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Numrering	Referens	Omslagsbild	Hitta
1.	Sorooshian, Shahryar, 1980, et al. (författare) Expedited analytical hierarchical process for multicriteria decision making 2022 Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151 Tidskriftsartikel (refereegranskat)abstract In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
2.	Sorooshian, Shahryar, 1980, et al. (författare) Performance of the decision-making trial and evaluation laboratory 2023 Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514 Tidskriftsartikel (refereegranskat)abstract Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
3.	Strömberg, Ann-Brith, 1961, et al. (författare) Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods 2020 Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
4.	Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings 2021 Samlingsverk (redaktörskap) (refereegranskat)abstract This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
5.	Gäfvert, Oliver, 1991- (författare) Topological and geometrical methods in data analysis 2021 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. The shape is described using a persistence module, which characterizes the topological features of the filtration, and the final step of the pipeline extracts algebraic invariants from this object. The second pipeline, referred to as the geometric data analysis (GDA) pipeline, associates an algebraic variety to a given data set and aims to describe the structure of this variety. Its structure is described using homology, an invariant which for most algebraic varieties can only be computed numerically using sampling methods.In Paper A we consider invariants on multi-parameter persistence modules. We explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.In Paper B we introduce an efficient algorithm to compute a minimal presentation of a multi-parameter persistent homology module, given a chain complex of free modules as input. Our approach extends previous work on this problem in the 2-parameter case, and draws on ideas underlying the F4 and F5 algorithms for Gröbner basis computation. In the r-parameter case, our algorithm computes a presentation for the homology of C ->F A ->G B, with modules of rank l,n,m respectively, in O(r2nr+1 + nrm + nr-1m2 + rn2 l) arithmetic operations. We implement this approach in our new software Muphasa, written in C++. In preliminary computational experiments on synthetic TDA examples, we compare our approach to a version of a classical approach based on Schreyer's algorithm, and find that ours is substantially faster and more memory efficient. In the course of developing our algorithm for computing presentations, we also introduce algorithms for the closely related problems of computing Gröbner bases for the image and kernel of the morphism G. This algorithm runs in time O(nrm + nr-1m2) and memory O(n2 + mn + nr + K), where K is the size of the output.Paper C analyzes the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in RN. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDD) of a certain variety called the hypothesis variety as the number of points in the configuration increases. Finally, we establish a connection to complexity of architectures of polynomial neural networks. For the problem of fitting an (N-1)-sphere to a configuration of m points in RN, we give a closed formula for the algebraic complexity of the hypothesis variety as m grows for the case of N=1. For the case N>1 we conjecture a generalization of this formula supported by numerical experiments.In Paper D we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing bottlenecks of the variety. Using geometric information such as the bottlenecks and the local reach we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et. al. (2019).
6.	Fotedar, Sunney, 1989, et al. (författare) A criterion space decomposition approach to generalized tri-objective tactical resource allocation 2023 Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20:1 Tidskriftsartikel (refereegranskat)abstract We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the generalized tactical resource allocation problem (GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the quadrant shrinking method (QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances.
7.	Fotedar, Sunney, 1989 (författare) Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops 2023 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item , multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory. In Paper I , we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II , we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III , we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV , using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap .
8.	Obradovic, Gabrijela, 1994, et al. (författare) Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model 2024 Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101 Tidskriftsartikel (refereegranskat)abstract Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
9.	Gerken, Jan, 1991, et al. (författare) Equivariance versus augmentation for spherical images 2022 Ingår i: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421 Konferensbidrag (refereegranskat)abstract We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.
10.	Brandes, Julia, et al. (författare) On generating functions in additive number theory, II: lower-order terms and applications to PDEs 2021 Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76 Tidskriftsartikel (refereegranskat)abstract We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) \| Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))\| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
11.	Ericsson, Niklas, 1968 (författare) A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain 2021 Ingår i: Computational Methods in Applied Mathematics. - : Walter de Gruyter GmbH. - 1609-4840 .- 1609-9389. ; 21:4 Tidskriftsartikel (refereegranskat)abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems. © 2021 Ericsson, published by De Gruyter 2021.
