On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

Ubiquitin and AP180 Regulate the Abundance of GLR-1 Glutamate Receptors at Postsynaptic Elements in C. elegans

AbstractRegulated delivery and removal of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) glutamate receptors (GluRs) from postsynaptic elements has been proposed as a mechanism for regulating synaptic strength. Here we test the role of ubiquitin in regulating synapses that contain a C. elegans GluR, GLR-1. GLR-1 receptors were ubiquitinated in vivo. Mutations that decreased ubiquitination of GLR-1 increased the abundance of GLR-1 at synapses and altered locomotion behavior in a manner that is consistent with increased synaptic strength. By contrast, overexpression of ubiquitin decreased the abundance of GLR-1 at synapses and decreased the density of GLR-1-containing synapses, and these effects were prevented by mutations in the unc-11 gene, which encodes a clathrin adaptin protein (AP180). These results suggest that ubiquitination of GLR-1 receptors regulates synaptic strength and the formation or stability of GLR-1-containing synapses

The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page

Statistical Computing on Non-Linear Spaces for Computational Anatomy

International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings

RIC-7 Promotes Neuropeptide Secretion

Secretion of neurotransmitters and neuropeptides is mediated by exocytosis of distinct secretory organelles, synaptic vesicles (SVs) and dense core vesicles (DCVs) respectively. Relatively little is known about factors that differentially regulate SV and DCV secretion. Here we identify a novel protein RIC-7 that is required for neuropeptide secretion in Caenorhabditis elegans. The RIC-7 protein is expressed in all neurons and is localized to presynaptic terminals. Imaging, electrophysiology, and behavioral analysis of ric-7 mutants indicates that acetylcholine release occurs normally, while neuropeptide release is significantly decreased. These results suggest that RIC-7 promotes DCV–mediated secretion

MAGI-1 Modulates AMPA Receptor Synaptic Localization and Behavioral Plasticity in Response to Prior Experience

It is well established that the efficacy of synaptic connections can be rapidly modified by neural activity, yet how the environment and prior experience modulate such synaptic and behavioral plasticity is only beginning to be understood. Here we show in C. elegans that the broadly conserved scaffolding molecule MAGI-1 is required for the plasticity observed in a glutamatergic circuit. This mechanosensory circuit mediates reversals in locomotion in response to touch stimulation, and the AMPA-type receptor (AMPAR) subunits GLR-1 and GLR-2, which are required for reversal behavior, are localized to ventral cord synapses in this circuit. We find that animals modulate GLR-1 and GLR-2 localization in response to prior mechanosensory stimulation; a specific isoform of MAGI-1 (MAGI-1L) is critical for this modulation. We show that MAGI-1L interacts with AMPARs through the intracellular domain of the GLR-2 subunit, which is required for the modulation of AMPAR synaptic localization by mechanical stimulation. In addition, mutations that prevent the ubiquitination of GLR-1 prevent the decrease in AMPAR localization observed in previously stimulated magi-1 mutants. Finally, we find that previously-stimulated animals later habituate to subsequent mechanostimulation more rapidly compared to animals initially reared without mechanical stimulation; MAGI-1L, GLR-1, and GLR-2 are required for this change in habituation kinetics. Our findings demonstrate that prior experience can cause long-term alterations in both behavioral plasticity and AMPAR localization at synapses in an intact animal, and indicate a new, direct role for MAGI/S-SCAM proteins in modulating AMPAR localization and function in the wake of variable sensory experience

Profiling Synaptic Proteins Identifies Regulators of Insulin Secretion and Lifespan

Cells are organized into distinct compartments to perform specific tasks with spatial precision. In neurons, presynaptic specializations are biochemically complex subcellular structures dedicated to neurotransmitter secretion. Activity-dependent changes in the abundance of presynaptic proteins are thought to endow synapses with different functional states; however, relatively little is known about the rules that govern changes in the composition of presynaptic terminals. We describe a genetic strategy to systematically analyze protein localization at Caenorhabditis elegans presynaptic specializations. Nine presynaptic proteins were GFP-tagged, allowing visualization of multiple presynaptic structures. Changes in the distribution and abundance of these proteins were quantified in 25 mutants that alter different aspects of neurotransmission. Global analysis of these data identified novel relationships between particular presynaptic components and provides a new method to compare gene functions by identifying shared protein localization phenotypes. Using this strategy, we identified several genes that regulate secretion of insulin-like growth factors (IGFs) and influence lifespan in a manner dependent on insulin/IGF signaling

PT-symmetry, indefinite metric, and nonlinear quantum mechanics

If a Hamiltonian of a quantum system is symmetric under space-time reflection, then the associated eigenvalues can be real. A conjugation operation for quantum states can then be defined in terms of space-time reflection, but the resulting Hilbert space inner product is not positive definite and gives rise to an interpretational difficulty. One way of resolving this difficulty is to introduce a superselection rule that excludes quantum states having negative norms. It is shown here that a quantum theory arising in this way gives an example of Kibble’s nonlinear quantum mechanics, with the property that the state space has a constant negative curvature. It then follows from the positive curvature theorem that the resulting quantum theory is not physically viable. This conclusion also has implications to other quantum theories obtained from the imposition of analogous superselection rules