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

Female brain size affects the assessment of male attractiveness during mate choice

Mate choice decisions are central in sexual selection theory aimed to understand how sexual traits evolve and their role in evolutionary diversification. We test the hypothesis that brain size and cognitive ability are important for accurate assessment of partner quality and that variation in brain size and cognitive ability underlies variation in mate choice. We compared sexual preference in guppy female lines selected for divergence in relative brain size, which we have previously shown to have substantial differences in cognitive ability. In a dichotomous choice test, large-brained and wild-type females showed strong preference for males with color traits that predict attractiveness in this species. In contrast, small-brained females showed no preference for males with these traits. In-depth analysis of optomotor response to color cues and gene expression of key opsins in the eye revealed that the observed differences were not due to differences in visual perception of color, indicating that differences in the ability to process indicators of attractiveness are responsible. We thus provide the first experimental support that individual variation in brain size affects mate choice decisions and conclude that differences in cognitive ability may be an important underlying mechanism behind variation in female mate choice

Fisheries

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A Novel Unsupervised Method to Identify Genes Important in the Anti-viral Response: Application to Interferon/Ribavirin in Hepatitis C Patients

Background: Treating hepatitis C with interferon/ribavirin results in a varied response in terms of decrease in viral titer and ultimate outcome. Marked responders have a sharp decline in viral titer within a few days of treatment initiation, whereas in other patients there is no effect on the virus (poor responders). Previous studies have shown that combination therapy modifies expression of hundreds of genes in vitro and in vivo. However, identifying which, if any, of these genes have a role in viral clearance remains challenging. Aims: The goal of this paper is to link viral levels with gene expression and thereby identify genes that may be responsible for early decrease in viral titer. Methods: Microarrays were performed on RNA isolated from PBMC of patients undergoing interferon/ribavirin therapy. Samples were collected at pre-treatment (day 0), and 1, 2, 7, 14 and 28 days after initiating treatment. A novel method was applied to identify genes that are linked to a decrease in viral titer during interferon/ribavirin treatment. The method uses the relationship between inter-patient gene expression based proximities and inter-patient viral titer based proximities to define the association between microarray gene expression measurements of each gene and viral-titer measurements. Results: We detected 36 unique genes whose expressions provide a clustering of patients that resembles viral titer based clustering of patients. These genes include IRF7, MX1, OASL and OAS2, viperin and many ISG's of unknown function. Conclusion: The genes identified by this method appear to play a major role in the reduction of hepatitis C virus during the early phase of treatment. The method has broad utility and can be used to analyze response to any group of factors influencing biological outcome such as antiviral drugs or anti-cancer agents where microarray data are available. © 2007 Brodsky et al

Sisyphus cooling and amplification by a superconducting qubit

Laser cooling of the atomic motion paved the way for remarkable achievements in the fields of quantum optics and atomic physics, including Bose-Einstein condensation and the trapping of atoms in optical lattices. More recently superconducting qubits were shown to act as artificial two-level atoms, displaying Rabi oscillations, Ramsey fringes, and further quantum effects. Coupling such qubits to resonators brought the superconducting circuits into the realm of quantum electrodynamics (circuit QED). It opened the perspective to use superconducting qubits as micro-coolers or to create a population inversion in the qubit to induce lasing behavior of the resonator. Furthering these analogies between quantum optical and superconducting systems we demonstrate here Sisyphus cooling of a low frequency LC oscillator coupled to a near-resonantly driven superconducting qubit. In the quantum optics setup the mechanical degrees of freedom of an atom are cooled by laser driving the atom's electronic degrees of freedom. Here the roles of the two degrees of freedom are played by the LC circuit and the qubit's levels, respectively. We also demonstrate the counterpart of the Sisyphus cooling, namely Sisyphus amplification. Parallel to the experimental demonstration we analyze the system theoretically and find quantitative agreement, which supports the interpretation and allows us to estimate system parameters.Comment: 7 pages, 4 figure

Estimating the number needed to treat from continuous outcomes in randomised controlled trials: methodological challenges and worked example using data from the UK Back Pain Exercise and Manipulation (BEAM) trial

