Probabilistic Reduced-Order Modeling for Stochastic Partial Differential Equations

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of very large systems of algebraic equations. We establish a physically inspired, data-driven coarse-grained model which learns a low- dimensional set of microstructural features that are predictive of the fine-grained model (FG) response. Once learned, those features provide a sharp distribution over the coarse scale effec- tive coefficients of the PDE that are most suitable for prediction of the fine scale model output. This ultimately allows to replace the computationally expensive FG by a generative proba- bilistic model based on evaluating the much cheaper CG several times. Sparsity enforcing pri- ors further increase predictive efficiency and reveal microstructural features that are important in predicting the FG response. Moreover, the model yields probabilistic rather than single-point predictions, which enables the quantification of the unavoidable epistemic uncertainty that is present due to the information loss that occurs during the coarse-graining process

Higgs boson pair production: top quark mass effects at NLO and NNLO

We compute next-to-next-to-leading order QCD corrections to the gluon-induced production cross section of Higgs boson pairs in the large top quark mass limit using the soft-virtual approximation. In the limit of infinitely-heavy top quark we confirm the results in the literature. We add two more expansion terms in the inverse top quark mass to the $M_t\to\infty$ result. Since the $1/M_t$ expansion converges poorly, we try to improve on it by factorizing the exact leading order cross section. We discuss two ways of doing that and conclude that the finite top quark mass effects shift the cross section at most by about 10\% at next-to-leading order and by about 5\% at next-to-next-to-leading order.Comment: 25 page

Virtual corrections to Higgs boson pair production in the large top quark mass limit

We calculate the three-loop matching coefficient $C_{HH}$, required for a consistent description of Higgs boson pair production in gluon fusion through next-to-next-to-leading order QCD in the heavy top quark approximation. We also compute the $gg \to HH$ amplitude in $m_t \to \infty$ approximation in the full theory and show its consistency with an earlier computation in heavy-top effective theory.Comment: 15 pages, 3 figure

Billiards and statistical mechanics

In this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise in the context of hard sphere systems when only one or two spheres are present. In particular we investigate the possibility of elliptic periodic orbits in the general construction of hyperbolic billiards. We show that if non-absolutely focusing components are present there can be elliptic periodic orbits with arbitrarily long free paths. Furthermore, we show that smooth stadium like billiards have elliptic periodic orbits for a large range of separation distances. In the second part we consider hard sphere systems with a large number of particles, which we model by the Boltzmann equation. We develop a new approach to derive hydrodynamic limits, which is based on classical methods of geometric singular perturbation theory of ordinary differential equations. This method provides new geometric and dynamical interpretations of hydrodynamic limits, in particular, for the of the dissipative Boltzmann equation.Ph.D.Committee Chair: Bunimovich, Leonid; Committee Member: Bonetto, Federico; Committee Member: Chow, Shui-Nee; Committee Member: Cvitanovic, Predrag; Committee Member: Weiss, Howar

A Special Tetradrachm Series of Euthydemos I

In diesem Beitrag werden Tetradrachmen des Euthydemos I. von Baktrien behandelt, die sich von den regulären Münzen des Königs unterscheiden: Der auffälligste Unterschied ist der frontale Blick des auf dem Revers abgebildeten Herakles. Obwohl andere Forscher diese Tetradrachmen als posthum bezeichnet haben, wird vorgeschlagen, dass sie zu Euthydemos’ Lebzeiten geprägt wurden, möglicherweise während des Krieges mit dem Seleukidenkönig Antiochos III.In this paper, tetradrachms of Euthydemos I of Bactria are discussed that differ from the regular coinage of the king: The most striking difference is the frontal glance of the seated Herakles depicted on the reverse. While other scholars have regarded these tetradrachms as posthumous, it is proposed that they were minted during Euthydemos’ lifetime, possibly during the war with the Seleukid king Antiochos III

Attempts to Decolonize Knowledge Production in Museum Practice

In the last decades, the pressure on museums, especially on ethnological museums in the global North, has increased considerably. They are criticized for reproducing neo-colonial power relations and knowledge orders through common representational practices. The recent debate on colonial collections and the necessity of restitution has further fueled the discussion about the role and legitimacy of museums. Ethnological museums need to fundamentally rethink their practices. Since 2015, two museums in Uganda (Kampala and Mbarara) and one in Switzerland (Zurich) have begun an unusual collaboration. They are conducting joint research in both countries, pursuing an approach of “reverse” and “reciprocal anthropology”, and creating exhibitions together in dialogue. This article provides insights into the dynamics of the cooperation process between the three museums. It addresses the challenges of collaborating on an equal footing, striven for in a transcontinental project framed by structural inequalities. Is it possible to integrate all points of view, orders of knowledge and interests? Each of the three museums involved is entangled in specific historical, economic, and political contexts that influence and limit their respective scopes of action, interests, and possibilities for assertion. Furthermore, there is always the danger that historically grown, internalized and unconscious relations of dominance come into play. Special attention is paid to the conditions and processes of knowledge creation