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• 251.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Elekta Instrument AB, Sweden.
A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images2017In: IFMBE Proceedings, Springer Verlag , 2017, p. 531-538Conference paper (Refereed)

CBCT images suffer from acute shading artifacts primarily due to scatter. Numerous image-domain correction algorithms have been proposed in the literature that use patient-specific planning CT images to estimate shading contributions in CBCT images. However, in the context of radiosurgery applications such as gamma knife, planning images are often acquired through MRI which impedes the use of polynomial fitting approaches for shading correction. We present a new shading correction approach that is independent of planning CT images. Our algorithm is based on the assumption that true CBCT images follow a uniform volumetric intensity distribution per material, and scatter perturbs this uniform texture by contributing cupping and shading artifacts in the image domain. The framework is a combination of fuzzy C-means coupled with a neighborhood regularization term and Otsu’s method. Experimental results on artificially simulated craniofacial CBCT images are provided to demonstrate the effectiveness of our algorithm. Spatial non-uniformity is reduced from 16% to 7% in soft tissue and from 44% to 8% in bone regions. With shading- correction, thresholding based segmentation accuracy for bone pixels is improved from 85% to 91% when compared to thresholding without shading-correction. The proposed algorithm is thus practical and qualifies as a p lug and p lay extension into any CBCT reconstruction software for shading correction.

• 252. Ashyralyev, Allaberen
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
Taylor's decomposition on four points for solving third-order linear time-varying systems2009In: Journal of the Franklin Institute, ISSN 0016-0032, E-ISSN 1879-2693, Vol. 346, no 7, p. 651-662Article in journal (Refereed)

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.

• 253. Asmussen, Sören
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
A Note on Skewness in Regenerative Simulation2011In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 40, no 1, p. 45-57Article in journal (Refereed)

The purpose of this article is to show, empirically and theoretically, that performance evaluation by means of regenerative simulation often involves random variables with distributions that are heavy tailed and heavily skewed. This, in turn, leads to the variance of estimators being poorly estimated, and confidence intervals having actual coverage quite different from (typically lower than) the nominal one. We illustrate these general ideas by estimating the mean occupancy and tail probabilities in M/G/1 queues, comparing confidence intervals computed from batch means to various intervals computed from regenerative cycles. In addition, we provide theoretical results on skewness to support the empirical findings.

• 254.
KTH, Superseded Departments, Mathematics.
The Collet-Eckmann condition for rational functions on the Riemann sphere2004Doctoral thesis, monograph (Other scientific)
• 255.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Mating Non-Renormalizable Quadratic Polynomials2009In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 287, no 1, p. 1-40Article in journal (Refereed)

In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.

• 256.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models2014In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 7, p. 811-835Article in journal (Refereed)

We consider the relativistic generalization of the quantum A (N-1) Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh-Feigin-Veselov-Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

• 257.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Theoretical Physics.

We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.

• 258.
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Automatic Control.
Association control in millimeterWave wireless access networks2014In: 2014 IEEE 19th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks, CAMAD 2014, 2014, p. 260-264Conference paper (Refereed)

The resource allocation problem of optimal assignment of the stations to the available access points in 60 GHz millimeterWave wireless access networks is investigated. The problem is posed as a multi-assignment optimization problem. The proposed solution method converts the initial problem to a minimum cost flow problem and allows to design an efficient algorithm by a combination of auction algorithms. The solution algorithm exploits the network optimization structure of the problem, and thus is much more powerful than computationally intensive general-purpose solvers. Theoretical and numerical results evince numerous properties, such as optimality, convergence, and scalability in comparison to existing approaches.

• 259. Atkin, Max R.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble2018In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 31, no 4, p. 1155-1196Article in journal (Refereed)

We study the probability distribution of the ratio between the second smallest and smallest eigenvalue in the n x n Laguerre unitary ensemble. The probability that this ratio is greater than r > 1 is expressed in terms of an n x n Hankel determinant with a perturbed Laguerre weight. The limiting probability distribution for the ratio as n -> infinity is found as an integral over (0, infinity) containing two functions q(1)(x) and q(2)(x). These functions satisfy a system of two coupled Painleve V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. We compute asymptotic behaviours of these functions as rx -> 0(+) and (r - 1)x -> infinity, as well as large n asymptotics for the associated Hankel determinants in several regimes of r and x.

