The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Latitudinal variation in monthly-scale reproductive synchrony among Acropora coral assemblages in the Indo-Pacific

Early research into coral reproductive biology suggested that spawning synchrony was driven by variations in the amplitude of environmental variables that are correlated with latitude, with synchrony predicted to break down at lower latitudes. More recent research has revealed that synchronous spawning, both within and among species, is a feature of all speciose coral assemblages, including equatorial reefs. Nonetheless, considerable variation in reproductive synchrony exists among locations and the hypothesis that the extent of spawning synchrony is correlated with latitude has not been formally tested on a large scale. Here, we use data from 90 sites throughout the Indo-Pacific and a quantitative index of reproductive synchrony applied at a monthly scale to demonstrate that, despite considerable spatial and temporal variation, there is no correlation between latitude and reproductive synchrony. Considering the critical role that successful reproduction plays in the persistence and recovery of coral reefs, research is urgently needed to understand the drivers underpinning variation in reproductive synchrony

Latitudinal variation in monthly-scale reproductive synchrony among Acropora coral assemblages in the Indo-Pacific

Early research into coral reproductive biology suggested that spawning synchrony was driven by variations in the amplitude of environmental variables that are correlated with latitude, with synchrony predicted to break down at lower latitudes. More recent research has revealed that synchronous spawning, both within and among species, is a feature of all speciose coral assemblages, including equatorial reefs. Nonetheless, considerable variation in reproductive synchrony exists among locations and the hypothesis that the extent of spawning synchrony is correlated with latitude has not been formally tested on a large scale. Here, we use data from 90 sites throughout the Indo-Pacific and a quantitative index of reproductive synchrony applied at a monthly scale to demonstrate that, despite considerable spatial and temporal variation, there is no correlation between latitude and reproductive synchrony. Considering the critical role that successful reproduction plays in the persistence and recovery of coral reefs, research is urgently needed to understand the drivers underpinning variation in reproductive synchrony

Observations of Past Lunar Landing Sites by the D-CIXS X-Ray Spectrometer on SMART-1

D-CIXS initial observations show a first unambiguous remote sensing of calcium in the lunar regolith. Data obtained are broadly consistent with current understanding of mare and highland composition. Ground truth is provided by the returned Apollo and Luna sample sets

Cytokine alterations in first-episode schizophrenia patients before and after antipsychotic treatment

Schizophrenia has been associated with central nervous system and peripheral immune system imbalances. However, most studies have not yielded conclusive results due to limitations such as small sample size, dissimilarities in the clinical status of patients and the high variability of cytokine levels within the normal human population. Here, we have attempted to account for these limitations by carrying out standardised multiplex immunoassay analyses of 9 cytokines in serum from 180 antipsychotic-naïve first-episode schizophrenia patients and 350 matched controls across 5 clinical cohorts. All subjects were matched for potential confounding factors including age, gender, smoking and body mass index. We found that the levels of interleukin (IL)-1RA, IL-10 and IL-15 were increased significantly in patients across the cohorts. We also found that the levels of IL-1RA and IL-10 were decreased in 32 patients who had been followed up and treated for 6. weeks with atypical antipsychotics. Interestingly, we found that the changes in IL-10 levels were significantly correlated with the improvements in negative, general and total symptom scores. These results indicate that mixed pro- and anti-inflammatory responses may be altered in first onset patients, suggesting a role in the aetiology of schizophrenia. The finding that only the anti-inflammatory cytokine IL-10 responded to treatment in parallel with symptom improvement suggests that this could be used as a potential treatment response biomarker in future studies of schizophrenia

Effect of quantum confinement on exciton-phonon interactions

We investigate the homogeneous linewidth of localized type-I excitons in type-II GaAs/AlAs superlattices. These localizing centers represent the intermediate case between quasi-two-dimensional (Q2D) and quasi-zero-dimensional localizations. The temperature dependence of the homogeneous linewidth is obtained with high precision from micro-photoluminescence spectra. We confirm the reduced interaction of the excitons with their environment with decreasing dimensionality except for the coupling to LO-phonons. The low-temperature limit for the linewidth of these localized excitons is five times smaller than that of Q2D excitons. The coefficient of exciton-acoustic-phonon interaction is 5 ~ 6 times smaller than that of Q2D excitons. An enhancement of the average exciton-LO-phonon interaction by localization is found in our sample. But this interaction is very sensitive to the detailed structure of the localizing centers.Comment: 6 pages, 4 figure

