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

Clubroot (Plasmodiophora brassicae Woronin): an agricultural and biological challenge worldwide

Clubroot disease and the causal microbe Plasmodiophora brassicae offer abundant challenges to agriculturists and biological scientists. This microbe is well fitted for the environments which it inhabits. Plasmodiophora brassicae exists in soil as microscopic well protected resting spores and then grows actively and reproduces while shielded inside the roots of host plants. The pathogen is active outside the host for only short periods. Consequently, scientific studies are made challenging by the biological context of the host and pathogen and the technology required to investigate and understand that relationship. Controlling clubroot disease is a challenge for farmers, crop consultants and plant pathology practitioners because of the limited options which are available. Full symptom expression happens solely in members of the Brassicaceae family. Currently, only a few genes expressing strong resistance to P. brassicae are known and readily available. Agrochemical control is similarly limited by difficulties in molecule formulation which combines efficacy with environmental acceptability. Manipulation of husbandry encouraging improvements in soil structure, texture, nutrient composition and moisture content can reduce populations of P. brassicae. Integrating such strategies with rotation and crop management will reduce but not eliminate this disease. There are indications that forms of biological competition may be mobilised as additions to integrated control strategies. The aim of this review is to chart key themes in the development of scientific biological understanding of this host-pathogen relationship by offering signposts to grapple with clubroot disease which devastates crops and their profitability. Particular attention is given to the link between soil and nutrient chemistry and activity of this microbe

On soft singularities at three loops and beyond

We report on further progress in understanding soft singularities of massless gauge theory scattering amplitudes. Recently, a set of equations was derived based on Sudakov factorization, constraining the soft anomalous dimension matrix of multi-leg scattering amplitudes to any loop order, and relating it to the cusp anomalous dimension. The minimal solution to these equations was shown to be a sum over color dipoles. Here we explore potential contributions to the soft anomalous dimension that go beyond the sum-over-dipoles formula. Such contributions are constrained by factorization and invariance under rescaling of parton momenta to be functions of conformally invariant cross ratios. Therefore, they must correlate the color and kinematic degrees of freedom of at least four hard partons, corresponding to gluon webs that connect four eikonal lines, which first appear at three loops. We analyze potential contributions, combining all available constraints, including Bose symmetry, the expected degree of transcendentality, and the singularity structure in the limit where two hard partons become collinear. We find that if the kinematic dependence is solely through products of logarithms of cross ratios, then at three loops there is a unique function that is consistent with all available constraints. If polylogarithms are allowed to appear as well, then at least two additional structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4; added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11, 5.12 and 5.29); 38 pages, 3 figure

Relation of gallbladder function and Helicobacter pylori infection to gastric mucosa inflammation in patients with symptomatic cholecystolithiasis

Background. Inflammatory alterations of the gastric mucosa are commonly caused by Helicobacter pylori (Hp) infection in patients with symptomatic gallstone disease. However, the additional pathogenetic role of an impaired gallbladder function leading to an increased alkaline duodenogastric reflux is controversially discussed. Aim:To investigate the relation of gallbladder function and Hp infection to gastric mucosa inflammation in patients with symptomatic gallstones prior to cholecystectomy. Patients: Seventy-three patients with symptomatic gallstones were studied by endoscopy and Hp testing. Methods: Gastritis classification was performed according to the updated Sydney System and gallbladder function was determined by total lipid concentration of gallbladder bile collected during mainly laparoscopic cholecystectomy. Results: Fifteen patients revealed no, 39 patients mild, and 19 moderate to marked gastritis. No significant differences for bile salts, phospholipids, cholesterol, or total lipids in gallbladder bile were found between these three groups of patients. However, while only 1 out of 54 (< 2%) patients with mild or no gastritis was found histologically positive for Hp, this infection could be detected in 14 (74%) out of 19 patients with moderate to marked gastritis. Conclusion: Moderate to marked gastric mucosa inflammation in gallstone patients is mainly caused by Hp infection, whereas gallbladder function is not related to the degree of gastritis. Thus, an increased alkaline duodenogastric reflux in gallstone patients seems to be of limited pathophysiological relevance. Copyright (c) 2006 S. Karger AG, Basel

Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level

SAMURAI is a tool for the automated numerical evaluation of one-loop corrections to any scattering amplitudes within the dimensional-regularization scheme. It is based on the decomposition of the integrand according to the OPP-approach, extended to accommodate an implementation of the generalized d-dimensional unitarity-cuts technique, and uses a polynomial interpolation exploiting the Discrete Fourier Transform. SAMURAI can process integrands written either as numerator of Feynman diagrams or as product of tree-level amplitudes. We discuss some applications, among which the 6- and 8-photon scattering in QED, and the 6-quark scattering in QCD. SAMURAI has been implemented as a Fortran90 library, publicly available, and it could be a useful module for the systematic evaluation of the virtual corrections oriented towards automating next-to-leading order calculations relevant for the LHC phenomenology.Comment: 35 pages, 7 figure