12.	Malik, Adam, 1991 (författare) Mathematical Modelling of Cell Migration and Polarization 2020 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract Cell migration plays a fundamental role in both development and disease. It is a complex process during which cells interact with one another and with their local environment. Mathematical modelling offers tools to investigate such processes and can give insights into the underlying biological details, and can also guide new experiments. The first two papers of this thesis are concerned with modelling durotaxis, which is the phenomena where cells migrate preferentially up a stiffness gradient. Two distinct mechanisms which potentially drive durotaxis are investigated. One is based on the hypothesis that adhesion sites of migrating cells become reinforced and have a longer lifespan on stiffer substrates. The second mechanism is based on cells being able to generate traction forces, the magnitude of which depend on the stiffness of the substrate. We find that both mechanisms can indeed give rise to biased migration up a stiffness gradient. Our results encourages new experiments which could determine the importance of the two mechanisms in durotaxis. The third paper is devoted to a population-level model of cancer cells in the brain of mice. The model incorporates diffusion tensor imaging data, which is used to guide the migration of the cells. Model simulations are compared to experimental data, and highlights the model’s difficulty in producing irregular growth patterns observed in the experiments. As a consequence, the findings encourage further model development. The fourth paper is concerned with modelling cell polarization, in the absence of environmental cues, referred to as spontaneous symmetry breaking. Polarization is an important part of cell migration, but also plays a role during division and differentiation. The model takes the form of a reaction diffusion system in 3D and describes the spatio-temporal evolution of three forms of Cdc42 in the cell. The model is able to produce biologically relevant patterns, and numerical simulations show how model parameters influence key features such as pattern formation and time to polarization.
13.	Zhao, D., et al. (författare) Low Phase-Rank Approximation 2022 Ingår i: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 639, s. 177-204 Tidskriftsartikel (refereegranskat)abstract In this paper, we propose and solve low phase-rank approximation problems, which serve as a counterpart to the well-known low-rank approximation problem and the Schmidt-Mirsky theorem. It is well known that a nonzero complex number can be specified by its gain and phase, and while it is generally accepted that the gains of a matrix may be defined by its singular values, there is no widely accepted definition for its phases. In this work, we consider sectorial matrices, whose numerical ranges do not contain the origin, and adopt the canonical angles of such matrices as their phases. Similarly to the rank of a matrix being defined as the number of its nonzero singular values, we define the phase-rank of a sectorial matrix as the number of its nonzero phases. While a low-rank approximation problem is associated with the matrix arithmetic mean, it turns out that a natural parallel for the low phase-rank approximation problem is to use the matrix geometric mean to measure the approximation error. Importantly, we derive a majorization inequality between the phases of the geometric mean and the arithmetic mean of the phases, similarly to the Ky-Fan inequality for eigenvalues of Hermitian matrices. A characterization of the solutions to the proposed problem, with the same flavor as the Schmidt-Mirsky theorem, is then obtained in the case where both the objective matrix and the approximant are restricted to be positive-imaginary. In addition, we provide an alternative formulation of the low phase-rank approximation problem using geodesic distances between sectorial matrices. The two formulations give rise to the exact same set of solutions when the involved matrices are additionally assumed to be unitary. © 2022 Elsevier Inc.
14.	Laksman, Efraim, 1983, et al. (författare) The stochastic opportunistic replacement problem, part III: improved bounding procedures 2020 Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733 Tidskriftsartikel (refereegranskat)abstract We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.
15.	Casarino, V., et al. (författare) On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one 2024 Ingår i: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891. ; 203:1, s. 205-219 Tidskriftsartikel (refereegranskat)abstract Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1, 1) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p < 8 were already known.
16.	Kavallaris, Nikos I., et al. (författare) On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions 2024 Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences. - 1937-1632 .- 1937-1179. ; 17:3, s. 1222-1268 Tidskriftsartikel (refereegranskat)abstract In this paper, we study a stochastic parabolic problem involving anonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixtureof a classical Brownian and a fractional Brownian motion with Hurst indexH ∈ (1/2, 1). We first establish local in time existence results and then exploreconditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals ofBrownian motion as well as tail estimates for the fractional Brownian motionwe provide analytic estimates for certain quantities of interest, such as upperbounds for quenching times and the corresponding quenching probabilities.The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analyticalresults demonstrate the non-trivial impact of the noise on the dynamics ofthe system. The analytic results are complemented with a detailed numericalstudy of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of theresults in this context are commented upon.
