This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND solutions), a vast class of algebraic structures encompassing groups, racks, and cycle sets. To ...each such solution there is associated a shelf (i.e., a self-distributive structure) which captures its major properties. We consider two (co)homology theories for LND solutions, one of which was previously known, in a reduced form, for biracks only. An explicit isomorphism between these theories is described. For groups and racks we recover their classical (co)homology, whereas for cycle sets we get new constructions. For a certain type of LND solutions, including quandles and non-degenerate cycle sets, the (co)homologies split into the degenerate and the normalized parts. We express 2-cocycles of our theories in terms of group cohomology, and, in the case of cycle sets, establish connexions with extensions. This leads to a construction of cycle sets with interesting properties.
The evolutionary potential of long‐lived species, such as forest trees, is fundamental for their local persistence under climate change (CC). Genome–environment association (GEA) analyses reveal if ...species in heterogeneous environments at the regional scale are under differential selection resulting in populations with potential preadaptation to CC within this area. In 79 natural Fagus sylvatica populations, neutral genetic patterns were characterized using 12 simple sequence repeat (SSR) markers, and genomic variation (144 single nucleotide polymorphisms (SNPs) out of 52 candidate genes) was related to 87 environmental predictors in the latent factor mixed model, logistic regressions and isolation by distance/environmental (IBD/IBE) tests. SSR diversity revealed relatedness at up to 150 m intertree distance but an absence of large‐scale spatial genetic structure and IBE. In the GEA analyses, 16 SNPs in 10 genes responded to one or several environmental predictors and IBE, corrected for IBD, was confirmed. The GEA often reflected the proposed gene functions, including indications for adaptation to water availability and temperature. Genomic divergence and the lack of large‐scale neutral genetic patterns suggest that gene flow allows the spread of advantageous alleles in adaptive genes. Thereby, adaptation processes are likely to take place in species occurring in heterogeneous environments, which might reduce their regional extinction risk under CC.
Plant populations can undergo very localized adaptation, allowing widely distributed populations to adapt to divergent habitats in spite of recurrent gene flow. Neotropical trees—whose large and ...undisturbed populations often span a variety of environmental conditions and local habitats—are particularly good models to study this process. Here, we explore patterns of adaptive divergence from large (i.e., regional) to small (i.e., microgeographic) spatial scales in the hyperdominant Amazonian tree Eperua falcata Aubl. (Fabaceae) under a replicated design involving two microhabitats (~300 m apart) in two study sites (~300 km apart). A three‐year reciprocal transplant illustrates that, beyond strong maternal effects and phenotypic plasticity, genetically driven divergence in seedling growth and leaf traits was detected both between seedlings originating from different regions, and between seedlings from different microhabitats. In parallel, a complementary genome scan for selection was carried out through whole‐genome sequencing of tree population pools. A set of 290 divergence outlier SNPs was detected at the regional scale (between study sites), while 185 SNPs located in the vicinity of 106 protein‐coding genes were detected as replicated outliers between microhabitats within regions. Outlier‐surrounding genomic regions are involved in a variety of physiological processes, including plant responses to stress (e.g., oxidative stress, hypoxia and metal toxicity) and biotic interactions. Together with evidence of microgeographic divergence in functional traits, the discovery of genomic candidates for microgeographic adaptive divergence represents a promising advance in our understanding of local adaptation, which probably operates across multiple spatial scales and underpins divergence and diversification in Neotropical trees.
see also the Perspective by Christopher W. Dick.
The pathophysiology of epilepsy has been historically grounded on hyperexcitability attributed to the oversimplified imbalance between excitation (E) and inhibition (I) in the brain. The decreased ...inhibition is mostly attributed to deficits in gamma-aminobutyric acid-containing (GABAergic) interneurons, the main source of inhibition in the central nervous system. However, the cell diversity, the wide range of spatiotemporal connectivity, and the distinct effects of the neurotransmitter GABA especially during development, must be considered to critically revisit the concept of hyperexcitability caused by decreased inhibition as a key characteristic in the development of epilepsy. Here, we will discuss that behind this known mechanism, there is a heterogeneity of GABAergic interneurons with distinct functions and sources, which have specific roles in controlling the neural network activity within the recruited microcircuit and altered network during the epileptogenic process.
This article is part of the Special Issue “NEWroscience 2018
•Excitation/inhibition (E–I) imbalance and seizures are tip of an iceberg in epilepsy.•Spatiotemporal synapses and interneuronal diversity control network activity.•Gamma-aminobutyric acid-containing (GABAergic) interneurons participate in different microcircuits recruited in epilepsy.•Hyperexcitability in epilepsy goes beyond of simply decreasing inhibition.
This paper explores the structure groups G(X,r) of finite non-degenerate set-theoretic solutions (X,r) to the Yang–Baxter equation. Namely, we construct a finite quotient $\overline {G}_{(X,r)}$ of ...G(X,r), generalizing the Coxeter-like groups introduced by Dehornoy for involutive solutions. This yields a finitary setting for testing injectivity: if X injects into G(X,r), then it also injects into $\overline {G}_{(X,r)}$. We shrink every solution to an injective one with the same structure group, and compute the rank of the abelianization of G(X,r). We show that multipermutation solutions are the only involutive solutions with diffuse structure groups; that only free abelian structure groups are bi-orderable; and that for the structure group of a self-distributive solution, the following conditions are equivalent: bi-orderable, left-orderable, abelian, free abelian and torsion free.
El artículo analiza la interpretación de Carl Schmitt sobre el artículo 48 de la Constitución de Weimar a la luz de las categorías de dictadura y estado de excepción. En este marco, se sostiene que ...Schmitt no fue un enemigo de la república de Weimar. Para desarrollar esto, se reconstruye cómo Schmitt identifica en el artículo 48 la herramienta idónea para enfrentar las crisis que amenazan a la república. En su visión, el artículo contiene una dictadura en cabeza del presidente destinada a defender la Constitución. Pero el cambio de matriz de la crisis de Weimar hacia 1929 lo lleva a modificar las implicancias concretas de esto. Así, entre 1921 y 1928, Schmitt defiende que el presidente puede adoptar todas las medidas necesarias para mantener el orden público –incluso violar determinadas cláusulas constitucionales– y suspender los derechos fundamentales enumerados en el artículo. Luego, entre 1929 y 1933, Schmitt amplía la noción de orden público para integrar la esfera de la economía. Apelando a la noción de praxis constitucional, Schmitt justifica el estado de emergencia económico y la facultad del presidente de dictar decretos con fuerza de ley. A su juicio, ambas cuestiones se encuadran dentro de los límites del artículo 48.
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