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• 1.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A Variant of Updating Page Rank in Evolving Tree graphs2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 31-49Conference paper (Refereed)

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.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
PageRank in evolving tree graphs2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 375-390Chapter in book (Refereed)

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.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Evaluation of Stopping Criteria for Ranks in Solving Linear Systems2019In: 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, p. 137-152Chapter in book (Refereed)

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.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, Makerere University, Kampala, Uganda. Department of Mathematics, Makerere University, Kampala, Uganda.
Nonlinearly  Perturbed Markov Chains  and  Information Networks2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 51-79Conference paper (Refereed)

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.

• 5. Abramov, V.
Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Stolin, A.Chalmers University of Techology.
Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Conference proceedings (editor) (Refereed)
• 6. Abramov, Viktor
Mälardalen University, School of Education, Culture and Communication.
Preface [Special issue devoted to the 4th Baltic-Nordic Workshop “Algebra, Geometry and Mathematical Physics”]2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 4Article in journal (Refereed)
• 7.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University. Mälardalen University.
Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 81-90Conference paper (Refereed)

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.

• 8.
Faculté des Sciences, Université de Sfax, Tunisia .
Université de Haute Alsace, France . Lund University.
Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras2010In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 43, no 26, p. 265204-Article in journal (Refereed)

In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

• 9.
WorldLight.com AB, Sweden.
Mälardalen University, School of Education, Culture and Communication.
The mathematics of internet search engines2008In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 104, no 2, p. 211-242Article in journal (Refereed)

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.

• 10.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A comparison of graph centrality measures based on random walks and their computation2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 121-135Conference paper (Refereed)

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.

• 11.
Shiraz Univ, Coll Sci, Dept Math, Shiraz, Iran..
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Shiraz Univ, Coll Sci, Dept Math, Shiraz, Iran..
Enveloping algebras of color hom-Lie algebras2019In: Turkish Journal of Mathematics, ISSN 1300-0098, E-ISSN 1303-6149, Vol. 43, no 1, p. 316-339Article in journal (Refereed)

In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincare- Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.

• 12.
Université de Haute-Alsace, Mulhouse, France. Université de Haute-Alsace, Mulhouse, France . Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras2014In: Springer Proceedings in Mathematics and Statistics, Berlin, Heidelberg: Springer, 2014, Vol. 85, p. 123-144Conference paper (Refereed)

The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced 3-Lie algebras

• 13.
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France. Mälardalen University, School of Education, Culture and Communication.
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)

As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

• 14.
Max Planck Institute for Gravitational Physics (AEI), Germany.
Université de Haute Alsace, France . Lund University, Sweden.
Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4, p. 043515-11Article in journal (Refereed)

The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction.

• 15.
Albert Einstein Institute, Golm, Germany.
Lund University.
Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems: July 21-25 2008, Lorentz Center, Leiden, The Netherlands, satellite conference of the fifth European Congress of Mathematics, Amer. Math. Soc. , 2009, Vol. 503, p. 1-25Chapter in book (Refereed)
• 16.
Universit́e de Haute Alsace, France .
Universit́e de Haute Alsace, France . Lund University.
Generalization of n-ary Nambu algebras and beyond2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, p. Article number 083501-Article in journal (Refereed)

The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

• 17.
Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach2018In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper (Refereed)

The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.

• 18.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Traditional and lazy pageranks for a line of nodes connected with complete graphs2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 391-412Chapter in book (Refereed)

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.

• 19.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
PageRank and perturbed Markov chains2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 233-247Conference paper (Refereed)

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.

• 20. Boulougari, Andromachi
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Application of a power-exponential function-based model to mortality rates forecasting2019In: Communications in Statistics: Case Studies, Data Analysis and Applications, E-ISSN 2373-7484, Vol. 5, no 1, p. 3-10Article in journal (Refereed)

There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.

