Functionally independent conservations laws in a quantum integrable model

We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability.Comment: 5 page

Vibration isolation for line of sight performance improvement

Diagrams of the Reaction Wheel Assembly (RWA) are presented along with charts and graphs illustrating jitter error model, induced vibration tests, radial displacement transfer function, and axial displacement power spectra density. The RWA isolator specification requirements are listed

Session, Segmented Session, and Acute RPE and Affective Responses to Self-selected Treadmill Exercise

Please view abstract in the attached PDF file

A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Inverse opal ceria–zirconia: architectural engineering for heterogeneous catalysis

The application of inverse opal structured materials is extended to the ceria–zirconia (Ce_(0.5)Zr_(0.5)O_2) system and the significance of material architecture on heterogeneous catalysis, specifically, chemical oxidation, is examined

Multiple Score Comparison: a network meta-analysis approach to comparison and external validation of prognostic scores

BACKGROUND Prediction models and prognostic scores have been increasingly popular in both clinical practice and clinical research settings, for example to aid in risk-based decision making or control for confounding. In many medical fields, a large number of prognostic scores are available, but practitioners may find it difficult to choose between them due to lack of external validation as well as lack of comparisons between them. METHODS Borrowing methodology from network meta-analysis, we describe an approach to Multiple Score Comparison meta-analysis (MSC) which permits concurrent external validation and comparisons of prognostic scores using individual patient data (IPD) arising from a large-scale international collaboration. We describe the challenges in adapting network meta-analysis to the MSC setting, for instance the need to explicitly include correlations between the scores on a cohort level, and how to deal with many multi-score studies. We propose first using IPD to make cohort-level aggregate discrimination or calibration scores, comparing all to a common comparator. Then, standard network meta-analysis techniques can be applied, taking care to consider correlation structures in cohorts with multiple scores. Transitivity, consistency and heterogeneity are also examined. RESULTS We provide a clinical application, comparing prognostic scores for 3-year mortality in patients with chronic obstructive pulmonary disease using data from a large-scale collaborative initiative. We focus on the discriminative properties of the prognostic scores. Our results show clear differences in performance, with ADO and eBODE showing higher discrimination with respect to mortality than other considered scores. The assumptions of transitivity and local and global consistency were not violated. Heterogeneity was small. CONCLUSIONS We applied a network meta-analytic methodology to externally validate and concurrently compare the prognostic properties of clinical scores. Our large-scale external validation indicates that the scores with the best discriminative properties to predict 3 year mortality in patients with COPD are ADO and eBODE

Effect of boundary conditions on diffusion in two-dimensional granular gases

We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which cause the coefficient of diffusion to be strongly dependent on the system size. On the other hand, in large enough systems with hard walls at the boundaries, diffusion is found to be independent of the system size. We compare the results obtained in this case with Langevin theory for an elastic gas. Good agreement is found. We then calculate the relaxation time and the influence of the mass for a particle of radius $R_s$ in a sea of particles of radius $R_b$. As granular gases are dissipative, we also study the influence of an external random force on the diffusion process in a forced dissipative system. In particular, we analyze differences in the mean square velocity and displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include

Regionalisation for lake level simulation – the case of Lake Tana in the Upper Blue Nile, Ethiopia

In this study lake levels of Lake Tana are simulated at daily time step by solving the water balance for all inflow and outflow processes. Since nearly 62% of the Lake Tana basin area is ungauged a regionalisation procedure is applied to estimate lake inflows from ungauged catchments. The procedure combines automated multi-objective calibration of a simple conceptual model and multiple regression analyses to establish relations between model parameters and catchment characteristics. <br><br> A relatively small number of studies are presented on Lake Tana's water balance. In most studies the water balance is solved at monthly time step and the water balance is simply closed by runoff contributions from ungauged catchments. Studies partly relied on simple <i>ad-hoc</i> procedures of area comparison to estimate runoff from ungauged catchments. In this study a regional model is developed that relies on principles of similarity of catchments characteristics. For runoff modelling the HBV-96 model is selected while multi-objective model calibration is by a Monte Carlo procedure. We aim to assess the closure term of Lake Tana's water balance, to assess model parameter uncertainty and to evaluate effectiveness of a multi-objective model calibration approach to make hydrological modeling results more plausible. <br><br> For the gauged catchments, model performance is assessed by the Nash-Sutcliffe coefficient and Relative Volumetric Error and resulted in satisfactory to good performance for six, large catchments. The regional model is validated and indicated satisfactory to good performance in most cases. Results show that runoff from ungauged catchments is as large as 527 mm per year for the simulation period and amounts to approximately 30% of Lake Tana stream inflow. Results of daily lake level simulation over the simulation period 1994–2003 show a water balance closure term of 85 mm per year that accounts to 2.7% of the total lake inflow. Lake level simulations are assessed by Nash Sutcliffe (0.91) and Relative Volume Error (2.71%) performance measures