On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation

A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian version as well as a second-order second-degree ordinary differential equation (ODE). As a byproduct we derive an auto-B\"acklund transformation, relating two copies of \pvi with different parameters. We also establish the analogous ordinary difference equations in the discrete counterpart of the chain. Such difference equations govern iterations of solutions of \pvi under B\"acklund transformations. Both discrete and continuous equations constitute a larger system which include partial difference equations, differential-difference equations and partial differential equations, all associated with the lattice Korteweg-de Vries equation subject to similarity constraints

Optical Gain from InAs Nanocrystal Quantum Dots in a Polymer Matrix

We report on the first observation of optical gain from InAs nanocrystal quantum dots emitting at 1.55 microns based on a three-beam, time resolved pump-probe technique. The nanocrystals were embedded into a transparent polymer matrix platform suitable for the fabrication of integrated photonic devices.Comment: 8 pages, 3 figures. This second version is excactly the same as the first. It is resubmitted to correct some format errors appeared in the pdf file of the first versio

On a Schwarzian PDE associated with the KdV Hierarchy

We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating equation for the entire hierarchy of Schwarzian KdV equations. We present its Lax pair, establish its connection with the SKdV hierarchy, its Miura relations to similar generating PDEs for the modified and regular KdV hierarchies and its Lagrangian structure. Finally we demonstrate that its similarity reductions lead to the {\it full} Painlev\'e VI equation, i.e. with four arbitary parameters.Comment: 11 page

Report of the panel on international programs

The panel recommends that NASA participate and take an active role in the continuous monitoring of existing regional networks, the realization of high resolution geopotential and topographic missions, the establishment of interconnection of the reference frames as defined by different space techniques, the development and implementation of automation for all ground-to-space observing systems, calibration and validation experiments for measuring techniques and data, the establishment of international space-based networks for real-time transmission of high density space data in standardized formats, tracking and support for non-NASA missions, and the extension of state-of-the art observing and analysis techniques to developing nations

Minimal Informationally Complete Measurements for Pure States

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PSI-complete) POVM. We show that a measurement with 2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D outcomes. We also consider PSI-complete POVMs that have only rank-one POVM elements and construct an example with 3D-2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PSI-complete POVM is left open.Comment: 2 figures, submitted for the Asher Peres festschrif

Quantum Control of a Single Qubit

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a non-projective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realises the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.Comment: 12 pages, 7 figures, v2 includes new references and minor change

Symptom Domain Groups of the Patient-Reported Outcomes Measurement Information System Tools Independently Predict Hospitalizations and Re-hospitalizations in Cirrhosis

Background Patient-Reported Outcomes Measurement Information System (PROMIS) tools can identify health-related quality of life (HRQOL) domains that could differentially affect disease progression. Cirrhotics are highly prone to hospitalizations and re-hospitalizations, but the current clinical prognostic models may be insufficient, and thus studying the contribution of individual HRQOL domains could improve prognostication. Aim Analyze the impact of individual HRQOL PROMIS domains in predicting time to all non-elective hospitalizations and re-hospitalizations in cirrhosis. Methods Outpatient cirrhotics were administered PROMIS computerized tools. The first non-elective hospitalization and subsequent re-hospitalizations after enrollment were recorded. Individual PROMIS domains significantly contributing toward these outcomes were generated using principal component analysis. Factor analysis revealed three major PROMIS domain groups: daily function (fatigue, physical function, social roles/activities and sleep issues), mood (anxiety, anger, and depression), and pain (pain behavior/impact) accounted for 77% of the variability. Cox proportional hazards regression modeling was used for these groups to evaluate time to first hospitalization and re-hospitalization. Results A total of 286 patients [57 years, MELD 13, 67% men, 40% hepatic encephalopathy (HE)] were enrolled. Patients were followed at 6-month (mth) intervals for a median of 38 mths (IQR 22–47), during which 31% were hospitalized [median IQR mths 12.5 (3–27)] and 12% were re-hospitalized [10.5 mths (3–28)]. Time to first hospitalization was predicted by HE, HR 1.5 (CI 1.01–2.5, p = 0.04) and daily function PROMIS group HR 1.4 (CI 1.1–1.8, p = 0.01), independently. In contrast, the pain PROMIS group were predictive of the time to re-hospitalization HR 1.6 (CI 1.1–2.3, p = 0.03) as was HE, HR 2.1 (CI 1.1–4.3, p = 0.03). Conclusions Daily function and pain HRQOL domain groups using PROMIS tools independently predict hospitalizations and re-hospitalizations in cirrhotic patients

Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations

We design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions. We obtain excellent numerical stability due to some new elements in the algorithm. The schemes are based on three- and five-wave approximate Riemann solvers of the HLL-type, with the novelty that we allow a varying normal magnetic field. This is achieved by considering the semi-conservative Godunov-Powell form of the MHD equations. We show that it is important to discretize the Godunov-Powell source term in the right way, and that the HLL-type solvers naturally provide a stable upwind discretization. Second-order versions of the ENO- and WENO-type reconstructions are proposed, together with precise modifications necessary to preserve positive pressure and density. Extending the discrete source term to second order while maintaining stability requires non-standard techniques, which we present. The first- and second-order schemes are tested on a suite of numerical experiments demonstrating impressive numerical resolution as well as stability, even on very fine meshe