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

Predicting "springback" using 3D surface representation techniques: A case study in sheet metal forming

The work presented in this papers is directed at mechanisms where by 3D surfaces can be represented to support the generation and application of classification techniques. Three different mechanisms are presented to allow for the representation of 3D surfaces in such a way that key features are retained while at the same time ensuring compatibility with prediction (classification) techniques. The three representation techniques are: (i) Local Geometry Matrices (LGMs) founded on the concept of local binary patterns, (ii) Local Distance Measure (LDM) founded on the idea that distances from edges (critical points) may be significant, and (iii) Point Series (PS) whereby local geometries are represented in terms of a linearisation of space. The representations are designed to capture the nature of 3D surfaces in terms of their local geometry and predict class labels associated with such local geometries. To act as a focus for the work the prediction of "springback" within the context of sheet metal forming is considered, where springback is a form of deformation that occurs (in a non-uniform manner) across a manufactured 3D surface as a result of the application of some sheet metal forming process. The evaluation of each of the techniques, and variations thereof, using sheet metal parts that have been manufactured especially for the purpose, is fully described. The paper also reports on a statistical significance test concerning the results

Precision Gauge Unification from Extra Yukawa Couplings

We investigate the impact of extra vector-like GUT multiplets on the predicted value of the strong coupling. We find in particular that Yukawa couplings between such extra multiplets and the MSSM Higgs doublets can resolve the familiar two-loop discrepancy between the SUSY GUT prediction and the measured value of alpha_3. Our analysis highlights the advantages of the holomorphic scheme, where the perturbative running of gauge couplings is saturated at one loop and further corrections are conveniently described in terms of wavefunction renormalization factors. If the gauge couplings as well as the extra Yukawas are of O(1) at the unification scale, the relevant two-loop correction can be obtained analytically. However, the effect persists also in the weakly-coupled domain, where possible non-perturbative corrections at the GUT scale are under better control.Comment: 26 pages, LaTeX. v6: Important early reference adde

Mellin Amplitudes for Dual Conformal Integrals

Motivated by recent work on the utility of Mellin space for representing conformal correlators in $AdS$/CFT, we study its suitability for representing dual conformal integrals of the type which appear in perturbative scattering amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for writing Mellin amplitudes for a large class of integrals in any dimension, and find explicit representations for several familiar toy integrals. However we show that the power of Mellin space is that it provides simple representations even for fully massive integrals, which except for the single case of the 4-mass box have not yet been computed by any available technology. Mellin space is also useful for exhibiting differential relations between various multi-loop integrals, and we show that certain higher-loop integrals may be written as integral operators acting on the fully massive scalar $n$-gon in $n$ dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very simple formula expressing the 6-mass double box as a single integral of the 6-mass scalar hexagon in 6 dimensions.Comment: 29+7 page

Patterns of primary care and mortality among patients with schizophrenia or diabetes: a cluster analysis approach to the retrospective study of healthcare utilization

Abstract Background Patients with schizophrenia have difficulty managing their medical healthcare needs, possibly resulting in delayed treatment and poor outcomes. We analyzed whether patients reduced primary care use over time, differentially by diagnosis with schizophrenia, diabetes, or both schizophrenia and diabetes. We also assessed whether such patterns of primary care use were a significant predictor of mortality over a 4-year period. Methods The Veterans Healthcare Administration (VA) is the largest integrated healthcare system in the United States. Administrative extracts of the VA's all-electronic medical records were studied. Patients over age 50 and diagnosed with schizophrenia in 2002 were age-matched 1:4 to diabetes patients. All patients were followed through 2005. Cluster analysis explored trajectories of primary care use. Proportional hazards regression modelled the impact of these primary care utilization trajectories on survival, controlling for demographic and clinical covariates. Results Patients comprised three diagnostic groups: diabetes only (n = 188,332), schizophrenia only (n = 40,109), and schizophrenia with diabetes (Scz-DM, n = 13,025). Cluster analysis revealed four distinct trajectories of primary care use: consistent over time, increasing over time, high and decreasing, low and decreasing. Patients with schizophrenia only were likely to have low-decreasing use (73% schizophrenia-only vs 54% Scz-DM vs 52% diabetes). Increasing use was least common among schizophrenia patients (4% vs 8% Scz-DM vs 7% diabetes) and was associated with improved survival. Low-decreasing primary care, compared to consistent use, was associated with shorter survival controlling for demographics and case-mix. The observational study was limited by reliance on administrative data. Conclusion Regular primary care and high levels of primary care were associated with better survival for patients with chronic illness, whether psychiatric or medical. For schizophrenia patients, with or without comorbid diabetes, primary care offers a survival benefit, suggesting that innovations in treatment retention targeting at-risk groups can offer significant promise of improving outcomes.http://deepblue.lib.umich.edu/bitstream/2027.42/78274/1/1472-6963-9-127.xmlhttp://deepblue.lib.umich.edu/bitstream/2027.42/78274/2/1472-6963-9-127.pdfPeer Reviewe