• 260.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Data gathering and analysis in gaming using Tobii Eye Tracking2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

E-sports is growing and the price pools in e-sports tournaments are increasing, Valves video game DotA 2 is one of the bigger e-sports. As professional gamers train to increase their skill, new tools to help the training might become very important. Eye tracking can give an extra training dimension for the gamer. The aim of this master thesis is to develop a Visual Attention Index for DotA 2, that is, a number that reflects the player’s visual attention during a game. Interviews with gamers combined with data collection from gamers with eye trackers and statistical methods were used to find relevant metrics to use in the work. The results show that linear regression did not work very well on the data set, however, since there were a low number of test persons, further data collection and testing needs to be done before any statistically significant conclusions can be drawn. Support Vector Machines (SVM) was also used and turned out to be an effective way of separating better players from less good players. A new SVM method, based on linear programming, was also tested and found to be efficient and easy to apply on the given data set.

• 261.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
The SVI implied volatility model and its calibration2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The SVI implied volatility model is a parametric model for stochastic implied volatility.The SVI is interesting because of the possibility to state explicit conditions on its parameters so that the model does not generate prices where static arbitrage opportunities can occur. Calibration of the SVI model to real market data requires non-linear optimization algorithms and can be quite time consuming. In recent years, methods to calibrate the SVI model that use its inherent structure to reduce the dimensions of the optimization problem have been invented in order to speed up the calibration. The ?first aim of this thesis is to justify the use of the model and the no static arbitrage conditions from a theoretic point of view. Important theorems by Kellerer and Lee and their proofs are discussed in detail and the conditions are carefully derived. The second aim is to implement the model so that it can be calibrated to real market implied volatility data. A calibration method is presented and the outcome of two numerical experiments validate it. The performance of the calibration method introduced in this thesis is measured in how big a fraction of the total market volume the method manages to ?t within the market spread. Tests show that the model manages to ?t most of the market volume inside the spread, even for options with short time to maturity. Further tests show that the model is capable to recalibrate an SVI parameter set that allows for static arbitrage opportunities into an SVI parameter set that does not.

• 262.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics2018In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 56, no 1, p. 434-455Article in journal (Refereed)

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.

• 263.
KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Aalto Univ ;Chinese Acad Sci.
Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 171, no 5, p. 745-767Article in journal (Refereed)

The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.

• 264.
KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Depts of Information and Computer Science and Applied Physics, Aalto University, Finland.
KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
Causal analysis, Correlation-Response, and Dynamic cavity2016In: International Meeting on High-Dimensional Data-Driven Science (HD3-2015), Institute of Physics (IOP), 2016, article id 012002Conference paper (Refereed)

The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non-equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.

• 265.
KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
Univ Havana, Dept Theoret Phys, Grp Complex Syst & Stat Phys, Havana, Cuba.. Univ Havana, Dept Theoret Phys, Grp Complex Syst & Stat Phys, Havana, Cuba.. Univ Havana, Dept Theoret Phys, Grp Complex Syst & Stat Phys, Havana, Cuba..
Exploring the diluted ferromagnetic p-spin model with a cavity master equation2018In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 5, article id 050103Article in journal (Refereed)

We introduce an alternative solution to Glauber multispin dynamics on random graphs. The solution is based on the recently introduced cavity master equation (CME), a time-closure turning the, in principle, exact dynamic cavity method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one Monte Carlo run on the same problem. We show that CME correctly models the ferromagnetic p-spin Glauber dynamics from high temperatures down to and below the spinoidal transition. We also show that CME allows an alternative exploration of the low-temperature spin-glass phase of the model.

• 266.
Division of Structural Mechanics, Lund Institute of Technology.
Kari, LeifKTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
Constitutive Models for Rubber IV: proceedings of the 4th European Conference for Constitutive Models for Rubber, ECCMR 2005, Stockholm, Sweden, 27-29 June 20052005Collection (editor) (Refereed)

The unique properties of elastomeric materials are taken advantage of in many engineering applications. Elastomeric units are used as couplings or mountings between stiff parts. Examples are shock absorbers, vibration insulators, flexible joints, seals and suspensions etc.

