Shadow Market Area for Air Pollutants

This study identifies the shadow market area of air pollutants based on the Gaussian plume model. Since pollutants are dispersed by wind, transport costs are irrelevant in its formation. Pollutant distribution on the ground level has an asymmetric bell-shape in the wind direction. Apart from the linear functions, the exponential and quadratic shadow price functions are considered for the compensation of health hazard of consumers, when the strict liability in the framework of Coase theorem applies. The shadow market area for pollutants is shell-shaped. This specific characteristic has an implication for market boundaries between polluters and their location decisions

Complete Bredon cohomology and its applications to hierarchically defined groups

By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class \LHFF of type Bredon-\FP_\infty admits a finite dimensional model for \EFG. We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional model for the classifying space for the family of virtually nilpotent subgroups. This allows us to prove that for \mF, the class of virtually cyclic groups, the class of \LHFF-groups contains all locally virtually soluble groups and all linear groups over $\mathbb C$ of integral characteristic.Comment: 14 page

Space-Efficient Graph Coarsening with Applications to Succinct Planar Encodings

We present a novel space-efficient graph coarsening technique for n-vertex planar graphs G, called cloud partition, which partitions the vertices V(G) into disjoint sets C of size O(log n) such that each C induces a connected subgraph of G. Using this partition ? we construct a so-called structure-maintaining minor F of G via specific contractions within the disjoint sets such that F has O(n/log n) vertices. The combination of (F, ?) is referred to as a cloud decomposition. For planar graphs we show that a cloud decomposition can be constructed in O(n) time and using O(n) bits. Given a cloud decomposition (F, ?) constructed for a planar graph G we are able to find a balanced separator of G in O(n/log n) time. Contrary to related publications, we do not make use of an embedding of the planar input graph. We generalize our cloud decomposition from planar graphs to H-minor-free graphs for any fixed graph H. This allows us to construct the succinct encoding scheme for H-minor-free graphs due to Blelloch and Farzan (CPM 2010) in O(n) time and O(n) bits improving both runtime and space by a factor of ?(log n). As an additional application of our cloud decomposition we show that, for H-minor-free graphs, a tree decomposition of width O(n^{1/2 + ?}) for any ? > 0 can be constructed in O(n) bits and a time linear in the size of the tree decomposition. A similar result by Izumi and Otachi (ICALP 2020) constructs a tree decomposition of width O(k ?n log n) for graphs of treewidth k ? ?n in sublinear space and polynomial time

Succinct Planar Encoding with Minor Operations

Let G be an unlabeled planar and simple n-vertex graph. Unlabeled graphs are graphs where the label-information is either not given or lost during the construction of data-structures. We present a succinct encoding of G that provides induced-minor operations, i.e., edge contractions and vertex deletions. Any sequence of such operations is processed in O(n) time in the word-RAM model. At all times the encoding provides constant time (per element output) neighborhood access and degree queries. Optional hash tables extend the encoding with constant expected time adjacency queries and edge-deletion (thus, all minor operations are supported) such that any number of edge deletions are computed in O(n) expected time. Constructing the encoding requires O(n) bits and O(n) time. The encoding requires ℋ(n) + o(n) bits of space with ℋ(n) being the entropy of encoding a planar graph with n vertices. Our data structure is based on the recent result of Holm et al. [ESA 2017] who presented a linear time contraction data structure that allows to maintain parallel edges and works for labeled graphs, but uses Θ(n log n) bits of space. We combine the techniques used by Holm et al. with novel ideas and the succinct encoding of Blelloch and Farzan [CPM 2010] for arbitrary separable graphs. Our result partially answers the question raised by Blelloch and Farzan whether their encoding can be modified to allow modifications of the graph

A Comparison of Germany and the United Kingdom Indicates That More SARS-CoV-2 Circulation and Less Restrictions in the Warm Season Might Reduce Overall COVID-19 Burden

