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A parameterized approximation algorithm for the Multiple Allocation k-Hub CenterMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

In the Multiple Allocation k-Hub Center (MAkHC), we are given a connected edge-weighted graph G, sets of clients C and hub locations H, where V (G) = C ∪ H, a set of demands D ⊆ C 2 and a positive integer k. A solution is a set of hubs H ⊆ H of size k such that every demand (a, b) is satisfied by a path starting in a, going through some vertex of H, and ending in b. The objective is to minimize the largest length of a path. We show that finding a (3 − ϵ)-approximation is NP-hard already for planar graphs. For arbitrary graphs, the approximation lower bound holds even if we parameterize by k and the value r of an optimal solution. An exact FPT algorithm is also unlikely when the parameter combines k and various graph widths, including pathwidth. To confront these barriers, we give a (2 + ϵ)-approximation algorithm parameterized by treewidth, and, as a byproduct, for unweighted planar graphs, we give a (2 + ϵ)-approximation algorithm parameterized by k and r. Compared to classical location problems, computing the length of a path depends on non-local decisions. This turns standard dynamic programming algorithms impractical, thus we introduce new ideas so that our algorithm approximates the length using only local information.

18th Colloquium on Mathematics and Foundations of Quantum TheoryA027 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

Joint colloquium of the groups of Dirk - André Deckert (LMU), Wojciech Dybalski (U Poznań), Felix Finster (U Regensburg), and Peter Pickl (U Tübingen). This time with talks: - 12:00-12:50 Janik Kruse -- Mourre theory and asymptotic observables in local relativistic quantum field theory - 13:20-14:10 Viet Hoang -- Effective polaron dynamics for an impurity particle interacting with a Fermi gas - 14:40-15:30 Paweł Duch -- Stochastic quantization of fractional $\Phi^4_3$ model of Euclidean quantum field theory

https://www.mathematik.uni-muenchen.de/~deckert/events/ws2324_cmfqt.php

Pattern Formation and Film Rupture in an Asymptotic Model of the Bénard– Marangoni problemMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Thin fluid films on heated planes exhibit the formation of spatially periodic structures. These can take the form of regular polygonal pattern, which was experimentally observed by Henri Bénard in 1900, or film rupture leading to dewetting phenomena. The emergence of these patterns is caused by the thermocapillary effect and the mathematical problem is known as the Bénard–Marangoni problem. In this talk, I will derive a deformational asymptotic model for the Bénard–Marangoni problem in the thin-film limit. In this model, the state of constant film height destabilises via a (conserved) long-wave instability and periodic solutions bifurcate via a subcritical pitchfork bifurcation. I will demonstrate that the bifurcation curve can be extended to a global bifurcation branch. Furthermore, periodic film-rupture solutions can be constructed as limit points of the bifurcation branch. The talk is based on joint work with Stefano Böhmer, Gabriele Brüll (both Lund) and Bastian Hilder.

Title: Aspects of constructive quantum field theory.A 027 (Theresienstraße 39, 80333 München)

Abstract: In this talk, I will try to motivate the subject of constructive quantum field theory which was born in the 70's as an attempt to give rigorous constructions of quantum field theory models on Minkowski space and also describe scaling limits of spin systems. We will focus on some examples which give a taste of the theory and then discuss recent advances and open problems.

Chimeric critical phenomena of non-local cascades at mixed-order phase transitionsOnline: attend (945856)

In systems with positive feedback, microscopic changes cause macroscopic effects, cascading up to length scales determined by the feedback range. Long-range feedback, in particular, generate cascades that can propagate at all distances resulting in abrupt transitions with critical scaling. These intriguing transitions, often called hybrid or mixed-order [1, 2], have been reported somewhere theoretically, somewhere numerically on both random and spatial graphs, typically in ad hoc models. In this talk, we will show that their critical phenomena can be cast in a coherent statistical mechanics framework, predicting two universality classes of mixed-order transitions by long-range cascades defined by the parity invariance of the underlying process [3]. We will provide finite-size scaling arguments based on hyperscaling above upper critical dimensions [4], predicting critical exponents having both mean-field and $d$-dimensional features –hence, their term "chimeric''– for any $d\geq2$ and show how parity invariance influences the geometry and lifetime of avalanches. We will demonstrate the validity of such framework in several synthetic and experimentally-driven cascade models, with a particular emphasis on interdependent processes [5, 6], given their recent observation in laboratory experiments [7].

[1] R. M. D’Souza, J. Gómez-Gardenes, J. Nagler, and A. Arena, Advances in Physics, 68(3):123–223, 2019. [2] C. Kuehn and C. Bick, Science advances, 7(16):eabe3824, 2021. [3] I. B., B. Gross, J.Kertész, S. Havlin, arXiv preprint arXiv:2401.09313, 2024. [4] B. Berche, T. Ellis, Y. Holovatch, and R. Kenna, SciPost Physics Lecture Notes, 060, 2022. [5] S. V. Buldyrev et al., Nature 464.7291, 1025-1028, 2010. [6] M. M. Danziger, I. B., S. Boccaletti, S. Havlin, Nature Physics, 15(2), 178-185, 2019. [7] I.B. et al.,Nature Physics 19, 1163–1170 (2023).

Derivation of the Vlasov Equation from Fermionic Many-Body Schrödinger Systems via Husimi MeasureA 027 (Theresienstraße 39, 80333 München)

Abstract:This work offers a derivation of the Vlasov equation from fermionic many-body Schrödinger systems, utilizing the Husimi measure as a connecting tool between classical mechanics and quantum mechanics. We start with an intuitive overview of the Vlasov equation, followed by a concise investigation of the many-body Schrödinger equation. The core of our discussion is about the usage of the Husimi measures to bridge these two equations. Participants will be introduced to the underlying formalism and techniques for the derivation process.

On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay AuctionsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

In first-price and all-pay auctions under the standard symmetric independent private-values model, we show that the unique Bayesian Coarse Correlated Equilibrium with symmetric, differentiable and strictly increasing bidding strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this result does not require assumptions on the prior distribution. The proof is based on a dual bound of the infinite-dimensional linear program. Numerical experiments without restrictions on bidding strategies show that for first-price auctions and discretisations up to 21 of the type and bid space, increasing discretisation sizes actually increase the concentration of Bayesian Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as the prior c.d.f. is concave. Such a concentration is also observed for all-pay auctions, independent of the prior distribution. Overall, our results imply that the equilibria of these important class of auctions are indeed learnable.

Early-Warning Signs and their Applications to Climate DynamicsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

In this talk, I am going to outline the recent history of the theory of early-warning signs for differential equations with a focus on stochastic dynamics near bifurcations. A particular emphasis will be put on the intertwining of the development of this theory with the simultaneous surge of interest in understanding applied geophysical systems and their tipping points.

Pathwise duality of interacting particle systems2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

In the study of Markov processes duality is an important tool used to prove various types of long-time behavior. There exist two approaches to Markov process duality: the algebraic one and the pathwise one. Using the well-known contact process as an example, this talk introduces the general idea of how to construct a pathwise duality for an interacting particle system. Afterwards, several different approaches how to construct pathwise dualities are presented. This is joint work with Jan M. Swart.