Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, ii) the analytic expression of the sectional curvature of this metric, iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

Energy minimization problem in two-level dissipative quantum control: meridian case

International audienceWe analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky-Lindblad equation. According to the Pontryagin Maximum Principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis concerning 2D solutions in the case where the Hamiltonian dynamics are integrable

Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity

We consider spatially homogeneous Lifshitz black hole solutions in five dimensional higher derivative gravity theories, which can be possible near horizon geometries of some systems that are interesting in the framework of gauge/gravity duality. We show the solutions belonging to the nine Bianchi classes in the pure R^2 gravity. We find that these black holes have zero entropy at non-zero temperatures and this property is the same as the case of BTZ black holes in new massive gravity at the critical point. In the most general quadratic curvature gravity theories, we find new solutions in Bianchi Type I and Type IX cases.Comment: 15 pages, no figure; v2, refs added, version to appear in JHE

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Induction of humoral immune response to multiple recombinant Rhipicephalus appendiculatus antigens and their effect on tick feeding success and pathogen transmission

BACKGROUND: Rhipicephalus appendiculatus is the primary vector of Theileria parva, the etiological agent of East Coast fever (ECF), a devastating disease of cattle in sub-Saharan Africa. We hypothesized that a vaccine targeting tick proteins that are involved in attachment and feeding might affect feeding success and possibly reduce tick-borne transmission of T. parva. Here we report the evaluation of a multivalent vaccine cocktail of tick antigens for their ability to reduce R. appendiculatus feeding success and possibly reduce tick-transmission of T. parva in a natural host-tick-parasite challenge model. METHODS: Cattle were inoculated with a multivalent antigen cocktail containing recombinant tick protective antigen subolesin as well as two additional R. appendiculatus saliva antigens: the cement protein TRP64, and three different histamine binding proteins. The cocktail also contained the T. parva sporozoite antigen p67C. The effect of vaccination on the feeding success of nymphal and adult R. appendiculatus ticks was evaluated together with the effect on transmission of T. parva using a tick challenge model. RESULTS: To our knowledge, this is the first evaluation of the anti-tick effects of these antigens in the natural host-tick-parasite combination. In spite of evidence of strong immune responses to all of the antigens in the cocktail, vaccination with this combination of tick and parasite antigens did not appear to effect tick feeding success or reduce transmission of T. parva. CONCLUSION: The results of this study highlight the importance of early evaluation of anti-tick vaccine candidates in biologically relevant challenge systems using the natural tick-host-parasite combination

Acute WNT signalling activation perturbs differentiation within the adult stomach and rapidly leads to tumour formation

A role for WNT signalling in gastric carcinogenesis has been suggested due to two major observations. First, patients with germline mutations in adenomatous polyposis coli (APC) are susceptible to stomach polyps and second, in gastric cancer, WNT activation confers a poor prognosis. However, the functional significance of deregulated WNT signalling in gastric homoeostasis and cancer is still unclear. In this study we have addressed this by investigating the immediate effects of WNT signalling activation within the stomach epithelium. We have specifically activated the WNT signalling pathway within the mouse adult gastric epithelium via deletion of either glycogen synthase kinase 3 (GSK3) or APC or via expression of a constitutively active β-catenin protein. WNT pathway deregulation dramatically affects stomach homoeostasis at very short latencies. In the corpus, there is rapid loss of parietal cells with fundic gland polyp (FGP) formation and adenomatous change, which are similar to those observed in familial adenomatous polyposis. In the antrum, adenomas occur from 4 days post-WNT activation. Taken together, these data show a pivotal role for WNT signalling in gastric homoeostasis, FGP formation and adenomagenesis. Loss of the parietal cell population and corresponding FGP formation, an early event in gastric carcinogenesis, as well as antral adenoma formation are immediate effects of nuclear β-catenin translocation and WNT target gene expression. Furthermore, our inducible murine model will permit a better understanding of the molecular changes required to drive tumourigenesis in the stomach