However, the complicated nature of the material behavior makes it difficult to accurately predict the performance of these units, using for example finite element modelling. It is therefore necessary that the constitutive model accurately capture relevant aspects of the mechanical behavior.

The latest development concerning constitutive modelling of rubber is collected in these proceedings. It is the fourth ECCMR-European Conference on Constitutive Modelling in a series on this subject.

Topics included in this volume are, Hyperelastic models, Strength, fracture & fatigue, Dynamic properties & the Fletcher-Gent effect, Micro-mechanical & statistical approaches, Stress softening, Viscoelasticity, Filler reinforcement, and Tyres, fiber & cord reinforced rubber.

• 267.
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
TOWARDS SHARP INAPPROXIMABILITY FOR ANY 2-CSP2010In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, Vol. 39, no 6, p. 2430-2463Article in journal (Refereed)

We continue the recent line of work on the connection between semidefinite programming (SDP)-based approximation algorithms and the unique games conjecture. Given any Boolean 2-CSP (or, more generally, any Boolean 2-CSP with real-valued "predicates"), we show how to reduce the search for a good inapproximability result to a certain numeric minimization problem. Furthermore, we give an SDP-based approximation algorithm and show that the approximation ratio of this algorithm on a certain restricted type of instances is exactly the inapproximability ratio yielded by our hardness result. We conjecture that the restricted type required for the hardness result is in fact no restriction, which would imply that these upper and lower bounds match exactly. This conjecture is supported by all existing results for specific 2-CSPs. As an application, we show that Max 2-AND is unique games-hard to approximate within 0.87435. This improves upon the best previous hardness of alpha(GW) + epsilon approximate to 0.87856 and comes very close to matching the approximation ratio of the best algorithm known, 0.87401. It also establishes that balanced instances of Max 2-AND, i.e., instances in which each variable occurs positively and negatively equally often, are not the hardest to approximate, as these can be approximated within a factor aGW and that Max Cut is not the hardest 2-CSP.

• 268.
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
Dense Subset Sum may be the hardest2016In: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2016Conference paper (Refereed)

The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t. It is an outstanding open question whether the O∗(2n/2)-time algorithm for Subset Sum by Horowitz and Sahni [J. ACM 1974] can be beaten in the worst-case setting by a "truly faster", O∗(2(0.5-δ)n)-time algorithm, with some constant δ &gt; 0. Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum. For every ∈ &gt; 0 we give a truly faster algorithm for instances with β ≤ 2(0.5-∈)n, as well as instances with β ≥ 20.661n. Consequently, we also obtain a characterization in terms of the popular density parameter n/log2 t: if all instances of density at least 1.003 admit a truly faster algorithm, then so does every instance. This goes against the current intuition that instances of density 1 are the hardest, and therefore is a step toward answering the open question in the affirmative. Our results stem from a novel combinatorial analysis of mixings of earlier algorithms for Subset Sum and a study of an extremal question in additive combinatorics connected to the problem of Uniquely Decodable Code Pairs in information theory.

• 269. Avgustinovich, S. V.
KTH, Superseded Departments, Mathematics.
The classification of some perfect codes2004In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 31, no 3, p. 313-318Article in journal (Refereed)

Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be the dimension of the vector space [C]. It is shown that if the rank of C is n - m + 2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n - m + 2, described by a Hamming code H and a set of MDS-codes D-h; h is an element of H, over an alphabet with four symbols. The case of rank n - m + 1 is much simpler: Any such code is a Vasil'ev code.

• 270. Avgustinovich, S. V.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On the structure of symmetry groups of Vasil'ev codes2005In: Problems of Information Transmission, ISSN 0032-9460, E-ISSN 1608-3253, Vol. 41, no 2, p. 105-112Article in journal (Refereed)

The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length n is always nontrivial; for codes of rank n - log(n + 1) + 1, an attainable upper bound on the order of the symmetry group is obtained.

