| 31. |
- Nursultanov, Medet, 1990, et al.
(författare)
-
Evolution of Time-Harmonic Electromagnetic and Acoustic Waves Along Waveguides
- 2018
-
Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 90:5
-
Tidskriftsartikel (refereegranskat)abstract
- We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder and prove estimates of the functional calculi of these first order non-self adjoint differential operators with non-smooth coefficients. Applying our new functional calculus, we obtain a one-to-one correspondence between polynomially bounded time-harmonic waves and functions in appropriate spectral subspaces.
|
|
| 32. |
- Ross, J., et al.
(författare)
-
ON THE MAXIMAL RANK PROBLEM FOR THE COMPLEX HOMOGENEOUS MONGE-AMPERE EQUATION
- 2019
-
Ingår i: Analysis & Pde. - : Mathematical Sciences Publishers. - 1948-206X .- 2157-5045. ; 12:2, s. 493-504
-
Tidskriftsartikel (refereegranskat)abstract
- We give examples of regular boundary data for the Dirichlet problem for the complex homogeneous Monge-Ampere equation over the unit disc, whose solution is completely degenerate on a nonempty open set and thus fails to have maximal rank.
|
|
| 33. |
- Andreotti, Eleonora, 1988, et al.
(författare)
-
Measuring stability of spectral clustering
- 2019
-
Ingår i: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 610, s. 673-697
-
Tidskriftsartikel (refereegranskat)abstract
- As an indicator of the stability of spectral clustering of an undirected weighted graph into k clusters, the kth spectral gap of the graph Laplacian is often considered. The k-th spectral gap is characterized here as an unstructured distance to ambiguity, namely as the minimal distance of the Laplacian to arbitrary symmetric matrices with vanishing kth spectral gap. As a more appropriate measure of stability, the structured distance to ambiguity of the k-clustering is introduced as the minimal distance of the Laplacian to Laplacians of the same graph with weights that are perturbed such that the k-th spectral gap vanishes. To compute a solution to this matrix nearness problem, a two-level iterative algorithm is proposed that uses a constrained gradient system of matrix differential equations in the inner iteration and a one-dimensional optimization of the perturbation size in the outer iteration. The structured and unstructured distances to ambiguity are compared on some example graphs. The numerical experiments show, in particular, that selecting the number k of clusters according to the criterion of maximal stability can lead to different results for the structured and unstructured stability indicators.
|
|
| 34. |
- Boström, Anders E, 1951
(författare)
-
Scattering of In-plane Elastic Waves by an Anisotropic Circle
- 2018
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 71:2, s. 139-155
-
Tidskriftsartikel (refereegranskat)abstract
- The 2D scattering of in-plane elastic waves by a circle is considered when the surrounding medium is isotropic and the medium inside the circle is anisotropic (orthotropic). The equations inside the circle are transformed to polar coordinates and then depend explicitly on the azimuthal angle through trigonometric functions. Making expansions in trigonometric series in the azimuthal coordinate give a coupled system of ordinary differential equations in the radial coordinate that is solved by power series expansions. With the solution inside the circle complete the scattering problem is solved essentially as in the classical case. The elements of the transition (T) matrix of the circle are given explicitly for low frequencies (long wavelengths). For low frequencies some numerical examples are given showing the strong influence of anisotropy.
|
|
| 35. |
- Cheraghchi, M., et al.
(författare)
-
Approximating linear threshold predicates
- 2012
-
Ingår i: ACM Transactions on Computation Theory. - : Association for Computing Machinery (ACM). - 1942-3462 .- 1942-3454. ; 4:1
-
Tidskriftsartikel (refereegranskat)abstract
- We study constraint satisfaction problems on the domain {-1, 1}, where the given constraints are homogeneous linear threshold predicates, that is, predicates of the form sgn(w 1 x 1 + · · · + w n x n ) for some positive integer weights w 1 , . . . , w n . Despite their simplicity, current techniques fall short of providing a classification of these predicates in terms of approximability. In fact, it is not easy to guess whether there exists a homogeneous linear threshold predicate that is approximation resistant or not. The focus of this article is to identify and study the approximation curve of a class of threshold predicates that allow for nontrivial approximation. Arguably the simplest such predicate is the majority predicate sgn(x 1 + · · · + x n ), for which we obtain an almost complete understanding of the asymptotic approximation curve, assuming the Unique Games Conjecture. Our techniques extend to a more general class of "majority-like" predicates and we obtain parallel results for them. In order to classify these predicates, we introduce the notion of Chow-robustness that might be of independent interest.
|
|
| 36. |
- Emamizadeh, B., et al.
(författare)
-
Optimal harvesting strategy based on rearrangements of functions
- 2018
-
Ingår i: Applied Mathematics and Computation. - Amsterdam : Elsevier. - 0096-3003 .- 1873-5649. ; 320, s. 677-690
-
Tidskriftsartikel (refereegranskat)abstract
- We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. © 2017 Elsevier Inc.
|
|
| 37. |
- Galindo-Prieto, Beatriz, et al.
(författare)
-
A new approach for variable influence on projection (VIP) in O2PLS models
- 2017
-
Ingår i: Chemometrics and Intelligent Laboratory Systems. - : Elsevier. - 0169-7439 .- 1873-3239. ; 160, s. 110-124
-
Tidskriftsartikel (refereegranskat)abstract
- A novel variable influence on projection approach for O2PLS® models, named VIPO2PLS, is presented in this paper. VIPO2PLS is a model-based method for judging the importance of variables. Its cornerstone is the 2-way formalism of the O2PLS models; i.e. the use of both predictive and orthogonal normalized loadings of the two modelled data matrices, and also a new weighting system based on the sum of squares of both data blocks (X, Y). The VIPO2PLS algorithm has been tested in one synthetic data set and two real cases, and the outcomes have been compared to the PLS-VIP, VIPOPLS, and i-PLS methods. The purpose is to achieve a sharper and enhanced model interpretation of O2PLS models by using the new VIPO2PLS method for assessing the importance of both X- and Y- variables.
|
|
| 38. |
- Benn, J., et al.