17.	Silvestrov, Sergei, Professor, 1970-, et al. (författare) Algebraic Structures and Applications 2020 Bok (refereegranskat)
18.	Anton, Rikard, et al. (författare) A fully discrete approximation of the one-dimensional stochastic heat equation 2020 Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press. - 0272-4979 .- 1464-3642. ; 40:1, s. 247-284 Tidskriftsartikel (refereegranskat)abstract A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space–time white noise is presented. The standard ﬁnite difference approximation is used in space and a stochastic exponential method is used for the temporal approximation. Observe that the proposed exponential scheme does not suffer from any kind of CFL-type step size restriction. When the drift term and the diffusion coefﬁcient are assumed to be globally Lipschitz this explicit time integrator allows for error bounds in Lq(Ω), for all q ≥ 2, improving some existing results in the literature. On top of this we also prove almost sure convergence of the numerical scheme. In the case of nonglobally Lipschitz coefﬁcients, under a strong assumption about pathwise uniqueness of the exact solution, convergence in probability of the numerical solution to the exact solution is proved. Numerical experiments are presented to illustrate the theoretical results.
19.	Araujo-Cabarcas, Juan Carlos, 1981-, et al. (författare) Shape optimization for the strong directional scattering of dielectric nanorods 2021 Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 122:8, s. 3683-3704 Tidskriftsartikel (refereegranskat)abstract In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.
20.	Araujo-Cabarcas, Juan Carlos, 1981-, et al. (författare) Shape optimization for the strong routing of light in periodic diffraction gratings 2023 Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 472 Tidskriftsartikel (refereegranskat)abstract In the quest for the development of faster and more reliable technologies, the ability to control the propagation, confinement, and emission of light has become crucial. The design of guide mode resonators and perfect absorbers has proven to be of fundamental importance. In this project, we consider the shape optimization of a periodic dielectric slab aiming at efficient directional routing of light to reproduce similar features of a guide mode resonator. For this, the design objective is to maximize the routing efficiency of an incoming wave. That is, the goal is to promote wave propagation along the periodic slab. A Helmholtz problem with a piecewise constant and periodic refractive index medium models the wave propagation, and an accurate Robin-to-Robin map models an exterior domain. We propose an optimal design strategy that consists of representing the dielectric interface by a finite Fourier formula and using its coefficients as the design variables. Moreover, we use a high order finite element (FE) discretization combined with a bilinear Transfinite Interpolation formula. This setting admits explicit differentiation with respect to the design variables, from where an exact discrete adjoint method computes the sensitivities. We show in detail how the sensitivities are obtained in the quasi-periodic discrete setting. The design strategy employs gradient-based numerical optimization, which consists of a BFGS quasi-Newton method with backtracking line search. As a test case example, we present results for the optimization of a so-called single port perfect absorber. We test our strategy for a variety of incoming wave angles and different polarizations. In all cases, we efficiently reach designs featuring high routing efficiencies that satisfy the required criteria.
21.	Engström, Christian (författare) On spectral enclosures for Maxwell’s equations with the Drude-Lorentz model 2024 Ingår i: Applied Mathematics Letters. - : Elsevier. - 0893-9659 .- 1873-5452. ; 155 Tidskriftsartikel (refereegranskat)abstract In this paper, we compare two approaches to derive spectral enclosures for Maxwell’s equations with the Drude–Lorentz model in possibly unbounded domains. The enclosures can be computed in the infinite-dimensional case as well as for the matrix-valued function obtained after a discretization. The enclosures are minimal given only the numerical ranges of the operator coefficients and we compare in the case of purely imaginary poles the derived enclosures with enclosures from the literature.
22.	Mousavi, Abbas, et al. (författare) How the waveguide acoustic black hole works: A study of possible damping mechanisms 2022 Ingår i: Journal of the Acoustical Society of America. - : Acoustical Society of America (ASA). - 0001-4966 .- 1520-8524. ; 151:6, s. 4279-4290 Tidskriftsartikel (refereegranskat)abstract The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.