Comparative study of nonlinear properties of EEG signals of a normal person and an epileptic patient

Background: Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results: Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak \textit{et al.} [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusions: In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.Comment: Keywords:EEG, epilepsy, Correlation dimension, Surrogate analysis, Hurst exponent. 9 page

Asymptotically Extrinsic Tamed Submanifolds

We study, from the extrinsic point of view, the structure at infinity of open submanifolds, ϕ : Mm → Mn(κ) isometrically immersed in the real space forms of constant sectional curvature κ ≤ 0.We shall use the decay of the second fundamental form of the so-called tamed immersions to obtain a description at infinity of the submanifold in the line of the structural results in Greene et al. (Int Math Res Not 1994:364–377, 1994) and Petrunin and Tuschmann (Math Ann 321:775–788, 2001) and an estimation from below of the number of its ends in terms of the volume growth of a special class of extrinsic domains, the extrinsic balls.Vicent Gimeno: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, and DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P. Vicente Palmer: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P, and Generalitat Valenciana Grant PrometeoII/2014/064. G. Pacelli Bessa: Work partially supported by CNPq- Brazil grant # 301581/2013-4

Inferring stabilizing mutations from protein phylogenies : application to influenza hemagglutinin

One selection pressure shaping sequence evolution is the requirement that a protein fold with sufficient stability to perform its biological functions. We present a conceptual framework that explains how this requirement causes the probability that a particular amino acid mutation is fixed during evolution to depend on its effect on protein stability. We mathematically formalize this framework to develop a Bayesian approach for inferring the stability effects of individual mutations from homologous protein sequences of known phylogeny. This approach is able to predict published experimentally measured mutational stability effects (ΔΔG values) with an accuracy that exceeds both a state-of-the-art physicochemical modeling program and the sequence-based consensus approach. As a further test, we use our phylogenetic inference approach to predict stabilizing mutations to influenza hemagglutinin. We introduce these mutations into a temperature-sensitive influenza virus with a defect in its hemagglutinin gene and experimentally demonstrate that some of the mutations allow the virus to grow at higher temperatures. Our work therefore describes a powerful new approach for predicting stabilizing mutations that can be successfully applied even to large, complex proteins such as hemagglutinin. This approach also makes a mathematical link between phylogenetics and experimentally measurable protein properties, potentially paving the way for more accurate analyses of molecular evolution

Environmental variables, habitat discontinuity and life history shaping the genetic structure of Pomatoschistus marmoratus

Coastal lagoons are semi-isolated ecosystems exposed to wide fluctuations of environmental conditions and showing habitat fragmentation. These features may play an important role in separating species into different populations, even at small spatial scales. In this study, we evaluate the concordance between mitochondrial (previous published data) and nuclear data analyzing the genetic variability of Pomatoschistus marmoratus in five localities, inside and outside the Mar Menor coastal lagoon (SE Spain) using eight microsatellites. High genetic diversity and similar levels of allele richness were observed across all loci and localities, although significant genic and genotypic differentiation was found between populations inside and outside the lagoon. In contrast to the FST values obtained from previous mitochondrial DNA analyses (control region), the microsatellite data exhibited significant differentiation among samples inside the Mar Menor and between lagoonal and marine samples. This pattern was corroborated using Cavalli-Sforza genetic distances. The habitat fragmentation inside the coastal lagoon and among lagoon and marine localities could be acting as a barrier to gene flow and contributing to the observed genetic structure. Our results from generalized additive models point a significant link between extreme lagoonal environmental conditions (mainly maximum salinity) and P. marmoratus genetic composition. Thereby, these environmental features could be also acting on genetic structure of coastal lagoon populations of P. marmoratus favoring their genetic divergence. The mating strategy of P. marmoratus could be also influencing our results obtained from mitochondrial and nuclear DNA. Therefore, a special consideration must be done in the selection of the DNA markers depending on the reproductive strategy of the species