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  • 1.
    Adelstrand, Carl
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Gavefalk, Sofia
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In times of regional geopolitical turmoil – why do some investment portfolios, equity funds, perform better than others? Is it simply luck, the effects of systematic risk or do factors such as investment styles and managerial skills play a significant part in the performance of a fund?

    As financial markets often reflect the macro environment, much of the previous year’s fluctuations of Eastern European stocks can be seen to derive from a number of geopolitical events; from the 2013 summer clashes between the Turkish police and opposing parties to the current issue concerning Russia and Ukraine. Needless to say, these events have affected return on equity in their regions and created a distressed environment for investors and equity fund managers investing in Eastern Europe.

    This thesis aims to explore how the aforementioned macroeconomic events impact the market and thus the portfolios of asset managers. The thesis also intends to provide aspects of eventual investment strategies that are more preferable than others under such circumstances, in order to mitigate the subsequent risks.

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  • 2.
    Afshar, Ardavan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A note on Halasz's Theorem in F-q[t]2023In: RESEARCH IN NUMBER THEORY, ISSN 2522-0160, Vol. 9, no 2, article id 24Article in journal (Refereed)
    Abstract [en]

    In the setting of the integers, Granville, Harper and Soundararajan showed that the upper bound in Halasz's Theorem can be improved for smoothly supported functions. We derive the analogous result for Halasz's Theorem in F-q[t], and then consider the converse question of when the general upper bound in this version of Halasz's Theorem is actually attained.

  • 3.
    Aghajani, Asadollah
    et al.
    School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Pointwise estimates for systems of coupled p-laplacian elliptic equations2023In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 22, no 3, p. 899-921Article in journal (Refereed)
    Abstract [en]

    This work examines positive solutions of systems of inequalities ±∆pu ≥ ρ(x)f (u), in Ω, where p = (p1, ..., pk), pi > 1 and ∆p is the diagonal-matrix diag(∆p1 , ..., ∆pk ), ∆pi is the pi-Laplace operator, Ω is an arbitrary domain (bounded or not) in RN (N ≥ 2), u = (u1, ..., uk)T and f = (f1, ..., fk)T are vector-valued functions and ρ(x) is a nonnegative function in Ω which is locally bounded. Using a maximum principle-based argument we provide explicit estimates on positive solutions u at each point x ∈ Ω, and as applications we find Liouville type results in unbounded domains such as RN, exterior domains or generally unbounded domains with the property that supx∈Ω dist(x, ∂Ω) = ∞, for various nonlinearities f and weights ρ. We also give explicit upper bounds on extremal parameters of related nonlinear multi-parameter eigenvalue problems in bounded domains.

  • 4.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hu, Yaozhong
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
    oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Mean-field backward stochastic differential equations and applications2022In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, article id 105196Article in journal (Refereed)
    Abstract [en]

    In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

  • 5.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Labed, Saloua
    Univ Mohamed Khider Biskra, Biskra, Algeria..
    Oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Yakhlef, Samia
    Univ Mohamed Khider Biskra, Biskra, Algeria..
    Singular Control Of Stochastic Volterra Integral Equations2022In: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 42, no 3, p. 1003-1017Article in journal (Refereed)
    Abstract [en]

    This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X-u,X-xi(t) =X(t) is given by X(t) = phi(t) + integral(t)(0) b (t, s, X(s), u(s)) ds + integral(t)(0) sigma (t, s, X(s), u(s)) dB(s) + integral(t )(0)h (t, s) d xi(s). Here dB(s) denotes the Brownian motion Ito type differential, xi denotes the singular control (singular in time t with respect to Lebesgue measure) and u denotes the regular control (absolutely continuous with respect to Lebesgue measure). Such systems may for example be used to model harvesting of populations with memory, where X(t) represents the population density at time t, and the singular control process xi represents the harvesting effort rate. The total income from the harvesting is represented by J(u, xi) = E[integral(T)(0) f(0)(t, X(t), u(t))dt + integral(T)(0) f(1)(t, X(t))d xi(t) + g(X(T))], for the given functions f(0), f(1) and g, where T > 0 is a constant denoting the terminal time of the harvesting. Note that it is important to allow the controls to be singular, because in some cases the optimal controls are of this type. Using Hida-Malliavin calculus, we prove sufficient conditions and necessary conditions of optimality of controls. As a consequence, we obtain a new type of backward stochastic Volterra integral equations with singular drift. Finally, to illustrate our results, we apply them to discuss optimal harvesting problems with possibly density dependent prices.