23.	Nepal, Surendra (författare) Models for capturing the penetration of a diffusant concentration into rubber : Numerical analysis and simulation 2024 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract Understanding the transport of diffusants into rubber plays an important role in forecasting the material's durability. In this regard, we study different models, conduct numerical analysis, and present simulation results that predict the evolution of the penetration front of diffusants.We start with a moving-boundary approach to model this phenomenon, employing a numerical scheme to approximate the diffusant profile and the position of the moving boundary capturing the penetration front. Our numerical scheme utilizes the Galerkin finite element method for space discretization and the backward Euler method for time discretization. We analyze both semi-discrete and fully discrete approximations of the weak solution to the model equations, proving error estimates and demonstrating good agreement between numerical and theoretical convergence rates. Numerically approximated penetration front of the diffusant recovers well the experimental data. As an alternative approach to finite element approximation, we introduce a random walk algorithm that employs a finite number of particles to approximate both the diffusant profile and the location of the penetration front. The transport of diffusants is due to unbiased randomness, while the evolution of the penetration front is based on biased randomness. Simulation results obtained via the random walk approach are comparable with the one based on the finite element method.In a multi-dimensional scenario, we consider a strongly coupled elliptic-parabolic two-scale system with nonlinear dispersion that describes particle transport in porous media. We construct two numerical schemes approximating the weak solution to the two-scale model equations. We present simulation results obtained with both schemes and compare them based on computational time and approximation errors in suitable norms. By introducing a precomputing strategy, the computational time for both schemes is significantly improved.
24.	Obradovic, Gabrijela, 1994, et al. (författare) Simultaneous scheduling of replacement and repair of common components in operating systems A multi-objective mathematical optimization model 2022 Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 0254-5330 .- 1572-9338. ; 322, s. 147-65 Tidskriftsartikel (refereegranskat)abstract In order for a system to stay operational, its components need maintenance. We consider two stakeholders-a system operator and a maintenance workshop-and a contract governing their joint activities. Components in the operating systems that are to be maintained are sent to the maintenance workshop, which should perform all maintenance activities on time in order to satisfy the contract. The maintained components are then sent back to be used in the operating systems. Our modeling of this system-of-systems includes stocks of damaged and repaired components, the workshop scheduling, and the planning of preventive maintenance for the operating systems. Our modeling is based on a mixed-binary linear optimization (MBLP) model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We generalize and extend this model with the flow of components through the workshop, including the stocks of spare components. The resulting scheduling model-a mixed-integer optimization (MILP) model-is then utilized to optimize the main contract in a bi-objective setting: maximizing the availability of repaired (or new) components and minimizing the costs of maintaining the operating systems over the time horizon. We analyze the main contract and briefly discuss a turn-around time contract. Our results concern the effect of our modeling on the levels of the stocks of components over time, in particular minimizing the risk for lack of spare components.
25.	Willsch, Dennis, et al. (författare) Benchmarking Advantage and D-Wave 2000Q quantum annealers with exact cover problems 2022 Ingår i: Quantum Information Processing. - : Springer Science and Business Media LLC. - 1570-0755 .- 1573-1332. ; 21:4 Tidskriftsartikel (refereegranskat)abstract We benchmark the quantum processing units of the largest quantum annealers to date, the 5000 + qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance.
26.	Åblad, Edvin, 1991, et al. (författare) Exact makespan minimization of unrelated parallel machines 2021 Ingår i: Open Journal of Mathematical Optimization. - : Cellule MathDoc/CEDRAM. - 2777-5860. ; 2 Tidskriftsartikel (refereegranskat)abstract We study methods for the exact solution of the unrelated parallel machine problem with makespan minimization, generally denoted as R\|\|Cmax. Our original application arises from the automotive assembly process where tasks needs to be distributed among several robots. This involves the solutions of several R\|\|Cmax instances, which proved hard for a MILP solver since the makespan objective induces weak LP relaxation bounds. To improve these bounds and to enable the solution of larger instances, we propose a branch–and–bound method based on a Lagrangian relaxation of the assignment constraints. For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. Our computational studies indicate that the proposed algorithm is competitive with state-of-the-art methods on different types of instances. Moreover, the impact of each proposed feature is analysed.
27.	Arkeryd, Leif, 1940, et al. (författare) On stationary solutions to normal, coplanar discrete Boltzmann equation models 2020 Ingår i: Communications in Mathematical Sciences. - 1539-6746 .- 1945-0796. ; 18:8, s. 2215-2234 Tidskriftsartikel (refereegranskat)abstract The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L-1- compactness for the integrated collision frequency and gain term. L-1-compactness of a sequence of approximations is obtained using the Kolmogorov-Riesz theorem and replaces the L-1-compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete.
