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• 1.
École polytechnique fédérale de Lausanne, Switzerland.
École polytechnique fédérale de Lausanne, Switzerland. École polytechnique fédérale de Lausanne, Switzerland.
Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems2019Ingår i: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, nr 6, s. 545-551Artikel i tidskrift (Refereegranskat)

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.

• 2.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank in evolving tree graphs2018Ingår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 375-390Kapitel i bok, del av antologi (Refereegranskat)

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.
University of California, Berkeley, USA.
Mälardalens högskola, Institutionen för matematik och fysik. University of Latvia, Latvia. University of Latvia, Latvia. University of Bonn, Germany.
Quantum finite multitape automata1999Ingår i: SOFSEM’99: Theory and Practice of Informatics: 26th Conference on Current Trends in Theory and Practice of Informatics Milovy, Czech Republic, November 27 — December 4, 1999 Proceedings, 1999, Vol. 1725, s. 340-348Konferensbidrag (Refereegranskat)

Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved Chat for some languages quantum finite automats may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multi-tape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automats. This is the first result on a problem which can be solved by a quantum computer but not by a deterministic or probabilistic computer. Additionally we discover unexpected probabilistic automata recognizing complicated languages.

• 4.
WorldLight.com AB, Sweden.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
The mathematics of internet search engines2008Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 104, nr 2, s. 211-242Artikel i tidskrift (Refereegranskat)

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.

• 5.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Forecasting the Stock Market: A Neural Network Approch2009Studentuppsats

Forecasting the stock market is a complex task, partly because of the random walk behavior of the stock price series. The task is further complicated by the noise, outliers and missing values that are common in financial time series. Despite of this, the subject receives a fair amount of attention, which probably can be attributed to the potential rewards that follows from being able to forecast the stock market.

Since artificial neural networks are capable of exploiting non-linear relations in the data, they are suitable to use when forecasting the stock market. In addition to this, they are able to outperform the classic autoregressive linear models.

The objective of this thesis is to investigate if the stock market can be forecasted, using the so called error correction neural network. This is accomplished through the development of a method aimed at finding the optimum forecast model.

The results of this thesis indicates that the developed method can be applied successfully when forecasting the stock market. Of the five stocks that were forecasted in this thesis using forecast models based on the developed method, all generated positive returns. This suggests that the stock market can be forecasted using neural networks.

• 6.
Umeå University.
Umeå University. Umeå University.
Fast multiplication of matrices over a finitely generated semiring2008Ingår i: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, nr 6, s. 230-234Artikel i tidskrift (Refereegranskat)
• 7.
École Polytechniques Fédérale de Lausanne, Switzerland.
Uppsala University, Uppsala, Sweden. Uppsala University, Uppsala, Sweden.
Temporal upscaling in micromagnetism via heterogeneous multiscale methods2019Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 345, s. 99-113Artikel i tidskrift (Refereegranskat)

We consider a multiscale strategy addressing the disparate scales in the Landau–Lifschitz equations in micromagnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic scale we are interested in simulating the dynamics of the magnetisation without fully resolving the microscopic scales.

The method follows the framework of heterogeneous multiscale methods and it has two main ingredients: a micro- and a macroscale model. The microscopic model is assumed to be known exactly whereas the macromodel is incomplete as it lacks effective quantities. The two models use different temporal and spatial scales and effective parameter values for the macromodel are computed on the fly, allowing for improved efficiency over traditional one-scale schemes.

For the analysis, we consider a single spin under a high frequency field and show that effective quantities can be obtained accurately with step-sizes much larger than the size of the microscopic scales required to resolve the microscopic features. Numerical results both for a single magnetic particle as well as a chain of interacting magnetic particles are given to validate the theory.

• 8.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. École Polytechniques Fédérale de Lausanne, Switzerland.
Uppsala University, Uppsala, Sweden.
An equation-free approach for second order multiscale hyperbolic problems in non-divergence form2018Ingår i: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 16, nr 8, s. 2317-2343Artikel i tidskrift (Refereegranskat)

The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale behavior, hence their effects should be accurately modelled in a numerical simulation. A direct numerical simulation is prohibitively expensive since a minimum of two points per wavelength are needed to resolve the small scales. A multiscale method, under the equation-free methodology, is proposed to approximate the coarse scale behaviour of the exact solution at a cost independent of the small scales in the problem. We prove convergence rates for the upscaled quantities in one as well as in multi-dimensional periodic settings. Moreover, numerical results in one and two dimensions are provided to support the theory.