  • 6.
    Ahari, Mostafa Tanhayi
    et al.
    Department of Physics, Indiana University, Bloomington, IN 47405, USA; Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA.
    Bandyopadhyay, Sumanta
    Nordita SU; Department of Physics, Washington University in St. Louis, USA.
    Nussinov, Zohar
    Department of Physics, Washington University in St. Louis, USA.
    Seidel, Alexander
    Department of Physics, Washington University in St. Louis, USA.
    Ortiz, Gerardo
    Department of Physics, Indiana University, Bloomington, IN 47405, USA.
    Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons2023In: SciPost Physics, E-ISSN 2542-4653, Vol. 15, no 2, article id 043Article in journal (Refereed)
    Abstract [en]

    We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor ν = 2/3. The emergent Entangled Pauli Principle (EPP), introduced in Phys. Rev. B 98, 161118(R) (2018) and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M-clustering property within any given number of Landau levels, that is, wave functions with Mth-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of Phys. Rev. X 1, 021015 (2011) to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

  • 7.
    Ahlin, Filip
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlstedt, Anton
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    As a result of a more globalized and industrial world, sustainability issues in terms of the environment and society has become an everyday heading in the financial world. The fact that companies should work actively towards sustainability and accountability is today a necessity rather than a choice. The purpose of this study is to research responsible investment (RI) and portfolio performance. To examine this relationship the study focuses on ESG where its dimensions will be included jointly through optimization, discussion and conclusion. The report outlines how ESG can be integrated into the investment process, but the weight of the study addresses the discussion of a portfolio's performance at the inclusion of ESG. Methods used are Modern Portfolio Theory (MPT) combined with the implementation of ESG according to "best-in-class". The results of the study lead towards the conclusion that ESG in addition to its positive effects, provided an accurate assessment, on sustainability also is financially arguable for investors.

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  • 8. Al Marjani, A.
    et al.
    Garivier, A.
    Proutiere, Alexandre
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Navigating to the Best Policy in Markov Decision Processes2021In: Advances in Neural Information Processing Systems, Neural Information Processing Systems Foundation (NIPS) , 2021, p. 25852-25864Conference paper (Refereed)
    Abstract [en]

    We investigate the classical active pure exploration problem in Markov Decision Processes, where the agent sequentially selects actions and, from the resulting system trajectory, aims at identifying the best policy as fast as possible. We propose a problem-dependent lower bound on the average number of steps required before a correct answer can be given with probability at least 1 - δ. We further provide the first algorithm with an instance-specific sample complexity in this setting. This algorithm addresses the general case of communicating MDPs; we also propose a variant with a reduced exploration rate (and hence faster convergence) under an additional ergodicity assumption. This work extends previous results relative to the generative setting [MP21], where the agent could at each step query the random outcome of any (state, action) pair. In contrast, we show here how to deal with the navigation constraints, induced by the online setting. Our analysis relies on an ergodic theorem for non-homogeneous Markov chains which we consider of wide interest in the analysis of Markov Decision Processes.

  • 9.
    Alam, Amit
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Inas, Yakub
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Analys av reporäntans påverkan på prissättningen av bostäder: Slår reporänteförändringar lika mycket på bostäder av olika storlek?2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of this study is to investigate whether changes of the repo rate has diverse effects on apartments of different sizes, targeting specific areas in Stockholm. A conclusion, that the effect of the repo rate differs for apartments of different sizes, was made based on regression analysis and hypothesis testing. The housing market is characterized by vast shifts and the repo rate has reached a historical low-point of -0.25 per cent. It is reflected upon how the central bank’s steering interest rate actually impacts the prices on the housing market and whether it has distinct effects on apartments of different sizes. Apartments sold between years 2005-2015 have been analyzed where the gravity of the repo rate has been taken into consideration and if its significance varies amongst apartments of different sizes. Important parameters concerning apartment prices have been utilized in the constructed model.

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  • 10.
    Aleksanyan, Hayk
    Yerevan State University.
    Nonlinear approximation by renormalized trigonometric system2012In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 47, no 2, p. 86-96Article in journal (Refereed)
    Abstract [en]

    We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions are found for system’s normalization to guarantee almost everywhere convergence, and convergence in Lp(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees convergence almost everywhere for functions from L1(T), or uniform convergence for continuous functions.

  • 11.
    Aleksanyan, Hayk
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Yerevan State University, Armenia.
    On greedy algorithm by renormed Franklin system2010In: East Journal on Approximations, ISSN 1310-6236, Vol. 16, no 3, p. 273-296Article in journal (Refereed)
    Abstract [en]

    We characterize the all weighted greedy algorithms with respect to Franklin system which converge uniformly for continuous functions and almost everywhere for integrable functions. In case, when the algorithm fails to satisfy our classification criteria, we construct a continuous function for which the corresponding approximation diverges unboundedly almost everywhere. Some applications to wavelet systems are also discussed. 

