Mathematisch-Naturwissenschaftliche Fakultät: Suche
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Gluing of metric measure spaces and the heat equation with homogeneous Dirichlet boundary values
(2020-07-09)
The first part of this thesis deals with gluing together several copies of an open subset of a metric measure space along the complement. This construction results in a metric measure space. We identify the Cheeger energy ......
Stochastic and deterministic models for the evolution of heterogeneous populations: Multiscale approximation and applications to melanoma T-cell therapy
(2020-07-24)
Stochastic modelling at the interface of mathematics and life sciences has gained great attention over the last decades. The study of many complex biological systems requires models taking random effects into account. Both ...
Faster Circuits for And-Or Paths and Binary Addition
(2020-07-24)
We consider the problem of constructing fast circuits both for binary addition and And-Or paths. And-Or paths are Boolean functions of the form t0 ∧ ( t1 ∨ ( t2 ∧ ( t3 ......
Supersymmetric methods in random matrix theory
(2021-12-02)
Randomness and chaos are key ingredients in the description of nature and are therefore central elements in mathematics and physics. A conducting metal becomes an insulator if there are enough random defects in its structure. ...
G-Global Algebraic K-Theory
(2021-11-09)
We develop the foundations of G-global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede on the other hand. Using this framework, we ...
In Silico Facets of Biochemical Research: Accounts from Protein Folding and Protein-Ligand Interaction Studies
(2020-09-04)
Exponential advancements in computer technology over the last five decades have ubiquitously benefited science and humanity as a whole. Consequent beneficiaries of this surge of computational power include all subfields ......
Global Timing Optimization in Chip Design
(2021-04-12)
In this thesis, we aim at solving the interconnect optimization problem comprehensively. By balancing global timing, routing, placement, and power constraints in a global model, we obtain solutions which outperform the ...
Geometric and topological recursion and invariants of the moduli space of curves
(2021-10-29)
A thread common to many problems of enumeration of surfaces is the idea that complicated cases can be recovered from simpler ones through a recursive procedure. Solving the problem for the simplest topologies and expressing ...
A geometric approach to the embedding calculus knot invariants
(2020-10-09)
In this thesis we consider two homotopy theoretic approaches to the study of spaces of knots: the theory of finite type invariants of Vassiliev and the embedding calculus of Goodwillie and Weiss, and address connections ...
Efficient Algorithms for Routing a Net Subject to VLSI Design Rules
(2020-12-17)
In this thesis we consider detailed routing, an important step in the design of integrated circuits. On large instances detailed routing requires packing millions of node-disjoint Steiner trees into a graph with hundreds ......