• 9.
Uppsala University, Uppsala, Sweden; École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Uppsala University, Uppsala, Sweden. Uppsala University, Uppsala, Sweden.
Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature2018Ingår i: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 44, nr 4, s. 1119-1151Artikel i tidskrift (Refereegranskat)

In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale concepts: the partitioned domain and the upscaling-based methodologies. The major challenge for both multiscale methods is to capture the correct value of magnetisation length accurately, which is affected by a random temperature-dependent force. Moreover, general limitations of these multiscale techniques in application to spin systems are discussed.

• 10.
Ecole polytechnique f´ed´erale de Lausanne, Switzerland.
University of Warwick, Coventry, UK. Uppsala University, Sweden.
Modelling long-range interactions in multiscale simulations of ferromagnetic materialsManuskript (preprint) (Övrigt vetenskapligt)

Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic approach handles the dynamics of spin magnetic moments of individual atoms, while the continuum approximations operate with volume-averaged quantities, such as magnetisation. One of the challenges for multiscale models in relation to physics of ferromagnets is the existence of the long-range dipole-dipole interactions between spins. The aim of the present paper is to demonstrate a way of including these interactions into existing atomistic-continuum coupling methods based on the partitioned-domain and the upscaling strategies. This is achieved by modelling the demagnetising field exclusively at the continuum level and coupling it to both scales. Such an approach relies on the atomistic expression for the magnetisation field converging to the continuum expression when the interatomic spacing approaches zero, which is demonstrated in this paper.

• 11.
Uppsala University, Sweden.
KTH, Stockholm.
A time dependent approach for removing the cell boundary error in elliptic homogenization problems2016Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, s. 206-227Artikel i tidskrift (Refereegranskat)

This paper concerns the cell-boundary error present in multiscale algorithms for elliptic homogenization problems. Typical multiscale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. To solve the micro model, boundary conditions are required on the boundary of the microscopic domain. Imposing a naive boundary condition leads to O(ε/η) error in the computation, where ε is the size of the microscopic variations in the media and η is the size of the micro-domain. The removal of this error in modern multiscale algorithms still remains an important open problem. In this paper, we present a time-dependent approach which is general in terms of dimension. We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of ε/η in the periodic setting. Additionally, we present numerical evidence showing that the method improves the O(ε/η) error to O(ε) in general non-periodic media.

• 12.
KTH, Stockholm.
KTH, Stockholm.
Analysis of heterogeneous multiscale methods for long time wave propagation problems2014Ingår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 12, nr 3, s. 1135-1166Artikel i tidskrift (Refereegranskat)

In this paper, we analyze a multiscale method developed under the heterogeneous multiscale method (HMM) framework for numerical approximation of multiscale wave propagation problems in periodic media. In particular, we are interested in the long time $O(\varepsilon^{-2})$ wave propagation, where $\varepsilon$ represents the size of the microscopic variations in the media. In large time scales, the solutions of multiscale wave equations exhibit $O(1)$ dispersive effects which are not observed in short time scales. A typical HMM has two main components: a macromodel and a micromodel. The macromodel is incomplete and lacks a set of local data. In the setting of multiscale PDEs, one has to solve for the full oscillatory problem over local microscopic domains of size $\eta=O(\varepsilon)$ to upscale the parameter values which are missing in the macroscopic model. In this paper, we prove that if the microproblems are consistent with the macroscopic solutions, the HMM approximates the unknown parameter values in the macromodel up to any desired order of accuracy in terms of $\varepsilon/\eta$.

• 13.
Uppsala University, Sweden.
KTH, Stockholm.
Estimates for the Upscaling Error in Heterogeneous Multiscale Methods for Wave Propagation Problems in Locally Periodic Media2017Ingår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 15, nr 2, s. 948-976Artikel i tidskrift (Refereegranskat)

This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the microscopic variations over a much larger physical domain of interest. The heterogeneous multiscale method (HMM) is an efficient framework to approximate the solutions of multiscale problems. In the HMM, one assumes an incomplete macroscopic model which is coupled to a known but expensive microscopic model. The micromodel is solved only locally to upscale the parameter values which are missing in the macromodel. The resulting macroscopic model can then be solved at a cost independent of the small scales in the problem. In general, the accuracy of the HMM is related to how good the upscaling step approximates the right macroscopic quantities. The analysis of the method that we consider here was previously addressed only in purely periodic media, although the method itself is numerically shown to be applicable to more general settings. In the present study, we consider a more realistic setting by assuming a locally periodic medium where slow and fast variations are allowed at the same time. We then prove that the HMM captures the right macroscopic effects. The generality of the tools and ideas in the analysis allows us to establish convergence rates in a multidimensional setting. The theoretical findings here imply an improved convergence rate in one dimension, which also justifies the numerical observations from our earlier study.