• 21.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Hom-associative Ore extensions2018In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, no 1, article id 012006Article in journal (Refereed)

We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

• 22.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Hom-associative Ore extensions and weak unitalizations2018In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 24, p. 174-194Article in journal (Refereed)

We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sucient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

• 23.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility2015In: 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, p. 53-66Conference paper (Refereed)

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such model can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. [3] presented a model where the underlying priceis governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi [2] transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American options prices. In a previous research of the authors (Canhanga et al. [1]), a particular case of Chiarella and Ziveyi [2] model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi [2].

1. Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. Perturbation methods for pricing European options in a model with two stochastic volatilities. 3rd SMTDA Conference Proceedings. 11-14 June 2014, Lisbon Porturgal, C. H. Skiadas (Ed.) 489-500 (2014).

2. Chiarella, C, and Ziveyi, J. American option pricing under two stochastic volatility processes. J. Appl. Math. Comput. 224:283–310 (2013).

3. Christoffersen, P.; Heston, S.; Jacobs, K. The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well. Manage. Sci. 55 (2) 1914-1932; (2009).

• 24.
DMI, Eduardo Mondlane University, Maputo, Mozambique.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility2017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1075-1087Article in journal (Refereed)

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).

• 25.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Pricing European Options Under Stochastic Volatilities Models2016In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 315-338Chapter in book (Refereed)

Interested by the volatility behavior, different models have been developed for option pricing. Starting from constant volatility model which did not succeed on capturing the effects of volatility smiles and skews; stochastic volatility models appearas a response to the weakness of the constant volatility models. Constant elasticity of volatility, Heston, Hull and White, Schöbel-Zhu, Schöbel-Zhu-Hull-Whiteand many others are examples of models where the volatility is itself a random process. Along the chapter we deal with this class of models and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. Christoffersen et al. in [4] proposed a model with two-factor stochastic volatilities where the correlation between the underlying asset price and the volatilities varies randomly. In the last section of this chapter we introduce a variation of Chiarella and Ziveyi model, which is a subclass of the model presented in [4] and we use the first order asymptotic expansion methods to determine the price of European options.

• 26.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 6, p. 1328-1349Article in journal (Refereed)

The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.

• 27.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Perturbation Methods for Pricing European Options in a Model with Two Stochastic Volatilities2015In: New Trends in Stochastic Modelling and Data Analysis / [ed] Raimondo Manca, Sally McClean, Christos H Skiadas, ISAST , 2015, p. 199-210Chapter in book (Refereed)

Financial models have to reflect the characteristics of markets in which they are developed to be able to predict the future behavior of a financial system. The nature of most trading environments is characterized by uncertainties which are expressed in mathematical models in terms of volatilities. In contrast to the classical Black-Scholes model with constant volatility, our model includes one fast-changing and another slow-changing stochastic volatilities of mean-reversion type. The different changing frequencies of volatilities can be interpreted as the effects of weekends and effects of seasons of the year (summer and winter) on the asset price.

We perform explicitly the transition from the real-world to the risk-neutral probability measure by introducing market prices of risk and applying Girsanov Theorem. To solve the boundary value problem for the partial differential equation that corresponds to the case of a European option, we perform both regular and singular multiscale expansions in fractional powers of the speed of mean-reversion factors. We then construct an approximate solution given by the two-dimensional Black-Scholes model plus some terms that expand the results obtained by Black and Scholes.

• 28.
Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Second Order Asymptotic Expansion for Pricing European Options in a Model with Two Stochastic Volatilities2015In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop, 30 June – 4 July 2015 University of Piraeus, Greece / [ed] C. H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 37-52Conference paper (Refereed)

Asset price processes with stochastic volatilities have been actively used by researchers in financial mathematics for valuing derivative securities. This type of models allows characterizing the uncertainties in the asset price process in financial markets. In a recent paper Chiarella and Ziveyi analyzed a model with two stochastic volatilities of mean reversion type with one variable changing fast and the other changing slowly. They used method of characteristics to solve the obtained partial differential equation and determine the price of an American option. Fouque et al presented also a similar model in which the volatility of the underlying asset is governed by two diffusion processes which are not of mean reversion type. They developed a first-order asymptotic expansion for the European option price via a perturbation method.

