection on its module of inner derivations and, furthermore, that the corresponding curvature operator has all the classical symmetries. Moreover, we present a construction procedure which allows one to associate a Kähler-Poisson algebra to a large class of Poisson algebras. From a more algebraic perspective, we introduce basic notions, such as morphisms and subalgebras, as well as direct sums and tensor products. Finally, we initiate a study of the moduli space of Kähler-Poisson algebras; i.e for a given Poisson algebra, one considers classes of metrics giving rise to non-isomorphic Kähler-Poisson algebras. As it turns out, even the simple case of a Poisson algebra generated by two variables gives rise to a nontrivial classification problem.
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| 35. |
- Albuhayri, Mohammed, et al.
(författare)
-
An Improved Asymptotics of Implied Volatility in the Gatheral Model
- 2022
-
Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer Nature. - 9783031178191 - 9783031178207 ; , s. 3-13
-
Konferensbidrag (refereegranskat)abstract
- We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference between the logarithmic security price and the logarithmic strike price.
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| 36. |
- Albuhayri, Mohammed, et al.
(författare)
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Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model
- 2019
-
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. 81-90
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 37. |
- Albuhayri, Mohammed, et al.
(författare)
-
Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model
- 2021
-
Ingår i: Applied Modeling Techniques and Data Analysis 2. - Hoboken, NJ, USA : John Wiley & Sons. - 9781786306746 ; , s. 27-38
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Bokkapitel (refereegranskat)abstract
- The double-mean-reverting model by Gatheral 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, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.
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| 38. |
- Albuhayri, Mohammed
(författare)
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Asymptotics of implied volatility in the Gatheral double stochastic volatility model
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider a market model of financial engineering with three factors represented by three correlated Brownian motions. The volatility of the risky asset in this model is the sum of two stochastic volatilities. The dynamic of each volatility is governed by a mean-reverting process. The first stochastic volatility of mean-reversion process reverts to the second volatility at a fast rate, while the second volatility moves slowly to a constant level over time with the state of the economy.The double mean-reverting model by Gatheral (2008) is motivated by empirical dynamics of the variance of the stock price. This model can be consistently calibrated to both the SPX options and the VIX options. However due to the lack of an explicit formula for both the European option price and the implied volatility, the calibration is usually done using time consuming methods like Monte Carlo simulation or the finite difference method.To solve the above issue, we use the method of asymptotic expansion developed by Pagliarani and Pascucci (2017). In paper A, we study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. We calculate explicitly the asymptotic expansions of implied volatility within a parabolic region up the second order. In paper B we improve the results obtain in paper A by calculating the asymptotic expansion of implied volatility under the Gatheral model up to order three. In paper C, we perform numerical studies on the asymptotic expansion up to the second order. The Monte-Carlo simulation is used as the benchmark value to check the accuracy of the expansions. We also proposed a partial calibration procedure using the expansions. The calibration procedure is implemented on real market data of daily implied volatility surfaces for an underlying market index and an underlying equity stock for periods both before and during the COVID-19 crisis. Finally, in paper D we check the performance of the third order expansion and compare it with the previous results.
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| 39. |
- Albuhayri, Mohammed, et al.
(författare)
-
Numerical Studies of the Implied Volatility Expansions up to Third Order under the Gatheral Model
- 2022
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The Gatheral double stochastic volatility model is a three-factor model with mean-reverting stochastic volatility that reverts to a stochastic long-run mean. Our previous paper investigated the performance of the first and second-order implied volatilities expansions under this model. Moreover, a simple partial calibration method has been proposed. This paper reviews and extends previous results to the third-order implied volatility expansions under the same model. Using Monte-Carlo simulation as the benchmark method, extensive numerical studies are conducted to investigate the accuracy and properties of the third-order expansion.
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| 40. |
- Alekseev, Aleksandr, et al.
(författare)
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On (σ,τ)-Derivations of Group Algebra as Category Characters
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 81-99
-
Konferensbidrag (refereegranskat)abstract
- For the space of (σ,τ)-derivations of the group algebra C[G] of a discrete countable group G, the decomposition theorem for the space of (σ,τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ,τ)-derivations are inner are obtained. Considered in details are cases of (σ,τ)-nilpotent groups and (σ,τ)-FC groups.