• 14.
KTH, Sweden.
Laboratoire POEMS, UMA, ENSTA ParisTech, Palaiseau, France.
A finite element heterogeneous multiscale method with improved control over the modeling error2016Ingår i: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 14, nr 2, s. 463-487Artikel i tidskrift (Refereegranskat)

Multiscale partial differential equations (PDEs) are difficult to solve by traditional numerical methods due to the need to resolve the small wavelengths in the media over the entire computational domain. We develop and analyze a Finite Element Heterogeneous Multiscale Method (FE-HMM) for approximating the homogenized solutions of multiscale PDEs of elliptic, parabolic, and hyperbolic type. Typical multiscale methods require a coupling between a micro and a macro model. Inspired from the homogenization theory, traditional FE-HMM schemes use elliptic PDEs as the micro model. We use, however, the second order wave equation as our micro model independent of the type of the problem on the macro level. This allows us to control the modeling error originating from the coupling between the different scales. In a spatially fully discrete a priori error analysis we prove that the modeling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media. We provide numerical examples in one and two dimensions confirming the theoretical results. Further examples show that the method captures the effective solutions in general non-periodic settings as well.

• 15.
Fatih University, Istanbul, Turkey.
Bogazici University, Istanbul, Turkey.
A note on the Taylor’s decomposition on four points for a third-order differential equation2007Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 188, nr 2, s. 1483-1490Artikel i tidskrift (Refereegranskat)

Taylor’s decomposition on four points is presented. Three-step difference schemesgenerated by the Taylor’s decomposition on four points for the numerical solutionsof an initial-value problem, a boundary-value problem and a nonlocal boundary-value problem for a third-order differential equation are constructed. Numerical examples are given.

• 16.
Fatih University, Istanbul, Turkey.
Royal Institute of Technology, Stockholm, Sweden. Fatih University, Istanbul, Turkey.
Taylor's decomposition on four points for solving third-order linear time-varying systems2009Ingår i: Journal of the Franklin Institute, ISSN 0016-0032, E-ISSN 1879-2693, Vol. 346, nr 7, s. 651-662Artikel i tidskrift (Refereegranskat)

In the present paper, the use of three-step difference schemes generated by Taylor's decomposition on four points for the numerical solutions of third-order time-varying linear dynamical systems is presented. The method is illustrated for the numerical analysis of an up-converter used in communication systems.

• 17.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Introduction to some modes of convergence: Theory and applications2017Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

This thesis aims to provide a brief exposition of some chosen modes of convergence; namely uniform convergence, pointwise convergence and L1 convergence. Theoretical discussion is complemented by simple applications to scientific computing. The latter include solving differential equations with various methods and estimating the convergence, as well as modelling problematic situations to investigate odd behaviors of usually convergent methods.

• 18.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Application of a power-exponential function-based model to mortality rates forecasting2019Ingår i: Communications in Statistics: Case Studies, Data Analysis and Applications, E-ISSN 2373-7484, Vol. 5, nr 1, s. 3-10Artikel i tidskrift (Refereegranskat)

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.

• 19.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Pricing American Style Asian OptionsUsing Dynamic Programming2010Självständigt arbete på avancerad nivå (masterexamen), 30 poäng / 45 hpStudentuppsats (Examensarbete)

The objective of this study is to implement a Java applet for calculating Bermudan/American-Asian call option prices and to obtain their respective optimal exercise strategies. Additionally, the study presents a computational time analysis and the effect of the variables on the option price.

• 20.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities2018Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, nr 6, s. 1328-1349Artikel i tidskrift (Refereegranskat)

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.