  • 12.
    Aleksanyan, Hayk
    Yerevan State University.
    On the greedy algorithm by the Haar system2010In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 45, no 3, p. 151-161Article in journal (Refereed)
    Abstract [en]

    The paper investigates the uniform and almost everywhere convergence of the greedy algorithm by the Haar system. Necessary and sufficient conditions for norming the functions of Haar system are obtained, which guarantee the uniformconvergence for functions from C[0, 1] and almost everywhere convergence for functions from L1[0, 1].

  • 13.
    Aleksanyan, Hayk
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh, UK.
    Regularity of boundary data in periodic homogenization of elliptic systems in layered media2017In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 154, no 1-2, p. 225-256Article in journal (Refereed)
    Abstract [en]

    In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed boundary data corresponding to the limiting (homogenized) problem. This issue has been addressed in recent papers by Gérard-Varet and Masmoudi (Acta Math. 209:133–178, 2012), and by Prange (SIAM J. Math. Anal. 45(1):345–387, 2012), however, not much is known about the regularity of this fixed data. The main objective of this note is to initiate a study of this problem, and to prove several regularity results in this connection.

  • 14.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Karakhanyan, Aram
    The University of Edinburgh.
    K-surfaces with free boundaries2017Manuscript (preprint) (Other academic)
  • 15.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Discrete balayage and boundary sandpile2019In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 138, no 1, p. 361-403Article in journal (Refereed)
    Abstract [en]

    We introduce a new lattice growth model, which we call the boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on Z(d) (d >= 2) onto the boundary of an (a priori) unknown domain. The latter evolves through sandpile dynamics, and has the property that the mass on the boundary is forced to stay below a prescribed threshold. Since finding the domain is part of the problem, the redistribution process is a discrete model of a free boundary problem, whose continuum limit is yet to be understood. We prove general results concerning our model. These include canonical representation of the model in terms of the smallest super-solution among a certain class of functions, uniform Lipschitz regularity of the scaled odometer function, and hence the convergence of a subsequence of the odometer and the visited sites, discrete symmetry properties, as well as directional monotonicity of the odometer function. The latter (in part) implies the Lipschitz regularity of the free boundary of the sandpile.

    As a direct application of some of the methods developed in this paper, combined with earlier results on the classical abelian sandpile, we show that the boundary of the scaling limit of an abelian sandpile is locally a Lipschitz graph.

  • 16.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sjölin, Per
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    L2-estimates for singular oscillatory integral operators2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 441, no 2, p. 529-548Article in journal (Refereed)
    Abstract [en]

    In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2L2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R3.

  • 17. Aleman, A.
    et al.
    Baranov, A.
    Belov, Y.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces2022In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2022, no 10, p. 7390-7419Article in journal (Refereed)
    Abstract [en]

    We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ℱWp, whose weight is not necessarily radial. We show that in the spaces ℱWp, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form ℘n, that is, finite-dimensional subspaces consisting of polynomials of degree at most n. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges' ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.

  • 18.
    Alexandersson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Haglund, J
    Wang, G
    On the schur expansion of jack polynomials2018In: 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018, Formal Power Series and Algebraic Combinatorics , 2018Conference paper (Refereed)
    Abstract [en]

    We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases. 

  • 19.
    Alexandersson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Haglund, James
    Univ Penn, Philadelphia, PA 19104 USA..
    Wang, George
    Univ Penn, Philadelphia, PA 19104 USA..
    Some conjectures on the Schur expansion of Jack polynomials2021In: Journal of Combinatorics, ISSN 2156-3527, E-ISSN 2150-959X, Vol. 12, no 2, p. 215-233Article in journal (Refereed)
    Abstract [en]

    We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.

  • 20.
    Alexandersson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sulzgruber, Robin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    P-Partitions and p-Positivity2021In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2021, no 14, p. 10848-10907Article in journal (Refereed)
    Abstract [en]

    Using the combinatorics of alpha-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that generating functions of reverse p-partitions expand positively into quasisymmetric power sums. Consequently, any nonnegative linear combination of such functions is p-positive whenever it is symmetric. As an application, we derive positivity results for chromatic quasisymmetric functions, unicellular and vertical strip LLT polynomials, multivariate Tutte polynomials, and the more general B-polynomials, matroid quasisymmetric functions, and certain Eulerian quasisymmetric functions, thus reproving and improving on numerous results in the literature.