• 271.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
Simulation and parameter estimation of spectrophotometric instruments ﻿2009Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The paper and the graphics industries use two instruments with different optical geometry (d/0 and 45/0) to measure the quality of paper prints. The instruments have been reported to yield incompatible measurements and even rank samples differently in some cases, causing communication problems between these sectors of industry.A preliminary investigation concluded that the inter-instrument difference could be significantly influenced by external factors (background, calibration, heterogeneity of the medium). A simple methodology for eliminating these external factors and thereby minimizing the instrument differences has been derived. The measurements showed that, when the external factors are eliminated, and there is no fluorescence or gloss influence, the inter-instrument difference becomes small, depends on the instrument geometry, and varies systematically with the scattering, absorption, and transmittance properties of the sample.A detailed description of the impact of the geometry on the results has been presented regarding a large sample range. Simulations with the radiative transfer model DORT2002 showed that the instruments measurements follow the physical radiative transfer model except in cases of samples with extreme properties. The conclusion is that the physical explanation of the geometrical inter-instrument differences is based on the different degree of light permeation from the two geometries, which eventually results in a different degree of influence from near-surface bulk scattering. It was also shown that the d/0 instrument fulfils the assumptions of a diffuse field of reflected light from the medium only for samples that resemble the perfect diffuser but it yields an anisotropic field of reflected light when there is significant absorption or transmittance. In the latter case, the 45/0 proves to be less anisotropic than the d/0.In the process, the computational performance of the DORT2002 has been significantly improved. After the modification of the DORT2002 in order to include the 45/0 geometry, the Gauss-Newton optimization algorithm for the solution of the inverse problem was qualified as the most appropriate one, after testing different optimization methods for performance, stability and accuracy. Finally, a new homotopic initial-value algorithm for routine tasks (spectral calculations) was introduced, which resulted in a further three-fold speedup of the whole algorithm.The paper and the graphics industries use two instruments with different optical geometry (d/0 and 45/0) to measure the quality of paper prints. The instruments have been reported to yield incompatible measurements and even rank samples differently in some cases, causing communication problems between these sectors of industry.A preliminary investigation concluded that the inter-instrument difference could be significantly influenced by external factors (background, calibration, heterogeneity of the medium). A simple methodology for eliminating these external factors and thereby minimizing the instrument differences has been derived. The measurements showed that, when the external factors are eliminated, and there is no fluorescence or gloss influence, the inter-instrument difference becomes small, depends on the instrument geometry, and varies systematically with the scattering, absorption, and transmittance properties of the sample.A detailed description of the impact of the geometry on the results has been presented regarding a large sample range. Simulations with the radiative transfer model DORT2002 showed that the instruments measurements follow the physical radiative transfer model except in cases of samples with extreme properties. The conclusion is that the physical explanation of the geometrical inter-instrument differences is based on the different degree of light permeation from the two geometries, which eventually results in a different degree of influence from near-surface bulk scattering. It was also shown that the d/0 instrument fulfils the assumptions of a diffuse field of reflected light from the medium only for samples that resemble the perfect diffuser but it yields an anisotropic field of reflected light when there is significant absorption or transmittance. In the latter case, the 45/0 proves to be less anisotropic than the d/0.In the process, the computational performance of the DORT2002 has been significantly improved. After the modification of the DORT2002 in order to include the 45/0 geometry, the Gauss-Newton optimization algorithm for the solution of the inverse problem was qualified as the most appropriate one, after testing different optimization methods for performance, stability and accuracy. Finally, a new homotopic initial-value algorithm for routine tasks (spectral calculations) was introduced, which resulted in a further three-fold speedup of the whole algorithm.

• 272.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Divergence-based spectral approximation with degree constraint as a concave optimization problemManuscript (preprint) (Other academic)

The Kullback-Leibler pseudo-distance, or divergence, can be used as a criterion for spectral approximation. Unfortunately this criterion is not convex over the most general classes of rational spectra. In this work it will be shown that divergence minimization is equivalent to a costrained entropy minimization problem, whose concave structure can be exploited in order to guarantee global convergence in the most general case.