• 21.
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. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. University of Central Florida.
Preface2012Ingår i: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 33, nr 7-9, s. 705-707Artikel i tidskrift (Övrigt vetenskapligt)
• 22.
University of Tuscia Largo dell’Universita, Italy.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy. Nanjing University, China.
On the Critical Strip of the Riemann zeta Fractional derivative2017Ingår i: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 151, s. 459-472Artikel i tidskrift (Refereegranskat)

The fractional derivative of the Dirichlet eta function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function on the critical strip. Its convergence is studied. In particular, its half-plane of convergence gives the possibility to better understand the fractional derivative of the Riemann zeta function and its critical strip. As an application, two signal processing networks, corresponding to the fractional derivative of the eta function and to its Fourier transform, respectively, are shortly described.

• 23.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Estimation and Testing the Quotient of Two Models2018Självständigt arbete på avancerad nivå (magisterexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

In the thesis, we introduce linear regression models such as Simple Linear Regression, Multiple Regression, and Polynomial Regression. We explain basic methods of the model parameters estimation, Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE). The properties of the estimates, and what assumptions need to be made for the model for the estimates to be the Best Linear Unbiased Estimates (BLUE) are given. The basic Bootstrap methods are introduced. The real world problem is simulated in order to see how measurement error affects the quotient of two estimated models.

• 24.
CNRS UMR 8163 STL, Universit´e Lille 3, 59653 Villeneuve d’Ascq, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. 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 Terms2013Ingår i: Artificial Intelligence in Medicine. Lecture Notes in Computer Science, vol. 7885 / [ed] Niels Peek, Roque Marín Morales, Mor Peleg, Berlin Heidelberg: Springer, 2013, s. 58-67Kapitel i bok, del av antologi (Refereegranskat)

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.

• 25.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
On the causes and effects of specialization: A mathematical approach2009Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on.

Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution.

The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.

• 26.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Applying Autonomous Methods for Signal Analysis and Correction with Applications in the ship Industry2018Självständigt arbete på avancerad nivå (masterexamen), 40 poäng / 60 hpStudentuppsats (Examensarbete)

The manufacturing and transportation industries generate a large amount of data sets which are often of inconsistent quality. The goal of this project is to find the mathematical principles of a system which learns automatically the essential statistical and analytical properties of datasets in order to detect and correct certain classes of faults in real time.

• 27.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A componentwise PageRank algorithm2015Ingår i: 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, s. 185-198Konferensbidrag (Refereegranskat)

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.

• 28.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Calculating PageRank in a changing network with added or removed edges2017Ingår i: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020052-1-020052-8, artikel-id 020052Konferensbidrag (Refereegranskat)

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

• 29.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Graph partitioning and a component wise PageRank algorithmManuskript (preprint) (Övrigt vetenskapligt)

In this article we will present a graph partitioning algorithm which partitions a graphinto two different types of components: the well known ‘strongly connected components’ as well as another type of components we call ‘connected acyclic component’. We will give analgorithm based on Tarjan’s algorithm for finding strongly connected components used to find such a partitioning. We will also show that the partitioning given by the algorithm is unique and that the underlying graph can be represented as a directed acyclic graph (similar to a pure strongly connected component partitioning). In the second part we will show how such an partitioning of a graph can be used to calculate PageRank of a graph effectively by calculating PageRank for different componentson the same ‘level’ in parallel as well as allowing for the use of different types of PageRankalgorithms for different types of components. To evaluate the method we have calculated PageRank on four large example graphs and compared it with a basic approach, as well as our algorithm in a serial as well as parallel implementation.

• 30.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Non-normalized PageRank and random walks on N-partite graphs2014Ingår i: SMTDA 2014 Proceedings / [ed] H. Skiadas (Ed), 2014, s. 193-202Konferensbidrag (Refereegranskat)

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.

• 31.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 223-247Kapitel i bok, del av antologi (Refereegranskat)

• 32.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank, Connecting a Line of Nodes with a Complete Graph2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)

The focus of this article is the PageRank algorithm originally defined by S. Brin and L. Page as the stationary distribution of a certain random walk on a graph used to rank homepages on the Internet. We will attempt to get a better understanding of how PageRank changes after you make some changes to the graph such as adding or removing edge between otherwise disjoint subgraphs. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others and different ways to combine the two. Both the ordinary normalized version of PageRank as well as a non-normalized version of PageRank found by solving corresponding linear system will be considered. We will see that it is possible to find explicit formulas for the PageRank in some simple link structures and using these formulas take a more in-depth look at the behavior of the ranking as the system changes.

