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 $v$ {\em dominates} a ray in the end if there are infinitely many paths connecting $v$ to the ray such that any two of these paths have only the vertex $v$ 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 Nd$_2$Fe$_{14}$B 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

Finance 1978-79

IPEDS Finance annual report contains the following information: • Revenues by source (e.g., tuition and fees, government, private gifts) • Expenses by function (e.g., instruction, research, plant maintenance and operation) • Scholarships, physical plant assets and indebtedness • Assets, liabilities and net assets • Different formats are used based on the institution’s accounting standard

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