The meta-abelian elliptic KZB associator and periods of Eisenstein series

We compute the image of Enriquez’ elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve.Our main result is an explicit formula for this image in terms of Eichler integrals of Eisenstein series, and is analogous to Deligne’s computation of the depth one quotient of the Drinfeld associator.We also show how to retrieve Zagier’s extended period polynomials of Eisenstein series, as well as the values at zero of Beilinson–Levin’s elliptic polylogarithms from the meta-abelian elliptic KZB associator

On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products

Two explicit sets of solutions to the double shuffle equations modulo products were introduced by Ecalle and Brown respectively. We place the two solutions into the same algebraic framework and compare them. We find that they agree up to and including depth four but differ in depth five by an explicit solution to the linearized double shuffle equations with an exotic pole structure

Influence of MgO overlayers on the electronic states of bct Co(001) thin film grown on bcc Fe(001)/GaAs(001

The spin polarization of the valence band electronic states of strained bcc Co(001) and MgO/Co(001) thin films grown onto a bcc Fe(001) seed layer on GaAs(001) are investigated by employing spin-resolved photoemission spectroscopy. The experimental results are compared with the calculated energy band structure of bcc and bct Co(001), and discussed in the framework of the interband transition model, which allows one to ascribe the observed spectral features to bands of given spin and spatial symmetry. In contrast to the positive spin polarization observed at the MgO/Fe(001) interface, a large negative spin polarization of the electronic states at the Fermi level is observed for the MgO/Co/Fe/GaAs(001) system. Such a large negative spin polarization is attributed to a change in the energy band structure at the bct Co/bcc Fe(001) interface

Exaggerated aggression and decreased anxiety in mice deficient in brain serotonin

Serotonin is a major neurotransmitter in the central nervous system (CNS). Dysregulation of serotonin transmission in the CNS is reported to be related to different psychiatric disorders in humans including depression, impulsive aggression and anxiety disorders. The most frequently prescribed antidepressants and anxiolytics target the serotonergic system. However, these drugs are not effective in 20–30% of cases. The causes of this failure as well as the molecular mechanisms involved in the origin of psychological disorders are poorly understood. Biosynthesis of serotonin in the CNS is initiated by tryptophan hydroxylase 2 (TPH2). In this study, we used Tph2-deficient (Tph2−/−) mice to evaluate the impact of serotonin depletion in the brain on mouse behavior. Tph2−/− mice exhibited increased depression-like behavior in the forced swim test but not in the tail suspension test. In addition, they showed decreased anxiety-like behavior in three different paradigms: elevated plus maze, marble burying and novelty-suppressed feeding tests. These phenotypes were accompanied by strong aggressiveness observed in the resident–intruder paradigm. Despite carrying only one copy of the gene, heterozygous Tph2+/− mice showed only 10% reduction in brain serotonin, which was not sufficient to modulate behavior in the tested paradigms. Our findings provide unequivocal evidence on the pivotal role of central serotonin in anxiety and aggression

Generic Fibrational Induction

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, a sound induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of a particular syntactic form. We establish the soundness of our generic induction rule by reducing induction to iteration. We then show how our generic induction rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The first of these lies outside the scope of Hermida and Jacobs' work because it is not polynomial, and as far as we are aware, no induction rules have been known to exist for the second and third in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.Comment: For Special Issue from CSL 201

Depletion of angiotensin-converting enzyme 2 reduces brain serotonin and impairs the running-induced neurogenic response

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordPhysical exercise induces cell proliferation in the adult hippocampus in rodents. Serotonin (5-HT) and angiotensin (Ang) II are important mediators of the pro-mitotic effect of physical activity. Here, we examine precursor cells in the adult brain of mice lacking angiotensin-converting enzyme (ACE) 2, and explore the effect of an acute running stimulus on neurogenesis. ACE2 metabolizes Ang II to Ang-(1-7) and is essential for the intestinal uptake of tryptophan (Trp), the 5-HT precursor. In ACE2-deficient mice, we observed a decrease in brain 5-HT levels and no increase in the number of BrdU-positive cells following exercise. Targeting the Ang II/AT1 axis by blocking the receptor, or experimentally increasing Trp/5-HT levels in the brain of ACE2-deficient mice, did not rescue the running-induced effect. Furthermore, mice lacking the Ang-(1-7) receptor, Mas, presented a normal neurogenic response to exercise. Our results identify ACE2 as a novel factor required for exercise-dependent modulation of adult neurogenesis and essential for 5-HT metabolism