A 3-component laser-Doppler velocimeter data acquisition and reduction system

A laser doppler velocimeter capable of measuring all three components of velocity simultaneously in low-speed flows is described. All the mean velocities, Reynolds stresses, and higher-order products can be evaluated. The approach followed is to split one of the two colors used in a 2-D system, thus creating a third set of beams which is then focused in the flow from an off-axis direction. The third velocity component is computed from the known geometry of the system. The laser optical hardware and the data acquisition electronics are described in detail. In addition, full operating procedures and listings of the software (written in BASIC and ASSEMBLY languages) are also included. Some typical measurements obtained with this system in a vortex/mixing layer interaction are presented and compared directly to those obtained with a cross-wire system

A Theory of Errors in Quantum Measurement

It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an observable are distributed normally. We obtain the probability distribution this implies for the outcome of a measurement, exactly for the case of 2x2 matrices and in the steepest descent approximation in general. Due to the phenomenon of `level repulsion', the probability distributions obtained are quite different from the Gaussian.Comment: Based on talk at "Spacetime and Fundamental Interactions: Quantum Aspects" A conference to honor A. P. Balachandran's 65th Birthda

Meta-analysis of the Cepheid Xpert® CT/NG assay for extragenital detection of Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG) infections.

Background Most studies evaluating extragenital testing performance for Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG) detection by the Xpert® CT/NG show high per cent agreement with comparison assays; however, the precision around positive per cent agreement is low and thus the values that have been reported are not highly informative. Therefore, a systematic review was conducted and data from five studies were combined to better assess positive per cent agreement.MethodsThe literature indexed on PubMed.gov was searched. Included studies were those that were an evaluation of the Xpert CT/NG assay with rectal and/or pharyngeal specimen types compared with another nucleic acid amplification test (NAAT), the Aptima transcription mediated amplification assay. A full Bayesian method was used for bivariate fixed-effect meta-analysis of positive and negative per cent agreement and pooled estimates (and 95% confidence intervals (CI)) were presented for each.ResultsThe pooled positive and negative per cent agreement for detection of CT in rectal specimens was 89.72% (95% CI: 84.97%, 93.64%) and 99.23% (95% CI: 98.74%, 99.60%), and in pharyngeal specimens, they were 89.96% (95% CI: 66.38%, 99.72%) and 99.62% (95% CI: 98.95%, 99.95%) respectively. For NG detection in rectal specimens, the pooled positive and negative per cent agreement was 92.75% (95% CI: 87.91%, 96.46%) and 99.75% (95% CI: 99.46%, 99.93%), and in pharyngeal specimens, they were 92.51% (95% CI: 85.84%, 97.18%) and 98.56% (95% CI: 97.69%, 99.23%) respectively.ConclusionsIt was found that the Xpert CT/NG assay performed similarly to the Aptima transcription mediated amplification assay for the detection of CT and NG in extragenital specimens. The Xpert assay has the benefit of providing faster results at the point-of-care, thus reducing the turnaround time for results, potentially enabling same-day treatment

Constant Rank Bimatrix Games are PPAD-hard

The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for constant rank games, and asked if there exists a polynomial time algorithm to compute an exact NE. Adsul et al. (2011) answered this question affirmatively for rank-$1$ games, leaving rank-2 and beyond unresolved. In this paper we show that NE computation in games with rank $\ge 3$, is PPAD-hard, settling a decade long open problem. Interestingly, this is the first instance that a problem with an FPTAS turns out to be PPAD-hard. Our reduction bypasses graphical games and game gadgets, and provides a simpler proof of PPAD-hardness for NE computation in bimatrix games. In addition, we get: * An equivalence between 2D-Linear-FIXP and PPAD, improving a result by Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD. * NE computation in a bimatrix game with convex set of Nash equilibria is as hard as solving a simple stochastic game. * Computing a symmetric NE of a symmetric bimatrix game with rank $\ge 6$ is PPAD-hard. * Computing a (1/poly(n))-approximate fixed-point of a (Linear-FIXP) piecewise-linear function is PPAD-hard. The status of rank-$2$ games remains unresolved

Competition and cooperation:aspects of dynamics in sandpiles

In this article, we review some of our approaches to granular dynamics, now well known to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they cooperate. A typical result of {\it cooperation} is the formation of stable bridges, signatures of spatiotemporal inhomogeneities; we review their geometrical characteristics and compare theoretical results with those of independent simulations. {\it Cooperative} excitations due to local density fluctuations are also responsible for relaxation at the angle of repose; the {\it competition} between these fluctuations and external driving forces, can, on the other hand, result in a (rare) collapse of the sandpile to the horizontal. Both these features are present in a theory reviewed here. An arena where the effects of cooperation versus competition are felt most keenly is granular compaction; we review here a random graph model, where three-spin interactions are used to model compaction under tapping. The compaction curve shows distinct regions where 'fast' and 'slow' dynamics apply, separated by what we have called the {\it single-particle relaxation threshold}. In the final section of this paper, we explore the effect of shape -- jagged vs. regular -- on the compaction of packings near their jamming limit. One of our major results is an entropic landscape that, while microscopically rough, manifests {\it Edwards' flatness} at a macroscopic level. Another major result is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction

How to measure the spreading width for decay of superdeformed nuclei

A new expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei is given within a simple two-level model. Using this expression, the spreading or tunneling width Gamma^downarrow for superdeformed decay can be expressed entirely in terms of experimentally known quantities. We show how to determine the tunneling matrix element V from the measured value of Gamma^downarrow and a statistical model of the energy levels. The accuracy of the two-level approximation is verified by considering the effects of the other normal-deformed states.Comment: 4 pages, 4 figure