• 273.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Fast, Globally Converging Algorithms for Spectral Moments ProblemsManuscript (preprint) (Other academic)

In this paper, we consider the matricial version of generalized moment problem with degree constraint. Specifically we focus on computing the solution that minimize the Kullback-Leibler criterion. Several strategies to find such optimum via descent methods are considered and their convergence studied. In particular a parameterization with better numerical properties is derived from a spectral factorization problem. Such parameterization, in addition to guaranteeing descent methods to be globally convergent, it appears to be very reliable in practice.

• 274.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Spectral Moment Problems: Generalizations, Implementation and Tuning2011Doctoral thesis, comprehensive summary (Other academic)

Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.

• 275.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
ARMA Identification of Graphical Models2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 5, p. 1167-1178Article in journal (Refereed)

Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data.

• 276.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Analys av variabler som påverkar lönsamheten i gymbranschen med multipel linjär regression2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis combines mathematical statistics with industrial economics and management to examine the profitability of the fitness industry in Sweden. The study was conducted with a dozen fitness businesses and the data mainly consisted of the companies’ annual reports from 2009 to 2014. The operating margin is the measure for profitability used in the calculations. A survey was conducted with multiple linear regressions to identify explanatory variables that affect the profitability and the extent of influence by these variables. The results of the regression analysis are discussed from economic aspects. This thesis contributes with strategic conclusions to the development of a business model for new and existing fitness businesses that aim to maximize profitability. The thesis can also be used as a tool in strategic development and give insight to how companies should approach the market. It includes an analysis of the competitive forces and external factors that may affect companies in the industry. Risk factors and growth opportunities are taken into account in the discussion about how companies can finance their operations. The regression analysis concludes that it is primarily the factors that affect the companies’ revenues and costs that have a significant impact on profitability. However, the results of the thesis also indicate that qualitative factors have a major impact on profitability.

• 277. Ayyer, A.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Bumping sequences and multispecies juggling2018In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 98, p. 100-126Article in journal (Refereed)

Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce “multispecies” juggling, which consist in having balls of different weights: when a ball is thrown it can possibly bump into a lighter ball that is then sent to a higher position, where it can in turn bump an even lighter ball, etc. We both study the case where the number of balls of each species is conserved and the case where the juggler sends back a ball of the species of its choice. In this latter case, we actually discuss three models: add-drop, annihilation and overwriting. The first two are generalisations of models presented in (ABCN) while the third one is new and its Markov chain has the ultra fast convergence property. We finally consider the case of several jugglers exchanging balls. In all models, we give explicit product formulas for the stationary probability and closed form expressions for the normalisation factor if known.

• 278. Ayyer, Arvind
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Some genelalized juggling processes (extended abstract)2015In: DMTCS proc. FPSAC'15, Nancy, France, 2015, p. 925-936Conference paper (Refereed)

We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models. We then consider the case of several jugglers exchanging balls. In all cases, we give explicit product formulas for the stationary probability and closed-form expressions for the normalization factor if known.

• 279. Ayyer, Arvind
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
An inhomogeneous multispecies TASEP on a ring2014In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 57, p. 21-43Article in journal (Refereed)

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove Lam and Williams' conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.

• 280. Ayyer, Arvind
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Correlations in the multispecies tasep and a conjecture by Lam2017In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 369, no 2, p. 1097-1125Article in journal (Refereed)

We study correlations in the multispecies TASEP on a ring. Results on the correlation of two adjacent points prove two conjectures by Thomas Lam on (a) the limiting direction of a reduced random walk in (A) over tilde (n-1) and (b) the asymptotic shape of a random integer partition with no hooks of length n, a so called n-core. We further investigate two-point correlations far apart and three-point nearest neighbour correlations and prove explicit formulas in almost all cases. These results can be seen as a finite strengthening of correlations in the TASEP speed process by Amir, Angel and Valko. We also give conjectures for certain higher order nearest neighbour correlations. We find an unexplained independence property (provably for two points, conjecturally for more points) between points that are closer in position than in value that deserves more study.

• 281.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av ett kösystem på IKEA Kungens Kurva2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Detta arbete har undersökt hur många betjäningsstationer avdelningen Byten och Återköp på IKEA Kungens Kurva behöver för att nå en förväntad kötid inom nio minuter.  Arbetet är uppdelat i en kvantitativ del samt en kvalitativ del.