28.	Bandara, L., et al. (författare) Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary 2021 Ingår i: Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze. - : Scuola Normale Superiore - Edizioni della Normale. - 0391-173X .- 2036-2145. ; 22:4, s. 1843-1878 Tidskriftsartikel (refereegranskat)abstract Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary conditions we demonstrate a Weyl law for the asymptotics of the eigenvalues of the Laplacian associated to a rough metric. Moreover, we obtain eigenvalue asymptotics for weighted Laplace equations associated to a rough metric. Of particular novelty is that the weight function is not assumed to be of fixed sign, and thus the eigenvalues may be both positive and negative. Key ingredients in the proofs were demonstrated by Birman and Solomjak nearly fifty years ago in their seminal work on eigenvalue asymptotics. In addition to determining the eigenvalue asymptotics in the rough Riemannian manifold setting for weighted Laplace equations, we also wish to promote their achievements which may have further applications to modern problems.
29.	Bauer, M., et al. (författare) Semi-invariant Riemannian metrics in hydrodynamics 2020 Ingår i: Calculus of Variations and Partial Differential Equations. - : Springer Science and Business Media LLC. - 0944-2669 .- 1432-0835. ; 59:2 Tidskriftsartikel (refereegranskat)abstract Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa-Holm equations are well-studied examples. A beautiful approach to well-posedness is to go from the Eulerian to a Lagrangian description. Geometrically it corresponds to a geodesic initial value problem on the infinite-dimensional group of diffeomorphisms with a right invariant Riemannian metric. By establishing regularity properties of the Riemannian spray one can then obtain local, and sometimes global, existence and uniqueness results. There are, however, many hydrodynamic-type equations, notably shallow water models and compressible Euler equations, where the underlying infinite-dimensional Riemannian structure is not fully right invariant, but still semi-invariant with respect to the subgroup of volume preserving diffeomorphisms. Here we study such metrics. For semi-invariant metrics of Sobolev Hk-type we give local and some global well-posedness results for the geodesic initial value problem. We also give results in the presence of a potential functional (corresponding to the fluid's internal energy). Our study reveals many pitfalls in going from fully right invariant to semi-invariant Sobolev metrics; the regularity requirements, for example, are higher. Nevertheless the key results, such as no loss or gain in regularity along geodesics, can be adopted.
30.	Frahm, J., et al. (författare) An extension problem related to the fractional Branson-Gover operators 2020 Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 278:5 Tidskriftsartikel (refereegranskat)abstract The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson-Gover operators. For Euclidean spaces we show that the fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of their properties. (C) 2019 Elsevier Inc. All rights reserved.
31.	Jensen, M., et al. (författare) Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions 2022 Ingår i: Ima Journal of Numerical Analysis. - : Oxford University Press (OUP). - 0272-4979 .- 1464-3642. ; 42:1, s. 199-228 Tidskriftsartikel (refereegranskat)abstract We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization and the backward Euler scheme for the temporal discretization. Furthermore, we prove uniqueness and higher regularity of the solution on creased domains and additional regularity in the interior of the domain. Due to a variational formulation with a cut-off functional, the convergence analysis does not require a discrete maximum principle, permitting approximation spaces suitable for adaptive mesh refinement, responding to the difference in regularity within the domain.
32.	Maurelli, M., et al. (författare) Incompressible Euler equations with stochastic forcing: A geometric approach 2023 Ingår i: Stochastic Processes and Their Applications. - : Elsevier BV. - 0304-4149. ; 159, s. 101-148 Tidskriftsartikel (refereegranskat)abstract We consider a stochastic version of Euler equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution in spaces of Sobolev mappings (of high enough regularity). Our approach combines techniques from stochastic analysis and infinite-dimensional geometry and provides a novel toolbox to establish local well-posedness of stochastic non-linear partial differential equations.(c) 2023 Elsevier B.V. All rights reserved.