• 33.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
PageRank for networks, graphs and Markov chains2017Ingår i: Theory of Probability and Mathematical Statistics, ISSN 0868-6904, Vol. 96, s. 61-83Artikel i tidskrift (Refereegranskat)

In this work it is described how a partitioning of a graph into components can be used to calculate PageRank in a large network and how such a partitioning can be used to re-calculate PageRank as the network changes. Although considered problem is that of calculating PageRank, it is worth to note that the same partitioning method could be used when working with Markov chains in general or solving linear systems as long as the method used for solving a single component is chosen appropriately. An algorithm for calculating PageRank using a modified partitioning of the graph into strongly connected components is described. Moreover, the paper focuses also on the calculation of PageRank in a changing graph from two different perspectives, by considering specific types of changes in the graph and calculating the difference in rank before and after certain types of edge additions or removals between components. Moreover, some common specific types of graphs for which it is possible to find analytic expressions for PageRank are considered, and in particular the complete bipartite graph and how PageRank can be calculated for such a graph. Finally, several open directions and problems are described.

• 34.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Using graph partitioning to calculate PageRank in a changing networkManuskript (preprint) (Övrigt vetenskapligt)

PageRank was first defined by S. Brinn and L. Page in 1998 in order to rank homepages on the Internet by ranking pages according to the stationary distribution of a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly different but equally important problem, namely how to improve the calculation of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between different strongly connected components in the network.

• 35.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Using graph partitioning to calculate PageRank in a changing network2016Ingår i: Proceedings of the 4th Stochastic Modeling Techniques and DataAnalysis International Conference with Demographics Workshop (SMTDA2016) / [ed] Christos H Skiadas, 2016, s. 155-164Konferensbidrag (Refereegranskat)

PageRank was first defined by S. Brinn and L. Page in 1998 in order to rank homepages on the Internet for use in search engines using a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly dierent but equally important problem, namely how to improve the calculation speed of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between dierent strongly connected components in the network.

• 36.
Mälardalens högskola, Institutionen för matematik och fysik.
Royal Institute of Technology,Stockholm, Sweden .
On two theorems of Quinzii and rent controlled housing allocation in Sweden2007Ingår i: International Game Theory Review, ISSN 0219-1989, Vol. 9, nr 3, s. 515-526Artikel i tidskrift (Refereegranskat)

The Swedish rent control system creates a white market for swapping rental contracts and a black market for selling rental contracts. Empirical data suggests that in this black-and-white market some people act according to utility functions that are both discontinuous and locally decreasing in money. We discuss Quinzii's theorem for the nonemptiness of the core of generalized house-swapping games, and show how it can be extended to cover the Swedish game. In a second part, we show how this theorem of Quinzii and her second theorem on nonemptiness of the core in two-sided models are both special cases of a more general theorem.

• 37.
Mälardalens högskola, Institutionen för matematik och fysik.
Mälardalens högskola, Institutionen för matematik och fysik. Mälardalens högskola, Institutionen för matematik och fysik.
Optimal Expected Rank in a Two-Sided Secretary Problem2007Ingår i: Operations Research, ISSN 0030-364X, Vol. 55, nr 5, s. 921-931Artikel i tidskrift (Refereegranskat)

In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.

• 38.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
Stockhom Univ.
Partner Search Heuristics in the Lab: Stability of Matchings Under Various Preference Structures2009Ingår i: Adaptive Behavior, ISSN 1059-7123, E-ISSN 1741-2633, Vol. 17, nr 6, s. 524-536Artikel i tidskrift (Refereegranskat)

When agents search for partners, the outcome is a matching. K. Eriksson and O. Häggström (2008)defined a measure of instability of matchings and proved that under a certain partner search heuristic,outcomes are likely to have low instability. They also showed that with regards to stability, the preferencestructure known as common preferences lie somewhere in between the extreme cases of homotypicand antithetical preferences. Following up on this theoretical work, we let human subjectssearch for a good partner in a computer game where preferences were set to be either common,homotypic, or antithetical. We find that total search effort and instability of the outcome vary in thepredicted ways with the preference structure and the number of agents. A set of simulations showthat these results are consistent with a model where agents use a simple search heuristic with a slightpossibility of error.