(1) Background: Between March 2020 and January 2022 severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) caused five infection waves in Europe. The first and the second wave was caused by wildtype SARS-CoV-2, while the following waves were caused by the variants of concern Alpha, Delta, and Omicron respectively. (2) Methods: In the present analysis, the first four waves were compared in Germany and the UK, in order to examine the COVID-19 epidemiology and its modulation by non-pharmaceutical interventions (NPI). (3) Results: The number of COVID-19 patients on intensive care units and the case fatality rate were used to estimate disease burden, the excess mortality to assess the net effect of NPI and other measures on the population. The UK was more severely affected by the first and the third wave while Germany was more affected by the second wave. The UK had a higher excess mortality during the first wave, afterwards the excess mortality in both countries was nearly identical. While most NPI were lifted in the UK in July 2021, the measures were kept and even aggravated in Germany. Nevertheless, in autumn 2021 Germany was much more affected, nearly resulting in a balanced sum of infections and deaths compared to the UK. Within the whole observation period, in Germany the number of COVID-19 patients on ICUs was up to four times higher than in the UK. Our results show that NPI have a limited effect on COVID-19 burden, seasonality plays a crucial role, and a higher virus circulation in a pre-wave situation could be beneficial. (4) Conclusions: Although Germany put much more effort and resources to fight the pandemic, the net balance of both countries was nearly identical, questioning the benefit of excessive ICU treatments and of the implementation of NPI, especially during the warm season

Prüfung verschiedener Untersuchungsverfahren zur Normung von Bissregistrierungsmaterialien

Die Ergebnisse zeigen in aller Deutlichkeit, daß die Bestimmung klinisch so relevanter Größen wie der Gesamtverarbeitungs- und Abbindezeit als auch der Standfestigkeit eines Bissregistrierungsmaterials auf erhebliche Schwierigkeiten stößt, wenn es darum geht, Verfahren zu definieren, die in einer Norm Anwendung finden könnten. Dabei sind es Fragen der Praktikabilität der Durchführung eines Versuches, seiner Reproduzierbarkeit bzw. seiner klinischen Relevanz. Es erscheint daher ratsam, auf differenzierte Versuchsaufbauten zu verzichten und vielmehr extrem einfache Aufbauten zu wählen, um das gewünschte Ziel zu erreichen. Zusammengefasst lassen sich die Ergebnisse der einzelnen Versuchsserien wie folgt beschreiben: - Im Rahmen der Kondymetermessung ließ sich - gut korreliert - ein Ansteigen der beim Einartikulieren eines Modells mit einem spezifischen Registrat zu erwartenden Kondylenverlagerung und ein Anstieg der Bisssperrung in Abhängigkeit von der Verarbeitungszeit erkennen. Allerdings war eine Korrelation dieser klinisch außerordentlich relevanten Werte mit den Ergebnissen der rheometrischen bzw. oszillometrischen Bestimmung der Verarbeitungszeit nicht möglich. - Die Kugeldruckhärtemessung erwies sich - bei korrekter Durchführung - als ein einfach handhabbares und im Sinne der Normung sinnvolles Verfahren zur Charakterisierung von Bissregistrierungsmassen. - Die von Zech und Reusch für Abformmaterialien angegebene Prüfungsapparatur eignet sich nicht für Bissregistrierungsmassen. Möglicherweise kann eine modifizierte Prüfung der Standfestigkeit nach DIN 24823 zum Erfolg führen. - Rheometrisch am Haake RS 80 ermittelte Verarbeitungszeiten zeigen zumindest bei Verwendung des gleichen Gerätes weitgehend Untersucher unabhängig.<BR

Finite Temperature Time-Dependent Effective Theory for the Phase Field in two-dimensional d-wave Neutral Superconductor

We derive finite temperature time-dependent effective actions for the phase of the pairing field, which are appropriate for a 2D electron system with both non-retarded d- and s-wave attraction. As for s-wave pairing the d-wave effective action contains terms with Landau damping, but their structure appears to be different from the s-wave case due to the fact that the Landau damping is determined by the quasiparticle group velocity v_{g}, which for d-wave pairing does not have the same direction as the non-interacting Fermi velocity v_{F}. We show that for d-wave pairing the Landau term has a linear low temperature dependence and in contrast to the s-wave case are important for all finite temperatures. A possible experimental observation of the phase excitations is discussed.Comment: 23 pages, RevTeX4, 10 EPS figures; final version to appear in PR