Background Reporting numbers needed to treat (NNT) improves interpretability of trial results. It is unusual that continuous outcomes are converted to numbers of individual responders to treatment (i.e., those who reach a particular threshold of change); and deteriorations prevented are only rarely considered. We consider how numbers needed to treat can be derived from continuous outcomes; illustrated with a worked example showing the methods and challenges. Methods We used data from the UK BEAM trial (n = 1, 334) of physical treatments for back pain; originally reported as showing, at best, small to moderate benefits. Participants were randomised to receive 'best care' in general practice, the comparator treatment, or one of three manual and/or exercise treatments: 'best care' plus manipulation, exercise, or manipulation followed by exercise. We used established consensus thresholds for improvement in Roland-Morris disability questionnaire scores at three and twelve months to derive NNTs for improvements and for benefits (improvements gained+deteriorations prevented). Results At three months, NNT estimates ranged from 5.1 (95% CI 3.4 to 10.7) to 9.0 (5.0 to 45.5) for exercise, 5.0 (3.4 to 9.8) to 5.4 (3.8 to 9.9) for manipulation, and 3.3 (2.5 to 4.9) to 4.8 (3.5 to 7.8) for manipulation followed by exercise. Corresponding between-group mean differences in the Roland-Morris disability questionnaire were 1.6 (0.8 to 2.3), 1.4 (0.6 to 2.1), and 1.9 (1.2 to 2.6) points. Conclusion In contrast to small mean differences originally reported, NNTs were small and could be attractive to clinicians, patients, and purchasers. NNTs can aid the interpretation of results of trials using continuous outcomes. Where possible, these should be reported alongside mean differences. Challenges remain in calculating NNTs for some continuous outcomes

Why I tense up when you watch me: inferior parietal cortex mediates an audience’s influence on motor performance

The presence of an evaluative audience can alter skilled motor performance through changes in force output. To investigate how this is mediated within the brain, we emulated real-time social monitoring of participants’ performance of a fine grip task during functional magnetic resonance neuroimaging. We observed an increase in force output during social evaluation that was accompanied by focal reductions in activity within bilateral inferior parietal cortex. Moreover, deactivation of the left inferior parietal cortex predicted both inter- and intra-individual differences in socially-induced change in grip force. Social evaluation also enhanced activation within the posterior superior temporal sulcus, which conveys visual information about others’ actions to the inferior parietal cortex. Interestingly, functional connectivity between these two regions was attenuated by social evaluation. Our data suggest that social evaluation can vary force output through the altered engagement of inferior parietal cortex; a region implicated in sensorimotor integration necessary for object manipulation, and a component of the action-observation network which integrates and facilitates performance of observed actions. Social-evaluative situations may induce high-level representational incoherence between one’s own intentioned action and the perceived intention of others which, by uncoupling the dynamics of sensorimotor facilitation, could ultimately perturbe motor output

A network medicine approach to quantify distance between hereditary disease modules on the interactome

We introduce a MeSH-based method that accurately quantifies similarity between heritable diseases at molecular level. This method effectively brings together the existing information about diseases that is scattered across the vast corpus of biomedical literature. We prove that sets of MeSH terms provide a highly descriptive representation of heritable disease and that the structure of MeSH provides a natural way of combining individual MeSH vocabularies. We show that our measure can be used effectively in the prediction of candidate disease genes. We developed a web application to query more than 28.5 million relationships between 7,574 hereditary diseases (96% of OMIM) based on our similarity measure

Screening of DUB activity and specificity by MALDI-TOF mass spectrometry

Deubiquitylases (DUBs) are key regulators of the ubiquitin system which cleave ubiquitin moieties from proteins and polyubiquitin chains. Several DUBs have been implicated in various diseases and are attractive drug targets. We have developed a sensitive and fast assay to quantify in vitro DUB enzyme activity using matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry. Unlike other current assays, this method uses unmodified substrates, such as diubiquitin topoisomers. By analyzing 42 human DUBs against all diubiquitin topoisomers we provide an extensive characterization of DUB activity and specificity. Our results confirm the high specificity of many members of the OTU and JAMM DUB families and highlight that all USPs tested display low linkage selectivity. We also demonstrate that this assay can be deployed to assess the potency and specificity of DUB inhibitors by profiling 11 compounds against a panel of 32 DUBs

The influence of the accessory genome on bacterial pathogen evolution

Bacterial pathogens exhibit significant variation in their genomic content of virulence factors. This reflects the abundance of strategies pathogens evolved to infect host organisms by suppressing host immunity. Molecular arms-races have been a strong driving force for the evolution of pathogenicity, with pathogens often encoding overlapping or redundant functions, such as type III protein secretion effectors and hosts encoding ever more sophisticated immune systems. The pathogens’ frequent exposure to other microbes, either in their host or in the environment, provides opportunities for the acquisition or interchange of mobile genetic elements. These DNA elements accessorise the core genome and can play major roles in shaping genome structure and altering the complement of virulence factors. Here, we review the different mobile genetic elements focusing on the more recent discoveries and highlighting their role in shaping bacterial pathogen evolution