  • 21.
    Alexandersson, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sulzgruber, Robin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    P-partitions and p-positivity2019In: FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics , 2019Conference paper (Refereed)
    Abstract [en]

    Using the combinatorics of a-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that generating functions of reverse P-partitions expand positively into quasisymmetric power sums. Consequently any nonnegative linear combination of such functions is p-positive whenever it is symmetric. We apply this method to derive positivity results for chromatic quasisymmetric functions and unicellular LLT polynomials. 

  • 22.
    Alexis, Sara
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Uludag, Ebru
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimering av antal flygplanssäten: Modellering med avseende på yta, intäkt och efterfrågan 2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    When managing the number of seats in a plane it is important to take into account the passenger intensity, i.e. how tightly the seats are located. The critical variable for these decisions is the distance between a point on one seat and the same point on the next seat. Critical variables that have small values , i.e. short distance, means more rows of seats and thus higher profits. Any unused space is an expensive waste due to the fact that the difference between profit and loss for a given flight can be as little as less than a cost of a seat.

    The purpose of this thesis is to develop a mathematical model to find the optimal seat allocation between classes in an airplane. The modeling shall be performed so that the revenues for the airlines and usage of the surface of the cabin are maximized and yet meet demand. This thesis also aims to investigate which different market strategies of airlines there are and how these affect the seat allocation.

    The report shows that the revenue and demand are not the only factors that affect the optimal number of seats for a class, but that there are also external factors that may play a role. The model's ranking in reality is difficult to assess because of the lack of realistic and reliable data that can be used for a basis for decisions

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  • 23.
    Al-Khalaf, Adnan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Gustafsson, Steve Oskar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Valuing Patents with Linear Regression: Identifying value indicators and using a linear regression model to value  patents2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis consist of two parts. The first part of the thesis will conduct a multiple regression on a data-set obtained from the Ocean Tomo’s auction results between 2006 to 2008 with the purpose to identify key value indicators and investigate to what extent it is possible to predict the value of a patent. The final regression model consist of the following covariates Average number of citings per year, share of active family members, age of the patent, average invested USD per year, and nine CPC’s as dummy variables. The second part of the thesis will investigate why it is difficult to value a patent and the different factors and changes that have contributed to a growing importance of patent valuation by applying theories from knowledge-based economy and industrial change. This is done by conducting a literature review and interviews.

    The results of this thesis states that it is only possible to construct a model that has an explanation degree of 50.21%. The complexity of a patents value derives from uncertainties about future context of the patent and non-quantifiable parameters of the patent. Furthermore we find evidence of a shift from tangible assets to intangible assets in industrial nations which motivates the growing importance of patent valuation.

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  • 24.
    Allen, Mark
    et al.
    Brigham Young Univ, Dept Math, Provo, UT 84602 USA..
    Kriventsov, Dennis
    Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA..
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The inhomogeneous boundary Harnack principle for fully nonlinear and p-Laplace equations2023In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 40, no 1, p. 133-156Article in journal (Refereed)
    Abstract [en]

    We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and p-Laplace-type equations with a right-hand side, as well as for the Laplace equa-tion on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.

  • 25.
    Altmann, Robert
    et al.
    Univ Augsburg, Inst Math, D-86159 Augsburg, Germany..
    Henning, Patrick
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. Ruhr Univ Bochum, Fak Math, D-44801 Bochum, Germany..
    Peterseim, Daniel
    Univ Augsburg, Inst Math, D-86159 Augsburg, Germany..
    Numerical homogenization beyond scale separation2021In: Acta Numerica, ISSN 0962-4929, E-ISSN 1474-0508, Vol. 30, p. 1-86, article id PII S0962492921000015Article in journal (Refereed)
    Abstract [en]

    Numerical homogenization is a methodology for the computational solution of multiscale partial differential equations. It aims at reducing complex large-scale problems to simplified numerical models valid on some target scale of interest, thereby accounting for the impact of features on smaller scales that are otherwise not resolved. While constructive approaches in the mathematical theory of homogenization are restricted to problems with a clear scale separation, modern numerical homogenization methods can accurately handle problems with a continuum of scales. This paper reviews such approaches embedded in a historical context and provides a unified variational framework for their design and numerical analysis. Apart from prototypical elliptic model problems, the class of partial differential equations covered here includes wave scattering in heterogeneous media and serves as a template for more general multi-physics problems.

  • 26.
    Alvfors, Oskar
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Björelind, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimization of Production Scheduling in the Dairy Industry2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis presents a case study of mathematical production scheduling optimization applied on Arla Foods AB’s production of dairy products. The scheduling was performed as a possible remedy for problems caused by overcrowded finished goods warehouse. Based on the scheduling, conclusions were made on whether the existing two-shift production is sufficient or if an additional night shift should be introduced. In parallel, an empirical and theoretical analysis on the perceived effects of night shift work on employees was conducted.

