42 research outputs found
Symmetry reduction of Brownian motion and Quantum Calogero-Moser systems
Let be a Riemannian -manifold. This paper is concerned with the
symmetry reduction of Brownian motion in and ramifications thereof in a
Hamiltonian context. Specializing to the case of polar actions we discuss
various versions of the stochastic Hamilton-Jacobi equation associated to the
symmetry reduction of Brownian motion and observe some similarities to the
Schr\"odinger equation of the quantum free particle reduction as described by
Feher and Pusztai. As an application we use this reduction scheme to derive
examples of quantum Calogero-Moser systems from a stochastic setting.Comment: V2 contains some improvements thanks to referees' suggestions; to
appear in Stochastics and Dynamic
Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of
nonholonomic mechanical systems with symmetries, using a technique called
Hamiltonization, which transforms nonholonomic systems into Hamiltonian
systems. We give a geometric account of the Hamiltonization, identify necessary
and sufficient conditions for Hamiltonization, and apply the conventional
Hamilton-Jacobi theory to the Hamiltonized systems. We show, under a certain
sufficient condition for Hamiltonization, that the solutions to the
Hamilton-Jacobi equation associated with the Hamiltonized system also solve the
nonholonomic Hamilton-Jacobi equation associated with the original Chaplygin
system. The results are illustrated through several examples.Comment: Accepted for publication in Journal of Geometry and Physic
Collisionless kinetic theory of rolling molecules
We derive a collisionless kinetic theory for an ensemble of molecules
undergoing nonholonomic rolling dynamics. We demonstrate that the existence of
nonholonomic constraints leads to problems in generalizing the standard methods
of statistical physics. In particular, we show that even though the energy of
the system is conserved, and the system is closed in the thermodynamic sense,
some fundamental features of statistical physics such as invariant measure do
not hold for such nonholonomic systems. Nevertheless, we are able to construct
a consistent kinetic theory using Hamilton's variational principle in
Lagrangian variables, by regarding the kinetic solution as being concentrated
on the constraint distribution. A cold fluid closure for the kinetic system is
also presented, along with a particular class of exact solutions of the kinetic
equations.Comment: Revised version; 31 pages, 1 figur
AP2γ: a new player on adult hippocampal neurogenesis regulation
Since the recognition that the mammalian brain retains the ability to generate newborn neurons with functional relevance throughout life, the matrix of molecular regulators that govern adult neurogenesis has been the focus of much interest. In a recent study published in Molecular Psychiatry, we demonstrate Activating Protein 2γ (AP2γ), a transcription factor previously implicated in cell fate determination in the developing cortex, as a novel player in the regulation of glutamatergic neurogenesis in the adult hippocampus. Using distinct experimental approaches, we showed that AP2γ is specifically present in a subpopulation of transient amplifying progenitors, where it acts as a crucial promoter of proliferation and differentiation of adult-born glutamatergic granule neurons. Strikingly, deficiency of AP2γ in the adult brain compromises the generation of new glutamatergic neurons, with impact on the function of cortico-limbic circuits. Here, we share our view on how AP2γ integrates the transcriptional orchestration of glutamatergic neurogenesis in the adult hippocampus, and consequently, how it emerges as a novel molecular candidate to study the translation of environmental pressures into alterations of brain neuroplasticity in homeostatic, but also in neuropathological contexts.Bial Foundation (427/14); Northern Portugal Regional Operational Programme (NORTE
2020); European Regional Development Fund (FEDER) (projects NORTE-01-0145-FEDER-000013 e NORTE-01-0145-FEDER-000023); Competitiveness Factors Operational Programme (COMPETE)info:eu-repo/semantics/publishedVersio
Integrable Euler top and nonholonomic Chaplygin ball
We discuss the Poisson structures, Lax matrices, -matrices, bi-hamiltonian
structures, the variables of separation and other attributes of the modern
theory of dynamical systems in application to the integrable Euler top and to
the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio
LR and L+R Systems
We consider coupled nonholonomic LR systems on the product of Lie groups. As
examples, we study -dimensional variants of the spherical support system and
the rubber Chaplygin sphere. For a special choice of the inertia operator, it
is proved that the rubber Chaplygin sphere, after reduction and a time
reparametrization becomes an integrable Hamiltonian system on the
--dimensional sphere. Also, we showed that an arbitrary L+R system
introduced by Fedorov can be seen as a reduced system of an appropriate coupled
LR system.Comment: 18 pages, 1 figur
Oligodendrocyte heterogeneity in the mouse juvenile and adult central nervous system
Oligodendrocytes have been considered as a functionally homogeneous population in the central nervous system (CNS). We performed single-cell RNA sequencing on 5072 cells of the oligodendrocyte lineage from 10 regions of the mouse juvenile and adult CNS. Thirteen distinct populations were identified, 12 of which represent a continuum from Pdgfra(+) oligodendrocyte precursor cells (OPCs) to distinct mature oligodendrocytes. Initial stages of differentiation were similar across the juvenile CNS, whereas subsets of mature oligodendrocytes were enriched in specific regions in the adult brain. Newly formed oligodendrocytes were detected in the adult CNS and were responsive to complex motor learning. A second Pdgfra(+) population, distinct from OPCs, was found along vessels. Our study reveals the dynamics of oligodendrocyte differentiation and maturation, uncoupling them at a transcriptional level and highlighting oligodendrocyte heterogeneity in the CNS
Social Innovations as Drivers of Social Change — Exploring Tarde’s Contribution to Social Innovation Theory Building
Regional Innovation and Research Policy Outlook: Policy Practices in Eight European Regions
This publication is part of a project called 'Practical Regional Research and Innovation policy in Action. The Efficient Tools for Regional Catching-up in New Member States'