Den kvantitativa delen av arbetet besvarade den matematiska frågeställningen där kön var modellerad enligt ett M|M|c-­‐system med Poissonfördelade ankomstintensiteter samt exponentialfördelade betjäningsintensiteter.  Resultatet var baserat på data från januari 2015.  I första hand reglerades antal betjäningsstationer för att nå en förväntad kötid under nio minuter.  I andra hand reglerades betjäningsintensiteten, om kötiden ännu inte uppnåtts.  Den kvalitativa delen av arbetet baserades på ett teoretiskt ramverk gällande Customer Relationship Management samt intervjuer med Avdelningschefen och Kundrelationschefen på IKEA Kungens Kurva.  Arbetets slutsats baserades på resultat från både den kvantitativa och den kvalitativa delen av arbetet.

Det matematiska resultatet presenterar antalet öppna betjäningsstationer som krävdes timme för timme under vardagar respektive helger för att nå en förväntad kötid under nio minuter.  Slutsatsen är att i de fall där den förväntade kötiden var strax över nio minuter kommer detta inte påverka kundrelationen, så länge en god betjäning ges, medan det matematiska resultatet bör tillämpas om den förväntade kötiden är långt över nio minuter.

• 282.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Recognition from collections of local features2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

An image matching system for object recognition in scenes of varying complexity was constructed in Matlab for evaluating the recognition quality of two types of image features: SURF (Speeded-Up Robust Features) and SIFT (Scale Invariant Feature Transform) using the affine Hough matching algorithm for finding matches between training and test images.

In the experimental part of the thesis, the matching was algorithm tested for varying number of image features extracted from the train and test images, namely 1000, 2000 and 3000 interest points. These experiments were carried out against 9 objects of different complexity, including difficulties such as repeating patterns on the image, down and upscaling of the object, cluttered scenes, silhouette features, partly occluded object and multiple known objects in the scene.

The work provides the directions for improvement of the given view-based recognition algorithm and suggests other possible ways to perform the object matching with higher quality.

• 283.
KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems.
KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems. KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems. KTH, Superseded Departments (pre-2005), Electrical Systems. KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems.
Distributed Two-stage Network Topology Processor for HVDC Grid Operation2017In: 2017 IEEE POWER & ENERGY SOCIETY GENERAL MEETING, IEEE , 2017Conference paper (Refereed)

This paper presents the results of an analysis of distributed two-stage coordination of network topology processor for HVDC grids. In the first stage of the two-stage processor, the substation topology is analyzed locally using an automated graph based algorithm. Thereafter, a distributed algorithm is proposed to used the neighboring information to realize the grid connectivity. For distributed islanding detection, the connectivity problem is formulated as a set of linear equations and solved iteratively using successive-over-relaxation method. The performance of the proposed methods versus conventional one-stage method has been tested in an islandinv, scenario for a 5-terminal HVDC grid.

• 284. Babuska, I.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, p. 2517-2539Article in journal (Refereed)

This work describes a solution to the validation challenge problem posed at the SANDIA Validation Challenge Workshop, May 21-23, 2006, NM. It presents and applies a general methodology to it. The solution entails several standard steps, namely selecting and fitting several models to the available prior information and then sequentially rejecting those which do not perform satisfactorily in the validation and accreditation experiments. The rejection procedures are based on Bayesian updates, where the prior density is related to the current candidate model and the posterior density is obtained by conditioning on the validation and accreditation experiments. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.

• 285. Babuska, I.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
Formulation of the static frame problem2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, p. 2496-2499Article in journal (Refereed)

This report describes a static framework validation challenge problem used in the SANDIA Validation Challenge Workshop, May 21-23, 2006. The challenge problem has clear engineering character, is simple to state and allows many different approaches to solve it. The regulatory assessment problem is to estimate the probability of a given vertical displacement to exceed a prescribed threshold.