33.	Modin, Klas, 1979, et al. (författare) Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey 2021 Ingår i: Arnold Mathematical Journal. - : Springer Science and Business Media LLC. - 2199-6792 .- 2199-6806. ; 7:3, s. 357-385 Tidskriftsartikel (refereegranskat)abstract Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for N= 2 , 3, or 4 point-vortices (and also more general Hamiltonian systems), based on symplectic reduction theory. The approach works on any two-dimensional manifold with a symmetry group; we illustrate it on the sphere, the plane, the hyperbolic plane, and the flat torus. A systematic study of integrability is prompted by advances in two-dimensional turbulence, bridging the long-time behaviour of 2D Euler equations with questions of point-vortex integrability. A gallery of solutions is given in the appendix.
34.	Samuelsson Kalm, Håkan, 1976 (författare) The dbar-equation, duality, and holomorphic forms on a reduced complex space 2021 Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 31:2, s. 1786-1820 Tidskriftsartikel (refereegranskat)abstract We solve the $\bar\partial$-equation for (p, q)-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain (p, q)-currents. In particular this gives a condition for the partial derivative-equation to be globally solvable. Our results also give information about holomorphic p-forms on singular spaces.
35.	Hellström, Fredrik, 1993, et al. (författare) Generalization Bounds via Information Density and Conditional Information Density 2020 Ingår i: IEEE Journal on Selected Areas in Information Theory. - 2641-8770. ; 1:3, s. 824-839 Tidskriftsartikel (refereegranskat)abstract We present a general approach, based on an exponential inequality, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds on its tail probability, for both the PAC-Bayesian and single-draw scenarios. Specifically, for the case of sub-Gaussian loss functions, we obtain novel bounds that depend on the information density between the training data and the output hypothesis. When suitably weakened, these bounds recover many of the information-theoretic bounds available in the literature. We also extend the proposed exponential-inequality approach to the setting recently introduced by Steinke and Zakynthinou (2020), where the learning algorithm depends on a randomly selected subset of the available training data. For this setup, we present bounds for bounded loss functions in terms of the conditional information density between the output hypothesis and the random variable determining the subset choice, given all training data. Through our approach, we recover the average generalization bound presented by Steinke and Zakynthinou (2020) and extend it to the PAC-Bayesian and singledraw scenarios. For the single-draw scenario, we also obtain novel bounds in terms of the conditional α-mutual information and the conditional maximal leakage.
36.	Araujo-Cabarcas, Juan Carlos, 1981-, et al. (författare) Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures 2020 Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 407 Tidskriftsartikel (refereegranskat)abstract In this paper we consider scattering resonance computations in optics when the resonators consist of frequency dependent and lossy materials, such as metals at optical frequencies. The proposed computational approach combines a novel hp-FEM strategy, based on dispersion analysis for complex frequencies, with a fast implementation of the nonlinear eigenvalue solver NLEIGS. Numerical computations illustrate that the pre-asymptotic phase is significantly reduced compared to standard uniform h and p strategies. Moreover, the efficiency grows with the refractive index contrast, which makes the new strategy highly attractive for metal-dielectric structures. The hp-refinement strategy together with the efficient parallel code result in highly accurate approximations and short runtimes on multi processor platforms.
37.	Engström, Christian, et al. (författare) A spectral projection based method for the numerical solution of wave equations with memory 2022 Ingår i: Applied Mathematics Letters. - : Elsevier. - 0893-9659 .- 1873-5452. ; 127 Tidskriftsartikel (refereegranskat)abstract In this paper, we compare two approaches to numerically approximate the solution of second-order Gurtin-Pipkin type of integro-differential equations. Both methods are based on a high-order Discontinous Galerkin approximation in space and the numerical inverse Laplace transform. In the first approach, we use functional calculus and the inverse Laplace transform to represent the solution. The spectral projections are then numerically computed and the approximation of the solution of the time-dependent problem is given by a summation of terms that are the product of projections of the data and the inverse Laplace transform of scalar functions. The second approach is the standard inverse Laplace transform technique. We show that the approach based on spectral projections can be very efficient when several time points are computed, and it is particularly interesting for parameter-dependent problems where the data or the kernel depends on a parameter.