In this chapter we consider the model given in Chiarella and Ziveyi. Instead of pricing American options we price European options by generalizing the techniques presented in Fouque et al to a more complex model with mean reverting stochastic volatility factors. We analyse both regular and singular perturbations to obtain an asymptotic expansion up to second order which can serve as an approximation for the price of non-path-dependent European options. Similar work is done in authors earlier work Canhanga et al where a first-order asymptotic expansion has been developed. Involving the second order terms has the advantage of capturing more accurately the effects of volatility smile and skew on the option pricing. Analytical approximation formula for pricing European Option is presented.

• 29.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility2017In: INCPAA 2016 Proceedings: 11th International Conference on Mathematical Problems in Engineering, Aerospace, and Sciences, ICNPAA 2016, La Rochelle, France, 4 - 8 July 2016. / [ed] S. Sivasundaram, 2017, Vol. 1798, p. 020035-1-020035-10, article id 020035Conference paper (Refereed)

After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes model was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced non-constant volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multi-factor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented an approximate formula for pricing American option.The huge calculation involved in the Chiarella and Ziveyi approach motivated us to investigate another approach to compute European option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present chapter we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.

• 30.
Norwegian University of Science and Technology.
Eilers, SorenUniversity of Copenhagen.Restorff, GunnarUniversity of the Faroe Islands.Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.
Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 20122013Collection (editor) (Refereed)
• 31.
University of Southern Denmark.
Lund University.
On the Exel crossed product of topological covering maps2009In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, ISSN 0167-8019, Vol. 108, no 3, p. 573-583Article in journal (Refereed)

For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C *-algebras C(X)⋊ α,ℒℕintroduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems.

• 32.
Norwegian University of Science and Technology (NTNU), Trondheim, Norway .
Mälardalen University, School of Education, Culture and Communication.
On the K-theory of the C*-algebra associated with a one-sided shift space2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 4, p. 272-279Article in journal (Refereed)

One-sided shift spaces are a special kind of non-invertible topological dynamical system with which one can associate a C*-algebra. We show how to construct the C*-algebra associated with a one-sided shift space as the Cuntz-Pimsner C*-algebra of a C*-correspondence and use this to compute its K-theory.

• 33.
University of Missouri.
The University of Iowa. University of Oklahoma. Technische Universität Berlin. Texas A&M University. Institute for Biomathematics and Biometry, Helmholtz Zentrum München. Lousiana State University. University of Colorado at Boulder. Mälardalen University, School of Education, Culture and Communication. University of Central Florida.
Preface2012In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 33, no 7-9, p. 705-707Article in journal (Other academic)
• 34.
Leiden University.
Silvestrov, SergeiMälardalen University, School of Education, Culture and Communication.Skau, ChristianNorwegian University of Science and Technology (NTNU), Norway.Tomiyama, JunUniversity of Tokyo, Japan.
Operator structures and dynamical systems2009Conference proceedings (editor) (Refereed)
• 35.
Leiden University, Netherlands .
Lund University. Lund University.
Algebraic curves for commuting elements in the \$q\$-deformed Heisenberg algebra2009In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 321, no 4, p. 1239-1255Article in journal (Refereed)

In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.

• 36.
CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. 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 Terms2013In: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885 / [ed] Niels Peek, Roque Marín Morales, Mor Peleg, Berlin Heidelberg: Springer, 2013, p. 58-67Chapter in book (Refereed)

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.

• 37. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication.
Decomposition of wavelet representations and Martin boundaries2012In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, no 3, p. 1043-1061Article in journal (Refereed)

We study a decomposition problem for a class of unitary representations associated with wavelet analysis, wavelet representations, but our framework is wider and has applications to multi-scale expansions arising in dynamical systems theory for non-invertible endomorphisms. Our main results offer a direct integral decomposition for the general wavelet representation, and we solve a question posed by Judith Packer. This entails a direct integral decomposition of the general wavelet representation. We further give a detailed analysis of the measures contributing to the decomposition into irreducible representations. We prove results for associated Martin boundaries, relevant for the understanding of wavelet filters and induced random walks, as well as classes of harmonic functions. Published by Elsevier Inc.