• 286. Babuska, I.
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
Galerkin finite element approximations of stochastic elliptic partial differential equations2004In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 42, no 2, p. 800-825Article in journal (Refereed)

We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method generates independent identically distributed approximations of the solution by sampling the coefficients of the equation and using a standard Galerkin finite element variational formulation. The Monte Carlo method then uses these approximations to compute corresponding sample averages. The second method is based on a finite dimensional approximation of the stochastic coefficients, turning the original stochastic problem into a deterministic parametric elliptic problem. A Galerkin finite element method, of either the h- or p-version, then approximates the corresponding deterministic solution, yielding approximations of the desired statistics. We present a priori error estimates and include a comparison of the computational work required by each numerical approximation to achieve a given accuracy. This comparison suggests intuitive conditions for an optimal selection of the numerical approximation.

• 287.
Mainz University, Department of Mathematics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Dynamical Symmetries in Supersymmetric Matrix2008In: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 13, p. 103-116Article in journal (Refereed)

We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).

• 288. Bachas, Constantin
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Nahm's equations, {$\scr N=1^*$} domain walls, and {D}-strings in {${\rm AdS}_5\times S_5$}2001In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 7, p. Paper 41,28-Article in journal (Refereed)

We consider the following two problems: classical domain walls in the = 1* mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS5 correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.

• 289.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Valuation of Contingent Convertible Bonds2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Contingent convertible bonds are hybrid capital instruments, contingent on some form of indicator of financial distress of the issuing bank. Following the financial crisis, these instruments are proposed as a solution to the moral hazard issue of banks too big to fail. With the increased capital requirements of the Basel III directive, contingent capital enables banks to increase their capitalization without issuing expensive equity. Also, in times of historically low interest rates, these instruments might be interesting for investors in search of higher yields, as well as long term investors wanting to implement countercyclical investment strategies. However, due to the high complexity of these instruments, valuation has proven diffcult. The purpose of this thesis is to value instruments contingent on the bank's common equity tier 1 to risk-weighted assets ratio. We build our model upon the work of Glasserman & Nouri (2012), and extend it to include contingency on risk-weighted assets, instant non-continuous conversion to equity, and a combination of fixed imposed loss and fixed conversion price as terms of conversion. We use a capital structure model in continuous time to define asset dynamics, asset claims and the event of conversion and liquidation of the bank. Thereafter we use two important results from Glasserman & Nouri (2012) to value the discounted cash flows to holders of debt and contingent debt. From this, we arrive at closed form solutions for the coupon rates of these securities.

• 290. Backelin, Jörgen
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Parity splits by triple point distances in X-trees2006In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, no 1, p. 1-18Article in journal (Refereed)

At the conference Dress defined parity split maps by triple point distance and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This article gives an answer to that question. The characterisation for X-trees can be easily described as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map for an X-tree, then so is the entire map. To ensure that the parity split map comes from an X-tree which is binary and phylogenetic, we add two more technical conditions also based on studying at most five points at a time.

• 291.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Dependence Modelling and Risk Analysis in a Joint Credit-Equity Framework2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis is set in the intersection between separate types of financial markets, with emphasis on joint risk modelling. Relying on empirical findings pointing toward the ex- istence of dependence across equity and corporate debt markets, a simulation framework intended to capture this property is developed. A few different types of models form building blocks of the framework, including stochastic processes describing the evolution of equity and credit risk factors in continuous time, as well as a credit rating based model, providing a mechanism for imposing dependent credit migrations and defaults for firms participating in the market. A flexible modelling framework results, proving capable of generating dependence of varying strength and shape, across as well as within studied markets. Particular focus is given to the way markets interact in the tails of the distributions. By means of simulation, it is highlighted that dependence as produced by the model tends to spread asymmetrically with simultaneously extreme outcomes occurring more frequently in lower than in upper tails. Attempts to fit the model to observed market data featuring historical stock index and corporate bond index values are promising as both marginal distributions and dependence connecting the investigated asset types appear largely replicable, although we conclude further validation remains.

• 292.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
Numerical simulation of an inertial spheroidal particle in Stokes flow2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Particle suspensions occur in many situations in nature and industry. In this master’s thesis, the motion of a single rigid spheroidal particle immersed in Stokes flow is studied numerically using a boundary integral method and a new specialized quadrature method known as quadrature by expansion (QBX). This method allows the spheroid to be massless or inertial, and placed in any kind of underlying Stokesian flow.