38.	Gardella, Eusebio, et al. (författare) Strongly outer actions of amenable groups on Z-stable nuclear C-algebras 2022 Ingår i:* Journal des Mathématiques Pures et Appliquées. - : Elsevier BV. - 0021-7824. ; 162, s. 76-123 Tidskriftsartikel (refereegranskat)abstract Let A be a separable, unital, simple, Z-stable, nuclear C*-algebra, and let alpha: G -+ Aut(A) be an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G on T(A) are finite and that their cardinality is bounded. We show that the following are equivalent: (1) alpha is strongly outer; (2) alpha (R) idZ has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to (3) alpha (R) idZ has finite Rokhlin dimension (in fact, at most 2). If partial differential eT(A) is furthermore compact, has finite covering dimension, and the orbit space partial differential eT(A)/G is Hausdorff, we generalize results by Matui and Sato to show that alpha is cocycle conjugate to alpha (R) idZ, even if alpha is not strongly outer. In particular, in this case the equivalences above hold for alpha in place of alpha (R) idZ. In the course of the proof, we develop equivariant versions of complemented partitions of unity and uniform property Gamma as technical tools of independent interest. (c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
39.	Heinrich, Katharina, et al. (författare) The space of twisted cubics 2021 Ingår i: Epijournal de Geometrie Algebrique. - : Centre pour la Communication Scientifique Directe (CCSD). - 2491-6765. ; 5, s. 1-22 Tidskriftsartikel (refereegranskat)abstract We consider the Cohen-Macaulay compactification of the space of twisted cubics in Pn. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t + 1. We show that the moduli scheme of CM-curves in P3 is isomorphic to the twisted cubic component of the Hilbert scheme. We also describe the compactification for twisted cubics in Pn
40.	Gyllingberg, Linnéa (författare) Mathematical models of biological interactions 2021 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract Mathematical models are used to describe and analyse different types of biological interactions. From self-propelled particle models capturing the collective motion of fish schools to models in mathematical neuroscience describing the interactions between neurons to individual-based models of ecological interactions. A question that arises for all such models is how we scale from one level to another. How do we scale from fish interactions to the movement of the school of fish? How do we scale from neuronal interactions to the functioning of the brain? How do we scale from animal competition to population dynamics? It is approaches to this question that we study in this thesis for two different systems. In paper I, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. The first is based on local interactions of the individuals and approximates the individual-based model well for small dispersal distances. The second approximates the long-range interactions of the individual-based model. Both approximations incorporate the demographic stochasticity from the individual-based model and show that dispersal stabilizes the population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the classical mean field approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Taken together, our results deepen the understanding of spatial population dynamics and introduces new approximate analytical descriptions.In paper II, we propose a model of social burst and glide motion in pairs of fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and pendulum-like tit-for-tat turn taking. Unlike self-propelled particle models, which assume that fish move at a constant speed, the model produces realistic motion of individual fish. Moreover, unlike previous studies where a random component is used for leadership switching to occur, we show that leadership switching, both periodic and chaotic, can be the result of from a deterministic interaction. We give several empirically testable predictions on how fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.
41.	Belomestny, Denis, et al. (författare) Weak solutions to gamma-driven stochastic differential equations 2023 Ingår i: Indagationes Mathematicae. - 0019-3577. ; 34:4, s. 820-829 Tidskriftsartikel (refereegranskat)abstract We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions.
42.	Bernhoff, Niclas, 1971- (författare) Compactness Property of the Linearized Boltzmann Collision Operator for a Mixture of Monatomic and Polyatomic Species 2024 Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 191:3 Tidskriftsartikel (refereegranskat)abstract The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were extended to multicomponent monatomic gases and polyatomic single species. For multicomponent polyatomic gases, the case where the polyatomicity is modelled by a discrete internal energy variable was considered lately. Here we consider the corresponding case for a continuous internal energy variable. Compactness results, stating that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a decomposition, such that the terms are, or at least are uniform limits of, Hilbert-Schmidt integral operators and therefore are compact operators. Moreover, bounds on-including coercivity of-the collision frequency are obtained for hard sphere like, as well as hard potentials with cutoff like, models, from which Fredholmness of the linearized collision operator follows, as well as its domain.