• 38.
University of Central Florida, US.
Texas A and M University, United sTATES. Lund University.
Irreducible wavelet representations and ergodic automorphisms on solenoids2011In: Operators and Matrices, ISSN 1846-3886, E-ISSN 1848-9974, Vol. 5, no 2, p. 201-219Article in journal (Refereed)

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.

• 39. Dutkay, Dorin Ervin
IRREDUCIBLE WAVELET REPRESENTATIONS AND ERGODIC AUTOMORPHISMS ON SOLENOIDS2011In: Operators and Matrices, ISSN 1846-3886, E-ISSN 1848-9974, Vol. 5, no 2, p. 201-219Article in journal (Refereed)

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, introduced in [13], and we present several equivalent formulations of the problem.

• 40.
Univ Cent Florida, Dept Math, 4000 Cent Florida Blvd,POB 161364, Orlando, FL 32816 USA..
Univ South Dakota, Dept Math Sci, 414 E Clark St, Vermillion, SD 57069 USA.. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
On Generalized Walsh Bases2019In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 163, no 1, p. 73-90Article in journal (Refereed)

This paper continues the study of orthonormal bases (ONB) of L2[0, 1] introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128-1139, 2014) by means of Cuntz algebra ON representations on L2[0, 1]. For N = 2, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery.

• 41. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication. Lund University.
REDUCIBILITY OF THE WAVELET REPRESENTATION ASSOCIATED TO THE CANTOR SET2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 10, p. 3657-3664Article in journal (Refereed)

We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representation is reducible.

• 42. Dutkay, Dorin Ervin
Mälardalen University, School of Education, Culture and Communication.
Wavelet Representations and Their Commutant2012In: Analysis for Science, Engineering and Beyond / [ed] Åström, Kalle; Persson, Lars-Erik; Silvestrov, Sergei D., Springer Berlin/Heidelberg, 2012, Vol. 6, p. 253-265Chapter in book (Refereed)

We study the reducibility of the wavelet representation associated to various QMF filters, including those associated to Cantor sets. We show there are connections between this problem, the harmonic analysis of transfer operators and the ergodic properties of shifts on solenoids. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.

• 43.
Lund University.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras2014In: Springer Proceedings in Mathematics and Statistics, Springer, 2014, Vol. 85, p. 37-59Conference paper (Refereed)

We consider a family of associative algebras, defined as the quotient of a free algebra with the ideal generated by a set of multi-parameter deformed commutation relations between four generators consisting of five quantum plane relations between pairs of generators and one sub-quadratic relation inter-linking all four generators. For generic parameter vectors, the center and the commutants of the two of the generators are described and conditions on the parameters for these commutants to be itself commutative or non-commutative are obtained.

• 44.
Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, Mulhouse, France.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Laboratoire de Mathématiques Informatique et Applications, Université de Haute Alsace, Mulhouse, France. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras2016In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 28, no 4, p. 657-673Article in journal (Refereed)

The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of (p, q)-deformations of Witt and Virasoro algebras as well as sl(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.

• 45.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
A componentwise PageRank algorithm2015In: 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, p. 185-198Conference paper (Refereed)

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.

• 46.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
An evaluation of centrality measures used in cluster analysis2014In: 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, p. 313-320Conference paper (Refereed)

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.

• 47.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Calculating PageRank in a changing network with added or removed edges2017In: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020052-1-020052-8, article id 020052Conference paper (Refereed)

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

• 48.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Generalisation of the Damping Factor in PageRank for Weighted Networks2014In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, Dmitrii; Martin-Löf, Anders, Springer International Publishing , 2014, p. 313-333Chapter in book (Refereed)

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.

• 49.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Non-normalized PageRank and random walks on N-partite graphs2014In: SMTDA 2014 Proceedings / [ed] H. Skiadas (Ed), 2014, p. 193-202Conference paper (Refereed)

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.

• 50.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, p. 223-247Chapter in book (Refereed)

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