GEODESIC BEHAVIOR FOR FINSLER METRICS OF CONSTANT POSITIVE FLAG CURVATURE ON S 2

International audienceWe study non-reversible Finsler metrics with constant flag curvature 1 on S 2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metric with constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on S 2 with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or has constant flag curvature

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) generally must contain terms in the potential that violate the custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs-quark couplings, that vacuum alignment will lead to up-down mass degeneration; this is not true if the vacua are not aligned.Comment: 16 pages, 1 figure. Title and abstract are modified, conclusions remain the same. Section on Yukawa couplings is extended. Published versio

Temporally divergent regulatory mechanisms govern neuronal diversification and maturation in the mouse and marmoset neocortex

Mammalian neocortical neurons span one of the most diverse cell type spectra of any tissue. Cortical neurons are born during embryonic development, and their maturation extends into postnatal life. The regulatory strategies underlying progressive neuronal development and maturation remain unclear. Here we present an integrated single-cell epigenomic and transcriptional analysis of individual mouse and marmoset cortical neuron classes, spanning both early postmitotic stages of identity acquisition and later stages of neuronal plasticity and circuit integration. We found that, in both species, the regulatory strategies controlling early and late stages of pan-neuronal development diverge. Early postmitotic neurons use more widely shared and evolutionarily conserved molecular regulatory programs. In contrast, programs active during later neuronal maturation are more brain- and neuron-specific and more evolutionarily divergent. Our work uncovers a temporal shift in regulatory choices during neuronal diversification and maturation in both mice and marmosets, which likely reflects unique evolutionary constraints on distinct events of neuronal development in the neocortex. The mechanisms underlying neuron specification and maturation are unclear. Here the authors provide an integrated epigenomic and transcriptomic analysis of mouse and marmoset neocortical neuronal classes. Pan-neuronal programs active during early development are more evolutionary conserved but not neuron-specific, whereas pan-neuronal programs active during later stages of maturation are more neuron- and species-specific

Expression of Lineage Transcription Factors Identifies Differences in Transition States of Induced Human Oligodendrocyte Differentiation

Oligodendrocytes (OLs) are critical for myelination and are implicated in several brain disorders. Directed differentiation of human-induced OLs (iOLs) from pluripotent stem cells can be achieved by forced expression of different combinations of the transcription factors SOX10 (S), OLIG2 (O), and NKX6.2 (N). Here, we applied quantitative image analysis and single-cell transcriptomics to compare different transcription factor (TF) combinations for their efficacy towards robust OL lineage conversion. Compared with S alone, the combination of SON increases the number of iOLs and generates iOLs with a more complex morphology and higher expression levels of myelin-marker genes. RNA velocity analysis of individual cells reveals that S generates a population of oligodendrocyte-precursor cells (OPCs) that appear to be more immature than those generated by SON and to display distinct molecular properties. Our work highlights that TFs for generating iOPCs or iOLs should be chosen depending on the intended application or research question, and that SON might be beneficial to study more mature iOLs while S might be better suited to investigate iOPC biology

The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors

Geodesic flows on Riemannian g.o. spaces

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.Comment: 12 pages, minor corrections, final versio