43.	Bernhoff, Niclas, 1971- (författare) Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas 2024 Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier. - 0022-247X .- 1096-0813. ; 537:1 Tidskriftsartikel (refereegranskat)abstract The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision frequency, and an integral operator is trivial. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for monatomic mixtures and polyatomic single species are more recently obtained. This work concerns the compactness of the operator for a multicomponent mixture of polyatomic species, where the polyatomicity is modeled by a discrete internal energy variable. With a probabilistic formulation of the collision operator as a starting point, compactness is obtained by proving that the integral operator is a sum of Hilbert-Schmidt integral operators and operators, which are uniform limits of Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. The assumptions are essentially generalizations of the Grad’s assumptions for monatomic single species. Self-adjointness of the linearized collision operator follows. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model. Then it follows that the linearized collision operator is a Fredholm operator, and its domain is also obtained.
44.	Bernhoff, Niclas, 1971- (författare) Linearized Boltzmann Collision Operator : I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures 2023 Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 183:1, s. 1-45 Tidskriftsartikel (refereegranskat)abstract The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some classical results for the linearized Boltzmann collision operator for monatomic single species to the case of polyatomic single species, while also reviewing corresponding results for multicomponent mixtures of monatomic species. The polyatomicity is modeled by a discrete internal energy variable, that can take a finite number of (given) different values. Results concerning the linearized Boltzmann collision operator being a nonnegative symmetric operator with a finite-dimensional kernel are reviewed. A compactness result, saying that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a splitting, such that the terms can be shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators and as such being compact operators. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model, from which Fredholmness of the linearized collision operator follows, as well as its domain.
45.	Bernhoff, Niclas, 1971- (författare) Linearized Boltzmann collision operator : II. Polyatomic molecules modeled by a continuous internal energy variable 2023 Ingår i: Kinetic and Related Models. - : American Institute of Mathematical Sciences. - 1937-5093 .- 1937-5077. ; 16:6, s. 828-849 Tidskriftsartikel (refereegranskat)abstract The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for mixtures and polyatomic single species where the polyatomicity is modeled by a discrete internal energy variable, are more recently obtained. In this work the compactness of the integral operator for polyatomic single species, for which the number of internal degrees of freedom is greater or equal to two and the polyatomicity is modeled by a continuous internal energy variable, is studied. Compactness of the integral operator is obtained by proving that its terms are, or, at least, can be approximated by, Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. Self-adjointness of the linearized collision operator follows. Moreover, bounds on -including coercivity of -the collision frequency, are obtained for some particular collision kernels -corresponding to hard sphere like models, but also hard potential with cut-off like models. Then it follows that the linearized collision operator is a Fredholm operator.
46.	Bågmark, Kasper, 1995, et al. (författare) An energy-based deep splitting method for the nonlinear filtering problem 2023 Ingår i: Partial Differential Equations and Applications. - : Springer Science and Business Media LLC. - 2662-2963 .- 2662-2971. ; 4:2 Tidskriftsartikel (refereegranskat)abstract The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on four examples, two linear in one and twenty dimensions and two nonlinear in one dimension. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.
47.	Casarino, V., et al. (författare) On the maximal operator of a general Ornstein-Uhlenbeck semigroup 2022 Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 301, s. 2393-2413 Tidskriftsartikel (refereegranskat)abstract If Q is a real, symmetric and positive definite n x n matrix, and B a real n x n matrix whose eigenvalues have negative real parts, we consider the Ornstein-Uhlenbeck semigroup on R-n with covariance Q and drift matrix B. Our main result says that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. The proof has a geometric gist and hinges on the "forbidden zones method" previously introduced by the third author.
48.	Cleanthous, G., et al. (författare) Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces 2020 Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 130:8, s. 4873-4891 Tidskriftsartikel (refereegranskat)abstract Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided. © 2020 Elsevier B.V.
49.	Eden, Michael, 1987-, et al. (författare) A multiscale quasilinear system for colloids deposition in porous media : Weak solvability and numerical simulation of a near-clogging scenario 2022 Ingår i: Nonlinear Analysis. - : Elsevier. - 1468-1218. ; 63 Tidskriftsartikel (refereegranskat)abstract We study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a 2D porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of not-necessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional elliptic cell problem. The reaction–diffusion system describes the macroscopic diffusion, aggregation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of this two-scale problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.
50.	Eisenmann, Monika, et al. (författare) Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations 2022 Ingår i: Bit Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 62:3, s. 803-48 Tidskriftsartikel (refereegranskat)abstract In this paper we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable but assumed to be convex. We show that the backward Euler-Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in Nochetto et al. (Commun Pure Appl Math 53(5):525-589, 2000). We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic p-Laplace equation.

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