    For the optimization, mixed integer programming was used to model the production context through a discrete time scheduling lot-sizing model developed in this thesis. The model developed and implemented on Arla Foods AB contributes to the research field through its feature of relatively low complexity enabling scheduling of extensive production systems when applied in industrial contexts where products may be categorized.

    The thesis concludes that mathematical production scheduling can solve Arla Foods AB’s production problematics and suggests reallocation of the existing shifts for the purpose of reduced costs and acceptable warehouse levels. This reallocation would incur production during inconvenient hours whereas management remedies reducing negative effects of night shift work are identified.

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  • 27.
    Ames, Ellery
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Andreasson, Håkan
    Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden..
    Logg, Anders
    Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden..
    Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity2019In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 99, no 2, article id 024012Article in journal (Refereed)
    Abstract [en]

    We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have nonvanishing angular momentum. As the parameters are tuned to more relativistic solutions (measured e.g., by an increasing redshift) we provide evidence for a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become locally rotationally symmetric about the matter density. The existence of a deficit angle in these regions is investigated.

  • 28.
    Amo-Navarro, Jesus
    et al.
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Conejero, J. Alberto
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Hoyas, Sergio
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives2021In: Mathematics, E-ISSN 2227-7390, Vol. 9, no 19, article id 2508Article in journal (Refereed)
    Abstract [en]

    In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.

  • 29.
    Amundsson, Karl
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Approximate Bayesian Learning of Partition Directed Acyclic Graphs2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Partition directed acyclic graphs (PDAGs) is a model whereby the conditional probability tables (CPTs) are partitioned into parts with equal probability. In this way, the number of parameters that need to be learned can be significantly reduced so that some problems become more computationally feasible. PDAGs have been shown to be connected to labeled DAGs (LDAGs) and the connection is summarized here. Furthermore, a clustering algorithm is compared to an exact algorithm for determining a PDAG. To evaluate the algorithm, we use it on simulated data where the expected result is known.

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  • 30.
    Andersson, Joel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On Invertibility of the Radon Transform and Compressive Sensing2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property.

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  • 31.
    Andersson, Joel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Boman, Jan
    Stockholm University.
    Stability estimates with a priori bound for the inverse local Radon transformManuscript (preprint) (Other academic)
    Abstract [en]

    We consider the inverse problem for the 2-dimensional weighted local Radon transform , where  is supported in  and is defined near . For weight functions satisfying a certain differential equation we give weak estimates of in terms of  for functions  that satisfies an a priori bound.

  • 32.
    Andersson, John
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    ALMOST EVERYWHERE REGULARITY FOR THE FREE BOUNDARY OF THE p-HARMONIC OBSTACLE PROBLEM p > 22021In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 32, no 3, p. 415-433Article in journal (Refereed)
    Abstract [en]

    Let u be a solution to the normalized p-harmonic obstacle problem with p > 2. That is, u is an element of W-1,W-p(B-1(0)), 2 < p < infinity, u >= 0 and div(vertical bar del u vertical bar(p-2) del u) = chi({u>0}) in B-1(0) where u(x) >= 0 and chi(A) is the characteristic function of the set A. The main result is that for almost every free boundary point with respect to the (n - 1)-Hausdorff measure, there is a neighborhood where the free boundary is a C-1,C-beta-graph. That is, for Hn-1- a.e. point x(0) is an element of partial derivative{u > 0}boolean AND B-1(0) there is an r > 0 such that B-r(x(0))boolean AND partial derivative{u > 0} is an element of C-1,C-beta.

  • 33.
    Andersson, Nicole
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Söderberg, Petra
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A study of the most important volume drivers for sparkling wine in Sweden2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This paper examines the factors that affect volume of sparkling wine sold at licensed Swedish liquor stores. Regression analysis is used to model the relationship between the identified parameters believed to have an impact on the volume sold.

    Social sustainability is also covered, and will be examined in the context of a deregulated alcohol market in the future. A 5C analysis and an analysis based on both WACOSS Social Sustainability framework and Social Life’s framework have been conducted.

    Results from the regression analysis show that the parameters which affected the volume sold fell into three categories: Country, what kind of grape, and price. Most parameters affected the volume sold in a positive way; except for wines from New Zealand and higher priced wine which reduce the volume sold.

    This thesis arrives at the conclusion that a regulated alcohol market is favorable in Sweden since the aim is to keep the alcohol consumption low and the overall public health high. 