A parameter study of the QBX method is presented, together with validation cases for spheroids in linear shear flow and quadratic flow. The QBX method is able to compute the force and torque on the spheroid as well as the resulting rigid body motion with small errors in a short time, typically less than one second per time step on a regular desktop computer. Novel results are presented for the motion of an inertial spheroid in quadratic flow, where in contrast to linear shear flow the shear rate is not constant. It is found that particle inertia induces a translational drift towards regions in the fluid with higher shear rate.

• 293. Baier, Stephan
ON PRIMES IN QUADRATIC PROGRESSIONS2009In: International Journal of Number Theory, ISSN 1793-0421, Vol. 5, no 6, p. 1017-1035Article in journal (Refereed)

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper by the authors [3].

• 294. Baker, Matthew
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Bitangents of tropical plane quartic curves2016In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 282, no 3-4, p. 1017-1031Article in journal (Refereed)

We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Whitney-Holder continuity of the SRB measure for transversal families of smooth unimodal maps2015In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 201, no 3, p. 773-844Article in journal (Refereed)

We consider families of nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure of , as a function of on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming existence of a transversal CE parameter, we find a positive measure set of CE parameters , and, for each , a set of polynomially recurrent parameters containing as a Lebesgue density point, and constants , , so that, for every -Holder function , In addition, for all , the renormalisation period of satisfies , and there are uniform bounds on the rates of mixing of for all with . If , the set contains almost all CE parameters. Lower bounds: Assuming existence of a transversal mixing Misiurewicz-Thurston parameter , we find a set of CE parameters accumulating at , a constant , and a function , so that C vertical bar t - t(0)vertical bar(1/2) >= vertical bar integral A(0)d mu(t) - integral A(0)d mu(t0) vertical bar >= C-1 vertical bar t - t(0)vertical bar(1/2), for all t is an element of Delta(MT)'.

• 296.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
On Constructing a Market Consistent Economic Scenario Generator2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
• 297. Balinsky, A.
KTH, Superseded Departments, Mathematics.
Generalized Hardy inequality for the magnetic Dirichlet forms2004In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 116, no 4-Jan, p. 507-521Article in journal (Refereed)

We obtain lower bounds for the magnetic Dirichlet form in dimensions d greater than or equal to 2. For d = 2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field B by an non-vanishing effective field which decays outside the support of B as dist( x, supp B)(-2). In the case d greater than or equal to 3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.

• 298.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Cauchy Integrals Method in the Study of Perturbations of Operators2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

We show that functions which are analytic on the open unit disc and fulfil the Hölder condition of order r  there, where r lies in the interval (0,1), are operator Hölder of order r on the set of all linear contractions on a Hilbert space. Further, it is known that analytic Lipschitz functions on the unit disc need not be operator Lipschitz. We show that under a certain additional integral condition, these functions are operator Lipschitz. The two results are shown by tools from operator theory including the Spectral theorem and dilations of contractions.

We also solve a problem related to theory of dilations which was arisen on a mathematical question- and answer site. More specificaly we show that, for a certain operator-valued polynomial, the von Neumann inequality is false.

• 299. Ball, Joseph A.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Extension of the nu-metric2012In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 6, no 1, p. 65-89Article in journal (Refereed)

We extend the nu-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.

• 300.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Modelling and Control of a Fixed-wing UAV for Landings on Mobile Landing Platforms2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Landing on mobile landing platforms could eliminate the need for landing gear. This would particularly benefit high altitude solar UAV, which typically have a very limited payload. Such landings would however require a precise and decoupled control of the UAV’s altitude and speed. In this thesis, a small UAV is modelled, and a flight control system suitable for such landings is developed.

The aerodynamic properties of the UAV were estimated using the vortex lattice method. Propeller performance data was obtained from the manufacturer and used in the propulsion model. The complete UAV model was validated using data from test flights. A comparison of period and damping of the dynamic modes showed a good agreement (<10% error) with the flight data, except for the phugoid damping, which was too low in the model.

The model was used to design two flight control systems, one consisting of three SISO loops for altitude, airspeed and course; and another using a TECS-based controller for airspeed and altitude. Extensive testing in simulation and flight revealed a superior performance of the TECS-based controller, especially in the ability to decouple altitude and airspeed responses.

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