Geodesics of Random Riemannian Metrics

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolutely continuous with respect to the law of the random metric, and we provide an explicit form for its Radon-Nikodym derivative. We use this result to prove a "local Markov property" along an unbounded geodesic, demonstrating that it eventually encounters any type of geometric phenomenon. We also develop in this paper some general results on conditional Gaussian measures. Our Main Theorem states that a geodesic chosen with random initial conditions (chosen independently of the metric) is almost surely not minimizing. To demonstrate this, we show that a minimizing geodesic is guaranteed to eventually pass over a certain "bump surface," which locally has constant positive curvature. By using Jacobi fields, we show that this is sufficient to destabilize the minimizing property.Comment: 55 pages. Supplementary material at arXiv:1206.494

Spin relaxation in (110) and (001) InAs/GaSb superlattices

We report an enhancement of the electron spin relaxation time (T1) in a (110) InAs/GaSb superlattice by more than an order of magnitude (25 times) relative to the corresponding (001) structure. The spin dynamics were measured using polarization sensitive pump probe techniques and a mid-infrared, subpicosecond PPLN OPO. Longer T1 times in (110) superlattices are attributed to the suppression of the native interface asymmetry and bulk inversion asymmetry contributions to the precessional D'yakonov Perel spin relaxation process. Calculations using a nonperturbative 14-band nanostructure model give good agreement with experiment and indicate that possible structural inversion asymmetry contributions to T1 associated with compositional mixing at the superlattice interfaces may limit the observed spin lifetime in (110) superlattices. Our findings have implications for potential spintronics applications using InAs/GaSb heterostructures.Comment: 4 pages, 2 figure

Results of Phase II Clinical Trial MPD-RC 101: Allogeneic Hematopoietic Stem Cell Transplantation Conditioned with Fludarabine/Melphalan in Patients with Myelofibrosis

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Indirect search for dark matter: prospects for GLAST

Possible indirect detection of neutralino, through its gamma-ray annihilation product, by the forthcoming GLAST satellite from our galactic halo, M31, M87 and the dwarf galaxies Draco and Sagittarius is studied. Gamma-ray fluxes are evaluated for the two representative energy thresholds, 0.1 GeV and 1.0 GeV, at which the spatial resolution of GLAST varies considerably. Apart from dwarfs which are described either by a modified Plummer profile or by a tidally-truncated King profiles, fluxes are compared for halos with central cusps and cores. It is demonstrated that substructures, irrespective of their profiles, enhance the gamma-ray emission only marginally. The expected gamma-ray intensity above 1 GeV at high galactic latitudes is consistent with the residual emission derived from EGRET data if the density profile has a central core and the neutralino mass is less than 50 GeV, whereas for a central cusp only a substantial enhancement would explain the observations. From M31, the flux can be detected above 0.1 GeV and 1.0 GeV by GLAST only if the neutralino mass is below 300 GeV and if the density profile has a central cusp, case in which a significant boost in the gamma-ray emission is produced by the central black hole. For Sagittarius, the flux above 0.1 GeV is detectable by GLAST provided the neutralino mass is below 50 GeV. From M87 and Draco the fluxes are always below the sensitivity limit of GLAST.Comment: 14 Pages, 7 Figures, 3 Tables, version to appear on Physical Review

Variational formulas and cocycle solutions for directed polymer and percolation models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Pegylated interferon alfa-2a for polycythemia vera or essential thrombocythemia resistant or intolerant to hydroxyurea

Prior studies have reported high response rates with recombinant interferon-a (rIFN-a) therapy in patients with essential thrombocythemia (ET) and polycythemia vera (PV). To further define the role of rIFN-a,we investigated the outcomes of pegylated-rIFN-a2a (PEG) therapy in ET and PV patients previously treated with hydroxyurea (HU). The Myeloproliferative Disorders Research Consortium (MPD-RC)-111 study was an investigator-initiated, international, multicenter, phase 2 trial evaluating the ability of PEG therapy to induce complete (CR) and partial (PR) hematologic responses in patients with high-risk ET or PVwho were either refractory or intolerant to HU. The study included 65 patients with ET and 50 patients with PV. The overall response rates (ORRs; CR/PR) at 12 monthswere 69.2%(43.1% and 26.2%) in ET patients and 60% (22% and 38%) in PV patients. CR rates were higher in CALR-mutated ET patients (56.5% vs 28.0%; P 5 .01), compared with those in subjects lacking a CALR mutation. The median absolute reduction in JAK2V617F variant allele fraction was 26% (range, 284%to 47%) in patients achieving a CR vs 14%(range, 218% to 56%) in patients with PR or nonresponse (NR). Therapy was associated with a significant rate of adverse events (AEs); most were manageable, and PEG discontinuation related to AEs occurred in only 13.9% of subjects. We conclude that PEG is an effective therapy for patients with ET or PV who were previously refractory and/or intolerant of HU