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

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

Troubling "understanding mathematics-in-depth": Its role in the identity work of student-teachers in England

Copyright @ The Author(s) 2013. This article is published with open access at Springerlink.comThis article has been made available through the Brunel Open Access Publishing Fund.In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop “understanding mathematics in-depth” in students in order for them to become successful mathematics teachers. We take a poststructural approach, so we are not interested in asking what such an understanding is, about the value of this approach or about the effectiveness of the MECs in developing this understanding in their participants. Instead we explore what positions this discourse of “understanding mathematics in-depth” makes available to MEC students. We do this by looking in detail at the “identity work” of two students, analysing how they use and are used by this discourse to position themselves as future mathematics teachers. In doing so, we show how even benign-looking social practices such as “understanding mathematics in-depth” are implicated in practices of inclusion and exclusion. We show this through detailed readings of interviews with two participants, one of whom fits with the dominant discourses in the MEC and the other who, despite passing the MEC, experiences tensions between her national identity work and MEC discourses. We argue that it is vital to explore “identity work” within teacher education contexts to ensure that becoming a successful mathematics teacher is equally available to all.King’s College Londo

Synthesis and Characterization of Tin Disulfide (SnS2) Nanowires

The ordered tin disulfide (SnS2) nanowire arrays were first fabricated by sulfurizing the Sn nanowires, which are embedded in the nanochannels of anodic aluminum oxide (AAO) template. SnS2nanowire arrays are highly ordered and highly dense. X-ray diffraction (XRD) and corresponding selected area electron diffraction (SAED) patterns demonstrate the SnS2nanowire is hexagonal polycrystalline. The study of UV/Visible/NIR absorption shows the SnS2nanowire is a wide-band semiconductor with three band gap energies (3.3, 4.4, and 5.8 eV)

Truncating and missense BMPR2 mutations differentially affect the severity of heritable pulmonary arterial hypertension

<p>Abstract</p> <p>Background</p> <p>Autosomal dominant inheritance of germline mutations in the bone morphogenetic protein receptor type 2 (<it>BMPR2</it>) gene are a major risk factor for pulmonary arterial hypertension (PAH). While previous studies demonstrated a difference in severity between <it>BMPR2 </it>mutation carriers and noncarriers, it is likely disease severity is not equal among <it>BMPR2 </it>mutations. We hypothesized that patients with missense <it>BMPR2 </it>mutations have more severe disease than those with truncating mutations.</p> <p>Methods</p> <p>Testing for <it>BMPR2 </it>mutations was performed in 169 patients with PAH (125 with a family history of PAH and 44 with sporadic disease). Of the 106 patients with a detectable <it>BMPR2 </it>mutation, lymphocytes were available in 96 to functionally assess the nonsense-mediated decay pathway of RNA surveillance. Phenotypic characteristics were compared between <it>BMPR2 </it>mutation carriers and noncarriers, as well as between those carriers with a missense versus truncating mutation.</p> <p>Results</p> <p>While there was a statistically significant difference in age at diagnosis between carriers and noncarriers, subgroup analysis revealed this to be the case only for females. Among carriers, there was no difference in age at diagnosis, death, or survival according to exonic location of the <it>BMPR2 </it>mutation. However, patients with missense mutations had statistically significant younger ages at diagnosis and death, as well as shorter survival from diagnosis to death or lung transplantation than those with truncating mutations. Consistent with this data, the majority of missense mutations were penetrant prior to age 36 years, while the majority of truncating mutations were penetrant after age 36 years.</p> <p>Conclusion</p> <p>In this cohort, <it>BMPR2 </it>mutation carriers have more severe PAH disease than noncarriers, but this is only the case for females. Among carriers, patients with missense mutations that escape nonsense-mediated decay have more severe disease than those with truncating mutations. These findings suggest that treatment and prevention strategies directed specifically at <it>BMPR2 </it>pathway defects may need to vary according to the type of mutation.</p

In vitro Induction of Entamoeba histolytica Cyst-like Structures from Trophozoites

