Maximal quadratic modules on *-rings

We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example of a maximal proper quadratic module is the cone of all positive semidefinite complex matrices of a fixed dimension. We show that the support of a maximal proper quadratic module is the symmetric part of a prime $\ast$-ideal, that every maximal proper quadratic module in a Noetherian $\ast$-ring comes from a maximal proper quadratic module in a simple artinian ring with involution and that maximal proper quadratic modules satisfy an intersection theorem. As an application we obtain the following extension of Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let $c$ be an element of the Weyl algebra $\mathcal{W}(d)$ which is not negative semidefinite in the Schr\" odinger representation. It is shown that under some conditions there exists an integer $k$ and elements $r_1,...,r_k \in \mathcal{W}(d)$ such that $\sum_{j=1}^k r_j c r_j^\ast$ is a finite sum of hermitian squares. This result is not a proper generalization however because we don't have the bound $k \le d$.Comment: 11 page

Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure

ANTICIPATION EFFECT ON KNEE JOINT STABILITY DURING PLANNED AND UN-PLANNED MOVEMENT TESTS IN LABORATORY

The purpose of this study was to investigate the anticipation effect on knee stability during functional test in laboratory. Ten healthy male subjects were recruited and instructed to perform a series of planned and un-planned stop-jumping tasks. Knee joint kinematics was measured by a motion analysis system. The subjects demonstrated different abduction and rotation angles for reactive tasks. This suggested that if knee abduction or rotational stability is considered as a primary measurement in documenting knee stability, such as in the investigation of rehabilitation progress after anterior cruciate ligament reconstruction, both planned and un-planned tasks should be considered as to take the anticipation effect into account

A Scalable, Self-Analyzing Digital Locking System for use on Quantum Optics Experiments

Digital control of optics experiments has many advantages over analog control systems, specifically in terms of scalability, cost, flexibility, and the integration of system information into one location. We present a digital control system, freely available for download online, specifically designed for quantum optics experiments that allows for automatic and sequential re-locking of optical components. We show how the inbuilt locking analysis tools, including a white-noise network analyzer, can be used to help optimize individual locks, and verify the long term stability of the digital system. Finally, we present an example of the benefits of digital locking for quantum optics by applying the code to a specific experiment used to characterize optical Schrodinger cat states.Comment: 7 pages, 5 figure

XAX: a multi-ton, multi-target detection system for dark matter, double beta decay and pp solar neutrinos

A multi-target detection system XAX, comprising concentric 10 ton targets of 136Xe and 129/131Xe, together with a geometrically similar or larger target of liquid Ar, is described. Each is configured as a two-phase scintillation/ionization TPC detector, enhanced by a full 4pi array of ultra-low radioactivity Quartz Photon Intensifying Detectors (QUPIDs) replacing the conventional photomultipliers for detection of scintillation light. It is shown that background levels in XAX can be reduced to the level required for dark matter particle (WIMP) mass measurement at a 10^-10 pb WIMP-nucleon cross section, with single-event sensitivity below 10^-11 pb. The use of multiple target elements allows for confirmation of the A^2 dependence of a coherent cross section, and the different Xe isotopes provide information on the spin-dependence of the dark matter interaction. The event rates observed by Xe and Ar would modulate annually with opposite phases from each other for WIMP mass >~100 GeV/c^2. The large target mass of 136Xe and high degree of background reduction allow neutrinoless double beta decay to be observed with lifetimes of 10^27-10^28 years, corresponding to the Majorana neutrino mass range 0.01-0.1 eV, the most likely range from observed neutrino mass differences. The use of a 136Xe-depleted 129/131Xe target will also allow measurement of the pp solar neutrino spectrum to a precision of 1-2%.Comment: 16 pages with 17 figure

And the winner is: galaxy mass

The environment is known to affect the formation and evolution of galaxies considerably best visible through the well-known morphology-density relationship. We study the effect of environment on the evolution of early-type galaxies for a sample of 3,360 galaxies morphologically selected by visual inspection from the SDSS in the redshift range 0.05<z<0.06, and analyse luminosity-weighted age, metallicity, and alpha/Fe ratio as function of environment and galaxy mass. We find that on average 10 per cent of early-type galaxies are rejuvenated through minor recent star formation. This fraction increases with both decreasing galaxy mass and decreasing environmental density. However, the bulk of the population obeys a well-defined scaling of age, metallicity, and alpha/Fe ratio with galaxy mass that is independent of environment. Our results contribute to the growing evidence in the recent literature that galaxy mass is the major driver of galaxy formation. Even the morphology-density relationship may actually be mass-driven, as the consequence of an environment dependent characteristic galaxy mass coupled with the fact that late-type galaxy morphologies are more prevalent in low-mass galaxies.Comment: 5 pages, proceedings of JENAM 2010, Symposium 2: "Environment and the formation of galaxies: 30 years later

Self-aligned nanoscale SQUID on a tip

A nanometer-sized superconducting quantum interference device (nanoSQUID) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 $\mu$m$^2$ displays flux sensitivity of 1.8$\cdot 10^{-6}$ $\Phi_0/\mathrm{Hz}^{1/2} and operates in fields as high as 0.6 T. With projected spin sensitivity of 65$\mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy.Comment: 14 manuscript pages, 5 figure

EXCESSIVE TIBIAL ROTATION IS RESTORED AFTER ANATOMICAL DOUBLE BUNDLE ANTERIOR CRUCIATE LIGAMENT RECONSTRUCTION

Recent studies suggested that tibial rotaion was not restored after single bundle anterior cruciate ligament (ACL) reconstruction. This study aimed to determine if excessive tibial rotation would be restored by anatomical double bundle ACL reconstruction. Ten male subjects with unilateral ACL injury were prospectively assessed with a high demanding task before and after ACL reconstruction. Knee kinematics during pivoting movement was measured by a motion analysis system. The tibial rotation was reduced in the reconstructed knee after ACL reconstruction than the deficient knee (

Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites

The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the electrons {\em within} each cell is taken into account exactly (including exchange and correlation effects), and the interaction {\em between} the cells is in second order (dipole) van der Waals approximation. No further approximations are made, in particular Landau level mixing and {\em in}complete spin polarization are accounted for. Therefore, our calculation comprises a, roughly speaking, complementary description of the bubble phase (in the special case of one and two electrons per bubble), which was proposed by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation. The phase diagram shows that in GaAs the paired phase is energetically more favorable than the single electron phase for, roughly speaking, filling factor $f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohr radii (for a more precise statement see Fig.s 4 and 5). If we start within the paired phase and increase magnetic field or decrease density, the pairs first undergo some singlet- triplet transitions before they break.Comment: 11 pages, 7 figure