# Publications

Sergei Silvestrov publications are indexed in several publication and citation databases.

**My publications 1992 - June 2015**

**Google Scholar **

Sergei Silvestrov at Google Scholar

**Research gate**

Sergei Silvestrov at Research Gate

**MathSciNet. Mathematical Reviews database for****publications in Mathematics (maintained by Americal Mathematical Society since 1940)**

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Note:* MathSciNet. Mathematical Reviews* is one of the most known, oldest and comprehensive databases reviewing mathematics publications. The database is run by the American Mathematical Society since 1940. It lists publications in selected established peer-reviewed mathematics sources of international journals, volumes, books, procedures, collective volumes, etc. MathSciNet access requires subscription (institutional or individual). Publications are listed in MathSciNet with some natural lag. Mathematics and Applied Mathematics publications published in non-mathematical journals or in proceedings Volumes for example might be absent from MathSciNet or registered with longer delays due to how MathSciNet collects information.

**DIVA (Mälardalen University publications database)**

**Latest 21 publications by Sergei Silvestrov registered in DIVA**

## DIVA registered latest publications

- A componentwise PageRank algorithm
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.

- A functional equation for the Riemann zeta fractional derivative
In this paper a functional equation for the fractional derivative of the Riemann zeta function is presented. The fractional derivative of the zeta function is computed by a generalization of the Grunwald-Letnikov fractional operator, which satisfies the generalized Leibniz rule. It is applied to the asymmetric functional equation of the Rieman zeta function in order to obtain the result sought. Moreover, further properties of this fractional derivative are proposed and discussed.

- A Note on Exploration of Sequence Spaces and Function Spaces on Interval [0,1] for DNA Sequencing
In [7] authors studied the sequence spaces and function spaces on interval [0,1]. Further they introduced new sequence spaces by using generalized p-summation method and proved these spaces of sequences and functions are Banach spaces. In this paper we extend the results of authors in [7] by introducing a new basis function and strongly p-summation method.

- A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set
In this paper, the Weierstrass-Mandelbrot function on the Cantor set is presented with emphasis on possible applications in science and engineering. An asymptotic estimation of its one-sided Fourier transform, in accordance with the simulation results, is analytically derived. Moreover, a time-frequency analysis of the Weierstrass-Mandelbrot function is provided by the numerical computation of its continuous wavelet transform.

- Algebra, Geometry and Mathematical Physics : Proceedings of the AGMP, Mulhouse, France, October 2011
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.

- An evaluation of centrality measures used in cluster analysis
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.

- An examination of the multi-peaked analytically extended function for approximation of lightning channel-base currents
A multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current wave-forms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge trans-fer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed.

- An Examination of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Channel-Base Currents
A multi-peaked version of the analytically extendedfunction (AEF) intended for approximation of multi-peaked light-ning current waveforms will be presented along with some of itsbasic properties. A general framework for estimating the parame-ters of the AEF using the Marquardt least-squares method(MLSM) for a waveform with an arbitrary (finite) number ofpeaks as well as a given charge transfer and specific energy willalso be described. This framework is used to find parameters forsome common single-peak wave-forms and some advantages anddisadvantages of the approach will be discussed.

- Analysis of Horizontal Thin-Wire Conductor Buried in Lossy Ground: New Model for Sommerfeld Type Integral
A new simple approximation that can be used for modeling of one type of Sommerfeld integrals typically occurring in the expressions that describe sources buried in the lossy ground, is proposed in the paper. The ground is treated as a linear, isotropic and homogenous medium of known electrical parameters. Proposed approximation has a form of a weighted exponential function with an additional complex constant term. The derivation procedure of this approximation is explained in detail, and the validation is done applying it in the analysis of a bare conductor fed in the center and immersed in the lossy ground at arbitrary depth. Wide range of ground and geometry parameters of interest has been taken into consideration.

- Analysis of shielded coupled microstrip line with partial dielectric support
A shielded coupled microstrip line with partial dielectric support is analysed using the hybrid boundary element method (HBEM) and the finite difference method (FDM). The HBEM is a combination of the equivalent electrodes method (EEM) and the boundary element method (BEM). The microstrip line characteristic parameters: the effective relative permittivity and the characteristic impedance are determined. “Odd” and “even” modes are taken into account. The results are compared with corresponding ones found in the literature.

- Application of the Marquardt Least Square Method to the Estimation of Pulse Function Parameters
Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functionsused for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse,Heidler’s and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove theability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.