(författare)
-
Currents and Finite Elements as Tools for Shape Space
- 2019
-
Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 61:8, s. 1197-1220
-
Tidskriftsartikel (refereegranskat)abstract
- The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper, we study a general representation of shapes as currents, which are based on linear spaces and are suitable for numerical discretization, being robust to noise. We develop the theory of currents for shape spaces by considering both the analytic and numerical aspects of the problem. In particular, we study the analytical properties of the current map and the norm that it induces on shapes. We determine the conditions under which the current determines the shape. We then provide a finite element-based discretization of the currents that is a practical computational tool for shapes. Finally, we demonstrate this approach on a variety of examples.
|
|
| 39. |
- Modin, Klas, 1979
(författare)
-
Geometry of Matrix Decompositions Seen Through Optimal Transport and Information Geometry
- 2017
-
Ingår i: Journal of Geometric Mechanics. - : American Institute of Mathematical Sciences (AIMS). - 1941-4889 .- 1941-4889 .- 1941-4897. ; 9:3, s. 335-390
-
Tidskriftsartikel (refereegranskat)abstract
- The space of probability densities is an infinite-dimensional Riemannian manifold, with Riemannian metrics in two flavors: Wasserstein and Fisher--Rao. The former is pivotal in optimal mass transport (OMT), whereas the latter occurs in information geometry---the differential geometric approach to statistics. The Riemannian structures restrict to the submanifold of multivariate Gaussian distributions, where they induce Riemannian metrics on the space of covariance matrices. Here we give a systematic description of classical matrix decompositions (or factorizations) in terms of Riemannian geometry and compatible principal bundle structures. Both Wasserstein and Fisher-Rao geometries are discussed. The link to matrices is obtained by considering OMT and information geometry in the category of linear transformations and multivariate Gaussian distributions. This way, OMT is directly related to the polar decomposition of matrices, whereas information geometry is directly related to the QR, Cholesky, spectral, and singular value decompositions. We also give a coherent description of gradient flow equations for the various decompositions; most flows are illustrated in numerical examples. The paper is a combination of previously known and original results. As a survey it covers the Riemannian geometry of OMT and polar decompositions (smooth and linear category), entropy gradient flows, and the Fisher--Rao metric and its geodesics on the statistical manifold of multivariate Gaussian distributions. The original contributions include new gradient flows associated with various matrix decompositions, new geometric interpretations of previously studied isospectral flows, and a new proof of the polar decomposition of matrices based an entropy gradient flow.
|
|
| 40. |
- Nyström, Ulrika, 1981
(författare)
-
Modelling of Concrete Structures Subjected to Blast and Fragment Loading
- 2013
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Betong är tack vare sin låga kostnad och sitt stora användningsområde ett av de mest använda byggmaterialen i modern tid. Dess stora energiabsorberande förmåga vid höga tryck, samt det sega beteende betongkonstruktioner har vid väl utformad armering, gör betongen också lämplig i skyddande konstruktioner. Responsen hos konstruktioner utsatta för extrem dynamisk belastning, så som stötvågs- och splitterbelastning, är dock förknippad med hög komplexitet och trots många år av forskning världen över är de fenomen som uppstår ännu inte helt klarlagda.Med målsättningen att öka kunskapen om betongkonstruktioners respons vid stötvågs- och splitterbelastning har litteraturstudier, teoretiska analyser och numeriska simuleringar använts på ett iterativt sätt. Den teoretiska grunden för betongmaterialets beteende, karaktärisering av stötvågs- och splitterlaster, lasternas verkan på betongkonstruktioner och dynamiska aspekter på vågpropagering behandlas i sammanläggningsdelen i denna avhandling. Därtill presenteras två numeriska studier. Den första numeriska studien var en jämförande studie av vilken relativ inverkan som tillsättning av stålfibrer i betong har på dess motståndsförmåga mot projektilinträngning. Det kunde konstateras att inträngningsdjupet var relativt opåverkat av fibertillsättningen medan kraterstorleken, på både fram och baksidan av den beskjutna kroppen, minskade. I den andra studien undersöktes responsen hos en armerad betongväggsstrimla vid kombinerad belastning av stötvåg och splitter. Det kunde konstateras att den totala skadan i väggelementet var starkt relaterat till skadan orsakad av enbart splitterbelastningen. Vidare framgick att väggstrimlans mittnedböjning var större för det kombinerade lastfallet än för den sammanlagda nedböjningen orsakad av stötvågs- respektive splitterbelastningarna separat. Detta tyder på en synergieffekt för de kombinerade lasterna. En tredje numerisk studie har utförts inom ramen för det presenterade arbetet. I denna studie har armeringens inverkan på betongens motståndsförmåga vid projektilbeskjutning undersökts. Slutsatsen drogs att armering kan ha viss betydelse för detta motstånd förutsatt att armeringen är lämpligt inlagd.I avhandlingen presenteras även en ny materialmodell (CDPM2) för dynamiskt belastad betong. Modellen har visat god förmåga att beskriva responsen vid ett stort antal lastfall, statiska så väl som dynamiska. I utvärdering av modellen har det visats att genom vissa modifieringar skulle modellens förmåga att beskriva responsen vid stora dynamiska laster kunna förbättras. Vissa riktlinjer för möjliga modifieringar har presenterats, men implementeringen och den vidare utvärderingen av dessa är inte en del av det presenterade arbetet.
|
|
