| 1. |
- Karlsson, Carl-Joar, 1995
(author)
-
Game theory and applications
- 2021
-
Licentiate thesis (other academic/artistic)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.
|
|
| 2. |
- Laksman, Efraim, 1983, et al.
(author)
-
The stochastic opportunistic replacement problem, part III: improved bounding procedures
- 2020
-
In: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
-
Journal article (peer-reviewed)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.
|
|
| 3. |
- Casarino, V., et al.
(author)
-
On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one
- 2024
-
In: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891. ; 203:1, s. 205-219
-
Journal article (peer-reviewed)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.
|
|
| 4. |
- Björnberg, Jakob, 1983, et al.
(author)
-
STABLE SHREDDED SPHERES AND CAUSAL RANDOM MAPS WITH LARGE FACES
- 2022
-
In: Annals of Probability. - 2168-894X .- 0091-1798. ; 50:5, s. 2056-2084
-
Journal article (peer-reviewed)abstract
- We introduce a new familiy of random compact metric spaces Sα for α ∈ (1, 2), which we call stable shredded spheres. They are constructed from excursions of α-stable Lévy processes on [0, 1] possessing no negative jumps. Informally, viewing the graph of the Lévy excursion in the plane, each jump of the process is “cut open” and replaced by a circle, and then all points on the graph at equal height, which are not separated by a jump, are identified. We show that the shredded spheres arise as scaling limits of models of causal random planar maps with large faces introduced by Di Francesco and Guitter. We also establish that their Hausdorff dimension is almost surely equal to α. Point identification in the shredded spheres is intimately connected to the presence of decrease points in stable spectrally positive Lévy processes, as studied by Bertoin in the 1990s.
|
|
| 5. |
- Brubaker, B., et al.
(author)
-
Colored five-vertex models and Demazure atoms
- 2021
-
In: Journal of Combinatorial Theory Series A. - : Elsevier BV. - 0097-3165 .- 1096-0899. ; 178
-
Journal article (peer-reviewed)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.
|
|
| 6. |
- Hellström, Fredrik, 1993, et al.
(author)
-
Generalization Bounds via Information Density and Conditional Information Density
- 2020
-
In: IEEE Journal on Selected Areas in Information Theory. - 2641-8770. ; 1:3, s. 824-839
-
Journal article (peer-reviewed)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.
|
|
| 7. |
- Holroyd, Alexander E., et al.
(author)
-
Minimal matchings of point processes
- 2022
-
In: Probability Theory and Related Fields. - : Springer Science and Business Media LLC. - 0178-8051 .- 1432-2064. ; 184:1-2, s. 571-611
-
Journal article (peer-reviewed)abstract
- Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider limits as gamma approaches 0, 1-, 1+ and infinity. We focus on dimension d = 1. We prove that almost surely no such matching has unmatched points. (This question is open for higher d). For each gamma < 1 we establish that there is almost surely a unique such matching, and that it can be expressed as a finitary factor of the points. Moreover, its typical edge length has finite rth moment if and only if r < 1 /2. In contrast, for gamma = 1 there are uncountably many matchings, while for gamma > 1 there are countably many, but it is impossible to choose one in a translation-invariant way. We obtain existence results in higher dimensions (covering many but not all cases). We address analogous questions for one-colour matchings also.
|
|
| 8. |
- Belomestny, Denis, et al.
(author)
-
Weak solutions to gamma-driven stochastic differential equations
- 2023
-
In: Indagationes Mathematicae. - 0019-3577. ; 34:4, s. 820-829
-
Journal article (peer-reviewed)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.
|
|
| 9. |
- Berndtsson, Bo, 1950
(author)
-
Bergman kernels for Paley-Wiener spaces and Nazarov’s proof of the Bourgain-Milman theorem
- 2022
-
In: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 18:2, s. 395-409
-
Journal article (peer-reviewed)abstract
- We give a general inequality for Bergman kernels of Bergman spaces defined by certain convex weights in Cn. We also discuss how this can be used in Nazarov’s proof of the BourgainMilman theorem, as a substitute for Hörmander’s estimates for the ¯∂-equation.
|
|
| 10. |
- Berndtsson, Bo, 1950
(author)
-
Plurisubharmonic functions and real submanifolds of ℂ n
- 2023
-
In: Indagationes Mathematicae. - : Elsevier BV. - 0019-3577. ; 34:2, s. 357-366
-
Journal article (peer-reviewed)abstract
- We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold M. Applications are given to the Hausdorff measure of the intersection of the variety with M and the exponential integrability of plurisubharmonic functions on M.
|
|
