| 1. |
- Xia, Jiacheng, 1991
(författare)
-
Vector-valued Eisenstein series of congruence types and their products
- 2019
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
|
|
| 2. |
- 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.
|
|
| 3. |
- Gustafsson, Henrik, 1988
(författare)
-
Automorphic string amplitudes
- 2015
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis explores the non-perturbative properties of higher derivative interactions appearing in the low-energy expansion of four-graviton scattering amplitudes in toroidal compactifications of type IIB string theory. We summarise the arguments for finding such higher derivative corrections in terms of automorphic forms using U-duality, supersymmetry and string perturbation theory. The perturbative and non-perturbative parts can then be studied from their Fourier expansions. To be able to compute such Fourier coefficients we use the adelic framework as an intermediate step which also gives a new perspective on the arithmetic content of the scattering amplitudes.We give a review of known methods for computing certain classes of Fourier coefficients from the mathematical literature as presented in Paper I of the appended papers, and of our own work in Paper II towards computing some of the remaining coefficients of interest in string theory.
|
|
| 4. |
- Martinsson, Anders, 1988
(författare)
-
Accessibility percolation and first-passage percolation on the hypercube
- 2015
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we consider two percolation models on the n-dimensional binary hypercube, known as accessibility percolation and first-passage percolation. First-passage percolation randomly assigns non-negative weights, called passage times, to the edges of a graph and considers the minimal total weight of a path between given end-points. This quantity is called the first-passage time. Accessibility percolation is a biologically inspired model which has appeared in the mathematical literature only recently. Here, the vertices of a graph are randomly assigned heights, or fitnesses, and a path is considered accessible if strictly ascending. We let and denote the all zeroes and all ones vertices respectively. A natural simplification of both models is the restriction to oriented paths, i.e. paths that only flip 0:s to 1:s. Paper I considers the existence of such accessible paths between and for fitnesses assigned according to the so-called House-of-Cards and Rough Mount Fuji models. In Paper II we consider the first-passage time between and in the case of independent standard exponential passage times. It is previously known that, in the oriented case, this quantity tends to 1 in probability as n tends to infinity. We show that without this restriction, the limit is instead . By adapting ideas in Paper II to unoriented accessibility percolation, we are able to determine a limiting probability for the existence of accessible paths from to the global fitness maximum. This is presented in Paper III.
|
|
| 5. |
- Nenashev, Gleb, 1992-
(författare)
-
On a class of commutative algebras associated to graphs
- 2016
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In 2004 Alexander Postnikov and Boris Shapiro introduced a class of commutative algebras for non-directed graphs. There are two main types of such algebras, algebras of the first type count spanning trees and algebras of the second type count spanning forests. These algebras have a number of interesting properties including an explicit formula for their Hilbert series. In this thesis we mainly work with the second type of algebras, we discover more properties of the original algebra and construct a few generalizations. In particular we prove that the algebra counting forests depends only on graphical matroid of the graph and converse. Furthermore, its "K-theoretic" filtration reconstructs the whole graph. We introduse $t$ labelled algebras of a graph, their Hilbert series contains complete information about the Tutte polynomial of the initial graph. Finally we introduce similar algebras for hypergraphs. To do this, we define spanning forests and trees of a hypergraph and the corresponding "hypergraphical" matroid.
|
|
| 6. |
|
|
| 7. |
- Palö Forsström, Malin, 1989
(författare)
-
On properties of generalizations of noise sensitivity
- 2015
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In 1999, Benjamini et. al. published a paper in which they introduced twodefinitions, noise sensitivity and noise stability, as measures of how sensitiveBoolean functions are to noise in their parameters. The parameters were assumedto be Boolean strings, and the noise consisted of each input bit changingtheir value with a small but positive probability. In the three papers appendedto this thesis, we study generalizations of these definitions to irreducible andreversible Markov chains.
|
|
| 8. |
|
|
| 9. |
- Balletti, Gabriele
(författare)
-
Classifications and volume bounds of lattice polytopes
- 2017
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional lattice polytopes with two lattice points in their strict interior. Up to unimodular equivalence thereare 22,673,449 such polytopes. This classification allows us to verify, for this case only, the sharp conjectural upper bound for the volume of a lattice polytope with interior points, and provides strong evidence for more general new inequalities on the coefficients of the h^*-polynomial in dimension three.
|
|
| 10. |
- Block, Hans
(författare)
-
Sport-sort : sorting algorithms and sport tournaments
- 1987
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Arrange a really short, thrilling and fair tournament! Execute parallel sorting in a machine of a new architecture! The author shows how these problems are connected. He designs several new tournament schemes, and analyses them both in theory and in extensive simulations. He uses only elementary mathematical and statistical methods. The results are much better than previous ones, and close to the theoretical limit. Now personal computers can be used to arrange tournaments which give the complete ranking list of several thousands of participants within only 20 - 30 rounds.
|
|
