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

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

Generalization of entropy based divergence measures for symbolic sequence analysis

Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theory and mathematical statistics. The uniqueness and versatility of this measure arise because of a number of attributes including generalization to any number of probability distributions and association of weights to the distributions. Furthermore, its entropic formulation allows its generalization in different statistical frameworks, such as, non-extensive Tsallis statistics and higher order Markovian statistics. We revisit these generalizations and propose a new generalization of JSD in the integrated Tsallis and Markovian statistical framework. We show that this generalization can be interpreted in terms of mutual information. We also investigate the performance of different JSD generalizations in deconstructing chimeric DNA sequences assembled from bacterial genomes including that of E. coli, S. enterica typhi, Y. pestis and H. influenzae. Our results show that the JSD generalizations bring in more pronounced improvements when the sequences being compared are from phylogenetically proximal organisms, which are often difficult to distinguish because of their compositional similarity. While small but noticeable improvements were observed with the Tsallis statistical JSD generalization, relatively large improvements were observed with the Markovian generalization. In contrast, the proposed Tsallis-Markovian generalization yielded more pronounced improvements relative to the Tsallis and Markovian generalizations, specifically when the sequences being compared arose from phylogenetically proximal organisms.publishedVersionFil: Ré, Miguel Ángel. Universidad Tecnológica Nacional. Facultad Regional Córdoba. Centro de Investigación en Informática para la Ingeniería. Departamento de Ciencias Básicas; Argentina.Fil: Ré, Miguel Ángel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Azad, Rajeev K. University of North Texas. College of Science. Department of Biological Sciences; Estados Unidos de América.Fil: Azad, Rajeev K. University of North Texas. College of Science. Department of Mathematics; Estados Unidos de América.Ciencias de la Información y Bioinformática (desarrollo de hardware va en 2.2 "Ingeniería Eléctrica, Electrónica y de Información" y los aspectos sociales van en 5.8 "Comunicación y Medios"

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

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

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

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

UEV-1 Is an Ubiquitin-Conjugating Enzyme Variant That Regulates Glutamate Receptor Trafficking in C. elegans Neurons

The regulation of AMPA-type glutamate receptor (AMPAR) membrane trafficking is a key mechanism by which neurons regulate synaptic strength and plasticity. AMPAR trafficking is modulated through a combination of receptor phosphorylation, ubiquitination, endocytosis, and recycling, yet the factors that mediate these processes are just beginning to be uncovered. Here we identify the ubiquitin-conjugating enzyme variant UEV-1 as a regulator of AMPAR trafficking in vivo. We identified mutations in uev-1 in a genetic screen for mutants with altered trafficking of the AMPAR subunit GLR-1 in C. elegans interneurons. Loss of uev-1 activity results in the accumulation of GLR-1 in elongated accretions in neuron cell bodies and along the ventral cord neurites. Mutants also have a corresponding behavioral defect—a decrease in spontaneous reversals in locomotion—consistent with diminished GLR-1 function. The localization of other synaptic proteins in uev-1-mutant interneurons appears normal, indicating that the GLR-1 trafficking defects are not due to gross deficiencies in synapse formation or overall protein trafficking. We provide evidence that GLR-1 accumulates at RAB-10-containing endosomes in uev-1 mutants, and that receptors arrive at these endosomes independent of clathrin-mediated endocytosis. UEV-1 homologs in other species bind to the ubiquitin-conjugating enzyme Ubc13 to create K63-linked polyubiquitin chains on substrate proteins. We find that whereas UEV-1 can interact with C. elegans UBC-13, global levels of K63-linked ubiquitination throughout nematodes appear to be unaffected in uev-1 mutants, even though UEV-1 is broadly expressed in most tissues. Nevertheless, ubc-13 mutants are similar in phenotype to uev-1 mutants, suggesting that the two proteins do work together to regulate GLR-1 trafficking. Our results suggest that UEV-1 could regulate a small subset of K63-linked ubiquitination events in nematodes, at least one of which is critical in regulating GLR-1 trafficking

On Rao distance asymptotic distribution

Preprint enviat per a la seva publicació en una revista científica.This paper is concerned with the study of the asymptotic properties of Rao distance maximum-likelihood estimation obtained from two independent samples of two statistical populations, under certain regularity conditions. These results allow the construction, by meaos of the Rao distance, of a statistical test to compare different populations, which may be regarded as an alternative to the standard likelihood ratio test. Furthermore, a geometrical model is supplied which can be used to obtain graphical outputs through numerical taxonomy methods or multidimensional scaling techniques. Finally, sorne of the previously-mentioned methods are illustrated by meaos of a specific example based on the univariate normal distribution