Lie algebra and invariant tensor technology for g2

Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representation gamma and the full set of invariant tensors that arise in relation thereto. A comprehensive listing of identities involving these tensors is given. This includes identities that depend on use of characteristic equations, especially for gamma, and a good body of results involving the quadratic, sextic and (the non-primitivity of) other Casimir operators of g2.Comment: 29 pages, LaTe

Simulation and measurement of hts josephson heterodyne oscillator

We report continuing investigations into practical applications of the ac Josephson effect as the basis for a voltage-tunable radio-frequency oscillator. We have previously demonstrated experimentally that useful power levels (10 s of nW) and linewidths of a few kHz can be achieved in the heterodyne output from a High-Temperature-Superconducting Resistive SQUID (HTS-RSQUID) operating in the frequency range 1-50 MHz. Those results were achieved with 2-junction R-SQUIDs incorporating current-biased shunt resistors of a few micro-ohms. We have now modified the fabrication procedures, and adjusted the shunt resistors and bias current values so that higher frequencies can be achieved. The Josephson junctions are of step-edge type, rather than the bi-crystal type used in our earlier work. The step-edge technique permits much more flexibility in the geometrical lay-out and utilizes the more cost-effective single-crystal MgO substrates. In the present paper, we report numerical simulations and experimental measurements on these devices in the frequency range up to 2 GHz

Districts Taking Charge of the Principal Pipeline

Six urban school districts received support from The Wallace Foundation to address the critical challenge of supplying schools with effective principals. The experiences of these districts may point the way to steps other districts might take toward this same goal. Since 2011, the districts have participated in the Principal Pipeline Initiative, which set forth a comprehensive strategy for strengthening school leadership in four interrelated domains of district policy and practice:Leader standards to which sites align job descriptions, preparation, selection, evaluation, and support.Preservice preparation that includes selective admissions to high-quality programs.Selective hiring, and placement based on a match between the candidate and the school.On-the-job evaluation and support addressing the capacity to improve teaching and learning, with support focused on needs identified by evaluation.The initiative also brought the expectation that district policies and practices related to school leaders would build the district's capacity to advance its educational priorities. The evaluation of the Principal Pipeline Initiative has a dual purpose: to analyze the processes of implementing the required components in the participating districts from 2011 through 2015; and then to assess the results achieved in schools led by principals whose experiences in standards-based preparation, hiring, evaluation, and support have been consistent with the initiative's requirements. This report addresses implementation of all components of the initiative as of 2014, viewing implementation in the context of districts' aims, constraints, and capacity

Cultivating Talent through a Principal Pipeline

This report, the second in a series, describes early results of Wallace's Principal Pipeline Initiative, a multi-year effort to improve school leadership in six urban school districts. The report describes changes in the six districts' practices to recruit, train and support new principals. It also offers early lessons for other districts considering changes to their own principal pipelines

Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis:A Brief Review

Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases, mortality. Understanding the biological mechanisms behind the progression of the disease, as well as developing new methods for quantitative predictions of disease progression in the presence/absence of various therapies is important for the success of therapeutic approaches. The aim of this study is to review various quantitative predictive modelling approaches for understanding rheumatoid arthritis. To this end, we start by briefly discussing the biology of this disease and some current treatment approaches, as well as emphasising some of the open problems in the field. Then, we review various mathematical mechanistic models derived to address some of these open problems. We discuss models that investigate the biological mechanisms behind the progression of the disease, as well as pharmacokinetic and pharmacodynamic models for various drug therapies. Furthermore, we highlight models aimed at optimising the costs of the treatments while taking into consideration the evolution of the disease and potential complications.Publisher PDFPeer reviewe

Regional and seasonal patterns of epipelagic fish assemblages from the central California Current

