Classical Functional Bethe Ansatz for SL(N)SL(N): separation of variables for the magnetic chain

The Functional Bethe Ansatz (FBA) proposed by Sklyanin is a method which gives separation variables for systems for which an $R$-matrix is known. Previously the FBA was only known for $SL(2)$ and $SL(3)$ (and associated) $R$-matrices. In this paper I advance Sklyanin's program by giving the FBA for certain systems with $SL(N)$ $R$-matrices. This is achieved by constructing rational functions \A(u) and \B(u) of the matrix elements of $T(u)$, so that, in the generic case, the zeros $x_i$ of \B(u) are the separation coordinates and the P_i=\A(x_i) provide their conjugate momenta. The method is illustrated with the magnetic chain and the Gaudin model, and its wider applicability is discussed.Comment: 14pp LaTex,DAMTP 94-1

An avionics sensitivity study. Volume 1: Operational considerations

Equipment and operational concepts affecting aircraft in the terminal area are reported. Curved approach applications and modified climb and descent procedures for minimum fuel consumption are considered. The curved approach study involves the application of MLS guidance to enable execution of the current visual approach to Washington National Airport under instrument flight conditions. The operational significance and the flight path control requirements involved in the application of curved approach paths to this situation are considered. Alternative flight path control regimes are considered to achieve minimum fuel consumption subject to constraints related to air traffic control requirements, flight crew and passenger reactions, and airframe and powerplant limitations

Design definition of a mechanical capacitor

A design study and analyses of a 10 kW-hr, 15 kW mechanical capacitor system was studied. It was determined that magnetically supported wheels constructed of advanced composites have the potential for high energy density and high power density. Structural concepts are analyzed that yield the highest energy density of any structural design yet reported. Particular attention was paid to the problem of 'friction' caused by magnetic and I to the second power R losses in the suspension and motor-generator subsystems, and low design friction levels have been achieved. The potentially long shelf life of this system, and the absence of wearing parts, provide superior performance over conventional flywheels supported with mechanical bearings. Costs and economies of energy storage wheels were reviewed briefly

Novel modeling of task versus rest brain state predictability using a dynamic time warping spectrum: comparisons and contrasts with other standard measures of brain dynamics

Dynamic time warping, or DTW, is a powerful and domain-general sequence alignment method for computing a similarity measure. Such dynamic programming-based techniques like DTW are now the backbone and driver of most bioinformatics methods and discoveries. In neuroscience it has had far less use, though this has begun to change. We wanted to explore new ways of applying DTW, not simply as a measure with which to cluster or compare similarity between features but in a conceptually different way. We have used DTW to provide a more interpretable spectral description of the data, compared to standard approaches such as the Fourier and related transforms. The DTW approach and standard discrete Fourier transform (DFT) are assessed against benchmark measures of neural dynamics. These include EEG microstates, EEG avalanches, and the sum squared error (SSE) from a multilayer perceptron (MLP) prediction of the EEG time series, and simultaneously acquired FMRI BOLD signal. We explored the relationships between these variables of interest in an EEG-FMRI dataset acquired during a standard cognitive task, which allowed us to explore how DTW differentially performs in different task settings. We found that despite strong correlations between DTW and DFT-spectra, DTW was a better predictor for almost every measure of brain dynamics. Using these DTW measures, we show that predictability is almost always higher in task than in rest states, which is consistent to other theoretical and empirical findings, providing additional evidence for the utility of the DTW approach

Neuropsychological and functional outcomes in recent-onset major depression, bipolar disorder and schizophrenia-spectrum disorders: a longitudinal cohort study

Functional disability is the lead contributor to burden of mental illness. Cognitive deficits frequently limit functional recovery, although whether changes in cognition and disability are longitudinally associated in recent-onset individuals remains unclear. Using a prospective, cohort design, 311 patients were recruited and assessed at baseline. One hundred and sixty-seven patients met eligibility criteria (M = 21.5 years old, s.d. = 4.8) and returned for follow-up (M = 20.6 months later, s.d. = 7.8). Two-hundred and thirty participants were included in the final analysis, comprising clinically stable patients with major depression (n = 71), bipolar disorder (BD; n = 61), schizophrenia-spectrum disorders (n = 35) and 63 healthy controls. Neuropsychological functioning and self-rated functional disability were examined using mixed-design, repeated-measures analysis, across diagnoses and cognitive clusters, covarying for relevant confounds. Clinical, neuropsychological and functional changes did not differ between diagnoses (all P40.05). Three reliable neuropsychological subgroups emerged through cluster analysis, characterized by psychomotor slowing, improved sustained attention, and improved verbal memory. Controlling for diagnosis and changes in residual symptoms, clusters with improved neuropsychological functioning observed greater reductions in functional disability than the psychomotor slowing cluster, which instead demonstrated a worsening in disability (Po0.01). Improved sustained attention was independently associated with greater likelihood of follow-up employment (Po0.01). Diagnosis of BD uniquely predicted both follow-up employment and independent living. Neuropsychological course appears to be independently predictive of subjective and objective functional outcomes. Importantly, cognitive phenotypes may reflect distinct pathophysiologies shared across major psychiatric conditions, and be ideal targets for personalized early intervention

Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry

We consider experimentally the instability and mass transport of a porous-medium flow in a Hele-Shaw geometry. In an initially stable configuration, a lighter fluid (water) is located over a heavier fluid (propylene glycol). The fluids mix via diffusion with some regions of the resulting mixture being heavier than either pure fluid. Density-driven convection occurs with downward penetrating dense fingers that transport mass much more effectively than diffusion alone. We investigate the initial instability and the quasi steady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6,000<Ra<90,000. The results have important implications for determining the time scales and rates of dissolution trapping of carbon dioxide in brine aquifers proposed as possible geologic repositories for sequestering carbon dioxide.Comment: 4 page, 3 figure

Oxygen isotopic and petrological constraints on the origin and relationship of IIE iron meteorites and H chondrites

New oxygen isotopic measurements of IIEs and H chondrites are indistinguishable — strengthening a possible common origin for these groups. Combining oxygen results with mineralogy, the nature of their parent body or bodies can be explored

The Behavior of Soluble Salt in Sharkey Clay

Soluble salt problems do exist and are significant in Arkansas. Studies have been conducted on Crowley silt loam (Typic Albaqualfs) which have established the behavior of soluble salt in that soil. The major objective of this study was to quantify the behavior of soluble salt in a second important Mississippi River Delta soil - the Sharkey (Vertic Haplaquepts). To this end, estimation of the downward redistribution of salt and the estimation of various components of the water balance for this soil served as specific objectives. Field studies were designed to monitor the movement of salt in the Sharkey soil and to characterize selected components of the water balance. In total, three tentative conclusions may be drawn from the data. First, the infiltration for the Sharkey soil was approximately three times that of the Crowley silt loam. The average value was 29 cm for the rice season. Second, levee seepage, while significant for small plots, was shown to be small for production-sized fields. Levee seepage remained relatively constant throughout the season and averaged 0.025 nvfym/d. And third, downward redistribution of salt was large and appeared to follow a pattern where a peak occurred at the surface and, possibly, at the lower soil depths