Exactly Marginal Deformations and Global Symmetries

We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a conserved current multiplet. Additionally, we find that the space of exactly marginal deformations, also called the "conformal manifold," is the quotient of the space of marginal couplings by the complexified continuous global symmetry group. This fact explains why exactly marginal deformations are ubiquitous in N=1 theories. Our method turns the problem of enumerating exactly marginal operators into a problem in group theory, and substantially extends and simplifies the previous analysis by Leigh and Strassler. We also briefly discuss how to apply our analysis to N=2 theories in three dimensions.Comment: 23 pages, 2 figure

Amblyopia and quality of life: a systematic review

Background/Aims Amblyopia is a common condition which can affect up to 5% of the general population. The health-related quality of life (HRQoL) implications of amblyopia and/or its treatment have been explored in the literature. Methods A systematic literature search was undertaken (16th-30th January 2007) to identify the HRQoL implications of amblyopia and/or its treatment. Results A total of 25 papers were included in the literature review. The HRQoL implications of amblyopia related specifically to amblyopia treatment, rather than the condition itself. These included the impact upon family life; social interactions; difficulties undertaking daily activities; and feelings and behaviour. The identified studies adopted a number of methodologies. The study populations included; children with the condition; parents of children with amblyopia; and adults who had undertaken amblyopia treatment as a child. Some studies developed their own measures of HRQoL, and others determined HRQoL through proxy measures. Conclusions The reported findings of the HRQoL implications are of importance when considering the management of cases of amblyopia. Further research is required to assess the immediate and long-term effects of amblyopia and/or its treatment upon HRQoL using a more standardised approach

The transcriptional repressor protein NsrR senses nitric oxide directly via a [2Fe-2S] cluster

The regulatory protein NsrR, a member of the Rrf2 family of transcription repressors, is specifically dedicated to sensing nitric oxide (NO) in a variety of pathogenic and non-pathogenic bacteria. It has been proposed that NO directly modulates NsrR activity by interacting with a predicted [Fe-S] cluster in the NsrR protein, but no experimental evidence has been published to support this hypothesis. Here we report the purification of NsrR from the obligate aerobe Streptomyces coelicolor. We demonstrate using UV-visible, near UV CD and EPR spectroscopy that the protein contains an NO-sensitive [2Fe-2S] cluster when purified from E. coli. Upon exposure of NsrR to NO, the cluster is nitrosylated, which results in the loss of DNA binding activity as detected by bandshift assays. Removal of the [2Fe-2S] cluster to generate apo-NsrR also resulted in loss of DNA binding activity. This is the first demonstration that NsrR contains an NO-sensitive [2Fe-2S] cluster that is required for DNA binding activity

No straight lines – young women’s perceptions of their mental health and wellbeing during and after pregnancy: a systematic review and meta-ethnography

Background: Young mothers face mental health challenges during and after pregnancy including increased rates of depression compared to older mothers. While the prevention of teenage pregnancy in countries such as the United States and the United Kingdom has been a focus for policy and research in recent decades, the need to understand young women’s own experiences has been highlighted. The aim of this meta-ethnography was to examine young women’s perceptions of their mental health and wellbeing during and after pregnancy to provide new understandings of those experiences. Methods: A systematic review and meta-ethnographic synthesis of qualitative research was conducted. Seven databases were systematically searched and forward and backward searching conducted. Papers were included if they were from Organisation for Economic Co-operation and Development countries and explored mental health and wellbeing experiences of young mothers (age under 20 in pregnancy; under 25 at time of research) as a primary research question – or where evidence about mental health and wellbeing from participants was foregrounded. Nineteen papers were identified and the Critical Appraisal Skills Programme checklist for qualitative research used to appraise the evidence. Following the seven-step process of meta-ethnography, key constructs were examined within each study and then translated into one another. Results: Seven translated themes were identified forming a new line of argument wherein mental health and wellbeing was analysed as relating to individual bodily experiences; tied into past and present relationships; underpinned by economic insecurity and entangled with feelings of societal surveillance. There were ‘no straight lines’ in young women’s experiences, which were more complex than dominant narratives around overcoming adversity suggest. Conclusions: The synthesis concludes that health and social care professionals need to reflect on the operation of power and stigma in young women’s lives and its impact on wellbeing. It adds to understanding of young women’s mental health and wellbeing during and after pregnancy as located in physical and structural factors rather than individual capacities alone

Cellular Robustness Conferred by Genetic Crosstalk Underlies Resistance against Chemotherapeutic Drug Doxorubicin in Fission Yeast

10.1371/journal.pone.0055041PLoS ONE81