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| 41. |
-
Algebra, Geometry and Mathematical Physics : AGMP, Mulhouse, France, October 2011
- 2014
-
Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more.The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.
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| 42. |
- Ameur, Yacin, et al.
(författare)
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Interpolation classes and matrix monotone functions
- 2007
-
Ingår i: Journal of operator theory. - 0379-4024 .- 1841-7744. ; 57:2, s. 409-427
-
Tidskriftsartikel (refereegranskat)abstract
- An interpolation function of order n is a positive function -/+ on (0, infinity) such that vertical bar vertical bar -/+ (A)(1/2) T -/+ (A)-(1/2) vertical bar vertical bar <= max(vertical bar vertical bar T vertical bar vertical bar, vertical bar A(1/2)TA(-1/2) vertical bar vertical bar) for all n x ii matrices T and A such that A is positive definite. By a theorem of Donoghue, the class C-n of interpolation functions of order n coincides with the class of functions -/+ such that for each n-subset S = {lambda i}(n)(i=1)of (0,infinity) there exists a positive Pick function h on (0, co) interpolating -/+ at S. This note comprises a study of the classes C-n and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*-algebras.
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| 43. |
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| 44. |
- Andersson, Fredrik K., et al.
(författare)
-
The mathematics of internet search engines
- 2008
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
-
Tidskriftsartikel (refereegranskat)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 45. |
- Anguzu, Collins, et al.
(författare)
-
A Comparison of Graph Centrality Measures Based on Lazy Random Walks
- 2021
-
Ingår i: Applied Modeling Techniquesand Data Analysis 1. - : John Wiley & Sons, Inc. Hoboken, NJ, USA. - 9781786306739 ; , s. 91-111
-
Bokkapitel (refereegranskat)abstract
- 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 by using some graph centralitymeasures. Since what constitutes as an important node varies from one network toanother, or even in applications on the same network, there is a large number ofdifferent centrality measures proposed in the literature. Due to the large amount ofdifferent centrality measures proposed in different fields, there is also a large amountof very similar or equivalent centrality measures (in the sense that they give the sameranks). In this chapter, we focus on the centrality measures based on powers of theadjacency matrix and those based on random walk. In this case, we show how someof these centrality measures are related, as well as their lazy variants.We will performsome experiments to demonstrate the similarities between the centrality measures.
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| 46. |
- Anguzu, Collins, et al.
(författare)
-
A comparison of graph centrality measures based on random walks and their computation
- 2019
-
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. 121-135
-
Konferensbidrag (refereegranskat)abstract
- 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.
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| 47. |
- Anguzu, Collins, et al.
(författare)
-
Algorithms for recalculating alpha and eigenvector centrality measures using graph partitioning techniques
- 2022
-
Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer Nature. - 9783031178191 ; , s. 541-562
-
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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| 48. |
- Arfa, Anja, et al.
(författare)
-
Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 33-60
-
Konferensbidrag (refereegranskat)abstract
- Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.
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| 49. |
- Armakan, Abdoreza, et al.
(författare)
-
Color Hom-Lie Algebras, Color Hom-Leibniz Algebras and Color Omni-Hom-Lie Algebras
- 2023
-
Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 61-79
-
Konferensbidrag (refereegranskat)abstract
- In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Lie algebra structures on a linear space is examined and it is shown that the underlying algebraic structure of the color omni-hom-Lie algebra is a color hom-Leibniz a algebra.
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| 50. |
- Armakan, Abdoreza, et al.
(författare)
-
Enveloping algebras of certain types of color hom-Lie algebras
- 2020
-
Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 - 9783030418502 ; , s. 257-284
-
Bokkapitel (refereegranskat)abstract
- In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free hom-associative color algebra on a hom-module is described for a certain type of color hom-Lie algebras and is applied to obtain the universal enveloping algebra of those hom-Lie color algebras. Finally, this construction is applied to obtain the extension of the well-known Poincaré–Birkhoff–Witt theorem for Lie algebras to the enveloping algebra of the certain types of color hom-Lie algebra such that some power of the twisting map is the identity map.
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