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See detailThe low-dimensional algebraic cohomology of infinite-dimensional Lie algebras of Virasoro-type
Ecker, Jill Marie-Anne UL

Doctoral thesis (2020)

In this doctoral thesis, the low-dimensional algebraic cohomology of infinite-dimensional Lie algebras of Virasoro-type is investigated. The considered Lie algebras include the Witt algebra, the Virasoro ... [more ▼]

In this doctoral thesis, the low-dimensional algebraic cohomology of infinite-dimensional Lie algebras of Virasoro-type is investigated. The considered Lie algebras include the Witt algebra, the Virasoro algebra and the multipoint Krichever-Novikov vector field algebra. We consider algebraic cohomology, meaning we do not put any constraints of continuity on the cochains. The Lie algebras are considered as abstract Lie algebras in the sense that we do not work with particular realizations of the Lie algebras. The results are thus independent of any underlying choice of topology. The thesis is self-contained, as it starts with a technical chapter introducing the definitions, concepts and methods that are used in the thesis. For motivational purposes, some time is spent on the interpretation of the low-dimensional cohomology. First results include the computation of the first and the third algebraic cohomology of the Witt and the Virasoro algebra with values in the trivial and the adjoint module, the second algebraic cohomology being known already. A canonical link between the low-dimensional cohomology of the Witt and the Virasoro algebra is exhibited by using the Hochschild-Serre spectral sequence. More results are given by the computation of the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in general tensor-densities modules. The study consists of a mix between elementary algebra and algorithmic analysis. Finally, some results concerning the low-dimensional algebraic cohomology of the multipoint Krichever-Novikov vector field algebra are derived. The thesis is concluded with an outlook containing possible short-term goals that could be achieved in the near future as well as some long-term goals. [less ▲]

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See detailContinuous Breuer-Major theorem: tightness and non-stationarity
Campese, Simon UL; Nourdin, Ivan UL; Nualart, David

in Annals of Probability (2020), 48(1), 147-177

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See detailBorders and COVID-19
Wille, Christian UL; Kanesu, Rebekka

in Borders in Perspective (2020), 4

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See detailBorder(ing)s in Times of COVID-19
Wille, Christian UL

in Borders in Perspective (2020), 4

Territorial borders and social demarcation processes are becoming dramatically more important during the coronavirus pandemic. A concise example is the 25th anniversary of the Schengen Agreement that ... [more ▼]

Territorial borders and social demarcation processes are becoming dramatically more important during the coronavirus pandemic. A concise example is the 25th anniversary of the Schengen Agreement that coincides with border control tightening and the closure of internal EU borders. At the same time, there is a certain degree of solidarity between the EU countries, which, at the end of March, slowly seems to be picking up speed. This includes not only the increasingly articulated concern to act in a coordinated manner both with the containment matters and the exit strategy. It is also shown in the increasing admission of critically ill patients from neighboring countries and the dispatch of medical supplies to particularly affected areas in other countries. [less ▲]

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See detailKummer theory for number fields and the reductions of algebraic numbers II
Perucca, Antonella UL; Sgobba, Pietro UL

in Uniform Distribution Theory (2020)

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number ... [more ▼]

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number lies in a given arithmetic progression. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if \ell^e is a prime power and a is a multiple of \ell (and a is a multiple of 4 if \ell=2), then the density of primes p of K such that the order of (G mod p) is congruent to a modulo \ell^e only depends on a through its \ell-adic valuation. [less ▲]

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See detailOxidation as Key Mechanism for Efficient Interface Passivation in Cu(In,Ga)Se2 Thin-Film Solar Cells
Werner, Florian UL; Veith-Wolf, Boris; Spindler, Conrad UL et al

in Physical Review Applied (2020)

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See detailThe atypical chemokine receptor ACKR3/CXCR7 is a broad-spectrum scavenger for opioid peptides.
Meyrath, Max; Szpakowska, Martyna; Zeiner, Julian et al

in Nature communications (2020), 11(1), 3033

Endogenous opioid peptides and prescription opioid drugs modulate pain, anxiety and stress by activating opioid receptors, currently classified into four subtypes. Here we demonstrate that ACKR3/CXCR7 ... [more ▼]

Endogenous opioid peptides and prescription opioid drugs modulate pain, anxiety and stress by activating opioid receptors, currently classified into four subtypes. Here we demonstrate that ACKR3/CXCR7, hitherto known as an atypical scavenger receptor for chemokines, is a broad-spectrum scavenger of opioid peptides. Phylogenetically, ACKR3 is intermediate between chemokine and opioid receptors and is present in various brain regions together with classical opioid receptors. Functionally, ACKR3 is a scavenger receptor for a wide variety of opioid peptides, especially enkephalins and dynorphins, reducing their availability for the classical opioid receptors. ACKR3 is not modulated by prescription opioids, but we show that an ACKR3-selective subnanomolar competitor peptide, LIH383, can restrain ACKR3's negative regulatory function on opioid peptides in rat brain and potentiate their activity towards classical receptors, which may open alternative therapeutic avenues for opioid-related disorders. Altogether, our results reveal that ACKR3 is an atypical opioid receptor with cross-family ligand selectivity. [less ▲]

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