  • 34.
    André, Léo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Prediction of French day-ahead electricity prices: Comparison between a deterministic and a stochastic approach2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis deals with the new flow-based computation method used in the Central Western Europe Area. This is done on the financial side. The main aim is to produce some robust methods for predicting. Two approaches are used: the first one is based on a deterministic and algorithmic method involving the study of the interaction between the fundamentals and the prices. The other one is a more statistical approach based on a time series modeling of the French flow-based prices. Both approaches have advantages and disadvantages which will be discussed in the following. The work is mainly based on global simulated data provided by CASC in their implementation phase of the flow-base in Western Europe.

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  • 35. Arakelyan, A.
    et al.
    Shah Gholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Multi-Phase Quadrature Domains and a Related Minimization Problem2016In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, p. 1-21Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.

  • 36.
    Aronsson, Petter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ronneback Thomson, Joachim
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimal löptidsallokering av bostadslån2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This Bachelor’s thesis introduces a dynamic method for allocation of adjustable-rate mortgages which can be used to reduce a growing social problem. The Swedish household’s debt has steadily increased and the primary cause is mortgages loans, used to fund the purchase of a real property. Because of a period of rising home prices, Swedes are mortgaged more than ever [1]. If interest rates go up there is an increased risk of not managing the interest charge which is the greatest expense for many households.

    However, there is an absence in the debate of the importance of efficient and safe mortgages. By means of the introduced dynamic method, this thesis optimizes the allocation of adjustable-rate mortgages, using both historical and future cases. In the forecasting case, expected interest charge and risk are being minimized. More specifically, the method consider three levels of risk which all values expected interest charge and risk differently. Further, the goal is to apply the dynamic method for decision support in reality and also commercialize as a business idea.

    Modeling mortgage as a network flow is essential for the dynamic method. This way enables analysis of mortgages during a period of time which is necessary for determining an optimal allocation of adjustable-rate mortgages. The result from the historical case shows that shorter adjustment periods have been more favorable. Though, to an extent lower than expected – only during seven out of the last seventeen years. In addition, the results from the forecasting case indicate that it is advantageous to choose longer adjustment periods. Finally introduces a business model for the startup company, Looptime AB, of which business idea is toadminister mortgages for households, residents’ associations and non-financial companies.

  • 37.
    Aurell, Alexander
    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
    Abstract [en]

    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.

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  • 38.
    Aurell, Erik
    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)
    Abstract [en]

    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.

  • 39.
    Axelsson, Rebecca
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Källsbo, Rebecca
    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
    Abstract [en]

    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.

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  • 40.
    Babaheidar, Persheng
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jernbeck, Michaela
    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
    Abstract [sv]

    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. 

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  • 41.
    Backman, Fredrik
    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
    Abstract [en]

    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.

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  • 42.
    Bagge, Joar
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Fast Ewald summation for Stokes flow with arbitrary periodicity2023In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 493, p. 112473-, article id 112473Article in journal (Refereed)
    Abstract [en]

    A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stokes flow to periodic boundary conditions in any number (three, two, one, or none) of the spatial directions, in a unified framework. The periodic potential is split into a short-range and a long-range part, where the latter is treated in Fourier space using the fast Fourier transform. A crucial component of the method is the modified kernels used to treat singular integration. We derive new modified kernels, and new improved truncation error estimates for the stokeslet and stresslet. An automated procedure for selecting parameters based on a given error tolerance is designed and tested. Analytical formulas for validation in the doubly and singly periodic cases are presented. We show that the computational time of the method scales like O(Nlog⁡N) for N sources and targets, and investigate how the time depends on the error tolerance and window function, i.e. the function used to smoothly spread irregular point data to a uniform grid. The method is fastest in the fully periodic case, while the run time in the free-space case is around three times as large. Furthermore, the highest efficiency is reached when applying the method to a uniform source distribution in a primary cell with low aspect ratio. The work presented in this paper enables efficient and accurate simulations of three-dimensional Stokes flow with arbitrary periodicity using e.g. boundary integral and potential methods.