• 39.
Pulchowk Campus, Institute of Engineering, Tribhuvan University, Nepal.
Pulchowk Campus, Institute of Engineering, Tribhuvan University, Nepal. Department of Mathematical Sciences, School of Science, Kathmandu University, Nepal. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A Survey on Queueing Systems with Mathematical Models and Applications2017Ingår i: American Journal of Operational Research, ISSN 2324-6537, E-ISSN 2324-6545, ISSN 2324-6537, Vol. 7, nr 1, s. 1-14Artikel i tidskrift (Refereegranskat)

Queuing systems consist of one or more servers that provide some sort of services to arriving customers. Almost everyone has some experience of tedious time being in a queue during several daily life activities. It is reasonable to accept that service should be provided to the one who arrives first in the queue. But this rule always may not work. Sometimes the last comer or the customer in the high priority gets service earlier than the one who is waiting in the queue for a long time. All these characteristics are the interesting areas of research in the queueing theory. In this paper, we present some of the previous works of various researchers with brief explanations. We then carry out some of the mathematical expressions which represent the different queueing behaviors. In almost all the literatures, these queueing behaviors are examined with the help of mathematical simulations. Based on the previous contributions of researchers, our specific point of attraction is to study the finite capacity queueing models in which limited number of customers are served by a single or multiple number of servers and the batch queueing models where arrival or service or both occur in a bulk. Furthermore, we present some performance measure equations of some queueing models together with necessary components used in the queueing theory. Finally, we report some applications of queueing systems in supply chain management pointing out some areas of research as further works.

• 40.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy.
Entropy and fractal antennas2016Ingår i: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 18, nr 3, artikel-id 84Artikel i tidskrift (Refereegranskat)

The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal antennas, is studied. In particular, their entropy is linked with the fractal geometrical shape and the physical performance.

• 41.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. University of Salerno, Italy.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A functional equation for the Riemann zeta fractional derivative2017Ingår i: Proceedings of INCPAA 2016, 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, s. 020063-1-020063-10, artikel-id UNSP 020063Konferensbidrag (Refereegranskat)

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.

• 42.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Fractional Derivative of Riemann zeta function and Main Properties2016Konferensbidrag (Övrigt vetenskapligt)

The Caputo-Ortigueira fractional derivative provides the fractional derivativeof complex functions. This derivative plays an important role in the number theory, and has been shown suitable for the analysis of the Dirichlet series, Hurwitz zeta function and Riemann zeta function. An integral representation for the fractional derivative of the Riemann zeta function was discovered. Since the Riemann zeta function is widely used in Physics, the unilateral Fourier transform of its fractional derivative is computed to investigate its applications in Quantum Theory and Signal Processing.

• 43.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei; Rančić, Milica, Springer, 2016, s. 337-353Kapitel i bok, del av antologi (Refereegranskat)

In the following chapter we describe a wavelet expansion theory for positivedefinite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterisation of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator is rewritten as a convolution product according to the fractional calculus of real distributions. In particular, the fractional derivative of the Gabor-Morlet wavelet is computed together with its plots and main properties.

• 44.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set2016Konferensbidrag (Övrigt vetenskapligt)

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.

• 45. Hagelin, N
Mälardalens högskola, Institutionen för matematik och fysik.
Hedge Fund Allocation under Higher Moments and Illiquidity2005Ingår i: HEDGE FUNDS: INSIGHTS IN PERFORMANCE MEASUREMENT, RISK ANALYSIS, AND PORTFOLIO ALLOCATION, John Wiley & Sons , 2005Kapitel i bok, del av antologi (Övrigt vetenskapligt)

We use the discrete-time dynamic investment model to evaluate the gains from including hedge funds in the investment opportunity set. In this multi-period framework, an investor's utility is affected by all moments of the return distribution. We assume that investors rebalance their portfolios on a monthly basis, and we compare the performance of portfolios which may include hedge funds versus portfolios consisting of stocks and bonds only. Our findings show that: (1) investors will allocate wealth to hedge funds even when they take into account deviations from normality in hedge fund returns. Those ex ante optimal allocations result in portfolios that ex post have higher geometric returns compared to the case in which hedge fund investing is not permitted; (2) investors that form portfolios taking all moments of the return distribution into account construct portfolios that are very similar to the portfolios being constructed by investors who care only about expected return and standard deviation, suggesting that the two first moments of the return distribution dominate higher moments; (3) the positive effect on capital growth from including hedge funds into the portfolios remains, although smaller, when the so-called "stale-pricing effect" is considered; and (4) lock-up periods and advance notice periods may force investors to have portfolios that deviate from their targeted ex ante optimal portfolios. Through a simple experiment we show that this inability to rebalance hedge fund allocations may seriously impact the benefits that hedge fund allocations appear to offer.

