Periodic orbit theory and spectral rigidity in pseudointegrable systems

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity $\Delta_3(L)$ using semiclassical quantum mechanics with $L$ reaching up to quite large values. We find that the diagonal approximation is applicable when averaging over a suitable energy interval. Comparing systems of various shapes we find that our results agree well with $\Delta_3$ calculated directly from the eigenvalues by spectral statistics. Therefore, additional terms as e.g. diffraction terms seem to be small in the case of the systems investigated in this work. By reducing the size of the corners, the spectral statistics of our pseudointegrable systems approaches the one of an integrable system, whereas very large differences between integrable and pseudointegrable systems occur, when the salient corners are large. Both types of behavior can be well understood by the properties of the periodic orbits in the system

Application of the Trace Formula in Pseudointegrable Systems

We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct diagonalization of the Schr\"odinger equation, that about the first 100 eigenvalues can be obtained directly from the periodic-orbit calculations in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.

α_1L-adrenoceptors mediate contraction of human erectile tissue

α1-adrenoceptor antagonists can impact upon sexual function and have potential in the treatment of erectile dysfunction. Human erectile tissue contains predominantly α1A-adrenoceptors, and here we examined whether contractions of this tissue are mediated by the functional phenotype, the α1L-adrenoceptor. Functional experiments using subtype selective agonists and antagonists, along with radioligand ([3H]tamsulosin) binding assays, were used to determine the α1-adrenoceptor population. A61603, a α1A-adrenoceptor agonist, was a full agonist with a potency 21-fold greater than that of noradrenaline. The α1A- and α1D-adrenoceptor antagonist tamsulosin antagonized noradrenaline responses with high affinity (pKD = 9.7 ± 0.3), whilst BMY7378 (100 nM) (α1D-adrenoceptor antagonist) failed to antagonize responses. In contrast, relatively low affinity estimates were obtained for both prazosin (pKD = 8.2 ± 0.1) and RS17053 (pKD = 6.9 ± 0.2), antagonists which discriminate between the α1A- and α1L-adrenoceptors. [3H]Tamsulosin bound with high affinity to the receptors of human erectile tissue (pKD = 10.3 ± 0.1) with a receptor density of 28.1 ± 1.4 fmol mg−1 protein. Prazosin displacement of [3H]tamsulosin binding revealed a single homogenous population of binding sites with a relatively low affinity for prazosin (pKi = 8.9). Taken together these data confirm that the receptor mediating contraction in human erectile tissue has the pharmacological properties of the α1L-adrenoceptor. Keywords: Erectile tissue, α1-adrenoceptor subtypes, α1L-adrenoceptor, Tamsulosin, Prazosi

Medication decision-making for patients with renal insufficiency in inpatient and outpatient care at a US Veterans Affairs Medical Centre: a qualitative, cognitive task analysis.

BackgroundMany studies identify factors that contribute to renal prescribing errors, but few examine how healthcare professionals (HCPs) detect and recover from an error or potential patient safety concern. Knowledge of this information could inform advanced error detection systems and decision support tools that help prevent prescribing errors.ObjectiveTo examine the cognitive strategies that HCPs used to recognise and manage medication-related problems for patients with renal insufficiency.DesignHCPs submitted documentation about medication-related incidents. We then conducted cognitive task analysis interviews. Qualitative data were analysed inductively.SettingInpatient and outpatient facilities at a major US Veterans Affairs Medical Centre.ParticipantsPhysicians, nurses and pharmacists who took action to prevent or resolve a renal-drug problem in patients with renal insufficiency.OutcomesEmergent themes from interviews, as related to recognition of renal-drug problems and decision-making processes.ResultsWe interviewed 20 HCPs. Results yielded a descriptive model of the decision-making process, comprised of three main stages: detect, gather information and act. These stages often followed a cyclical path due largely to the gradual decline of patients' renal function. Most HCPs relied on being vigilant to detect patients' renal-drug problems rather than relying on systems to detect unanticipated cues. At each stage, HCPs relied on different cognitive cues depending on medication type: for renally eliminated medications, HCPs focused on gathering renal dosing guidelines, while for nephrotoxic medications, HCPs investigated the need for particular medication therapy, and if warranted, safer alternatives.ConclusionsOur model is useful for trainees so they can gain familiarity with managing renal-drug problems. Based on findings, improvements are warranted for three aspects of healthcare systems: (1) supporting the cyclical nature of renal-drug problem management via longitudinal tracking mechanisms, (2) providing tools to alleviate HCPs' heavy reliance on vigilance and (3) supporting HCPs' different decision-making needs for renally eliminated versus nephrotoxic medications

