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Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points is known as the maximum likelihood (ML) degree. When the variety is smooth, it coincides with the Euler characteristic. We introduce degeneration techniques that are inspired by the soft limits in CEGM theory, and we answer several questions raised in the physics literature. These pertain to bounded regions in discriminantal arrangements and to moduli spaces of point configurations. We present theory and practise, connecting complex geometry, tropical combinatorics, and numerical nonlinear algebra.

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of D-modules. We present an overview and uncover new relations between these approaches. We also provide new algorithmic tools.

The development of new diagnostic methods resulted in the discovery of novel hepaciviruses in wild populations of the bank vole (Myodes glareolus, syn. Clethrionomys glareolus). The naturally infected voles demonstrate signs of hepatitis similar to those induced by hepatitis C virus (HCV) in humans. The aim of the present research was to investigate the geographical distribution of bank vole-associated hepaciviruses (BvHVs) and their genetic diversity in Europe. Real-time reverse transcription polymerase chain reaction (RT-qPCR) screening revealed BvHV RNA in 442 out of 1838 (24.0%) bank voles from nine European countries and in one of seven northern red-backed voles (Myodes rutilus, syn. Clethrionomys rutilus). BvHV RNA was not found in any other small mammal species (n = 23) tested here. Phylogenetic and isolation-by-distance analyses confirmed the occurrence of both BvHV species (Hepacivirus F and Hepacivirus J) and their sympatric occurrence at several trapping sites in two countries. The broad geographical distribution of BvHVs across Europe was associated with their presence in bank voles of different evolutionary lineages. The extensive geographical distribution and high levels of genetic diversity of BvHVs, as well as the high population fluctuations of bank voles and occasional commensalism in some parts of Europe warrant future studies on the zoonotic potential of BvHVs.

The picornavirus named ‘Ljungan virus’ (LV, species Parechovirus B) has been detected in a dozen small mammal species from across Europe, but detailed information on its genetic diversity and host specificity is lacking. Here, we analyze the evolutionary relationships of LV variants circulating in free-living mammal populations by comparing the phylogenetics of the VP1 region (encoding the capsid protein and associated with LV serotype) and the 3Dpol region (encoding the RNA polymerase) from 24 LV RNA-positive animals and a fragment of the 5′ untranslated region (UTR) sequence (used for defining strains) in sympatric small mammals. We define three new VP1 genotypes: two in bank voles (Myodes glareolus) (genotype 8 from Finland, Sweden, France, and Italy, and genotype 9 from France and Italy) and one in field voles (Microtus arvalis) (genotype 7 from Finland). There are several other indications that LV variants are host-specific, at least in parts of their range. Our results suggest that LV evolution is rapid, ongoing and affected by genetic drift, purifying selection, spillover and host evolutionary history. Although recent studies suggest that LV does not have zoonotic potential, its widespread geographical and host distribution in natural populations of well-characterized small mammals could make it useful as a model for studying RNA virus evolution and transmission.