Universal Polynomials for Severi Degrees of Toric Surfaces

The Severi variety parameterizes plane curves of degree d with delta nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of P^2. Fomin and Mikhalkin (2009) proved the 1995 conjecture that, for fixed delta, Severi degrees are eventually polynomial in d. In this paper, we study the Severi varieties corresponding to a large family of toric surfaces. We prove the analogous result that the Severi degrees are eventually polynomial as a function of the multidegree. More surprisingly, we show that the Severi degrees are also eventually polynomial "as a function of the surface". We illustrate our theorems by explicit computing, for a small number of nodes, the Severi degree of any large enough Hirzebruch surface and of a singular surface. Our strategy is to use tropical geometry to express Severi degrees in terms of Brugalle and Mikhalkin's floor diagrams, and study those combinatorial objects in detail. An important ingredient in the proof is the polynomiality of the discrete volume of a variable facet-unimodular polytope.Comment: 30 pages, 10 figures; minor modifications, included an explicit computation for some singular toric surfaces in Section 6.

Detection and Prevalence Patterns of Group I Coronaviruses in Bats, Northern Germany

The virus is probably maintained on the population level by amplification and transmission in maternity colonies

Regionale Standards: Ausgabe 2019

Die "Regionalen Standards" gehen zurück auf die Initiative eines gemeinsamen Arbeitskreises, bestehend aus Vertretern des Statistischen Bundesamtes, der Arbeitsgemeinschaft Sozialwissenschaftlicher Institute e.V. (ASI) und des ADM Arbeitskreis Deutscher Markt- und Sozialforschungsinstitute e.V. Sie stellen ein Angebot für die Forschung in der Bundesrepublik Deutschland dar. Die "Regionalen Standards" beschreiben Gebietsabgrenzungen und Instrumente zur Typisierung von Regionen, wie sie in der Bundesrepublik Deutschland von der amtlichen Statistik und/oder der Markt- und Sozialforschung in gewisser Regelmäßigkeit eingesetzt werden. Zusätzlich werden Datensätze aus unterschiedlichen Quellen vorgestellt, die für die Regionalisierung von Bevölkerungsumfragen genutzt werden können und für die Forschung (teils jedoch mit Einschränkungen) zur Verfügung stehen

Data from: Conservation genetics of the pond bat (Myotis dasycneme) with special focus on the populations in northwestern Germany and Jutland, Denmark

Conservation genetics is important in the management of endangered species, helping to understand their connectivity and long-term viability, thus identifying populations of importance for conservation. The pond bat (Myotis dasycneme) is a rare species classified as ‘Near threatened’ with a wide but patchy Palearctic distribution. A total of 277 samples representing populations in Denmark, Germany, Latvia, Hungary and Russia were used in the genetic analyses; 224 samples representing Denmark, Germany and Russia were analysed at 10 microsatellite loci; 241 samples representing all areas were analysed using mitochondrial D-loop and cytochrome B sequences. A Bayesian clustering approach revealed two poorly resolved clusters, one representing the Danish and German group and the other the Russian group. However, significantly, different pairwise FST and DEST estimates were observed between the Danish and German group, and between the Danish and Russian group suggesting a recent population structure. These conflicting results might be attributed to the effect of migration or low resolution due to the number of microsatellite markers used. After concatenating the two mitochondrial sequences, analysis detected significant genetic differentiation between all populations, probably due to genetic drift combined with a founder event. The phylogenetic tree suggested a closer relationship between Russian and Northern European populations compared to the Hungarian population, implying that the latter belongs to an older ancestral population. This was supported by the observed haplotype network and higher nucleotide diversity in this population. The genetic structuring observed in the Danish/German pond bat stresses the need for a cross border management between the two countries. Further, the pronounced mtDNA structuring, together with the indicated migration between nearby populations suggest philopatric female behavior but male migration, emphasizes the importance of protecting suitable habitat mosaics to maintain a continuum of patches with dense pond bat populations across the species’ distribution range