Smoothing a program soundly and robustly

We study the foundations of smooth interpretation, a recently-proposed program approximation scheme that facilitates the use of local numerical search techniques (e.g., gradient descent) in program analysis and synthesis. While the popular techniques for local optimization works well only on relatively smooth functions, functions encoded by real-world programs are infested with discontinuities and local irregular features. Smooth interpretation attenuates such features by taking the convolution of the program with a Gaussian function, effectively replacing discontinuous switches in the program by continuous transitions. In doing so, it extends to programs the notion of Gaussian smoothing, a popular signal-processing technique used to filter noise and discontinuities from signals. Exact Gaussian smoothing of programs is undecidable, so algorithmic implementations of smooth interpretation must necessarily be approximate. In this paper, we characterize the approximations carried out by such algorithms. First, we identify three correctness properties—soundness, robustness, and β-robustness—that an approximate smooth interpreter should satisfy. In particular, a smooth interpreter is sound if it computes an abstraction of a program’s “smoothed” semantics, and robust if it has arbitrary-order derivatives in the input variables at every point in its input space. Second, we describe the design of an approximate smooth interpreter that provably satisfies these properties. The interpreter combines program abstraction using a new domain with symbolic calculation of convolution.National Science Foundation (U.S.) (Grant CCF-0953507)Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laborator

Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.Comment: 16 pages, to appear in Phys. Rev.

Back Reaction Problem in the Inflationary Universe

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.Comment: 17 page

Refinement of the Spitzer Space Telescope Pointing History Based on Image Registration Corrections from Multiple Data Channels

Position reconstruction for images acquired by the Infrared Array Camera (IRAC), one of the science instruments onboard the Spitzer Space Telescope, is a multistep procedure that is part of the routine processing done at the Spitzer Science Center (SSC). The IRAC instrument simultaneously images two different sky footprints, each with two independent infrared passbands (channels). The accuracy of the initial Spitzer pointing reconstruction is typically slightly better than 1". The well‐known technique of position matching imaged point sources to even more accurate star catalogs to refine the pointing further is implemented for SSC processing of IRAC data as well. Beyond that, the optimal processing of redundant pointing information from multiple instrument channels to yield an even better solution is also performed at the SSC. Our multichannel data processing approach is particularly beneficial when the star‐catalog matches are sparse in one channel but copious in others. A thorough review of the algorithm as implemented for the Spitzer mission reveals that the mathematical formalism can be fairly easily generalized for application to other astronomy missions. The computation of pointing uncertainties, the interpolation of pointing corrections and their uncertainties between measurements, and the estimation of random‐walk deviations from linearity are special areas of importance when implementing the method. After performing the operations described in this paper on the initial Spitzer pointing, the uncertainty in the observatory pointing history file is reduced 10–15 fold

Design of the Spitzer Space Telescope Heritage Archive

It is predicted that Spitzer Space Telescope’s cryogen will run out in April 2009, and the final reprocessing for the cryogenic mission is scheduled to end in April 2011, at which time the Spitzer archive will be transferred to the NASA/IPAC Infrared Science Archive (IRSA) for long-term curation. The Spitzer Science Center (SSC) and IRSA are collaborating to design and deploy the Spitzer Heritage Archive (SHA), which will supersede the current Spitzer archive. It will initially contain the raw and final reprocessed cryogenic science products, and will eventually incorporate the final products from the Warm mission. The SHA will be accompanied by tools deemed necessary to extract the full science content of the archive and by comprehensive documentation