- Application of the multi-peaked analytically extended function to representation of some measured lightning currents
A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function's parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the p-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.

- Approximation Methods of European Option Pricing in Multiscale Stochastic Volatility Model
In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model , in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown by Christoffersen, Heston and Jacobs. We consider one specific type of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this chapter is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi using method of characteristics, Fourier and bivariate Laplace transforms.

- Asian Options, Jump-Diffusion Processes on a Lattice, and Vandermonde Matrices
Asian options are options whose value depends on the average asset price during its lifetime. They are useful because they are less subject to price manipulations. We consider Asian option pricing on a lattice where the underlying asset follows the Merton–Bates jump-diffusion model. We describe the construction of the lattice using the moment matching technique which results in an equation system described by a Vandermonde matrix. Using some properties of Vandermonde matrices we calculate the jump probabilities of the resulting system. Some conditions on the possible jump sizes in the lattice are also given.

- Asymptotic expansions for stationary and quasi-stationary distributions of perturbed semi-Markov processes
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.

- Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing 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.

- Asymptotic expansions for stationary distributions of perturbed semi-markov processes
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.

- Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras
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.

- Calculating PageRank in a changing network with added or removed edges
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

- Centralizers in Ore extensions over polynomial rings
In this paper we consider centralizers of single elements in Ore extensions of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as an algebra. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

- Common Fixed Point Results for Family of Generalized Multivalued F-contraction Mappings in Ordered Metric Spaces
In this paper, we study the existence of common fixed points of family of multivalued mappings satisfying generalized F-contractive conditions in ordered metric spaces. These results establish some of the general common fixed point theorems for family of multivalued maps.

- Common Fixed Points of Weakly Commuting Multivalued Mappings on a Domain of Sets Endowed with Directed Graph
In this paper, the existence of coincidence points and common fixed points for multivalued mappings satisfying certain graphic ψ- contraction contractive conditions with set-valued domain endowed with a graph, without appealing to continuity, is established. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

- Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras
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.

- Commutants in Crossed Product Algebras for Piece-Wise Constant Functions
In this paper we consider crossed product algebras of algebras of piecewiseconstant functions on the real line with Z. For an increasing sequence of algebras (in which case the commutants form a decreasing sequence), we describe the set difference between the corresponding commutants.

- Comparing the landcapes of common retroviral insertion sites across tumor models
Retroviral tagging represents an important technique, which allows researchers to screen for candidate cancer genes. The technique is based on the integration of retroviral sequences into the genome of a host organism, which might then lead to the artificial inhibition or expression of proximal genetic elements. The identification of potential cancer genes in this framework involves the detection of genomic regions (common insertion sites; CIS) which contain a number of such viral integration sites that is greater than expected by chance. During the last two decades, a number of different methods have been discussed for the identification of such loci and the respective techniques have been applied to a variety of different retroviruses and/or tumor models. We have previously established a retrovirus driven brain tumor model and reported the CISs which were found based on a Monte Carlo statistics derived detection paradigm. In this study, we consider a recently proposed alternative graph theory based method for identifying CISs and compare the resulting CIS landscape in our brain tumor dataset to those obtained when using the Monte Carlo approach. Finally, we also employ the graph-based method to compare the CIS landscape in our brain tumor model with those of other published retroviral tumor models.

- Comparison of Clustering Approaches through Their Application to Pharmacovigilance Terms
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.

- Comparison of TL, Point-Matching and Hybrid Circuit Method Analysis of a Horizontal Dipole Antenna Immersed in Lossy Soil
HF analysis of a horizontal dipole antenna buried in lossy ground has been performed in this paper. The soil is treated as a homogenous half-space of known electrical parameters. The authors compare the range of applicability of two forms of transmission line model , a hybrid circuit method, and a point-matching method in such analysis.

- Computing Burchnall–Chaundy Polynomials with Determinants
In this expository paper we discuss a way of computing the Burchnall-Chaundy polynomial of two commuting differential operators using a determinant.We describe how the algorithm can be generalized to general Ore extensions, andwhich properties of the algorithm that are preserved.

- Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases
In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process.

- Crossed Product Algebras for Piece-Wise Constant Functions
In this paper we consider algebras of functions that are constant on the sets of a partition. We describe the crossed product algebras of the mentioned algebras with Z. We show that the function algebra is isomorphic to the algebra of all functions on some set. We also describe the commutant of the function algebra and finish by giving an example of piece-wise constant functions on a real line.