Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures

In a previous paper (math-ph/0205016) an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CP(N) as well as other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived.Comment: 26 pages, no figures; minor edits, to be published in J. Geom. Phy

A comparative analysis of projected impacts of climate change on river runoff from global and catchment-scale hydrological models

We present a comparative analysis of projected impacts of climate change on river runoff from two types of distributed hydrological model, a global hydrological model (GHM) and catchment-scale hydrological models (CHM). Analyses are conducted for six catchments that are global in coverage and feature strong contrasts in spatial scale as well as climatic and development conditions. These include the Liard (Canada), Mekong (SE Asia), Okavango (SW Africa), Rio Grande (Brazil), Xiangu (China) and Harper's Brook (UK). A single GHM (Mac-PDM.09) is applied to all catchments whilst different CHMs are applied for each catchment. The CHMs typically simulate water resources impacts based on a more explicit representation of catchment water resources than that available from the GHM, and the CHMs include river routing. Simulations of average annual runoff, mean monthly runoff and high (Q5) and low (Q95) monthly runoff under baseline (1961-1990) and climate change scenarios are presented. We compare the simulated runoff response of each hydrological model to (1) prescribed increases in global mean temperature from the HadCM3 climate model and (2)a prescribed increase in global-mean temperature of 2oC for seven GCMs to explore response to climate model and structural uncertainty. We find that differences in projected changes of mean annual runoff between the two types of hydrological model can be substantial for a given GCM, and they are generally larger for indicators of high and low flow. However, they are relatively small in comparison to the range of projections across the seven GCMs. Hence, for the six catchments and seven GCMs we considered, climate model structural uncertainty is greater than the uncertainty associated with the type of hydrological model applied. Moreover, shifts in the seasonal cycle of runoff with climate change are presented similarly by both hydrological models, although for some catchments the monthly timing of high and low flows differs.This implies that for studies that seek to quantify and assess the role of climate model uncertainty on catchment-scale runoff, it may be equally as feasible to apply a GHM as it is to apply a CHM, especially when climate modelling uncertainty across the range of available GCMs is as large as it currently is. Whilst the GHM is able to represent the broad climate change signal that is represented by the CHMs, we find, however, that for some catchments there are differences between GHMs and CHMs in mean annual runoff due to differences in potential evaporation estimation methods, in the representation of the seasonality of runoff, and in the magnitude of changes in extreme monthly runoff, all of which have implications for future water management issues

Functional evolution of the feeding system in rodents

The masticatory musculature of rodents has evolved to enable both gnawing at the incisors and chewing at the molars. In particular, the masseter muscle is highly specialised, having extended anteriorly to originate from the rostrum. All living rodents have achieved this masseteric expansion in one of three ways, known as the sciuromorph, hystricomorph and myomorph conditions. Here, we used finite element analysis (FEA) to investigate the biomechanical implications of these three morphologies, in a squirrel, guinea pig and rat. In particular, we wished to determine whether each of the three morphologies is better adapted for either gnawing or chewing. Results show that squirrels are more efficient at muscle-bite force transmission during incisor gnawing than guinea pigs, and that guinea pigs are more efficient at molar chewing than squirrels. This matches the known diet of nuts and seeds that squirrels gnaw, and of grasses that guinea pigs grind down with their molars. Surprisingly, results also indicate that rats are more efficient as well as more versatile feeders than both the squirrel and guinea pig. There seems to be no compromise in biting efficiency to accommodate the wider range of foodstuffs and the more general feeding behaviour adopted by rats. Our results show that the morphology of the skull and masticatory muscles have allowed squirrels to specialise as gnawers and guinea pigs as chewers, but that rats are high-performance generalists, which helps explain their overwhelming success as a group

Tensor hypercontraction: A universal technique for the resolution of matrix elements of local, finite-range NN-body potentials in many-body quantum problems

Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the eXact Tensor HyperContraction (X-THC) method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchange-like" contractions.Comment: Third version of the manuscript after referee's comments. In press in PRL. Main text: 4 pages, 2 figures, 1 table; Supplemental material (also included): 14 pages, 2 figures, 2 table

Review of Labor and Employment Decisions from the United States Supreme Court’s 2008–2009 Term

In its most recently completed Term, the United States Supreme Court decided eight labor and employment law cases of some consequence. The decided cases covered a broad array of labor and employment subjects, including: the Employee Retirement Income Security Act (ERISA), Title VII of the Civil Rights Act of 1964 (Title VII), the Age Discrimination in Employment Act (ADEA), public sector labor law, and private sector labor law. Practitioners who specialize in a particular area might be tempted to focus on only the cases in their area. Academics might be tempted to try to devise some economic or logical theory that ties together these diverse decisions. However, after even modest reflection, it is apparent that the best way to understand the underlying dynamics of the Supreme Court’s 2008–2009 Term with respect to labor and employment law cases is to consider the voting patterns of the individual justices and the Court’s overall vote in each case. The labor and employment law decisions from the Court’s 2008–2009 Term might be divided into two categories: “broad consensus” cases, which are decided by at least a 6-3 vote of the justices, and “close cases,” which are decided by a bare 5-4 vote. Even though a 6-3 vote indicates significant disagreement among the justices, we might call it a “broad consensus” in that, as we will see, a six-vote majority includes at least one justice from both the liberal and conservative wings of the Court. It is very revealing to first divide the Court’s decisions in this fashion and then arrange the decisions and the votes of the justices chronologically. Although the insight gained from this exercise will not surprise followers of the Court, even dedicated students of the Court will be impressed by its predictability in deciding the labor and employment law cases this last Term

FAST: A multi-processed environment for visualization of computational fluid dynamics

Three-dimensional, unsteady, multi-zoned fluid dynamics simulations over full scale aircraft are typical of the problems being investigated at NASA Ames' Numerical Aerodynamic Simulation (NAS) facility on CRAY2 and CRAY-YMP supercomputers. With multiple processor workstations available in the 10-30 Mflop range, we feel that these new developments in scientific computing warrant a new approach to the design and implementation of analysis tools. These larger, more complex problems create a need for new visualization techniques not possible with the existing software or systems available as of this writing. The visualization techniques will change as the supercomputing environment, and hence the scientific methods employed, evolves even further. The Flow Analysis Software Toolkit (FAST), an implementation of a software system for fluid mechanics analysis, is discussed

Climate Science, Development Practice, and Policy Interactions in Dryland Agroecological Systems

The literature on drought, livelihoods, and poverty suggests that dryland residents are especially vulnerable to climate change. However, assessing this vulnerability and sharing lessons between dryland communities on how to reduce vulnerability has proven difficult because of multiple definitions of vulnerability, complexities in quantification, and the temporal and spatial variability inherent in dryland agroecological systems. In this closing editorial, we review how we have addressed these challenges through a series of structured, multiscale, and interdisciplinary vulnerability assessment case studies from drylands in West Africa, southern Africa, Mediterranean Europe, Asia, and Latin America. These case studies adopt a common vulnerability framework but employ different approaches to measuring and assessing vulnerability. By comparing methods and results across these cases, we draw out the following key lessons: (1) Our studies show the utility of using consistent conceptual frameworks for vulnerability assessments even when quite different methodological approaches are taken; (2) Utilizing narratives and scenarios to capture the dynamics of dryland agroecological systems shows that vulnerability to climate change may depend more on access to financial, political, and institutional assets than to exposure to environmental change; (3) Our analysis shows that although the results of quantitative models seem authoritative, they may be treated too literally as predictions of the future by policy makers looking for evidence to support different strategies. In conclusion, we acknowledge there is a healthy tension between bottom-up/ qualitative/place-based approaches and top-down/quantitative/generalizable approaches, and we encourage researchers from different disciplines with different disciplinary languages, to talk, collaborate, and engage effectively with each other and with stakeholders at all levels