Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

A phase 1 trial dose-escalation study of tipifarnib on a week-on, week-off schedule in relapsed, refractory or high-risk myeloid leukemia.

Inhibition of farnesyltransferase (FT) activity has been associated with in vitro and in vivo anti-leukemia activity. We report the results of a phase 1 dose-escalation study of tipifarnib, an oral FT inhibitor, in patients with relapsed, refractory or newly diagnosed (if over age 70) acute myelogenous leukemia (AML), on a week-on, week-off schedule. Forty-four patients were enrolled, two patients were newly diagnosed, and the rest were relapsed or refractory to previous treatment, with a median age of 61 (range 33-79). The maximum tolerated dose was determined to be 1200 mg given orally twice daily (b.i.d.) on this schedule. Cycle 1 dose-limiting toxicities were hepatic and renal. There were three complete remissions seen, two at the 1200 mg b.i.d. dose and one at the 1000 mg b.i.d. dose, with minor responses seen at the 1400 mg b.i.d. dose level. Pharmacokinetic studies performed at doses of 1400 mg b.i.d. showed linear behavior with minimal accumulation between days 1-5. Tipifarnib administered on a week-on, week-off schedule shows activity at higher doses, and represents an option for future clinical trials in AML

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.Comment: 13 page

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio

An archival case study : revisiting the life and political economy of Lauchlin Currie

This paper forms part of a wider project to show the significance of archival material on distinguished economists, in this case Lauchlin Currie (1902-93), who studied and taught at Harvard before entering government service at the US Treasury and Federal Reserve Board as the intellectual leader of Roosevelt's New Deal, 1934-39, as FDR's White House economic adviser in peace and war, 1939-45, and as a post-war development economist. It discusses the uses made of the written and oral material available when the author was writing his intellectual biography of Currie (Duke University Press 1990) while Currie was still alive, and the significance of the material that has come to light after Currie's death

Discrepancies in central review re-testing of patients with ER-positive and HER2-negative breast cancer in the OPTIMA prelim randomised clinical trial

BACKGROUND: There is limited data on results of central re-testing of samples from patients with invasive breast cancer categorised in their local hospital laboratories as oestrogen receptor (ER) positive and human epidermal growth factor receptor homologue 2 (HER2) negative. METHODS: The Optimal Personalised Treatment of early breast cancer usIng Multiparameter Analysis preliminary study (OPTIMA prelim) was the feasibility phase of a randomised controlled trial to validate the use of multiparameter assay-directed chemotherapy decisions in the UK National Health Service (NHS). Eligibility criteria included ER positivity and HER2 negativity. Central re-testing of receptor status was mandatory. RESULTS: Of the 431 patients tested centrally, discrepant results between central and local laboratory results were identified in only 19 (4.4%; 95% confidence interval 2.5–6.3%) patients (with 21 tumours). On central review, seven patients had cancers that were ER-negative (1.6%) and 13 (3.0%) patients with 15 tumours had HER2-positive disease, including one tumour discrepant for both biomarkers. CONCLUSIONS: Central re-testing of receptor status of invasive breast cancers in the UK NHS setting shows a high level of reproducibility in categorising tumours as ER-positive and HER2-negative, and raises questions regarding the cost effectiveness and clinical value of central re-testing in this sub-group of breast cancers in this setting

Quantum resource estimates for computing elliptic curve discrete logarithms

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve defined over an $n$-bit prime field can be computed on a quantum computer with at most $9n + 2\lceil\log_2(n)\rceil+10$ qubits using a quantum circuit of at most $448 n^3 \log_2(n) + 4090 n^3$ Toffoli gates. We are able to classically simulate the Toffoli networks corresponding to the controlled elliptic curve point addition as the core piece of Shor's algorithm for the NIST standard curves P-192, P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to recent resource estimates for Shor's factoring algorithm. The results also support estimates given earlier by Proos and Zalka and indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added. ASIACRYPT 201

Neuromuscular Blockade with Rocuronium Bromide Increases the Tolerance of Acute Normovolemic Anemia in Anesthetized Pigs

Background: The patient's individual anemia tolerance is pivotal when blood transfusions become necessary, but are not feasible for some reason. To date, the effects of neuromuscular blockade (NMB) on anemia tolerance have not been investigated. Methods: 14 anesthetized and mechanically ventilated pigs were randomly assigned to the Roc group (3.78 mg/kg rocuronium bromide followed by continuous infusion of 1 mg/kg/min, n = 7) or to the Sal group (administration of the corresponding volume of normal saline, n = 7). Subsequently, acute normovolemic anemia was induced by simultaneous exchange of whole blood for a 6% hydroxyethyl starch solution (130/0.4) until a sudden decrease of total body O-2 consumption (VO2) indicated a critical limitation of O-2 transport capacity. The Hb concentration quantified at this time point (Hb(crit)) was the primary end-point of the protocol. Secondary endpoints were parameters of hemodynamics, O-2 transport and tissue oxygenation. Results: Hb(crit) was significantly lower in the Roc group (2.4 +/- 0.5 vs. 3.2 +/- 0.7 g/dl) reflecting increased anemia tolerance. NMB with rocuronium bromide reduced skeletal muscular VO2 and total body O-2 extraction rate. As the cardiac index increased simultaneously, total body VO2 only decreased marginally in the Roc group (change of VO2 relative to baseline -1.7 +/- 0.8 vs. 3.2 +/- 1.9% in the Sal group, p < 0.05). Conclusion: Deep NMB with rocuronium bromide increases the tolerance of acute normovolemic anemia. The underlying mechanism most likely involves a reduction of skeletal muscular VO2. During acellular treatment of an acute blood loss, NMB might play an adjuvant role in situations where profound stages of normovolemic anemia have to be tolerated (e.g. bridging an unexpected blood loss until blood products become available for transfusion). Copyright (C) 2011 S. Karger AG, Base

Bioprosthetic mitral valve thrombosis less than one year after replacement and an ablative MAZE procedure: a case report

Occurrence of bioprosthetic valve thrombosis less than a year after replacement is very uncommon. Here, we describe a case of a 57 year old male, who presented 10 months after receiving a bioprosthetic mitral valve replacement with a two week history of dyspnea on exertion, worsening orthopnea and decreased exercise tolerance. Echocardiography revealed severe mitral regurgitation (MR), thrombosis of the posterior mitral leaflet, left atrial (LA) mural thrombus and a depressed left ventricular ejection fraction of twenty-five percent. Given severe clot burden and decompensated heart failure (New York Heart Association - NYHA class III) repeat sternotomy was done to replace the bioprosthetic mitral valve and remove LA mural thrombus. MR was resolved postoperatively. This brief report further reviews promoting factors, established guidelines and management strategies of bioprosthetic valve thrombosis