The coastal Pacific Ocean off northern and central California encompasses the strongest seasonal upwelling zone in the California Current ecosystem. Headlands and bays here generate complex circulation features and confer unusual oceanographic complexity. We sampled the coastal epipelagic fish community of this region with a surface trawl in the summer and fall of 2000–05 to assess patterns of spatial and temporal community structure. Fifty-three species of fish were captured in 218 hauls at 34 fixed stations, with clupeiform species dominating. To examine spatial patterns, samples were grouped by location relative to a prominent headland at Point Reyes and the resulting two regions, north coast and Gulf of the Farallones, were plotted by using nonmetric multidimensional scaling. Seasonal and interannual patterns were also examined, and representative species were identified for each distinct community. Seven oceanographic variables measured concurrently with trawling were plotted by principal components analysis and tested for correlation with biotic patterns. We found significant differences in community structure by region, year, and season, but no interaction among main effects. Significant differences in oceanographic conditions mirrored the biotic patterns, and a match between biotic and hydrographic structure was detected. Dissimilarity between assemblages was mostly the result of differences in abundance and frequency of occurrence of about twelve common species. Community patterns were best described by a subset of hydrographic variables, including water depth, distance from shore, and any one of several correlated variables associated with upwelling intensity. Rather than discrete communities with clear borders and distinct member species, we found gradients in community structure and identified stations with similar fish communities by region and by proximity to features such as the San Francisco Bay

Geometrical foundations of fractional supersymmetry

A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When $q$ is a root of unity the algebra is found to have a non-trivial Hopf structure, extending that associated with the anyonic line. One-dimensional ordinary/fractional superspace is identified with the braided line when $q$ is a root of unity, so that one-dimensional ordinary/fractional supersymmetry can be viewed as invariance under translation along this line. In our construction of fractional supersymmetry the $q$-deformed bosons play a role exactly analogous to that of the fermions in the familiar supersymmetric case.Comment: 42 pages, LaTeX. To appear in Int. J. Mod. Phys.

Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments

A spectrogram of a ship wake is a heat map that visualises the time-dependent frequency spectrum of surface height measurements taken at a single point as the ship travels by. Spectrograms are easy to compute and, if properly interpreted, have the potential to provide crucial information about various properties of the ship in question. Here we use geometrical arguments and analysis of an idealised mathematical model to identify features of spectrograms, concentrating on the effects of a finite-depth channel. Our results depend heavily on whether the flow regime is subcritical or supercritical. To support our theoretical predictions, we compare with data taken from experiments we conducted in a model test basin using a variety of realistic ship hulls. Finally, we note that vessels with a high aspect ratio appear to produce spectrogram data that contains periodic patterns. We can reproduce this behaviour in our mathematical model by using a so-called two-point wavemaker. These results highlight the role of wave interference effects in spectrograms of ship wakes.Comment: 14 pages, 7 figure

Six Districts Begin the Principal Pipeline Initiative

This first report of an ongoing evaluation of The Wallace Foundation's Principal Pipeline Initiative describes the six participating school districts' plans and activities during the first year of their grants. The evaluation, conducted by Policy Studies Associates and the RAND Corporation, isintended to inform policy makers and practitioners about the process of carrying out new policies and practices for school leadership and about the results of investments in the Principal Pipeline Initiative. This report is based on collection and analysis of qualitative data, including the districts' proposals, work plans, and progress reports and semi-structured interviews in spring 2012 with 91 administrators employed by districts and their partner institutions. Leaders in all districts report wanting to enlarge their pools of strong applicants for principal positions and to identify and cultivate leadership talent as early as possible in educators' careers.Districts are actively working on allrequired pipeline components: (1) with stakeholder participation, they have developed standards and identified competencies for principals, which they plan to use to guide principal training, hiring, evaluation, and support; (2) they are initiating or strengthening partnerships with university training programs; (3) for hiring, they have standard performance tasks and are developing systems to capture data on candidates' experience; (4) they have diagnostic evaluation tools and are working to build the capacity of principals' supervisors and mentors to support principals' skill development. In addition, all are also bolstering district-run training programs for graduates of university training programs who aspire to become principals