  • 43.
    Bakan, Andrew
    et al.
    Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 01601, Ukraine.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Exponential Integral Representations of Theta Functions2020In: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 20, no 3-4, p. 591-621Article in journal (Refereed)
    Abstract [en]

    Let Θ3(z) : = ∑ n∈Zexp (i πn2z) be the standard Jacobi theta function, which is holomorphic and zero-free in the upper half-plane H:={z∈C|Imz&gt;0}, and takes positive values along i R&gt; 0, the positive imaginary axis, where R&gt; 0: = (0 , + ∞). We define its logarithm log Θ3(z) which is uniquely determined by the requirements that it should be holomorphic in H and real-valued on i R&gt; 0. We derive an integral representation of log Θ3(z) when z belongs to the hyperbolic quadrilateral F□||:={z∈C|Imz&gt;0,-1≤Rez≤1,|2z-1|&gt;1,|2z+1|&gt;1}.Since every point of H is equivalent to at least one point in F□|| under the theta subgroup of the modular group on the upper half-plane, this representation carries over in modified form to all of H via the identity recorded by Berndt. The logarithms of the related Jacobi theta functions Θ4 and Θ2 may be conveniently expressed in terms of log Θ3 via functional equations, and hence get controlled as well. Our approach is based on a study of the logarithm of the Gauss hypergeometric function for a specific choice of the parameters. This has connections with the study of the universally starlike mappings introduced by Ruscheweyh, Salinas, and Sugawa.

  • 44.
    Bakan, Andrew
    et al.
    Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine..
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Montes-Rodriguez, Alfonso
    Univ Seville, Dept Math Anal, ES-41004 Seville, Spain..
    Radchenko, Danylo
    Swiss Fed Inst Technol Zurich ETHZ, Dept Math, CH-8092 Zurich, Switzerland..
    Viazovska, Maryna
    Swiss Fed Inst Technol Lausanne EPFL, Inst Math, CH-1015 Lausanne, Switzerland..
    Fourier uniqueness in even dimensions2021In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 118, no 15, article id e2023227118Article in journal (Refereed)
    Abstract [en]

    In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discrete set, with the striking application of resolving the sphere packing problem in dimensions d = 8 and d = 24. In this short note, we present an alternative approach to such results, viable in even dimensions, based instead on the uniqueness theory for the KleinGordon equation. Since the existing method for the Klein-Gordon uniqueness theory is based on the study of iterations of Gauss-type maps, this suggests a connection between the latter and methods involving modular forms. The derivation of Fourier uniqueness from the Klein-Gordon theory supplies conditions on the given test function for Fourier interpolation, which are hoped to be optimal or close to optimal.

  • 45.
    Balmer, Georg Robert
    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
    Abstract [en]

    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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  • 46.
    Barbero, G. J. Fernando
    et al.
    IEM CSIC, Inst Estruct Mat, Serrano 123, Madrid 28006, Spain.;Inst Gregorio Millan UC3M, Grp Teorias Campos & Fis Estadist, Ave Univ 30, Leganes 28911, Spain..
    Basquens, Marc
    KTH, School of Industrial Engineering and Management (ITM), Energy Technology, Applied Thermodynamics and Refrigeration. Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Leganes 28911, Spain..
    Villasenor, Eduardo J. S.
    Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Leganes 28911, Spain.;Inst Gregorio Millan UC3M, Grp Teorias Campos & Fis Estadist, Ave Univ 30, Leganes 28911, Spain..
    Euclidean self-dual gravity: Ashtekar variables without gauge fixing2024In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 109, no 6, article id 064047Article in journal (Refereed)
    Abstract [en]

    The Gotay-Nester-Hinds method is used in this paper to study the Hamiltonian formulation of the Euclidean self-dual action. This action can be used to arrive at the complex Ashtekar formulation of general relativity or a real connection formulation for Euclidean general relativity. The main result of the paper is a derivation of the Ashtekar formulation for Euclidean gravity without using any gauge fixing. It is interesting to compare this derivation with the one corresponding to the Holst action. In particular it is worth noting that no "tertiary" constraints appear in the case considered in the present paper.

  • 47.
    Barhoumi, Ahmad
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). University of Michigan, East Hall, 530 Church St., Ann Arbor, MI 48109, USA.
    Lisovyy, Oleg
    Institut Denis-Poisson, Université de Tours, CNRS, Parc de Grandmont, 37200, Tours, France, Parc de Grandmont.
    Miller, Peter D.
    Department of Mathematics, University of Michigan, East Hall, 530 Church St., Ann Arbor, MI, 48109, USA, East Hall, 530 Church St..
    Prokhorov, Andrei
    Department of Mathematics, University of Michigan, East Hall, 530 Church St., Ann Arbor, MI, 48109, USA, East Hall, 530 Church St.; St. Petersburg State University, Universitetskaya emb. 7/9, 199034, St. Petersburg, Russia, Universitetskaya emb. 7/9.
    Painlevé-III Monodromy Maps Under the D<inf>6</inf> → D<inf>8</inf> Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions2024In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 20, article id 19Article in journal (Refereed)
    Abstract [en]