Reducible connections and non-local symmetries of the self-dual Yang-Mills equations

We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat $\mathbb{R}^4$. We show how all such connections lie in the orbit of the flat connection on $\mathbb{R}^4$ under the action of non-local symmetries of the self-dual Yang-Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang-Mills equations that are analogous to harmonic maps of finite type.Comment: AMSLatex, 15 pages, no figures. Corrected in line with the referee's comments. In particular, restriction to simply-connected open sets now explicitly stated. Version to appear in Communications in Mathematical Physic

Algebraic construction of the Darboux matrix revisited

We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the Darboux-Backlund transformation, based on different lambda-dependencies of the Darboux matrix: polynomial, sum of partial fractions, or the transfer matrix form. We derive symmetric N-soliton formulas in the general case. The matrix spectral parameter and dressing actions in loop groups are also discussed. We describe reductions to twisted loop groups, unitary reductions, the matrix Lax pair for the KdV equation and reductions of chiral models (harmonic maps) to SU(n) and to Grassmann spaces. We show that in the KdV case the nilpotent Darboux matrix generates the binary Darboux transformation. The paper is intended as a review of known results (usually presented in a novel context) but some new results are included as well, e.g., general compact formulas for N-soliton surfaces and linear and bilinear constraints on the nonisospectral Lax pair matrices which are preserved by Darboux transformations.Comment: Review paper (61 pages). To be published in the Special Issue "Nonlinearity and Geometry: Connections with Integrability" of J. Phys. A: Math. Theor. (2009), devoted to the subject of the Second Workshop on Nonlinearity and Geometry ("Darboux Days"), Bedlewo, Poland (April 2008

A comparison of HAART outcomes between the US military HIV Natural History Study (NHS) and HIV Atlanta Veterans Affairs Cohort Study (HAVACS).

INTRODUCTION: The Department of Defense (DoD) and the Department of Veterans Affairs (VA) provide comprehensive HIV treatment and care to their beneficiaries with open access and few costs to the patient. Individuals who receive HIV care in the VA have higher rates of substance abuse, homelessness and unemployment than individuals who receive HIV care in the DoD. A comparison between individuals receiving HIV treatment and care from the DoD and the VA provides an opportunity to explore the impact of individual-level characteristics on clinical outcomes within two healthcare systems that are optimized for clinic retention and medication adherence. METHODS: Data were collected on 1065 patients from the HIV Atlanta VA Cohort Study (HAVACS) and 1199 patients from the US Military HIV Natural History Study (NHS). Patients were eligible if they had an HIV diagnosis and began HAART between January 1, 1996 and June 30, 2010. The analysis examined the survival from HAART initiation to all-cause mortality or an AIDS event. RESULTS: Although there was substantial between-cohort heterogeneity and the 12-year survival of participants in NHS was significantly higher than in HAVACS in crude analyses, this survival disparity was reduced from 21.5% to 1.6% (mortality only) and 26.8% to 4.1% (combined mortality or AIDS) when controlling for clinical and demographic variables. CONCLUSION: We assessed the clinical outcomes for individuals with HIV from two very similar government-sponsored healthcare systems that reduced or eliminated many barriers associated with accessing treatment and care. After controlling for clinical and demographic variables, both 12-year survival and AIDS-free survival rates were similar for the two study cohorts who have open access to care and medication despite dramatic differences in socioeconomic and behavioral characteristics

Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters

We report a first-principles theoretical study of hyperfine interactions, zero-point effects and defect energetics of muonium and hydrogen impurities in silicon and germanium. The spin-polarized density functional method is used, with the crystalline orbitals expanded in all-electron Gaussian basis sets. The behaviour of hydrogen and muonium impurities at both the tetrahedral and bond-centred sites is investigated within a supercell approximation. To describe the zero-point motion of the impurities, a double adiabatic approximation is employed in which the electron, muon/proton and host lattice degrees of freedom are decoupled. Within this approximation the relaxation of the atoms of the host lattice may differ for the muon and proton, although in practice the difference is found to be slight. With the inclusion of zero-point motion the tetrahedral site is energetically preferred over the bond-centred site in both silicon and germanium. The hyperfine and superhyperfine parameters, calculated as averages over the motion of the muon, agree reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.