Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups

The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the field of computer algebra. As is known, almost all irreducible polynomials with integer coefficients have only trivial exponent lattices. However, the algorithms in the literature have difficulty in proving such triviality for a generic polynomial. In this paper, the relations between the Galois group (respectively, \emph{the Galois-like groups}) and the triviality of the exponent lattice of a polynomial are investigated. The \bbbq\emph{-trivial} pairs, which are at the heart of the relations between the Galois group and the triviality of the exponent lattice of a polynomial, are characterized. An effective algorithm is developed to recognize these pairs. Based on this, a new algorithm is designed to prove the triviality of the exponent lattice of a generic irreducible polynomial, which considerably improves a state-of-the-art algorithm of the same type when the polynomial degree becomes larger. In addition, the concept of the Galois-like groups of a polynomial is introduced. Some properties of the Galois-like groups are proved and, more importantly, a sufficient and necessary condition is given for a polynomial (which is not necessarily irreducible) to have trivial exponent lattice.Comment: 19 pages,2 figure

Effects of the fatty acid amide hydrolase inhibitor URB597 on coping behavior under challenging conditions in mice

RATIONALE: Recent evidence suggests that in addition to controlling emotional behavior in general, endocannabinoid signaling is engaged in shaping behavioral responses to challenges. This important function of endocannabinoids is still poorly understood. OBJECTIVES: Here we investigated the impact of blockade of fatty acid amide hydrolase (FAAH), the degrading enzyme of anandamide on behavioral responses induced by challenges of different intensity. METHODS: Mice treated with FAAH inhibitor URB597 were either manually restrained on their backs (back test) or received foot-shocks. RESULTS: The behavior of mice showed bimodal distribution in the back test: they either predominantly showed escape attempts or equally distributed time between passivity and escape. URB597 increased escapes in animals with low escape scores. No effects were noticed in mice showing high escape scores, which is likely due to a ceiling effect. We hypothesized that stronger stressors would wash out individual differences in coping; therefore, we exposed mice to foot-shocks that decreased locomotion and increased freezing in all mice. URB597 ameliorated both responses. The re-exposure of mice to the shock cage 14 days later without delivering shocks or treatment was followed by reduced and fragmented sleep as shown by electrophysiological recordings. Surprisingly, sleep was more disturbed after the reminder than after shocks in rats receiving vehicle before foot-shocks. These reminder-induced disturbances were abolished by URB597 administered before shocks. CONCLUSIONS: These findings suggest that FAAH blockade has an important role in the selection of behavioral responses under challenging conditions and-judging from its long-term effects-that it influences the cognitive appraisal of the challenge

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.Comment: 39 pages, 12 figures, 2 tables. Chapter of the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action 1304. Minor corrections to match published versio

Investigating the effect of independent blinded digital image assessment on the STOP GAP trial

Background Blinding is the process of keeping treatment assignment hidden and is used to minimise the possibility of bias. Trials at high risk of bias have been shown to report larger treatment effects than low risk studies. In dermatology, one popular method of blinding is to have independent outcome assessors who are unaware of treatment allocation assessing the end point using digital photographs. However, this can be complex, expensive and time-consuming. The objective of this study was to compare the effect of blinded and unblinded outcome assessment on the results of the STOP GAP trial. Methods The STOP GAP trial compared prednisolone to ciclosporin in treating pyoderma gangrenosum. Participants’ lesions were measured at baseline and 6 weeks to calculate the primary outcome, speed of healing. Independent blinded assessors obtained measurements from digital photographs using specialist software. In addition, unblinded treating clinicians estimated lesion area by measuring length and width. The primary outcome was determined using blinded measurements where available, otherwise unblinded measurements were used (method referred to as trial measurements). In this study, agreement between the trial and unblinded measurements was determined using the intraclass correlation coefficient (ICC). The STOP GAP primary analysis was repeated using unblinded measurements only. We introduced differential and non-differential error in unblinded measurements and investigated the effect on the STOP GAP primary analysis. Results 86 (80%) of the 108 patients were assessed using digital images. Agreement between trial and unblinded measurements was excellent (ICC=0.92 at baseline; 0.83 at 6 weeks). There was no evidence that the results of the trial primary analysis differed according to how the primary outcome was assessed (p-value for homogeneity = 1.00). Conclusions Blinded digital image assessment in STOP GAP did not meaningfully alter trial conclusions compared with unblinded assessment. However, as the process brought added accuracy and credibility to the trial it was considered worthwhile. These findings question the usefulness of digital image assessment in a trial with an objective outcome and where bias is not expected to be excessive. Further research should investigate if there are alternative, less complex ways of incorporating blinding in clinical trials

Milk Lacking α-Casein Leads to Permanent Reduction in Body Size in Mice

The major physiological function of milk is the transport of amino acids, carbohydrates, lipids and minerals to mammalian offspring. Caseins, the major milk proteins, are secreted in the form of a micelle consisting of protein and calcium-phosphate

Subtype-associated differences in HIV-1 reverse transcription affect the viral replication