    The third Painlevé equation in its generic form, often referred to as Painlevé-III(D6), is given by [Formula Presented] Starting from a generic initial solution u0 (x) corresponding to parameters α, β, denoted as the triple (u0 (x), α, β), we apply an explicit Bäcklund transformation to generate a family of solutions (un (x), α + 4n, β + 4n) indexed by n ∈ N. We study the large n behavior of the solutions (un (x), α + 4n, β + 4n) under the scaling x = z/n in two different ways: (a) analyzing the convergence properties of series solutions to the equation, and (b) using a Riemann–Hilbert representation of the solution un (z/n). Our main result is a proof that the limit of solutions un (z/n) exists and is given by a solution of the degenerate Painlevé-III equation, known as Painlevé-III(D8), [Formula Presented]. z A notable application of our result is to rational solutions of Painlevé-III(D6), which are constructed using the seed solution (1, 4m, −4m) where m ∈ C\(Z +12) and can be written as a particular ratio of Umemura polynomials. We identify the limiting solution in terms of both its initial condition at z = 0 when it is well defined, and by its monodromy data in the general case. Furthermore, as a consequence of our analysis, we deduce the asymptotic behavior of generic solutions of Painlevé-III, both D6 and D8 at z = 0. We also deduce the large n behavior of the Umemura polynomials in a neighborhood of z = 0.

  • 48. Barreiro-Gomez, J.
    et al.
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Duncan, T. E.
    Pasik-Duncan, B.
    Tembine, H.
    Fractional Mean-Field-Type Games under Non-Quadratic Costs: A Direct Method2019In: Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc. , 2019, p. 293-298Conference paper (Refereed)
    Abstract [en]

    This work examines the solvability of fractional conditional mean-field-type games. The evolution of the state is described by a time-fractional stochastic dynamics driven by jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motion and multi-fractional Brownian motion. The cost functional is non-quadratic and includes a fractional-integral of an higher order polynomial. We provide semi-explicitly the equilibrium strategies in state-and-conditional mean-field-type feedback form for all decision-makers. 

  • 49.
    Bartold, Martina
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Wachtmeister, Caroline
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Studie av korrelation mellan valutapar relaterade till Skandinavien2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Is there a correlation between exchange rates for currency pairs related to Scandinavia? How can this information be used in foreign exchange trading?

    This Bachelor’s thesis in Mathematical Statistics and Industrial Management aims to investigate the correlation between prices for currency pairs on the Scandinavian market. The problem formulation for the mathematical part has been designed in cooperation with Pär Hellström, a Senior Quant Trader at the electronic foreign exchange trading department at SEB. Pärs main responsibilities is to manage and develop models that are used for algorithmic currency trading. The result of the correlation study is supposed to contribute additional knowledge about the correlation on the Scandinavian currency market.

    The Bachelor’s thesis is divided into several parts. The purpose of the first part is to give a background about currency trading, electronic foreign exchange trading and algorithmic trading.

    In the subsequent part in Mathematical Statistics the correlation study is conducted. The study of correlation is made for a long time interval and for a number of shorter time intervals over the same time period in order to determine if there are periods when the correlation of the studied currency pairs change drastically. Data for the currency pairs are modified and a simple linear regression is performed for two currency pairs at a time. Based on the regressions, correlation coefficients and their significance is calculated. The correlation study shows that for the longer time interval there is a significant and strong or very strong correlation or anticorrelation between several of the currency pairs related to Scandinavia. Furthermore, the correlation study shows that the correlation is dependent on the studied time interval and that all combinations of currency pairs exhibit correlation changes over time. The changes in correlation between two currency pairs are primarily due

    to a large price change for one or both of the currency pairs.

    The Bachelor’s thesis concludes with a discussion about why correlation should be taken into account in currency trading and whether correlation should be used in algorithmic currency trading. Based on articles and theories of behavioral finance it is also discussed what differentiates a traditional currency trader and algorithmic foreign exchange trading. We have come to the conclusion that correlation should be considered in algorithmic currency trading. The behavioral aspect of a traditional trader is the trader’s emotional reactions and the psychological factors when trading, while the behavioral aspect of a trading algorithm is the construction of the trading algorithm by humans.

  • 50.
    Bayer, Christian
    et al.
    Weierstrass Institute for Applied Analysis and Stochastics.
    Hoel, Håkon
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Kadir, Ashraful
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Plechac, Petr
    Dept. of Mathematical Sciences, University of Delaware.
    Sandberg, Mattias
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Tempone, Raul
    Division of Mathematics, King Abdullah University of Science and Technology.
    How accurate is molecular dynamics?2012Report (Other academic)
    Abstract [en]

    Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding hitting time Hamilton-Jacobi equation for non ergodic dynamics, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on theBorn-Oppenheimer approximation, Schrödinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy.

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