The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet space of all smooth functions on the circle.Comment: 17 page

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Comments on D-brane Interactions in PP-wave Backgrounds

We calculate the interaction potential between widely separated D-branes in PP-wave backgrounds in string theory as well as in low-energy supergravity. Timelike and spacelike orientations are qualitatively different but in both cases the effective brane tensions and RR charges take the same values as in Minkowski space in accordance with the expectations from the sigma model perturbation theory.Comment: Latex, 22 pages. Typos corrected and a reference added, final versio

Spin-polarized current amplification and spin injection in magnetic bipolar transistors

The magnetic bipolar transistor (MBT) is a bipolar junction transistor with an equilibrium and nonequilibrium spin (magnetization) in the emitter, base, or collector. The low-injection theory of spin-polarized transport through MBTs and of a more general case of an array of magnetic {\it p-n} junctions is developed and illustrated on several important cases. Two main physical phenomena are discussed: electrical spin injection and spin control of current amplification (magnetoamplification). It is shown that a source spin can be injected from the emitter to the collector. If the base of an MBT has an equilibrium magnetization, the spin can be injected from the base to the collector by intrinsic spin injection. The resulting spin accumulation in the collector is proportional to $\exp(qV_{be}/k_BT)$, where $q$ is the proton charge, $V_{be}$ is the bias in the emitter-base junction, and $k_B T$ is the thermal energy. To control the electrical current through MBTs both the equilibrium and the nonequilibrium spin can be employed. The equilibrium spin controls the magnitude of the equilibrium electron and hole densities, thereby controlling the currents. Increasing the equilibrium spin polarization of the base (emitter) increases (decreases) the current amplification. If there is a nonequilibrium spin in the emitter, and the base or the emitter has an equilibrium spin, a spin-valve effect can lead to a giant magnetoamplification effect, where the current amplifications for the parallel and antiparallel orientations of the the equilibrium and nonequilibrium spins differ significantly. The theory is elucidated using qualitative analyses and is illustrated on an MBT example with generic materials parameters.Comment: 14 PRB-style pages, 10 figure

Validating automated segmentation tools in the assessment of caudate atrophy in Huntington's disease

Background: Neuroimaging shows considerable promise in generating sensitive and objective outcome measures for therapeutic trials across a range of neurodegenerative conditions. For volumetric measures the current gold standard is manual delineation, which is unfeasible for samples sizes required for large clinical trials.Methods: Using a cohort of early Huntington's disease (HD) patients (n = 46) and controls (n = 35), we compared the performance of four automated segmentation tools (FIRST, FreeSurfer, STEPS, MALP-EM) with manual delineation for generating cross-sectional caudate volume, a region known to be vulnerable in HD. We then examined the effect of each of these baseline regions on the ability to detect change over 15 months using the established longitudinal Caudate Boundary Shift Integral (cBSI) method, an automated longitudinal pipeline requiring a baseline caudate region as an input.Results: All tools, except Freesurfer, generated significantly smaller caudate volumes than the manually derived regions. Jaccard indices showed poorer levels of overlap between each automated segmentation and manual delineation in the HD patients compared with controls. Nevertheless, each method was able to demonstrate significant group differences in volume (p < 0.001). STEPS performed best qualitatively as well as quantitively in the baseline analysis. Caudate atrophy measures generated by the cBSI using automated baseline regions were largely consistent with those derived from a manually segmented baseline, with STEPS providing the most robust cBSI values across both control and HD groups.Conclusions: Atrophy measures from the cBSI were relatively robust to differences in baseline segmentation technique, suggesting that fully automated pipelines could be used to generate outcome measures for clinical trials.Neurological Motor Disorder

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix

Testing a longitudinal compensation model in premanifest Huntington's disease

Neurological Motor Disorder

Land management shapes drought responses of dominant soil microbial taxa across grasslands

Soil microbial communities are dominated by a relatively small number of taxa that may play outsized roles in ecosystem functioning, yet little is known about their capacities to resist and recover from climate extremes such as drought, or how environmental context mediates those responses. Here, we imposed an in situ experimental drought across 30 diverse UK grassland sites with contrasting management intensities and found that: (1) the majority of dominant bacterial (85%) and fungal (89%) taxa exhibit resistant or opportunistic drought strategies, possibly contributing to their ubiquity and dominance across sites; and (2) intensive grassland management decreases the proportion of drought-sensitive and non-resilient dominant bacteria—likely via alleviation of nutrient limitation and pH-related stress under fertilisation and liming—but has the opposite impact on dominant fungi. Our results suggest a potential mechanism by which intensive management promotes bacteria over fungi under drought with implications for soil functioning