Background: The impact of the products of the pol gene, specifically, reverse transcriptase (RT) on HIV-1 replication, evolution, and acquisition of drug resistance has been thoroughly characterized for subtype B. For subtype C, which accounts of almost 60% of HIV cases worldwide, much less is known. It has been reported that subtype C HIV-1 isolates have a lower replication capacity than B; however, the basis of these differences remains unclear. Results: We analyzed the impact of the pol gene products from HIV-1 B and C subtypes on the maturation of HIV virions, accumulation of reverse transcription products, integration of viral DNA, frequency of point mutations in provirus and overall viral replication. Recombinant HIV-1 viruses of B and C subtypes comprising the pol fragments encoding protease, integrase and either the whole RT or a chimeric RT from different isolates of the C and B subtypes, were used for infection of cells expressing CXCR4 or CCR5 co-receptors. The viruses carrying different fragments of pol from the isolates of B and C subtypes did not reveal differences in Gag and GagPol processing and viral RNA incorporation into the virions. However, the presence of the whole RT from subtype C, or the chimeric RT containing either the polymerase or the connection and RNase H domains from C isolates, caused significantly slower viral replication regardless of B or C viral backbone. Subtype C RT carrying viruses displayed lower levels of accumulation of strong-stop cDNA in permeabilized virions during endogenous reverse transcription, and decreased accumulation of both strong-stop and positive strand reverse transcription products in infected cells and in isolated reverse transcription complexes. This decreased accumulation correlated with lower levels of viral DNA integration in cells infected with viruses carrying the whole RT or RT domains from subtype C isolates. The single viral genome assay analysis did not reveal significant differences in the frequency of point mutations between the RT from B or C subtypes. Conclusions: These data suggest that the whole RT as well as distinct polymerase and connection-RNase H domains from subtype C HIV-1 confer a lower level of accumulation of reverse transcripts in the virions and reverse transcription complexes as compared to subtype B, resulting in a lower overall level of virus replication

HIV-1 pol Diversity among Female Bar and Hotel Workers in Northern Tanzania

A national ART program was launched in Tanzania in October 2004. Due to the existence of multiple HIV-1 subtypes and recombinant viruses co-circulating in Tanzania, it is important to monitor rates of drug resistance. The present study determined the prevalence of HIV-1 drug resistance mutations among ART-naive female bar and hotel workers, a high-risk population for HIV-1 infection in Moshi, Tanzania. A partial HIV-1 pol gene was analyzed by single-genome amplification and sequencing in 45 subjects (622 pol sequences total; median number of sequences per subject, 13; IQR 5–20) in samples collected in 2005. The prevalence of HIV-1 subtypes A1, C, and D, and inter-subtype recombinant viruses, was 36%, 29%, 9% and 27%, respectively. Thirteen different recombination patterns included D/A1/D, C/A1, A1/C/A1, A1/U/A1, C/U/A1, C/A1, U/D/U, D/A1/D, A1/C, A1/C, A2/C/A2, CRF10_CD/C/CRF10_CD and CRF35_AD/A1/CRF35_AD. CRF35_AD was identified in Tanzania for the first time. All recombinant viruses in this study were unique, suggesting ongoing recombination processes among circulating HIV-1 variants. The prevalence of multiple infections in this population was 16% (n = 7). Primary HIV-1 drug resistance mutations to RT inhibitors were identified in three (7%) subjects (K65R plus Y181C; N60D; and V106M). In some subjects, polymorphisms were observed at the RT positions 41, 69, 75, 98, 101, 179, 190, and 215. Secondary mutations associated with NNRTIs were observed at the RT positions 90 (7%) and 138 (6%). In the protease gene, three subjects (7%) had M46I/L mutations. All subjects in this study had HIV-1 subtype-specific natural polymorphisms at positions 36, 69, 89 and 93 that are associated with drug resistance in HIV-1 subtype B. These results suggested that HIV-1 drug resistance mutations and natural polymorphisms existed in this population before the initiation of the national ART program. With increasing use of ARV, these results highlight the importance of drug resistance monitoring in Tanzania

Review of genetic factors in intestinal malrotation

Intestinal malrotation is well covered in the surgical literature from the point of view of operative management, but few reviews to date have attempted to provide a comprehensive examination of the topic from the point of view of aetiology, in particular genetic aetiology. Following a brief overview of molecular embryology of midgut rotation, we present in this article instances of and case reports and case series of intestinal malrotation in which a genetic aetiology is likely. Autosomal dominant, autosomal recessive, X-linked and chromosomal forms of the disorder are represented. Most occur in syndromic form, that is to say, in association with other malformations. In many instances, recognition of a specific syndrome is possible, one of several examples discussed being the recently described association of intestinal malrotation with alveolar capillary dysplasia, due to mutations in the forkhead box transcription factor FOXF1. New advances in sequencing technology mean that the identification of the genes mutated in these disorders is more accessible than ever, and paediatric surgeons are encouraged to refer to their colleagues in clinical genetics where a genetic aetiology seems likely