432 research outputs found
On tree-decompositions of one-ended graphs
A graph is one-ended if it contains a ray (a one way infinite path) and
whenever we remove a finite number of vertices from the graph then what remains
has only one component which contains rays. A vertex {\em dominates} a ray
in the end if there are infinitely many paths connecting to the ray such
that any two of these paths have only the vertex in common. We prove that
if a one-ended graph contains no ray which is dominated by a vertex and no
infinite family of pairwise disjoint rays, then it has a tree-decomposition
such that the decomposition tree is one-ended and the tree-decomposition is
invariant under the group of automorphisms.
This can be applied to prove a conjecture of Halin from 2000 that the
automorphism group of such a graph cannot be countably infinite and solves a
recent problem of Boutin and Imrich. Furthermore, it implies that every
transitive one-ended graph contains an infinite family of pairwise disjoint
rays
Model-Based Design of Process Strategies for Cell Culture Bioprocesses: State of the Art and New Perspectives
Production processes for biopharmaceuticals with mammalian cells have to provide a nearly optimal environment to promote cell growth and product formation. Design and operation of a bioreactor are complex tasks, not only with respect to reactor configuration and size but also with respect to the mode of operation. New concepts for the design and layout of process strategies are required to meet regulatory demands and to guarantee efficient, safe, and reproducible biopharmaceutical production. Key elements are critical process parameters (CPPs), which affect critical quality attributes (CQAs), quality by design (QbD), process analytical tools (PAT), and design of experiment (DoE). In this chapter, some fundamentals including process and control strategies as well as concepts for process development are discussed. Examples for novel model-based concepts for the design of experiments to identify suitable fed-batch-feeding strategies are shown
Compositional optimization of hard-magnetic phases with machine-learning models
Machine Learning (ML) plays an increasingly important role in the discovery
and design of new materials. In this paper, we demonstrate the potential of ML
for materials research using hard-magnetic phases as an illustrative case. We
build kernel-based ML models to predict optimal chemical compositions for new
permanent magnets, which are key components in many green-energy technologies.
The magnetic-property data used for training and testing the ML models are
obtained from a combinatorial high-throughput screening based on
density-functional theory calculations. Our straightforward choice of
describing the different configurations enables the subsequent use of the ML
models for compositional optimization and thereby the prediction of promising
substitutes of state-of-the-art magnetic materials like NdFeB with
similar intrinsic hard-magnetic properties but a lower amount of critical
rare-earth elements.Comment: 12 pages, 6 figure
Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients
We provide formulas for the Chern classes of linear submanifolds of the
moduli spaces of Abelian differentials and hence for their Euler
characteristic. This includes as special case the moduli spaces of
k-differentials, for which we set up the full intersection theory package and
implement it in the sage-program diffstrata.
As an application, we give an algebraic proof of the theorems of
Deligne-Mostow and Thurston that suitable compactifications of moduli spaces of
k-differentials on the 5-punctured projective line with weights satisfying the
INT-condition are quotients of the complex two-ball
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Liquid-liquid phase separation and intermolecular interactions in dense protein solutions
Highly concentrated protein solution were found to yield a large number of different phases, like amorphous aggregates, gels, crystals, or a liquid-liquid phase separation, which are all governed by the underlying protein-protein interactions in water. The interactions in dense protein solutions are highly complex, changes in the aqueous environment influence the inter- and intramolecular interactions, the protein-solvent interactions, and the solvent-solvent interactions. In this thesis, small angle X-ray scattering in combination with hydrostatic pressure perturbation was used to investigate the intermolecular interaction potential and the resulting phase behavior of dense lysozyme solutions. A reentrant liquid-liquid phase separation at elevated pressures was discovered, which could be ascribed to the solvent mediated protein-protein interactions.Hochkonzentrierte Proteinlösungen können eine Vielzahl verschiedener Phasen bilden, wie zum Beispiel amorphe Aggregate, Gele, Kristalle oder eine flüssig/flüssig-Phasentrennung, welche alle durch die zugrundeliegenden Protein-Protein-Wechselwirkungen beeinflusst werden. Die Wechselwirkungen in dichten Proteinlösungen sind sehr komplex, Änderungen in der wässrigen Umgebung beeinflussen die inter- und intramolekularen Wechselwirkungen, die Protein-Lösungsmittel-Wechselwirkungen und die Wechselwirkungen im Lösungsmittel selbst. Röntgenkleinwinkelstreuung in Kombination mit hohen hydrostatischen Drücken wurde in dieser Arbeit genutzt, um das intermolekulare Wechselwirkungspotential und das daraus resultierende Phasenverhalten von hochkonzentrierten Lysozymlösungen zu untersuchen. Eine Wiedereintrittsverhalten der flüssig/flüssig-Phasentrennung bei erhöhten Drücken wurde entdeckt, welches sich auf die durch die wässrige Lösung vermittelte Protein-Protein-Wechselwirkung zurückführen lassen konnte
A tale of two moduli spaces: logarithmic and multi-scale differentials
Multi-scale differentials are constructed in [BCGGM3], from the viewpoint of
flat and complex geometry, for the purpose of compactifying moduli spaces of
curves together with a differential with prescribed orders of zeros and poles.
Logarithmic differentials are constructed in [MW20], as a generalization of
stable rubber maps from Gromov--Witten theory. Modulo the global residue
condition that isolates the main components of the compactification, we show
that these two kinds of differentials are equivalent, and establish an
isomorphism of their (coarse) moduli stacks. Moreover, we describe the rubber
and multi-scale spaces as an explicit blowup of the moduli space of stable
pointed rational curves in the case of genus zero, and as a global blowup of
the incidence variety compactification for arbitrary genera, which implies
their projectivity. We also propose a refined double ramification cycle formula
in the twisted Hodge bundle which interacts with the universal line bundle
class.Comment: 54 pages. Comments very welcome
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