• 46.
Stockholm University.
Stockholm University. Mälardalens högskola, Institutionen för matematik och fysik.
Gains from Adding Funds of Hedge Funds to Portfolios of Traditional Assets: An International Perspective2005Ingår i: FUNDS OF HEDGE FUNDS: Performance, Assessment, Diversification, and Statistical Properties, BUTTERWORTH HEINEMANN , 2005, s. 171-187Kapitel i bok, del av antologi (Övrigt vetenskapligt)

We investigate the certainty-equivalent wealth gain from adding funds of hedge funds to portfolios of traditional assets for investors in G7 countries. The allows us to incorporate the effect of currency exposure and different proxies of equity performance. We find that for many investors, access to funds of hedge funds is as valuable as access to international equity markets. Difference between investors in different countries are documented. These differences are due to the relative performance of the different equity markets as well as the fact that hedge fund exposure contains currency exposure that vigilant investors should take care in hedging to reduce unnecessary volatility.

• 47.
LIM&BIO (EA3969), Université Paris 13, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Université Paris 13, France. Universiteá Lille, Villeneuve d'Ascq, France. Universiteá Lille, Villeneuve d'Ascq, France. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Combining Compositionality and Pagerank for the Identification of Semantic Relations between Biomedical Words2012Ingår i: BioNLP: Proceedings of the 2012 Workshop on Biomedical Natural Language Processing, 2012, s. 109-117Konferensbidrag (Refereegranskat)

The acquisition of semantic resources and relations is an important task for several applications, such as query expansion, information retrieval and extraction, machine translation. However, their validity should also be computed and indicated, especially for automatic systems and applications. We exploit the compositionality based methods for the acquisition of synonymy relations and of indicators of these synonyms. We then apply pagerank-derived algorithm to the obtained semantic graph in order to filter out the acquired synonyms. Evaluation performed with two independent experts indicates that the quality of synonyms is systematically improved by 10 to 15% after their filtering.

• 48.
LIMSI-CNRS, Orsay, France.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Term Ranking Adaptation to the Domain: Genetic Algorithm-Based Optimisation of the C-Value2014Ingår i: Advances in Natural Language Processing: 9th International Conference on NLP, PolTAL 2014, Warsaw, Poland, September 17-19, 2014. Proceedings, Springer International Publishing , 2014, Vol. 8686, s. 71-83Konferensbidrag (Refereegranskat)

Term extraction methods based on linguistic rules have been proposed to help the terminology building from corpora. As they face the difficulty of identifying the relevant terms among the noun phrases extracted, statistical measures have been proposed. However, the term selection results may depend on corpus and strong assumptions reflecting specific terminological practice. We tackle this problem by proposing a parametrised C-Value which optimally considers the length and the syntactic roles of the nested terms thanks to a genetic algorithm. We compare its impact on the ranking of terms extracted from three corpora. Results show average precision increased by 9% above the frequency-based ranking and by 12% above the C-Value-based ranking.

• 49.
Mälardalens högskola, Institutionen för matematik och fysik.
A Global Optimization Approach for Integrated Design and Parameter Estimation in Process Engineering2006Övrigt (Övrigt vetenskapligt)
• 50.
Mälardalens högskola, Institutionen för matematik och fysik.
An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization2008Ingår i: Journal of Global Optimization, ISSN 1573-2916, Vol. 41, nr 3, s. 447-464Artikel i tidskrift (Refereegranskat)

Powerful response surface methods based on kriging and radial basis function (RBF) interpolation have been developed for expensive, i.e. computationally costly, global nonconvex optimization. We have implemented some of these methods in the solvers rbfSolve and EGO in the TOMLAB Optimization Environment (http://www.tomopt.com/tomlab/). In this paper we study algorithms based on RBF interpolation. The practical performance of the RBF algorithm is sensitive to the initial experimental design, and to the static choice of target values. A new adaptive radial basis interpolation (ARBF) algorithm, suitable for parallel implementation, is presented. The algorithm is described in detail and its efficiency is analyzed on the standard test problem set of Dixon-Szego. Results show that it outperforms the published results of rbfSolve and several other solvers.

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