Inhibition of encystment can be conceived as a potentially useful mechanism to block the transmission of Entamoeba histolytica under natural conditions. Unfortunately, amoeba encystment has not been achieved in vitro and drugs inhibiting the formation of cysts are not available. Luminal conditions inducing encystment in vivo are also unknown, but cellular stress such as exposure to reactive oxygen species from immune cells or intestinal microbiota could be involved. A role for certain divalent cations as cofactors of enzymes involved in excystment has also been described. In this study, we show that trophozoite cultures, treated with hydrogen peroxide in the presence of trace amounts of several cations, transform into small-sized spherical and refringent structures that exhibit resistance to different detergents. Ultrastructural analysis under scanning and transmission electron microscopy revealed multinucleated structures (some with four nuclei) with smooth, thick membranes and multiple vacuoles. Staining with calcofluor white, as well as an ELISA binding assay using wheat germ agglutinin, demonstrated the presence of polymers of N-acetylglucosamine (chitin), which is the primary component of the natural cyst walls. Over-expression of glucosamine 6-phosphate isomerase, likely to be the rate-limiting enzyme in the chitin synthesis pathway, was also confirmed by RT-PCR. These results suggest that E. histolytica trophozoites activated encystment pathways when exposed to our treatment

Similarities and Differences in Chinese and Caucasian Adults' Use of Facial Cues for Trustworthiness Judgments

All cultural groups in the world place paramount value on interpersonal trust. Existing research suggests that although accurate judgments of another's trustworthiness require extensive interactions with the person, we often make trustworthiness judgments based on facial cues on the first encounter. However, little is known about what facial cues are used for such judgments and what the bases are on which individuals make their trustworthiness judgments.In the present study, we tested the hypothesis that individuals may use facial attractiveness cues as a “shortcut” for judging another's trustworthiness due to the lack of other more informative and in-depth information about trustworthiness. Using data-driven statistical models of 3D Caucasian faces, we compared facial cues used for judging the trustworthiness of Caucasian faces by Caucasian participants who were highly experienced with Caucasian faces, and the facial cues used by Chinese participants who were unfamiliar with Caucasian faces. We found that Chinese and Caucasian participants used similar facial cues to judge trustworthiness. Also, both Chinese and Caucasian participants used almost identical facial cues for judging trustworthiness and attractiveness.The results suggest that without opportunities to interact with another person extensively, we use the less racially specific and more universal attractiveness cues as a “shortcut” for trustworthiness judgments

Analysis of gene mutations associated with isoniazid, rifampicin and ethambutol resistance among Mycobacterium tuberculosis isolates from Ethiopia

<p>Abstract</p> <p>Background</p> <p>The emergence of drug resistance is one of the most important threats to tuberculosis control programs. This study was aimed to analyze the frequency of gene mutations associated with resistance to isoniazid (INH), rifampicin (RMP) and ethambutol (EMB) among <it>Mycobacterium tuberculosis </it>isolates from Northwest Ethiopia, and to assess the performance of the GenoType^®MTBDRplus and GenoType^®MTBDRsl assays as compared to the BacT/ALERT 3D system.</p> <p>Methods</p> <p>Two hundred sixty <it>Mycobacterium tuberculosis </it>isolates from smear positive tuberculosis patients diagnosed between March 2009 and July 2009 were included in this study. Drug susceptibility tests were performed in the Institute of Medical Microbiology and Epidemiology of Infectious Diseases, University Hospital of Leipzig, Germany.</p> <p>Results</p> <p>Of 260 isolates, mutations conferring resistance to INH, RMP, or EMB were detected in 35, 15, and 8 isolates, respectively, while multidrug resistance (MDR) was present in 13 of the isolates. Of 35 INH resistant strains, 33 had mutations in the <it>katG </it>gene at Ser315Thr 1 and two strains had mutation in the <it>inhA </it>gene at C15T. Among 15 RMP resistant isolates, 11 had <it>rpoB </it>gene mutation at Ser531Leu, one at His526Asp, and three strains had mutations only at the wild type probes. Of 8 EMB resistant strains, two had mutations in the <it>embB </it>gene at Met306Ile, one at Met306Val, and five strains had mutations only at the wild type probes. The GenoType^®MTBDRplus assay had a sensitivity of 92% and specificity of 99% for INH resistance, and 100% sensitivity and specificity to detect RMP resistance and MDR. The GenoType^®MTBDRsl assay had a sensitivity of 42% and specificity of 100% for EMB resistance.</p> <p>Conclusion</p> <p>The dominance of single gene mutations associated with the resistance to INH and RMP was observed in the codon 315 of the <it>katG </it>gene and codon 531 of the <it>rpoB </it>gene, respectively. The GenoType^®MTBDRplus assay is a sensitive and specific tool for diagnosis of resistance to INH, RMP and MDR. However, the GenoType^®MTBDRsl assay shows limitations in detecting resistance to EMB.</p