Next-to-leading order QCD predictions for Z0H0+jetZ^0 H^0 + {\rm jet} production at LHC

We calculate the complete next-to-leading order (NLO) QCD corrections to the $Z^0H^0$ production in association with a jet at the LHC. We study the impacts of the NLO QCD radiative corrections to the integrated and differential cross sections and the dependence of the cross section on the factorization/renormalization scale. We present the transverse momentum distributions of the final $Z^0$-, Higgs-boson and leading-jet. We find that the NLO QCD corrections significantly modify the physical observables, and obviously reduce the scale uncertainty of the LO cross section. The QCD K-factors can be 1.183 and 1.180 at the $\sqrt{s}=14 TeV$ and $\sqrt{s}=7 TeV$ LHC respectively, when we adopt the inclusive event selection scheme with $p_{T,j}^{cut}=50 GeV$, $m_H=120 GeV$ and $\mu=\mu_r=\mu_f=\mu_0 \equiv 1/2(m_Z+m_H)$. Furthermore, we make the comparison between the two scale choices, $\mu=\mu_0$ and $\mu=\mu_1=1/2(E_{T}^{Z}+E_{T}^{H}+ \sum_{j}E_{T}^{jet})$, and find the scale choice $\mu=\mu_1$ seems to be more appropriate than the fixed scale $\mu=\mu_0$.Comment: 18 pages, 7 figure

Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure

The convective storm initiation project

Copyright @ 2007 AMSThe Convective Storm Initiation Project (CSIP) is an international project to understand precisely where, when, and how convective clouds form and develop into showers in the mainly maritime environment of southern England. A major aim of CSIP is to compare the results of the very high resolution Met Office weather forecasting model with detailed observations of the early stages of convective clouds and to use the newly gained understanding to improve the predictions of the model. A large array of ground-based instruments plus two instrumented aircraft, from the U.K. National Centre for Atmospheric Science (NCAS) and the German Institute for Meteorology and Climate Research (IMK), Karlsruhe, were deployed in southern England, over an area centered on the meteorological radars at Chilbolton, during the summers of 2004 and 2005. In addition to a variety of ground-based remote-sensing instruments, numerous rawin-sondes were released at one- to two-hourly intervals from six closely spaced sites. The Met Office weather radar network and Meteosat satellite imagery were used to provide context for the observations made by the instruments deployed during CSIP. This article presents an overview of the CSIP field campaign and examples from CSIP of the types of convective initiation phenomena that are typical in the United Kingdom. It shows the way in which certain kinds of observational data are able to reveal these phenomena and gives an explanation of how the analyses of data from the field campaign will be used in the development of an improved very high resolution NWP model for operational use.This work is funded by the National Environment Research Council following an initial award from the HEFCE Joint Infrastructure Fund

Obstructive sleep apnea in Treacher Collins syndrome

The aim of the present study was to investigate the prevalence of obstructive sleep apnea syndrome (OSAS) among the Norwegian population with Treacher Collins syndrome (TCS). A secondary aim was to establish whether TCS phenotype severity is associated with OSAS severity. A prospective case study design was used. Individuals who were 5 years old and above with a known diagnosis of TCS in Norway were invited to participate in a study. The study included genetic testing, medical and dental examinations and polysomnography. All participants demonstrated disturbed respiration during sleep; 18/19 met the diagnostic criteria for OSAS. Subjectively evaluated snoring was not a reliable predictor of OSAS. We found no significant association between TCS phenotype severity and the severity of OSAS. OSAS is common in TCS, but there is no association with the phenotype severity. Individuals diagnosed with TCS must undergo sleep studies to identify the presence of OSAS

Leveraging icebreaking tasks to facilitate uptake of voice communication in multiplayer games

Voice Communication (VC) is widely employed by developers as an essential component of online games. Typically, it is assumed that communications through this mechanism will be helpful and enjoyable, but existing literature suggests that the entry into VC can be problematic. In this paper, we present a study that attempts to mitigate player discomfort when first engaging with VC with strangers, through the use of traditional icebreaking tasks. We integrate these into the game RET, an online cooperative first person shooter which requires effective communication for players to succeed. An online user study with 18 participants suggests that icebreaking tasks can contribute to a positive VC experience, but their inclusion also creates further issues to be considered for successful integration