| 1. |
- 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.
|
|
| 2. |
- 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.
|
|
| 3. |
- 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.
|
|
| 4. |
- Kim, Inkang, et al.
(författare)
-
Toledo invariant of lattices in SU(2,1) via symmetric square
- 2020
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 1089-7658 .- 0022-2488. ; 61:11
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we address the issue of the quaternionic Toledo invariant to study the character variety of two-dimensional complex hyperbolic uniform lattices into SU(n, 2), n ≥ 4. We construct four distinct representations to prove that the character variety contains at least seven distinct components. We also show the existence of holomorphic horizontal lift to various period domains of SU(n, 2).
|
|
| 5. |
- 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.
|
|
| 6. |
- Karlsson, Carl-Joar, 1995
(författare)
-
Game theory and applications
- 2021
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Individual-level interactions and decisions spread though populations and change the collective-level dynamics in an intricate way. Nevertheless, game theory is well suited for the unification of these viewpoints. This thesis introduces the works The strength of diversity and Decisions and disease: a mechanism for the evolution of cooperation, which show that games have broad applications in population dynamics modeling. In The strength of diversity we calculate the equilibrium strategies of the so-called game of teams. The game of teams is an individual-level competition between teams, and a team's strategy in this context is a distribution of strength over the team members. It turns out that the equilibrium strategies are flat distributions or 'alternating' flat distributions whenever there exists equilibrium strategies. In Decisions and disease: a mechanism for the evolution of cooperation we combine the classic SIR and SIS models from epidemiology with the prisoner's dilemma game. The transmission rate is computed as the average over defecting and cooperating individuals, and the individuals are subjected to a replicator equation that takes into account the portion of infectious members of the population. We compute the steady state solutions and interpret the results.
|
|
| 7. |
- Balkanova, O., et al.
(författare)
-
NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT
- 2021
-
Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 149:2, s. 509-523
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider the family {L-j(s)}(j=1)(infinity) of L-functions associated to an orthonormal basis {u(j)}(j=1)(infinity) of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues {lambda(j) = kappa(2)(j) + 1/4}(j=1)(infinity). We prove the following effective non-vanishing result: At least 50% of the central values L-j(1/2) with kappa(j) <= T do not vanish as T -> infinity. Furthermore, we establish effective non-vanishing results in short intervals.
|
|
| 8. |
- Brubaker, B., et al.
(författare)
-
Colored five-vertex models and Demazure atoms
- 2021
-
Ingår i: Journal of Combinatorial Theory Series A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 178
-
Tidskriftsartikel (refereegranskat)abstract
- Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a byproduct, we will construct Demazure atoms on Kashiwara's B-infinity crystal and give new algorithms for computing Lascoux-Schutzenberger keys. (C) 2020 Elsevier Inc. All rights reserved.
|
|
| 9. |
- Mertens, M. H., et al.
(författare)
-
Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms
- 2021
-
Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 28:2, s. 511-561
-
Tidskriftsartikel (refereegranskat)abstract
- The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals. Applications beyond number theory range from combinatorics, geometry, and representation theory to string theory and conformal field theory. We unify these relaxed notions in the framework of vector-valued modular forms by introducing a new class of SL2(Z)-representations: virtually real-arithmetic types. The key point of the paper is that virtually real-arithmetic types are in general not completely reducible. We obtain a rationality result for Fourier and Taylor coefficients of associated modular forms.
|
|
| 10. |
- Westerholt-Raum, Martin, 1985, et al.
(författare)
-
All modular forms of weight 2 can be expressed by Eisenstein series
- 2020
-
Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2522-0160 .- 2363-9555. ; 6:3
-
Tidskriftsartikel (refereegranskat)abstract
- We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L-values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.
|
|
