On the existence of star products on quotient spaces of linear Hamiltonian torus actions

We discuss BFV deformation quantization of singular symplectic quotient spaces in the special case of linear Hamiltonian torus actions. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms, Gotay and Jennings for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.Comment: 9 pages, 4 figures, uses psfra

The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.Comment: 14 pages, 5 figures, REVTeX4, submitted to PRB; clarification of the diagrammatic technique added, one figure update

An HST Snapshot Survey of Proto-Planetary Nebulae Candidates: Two Types of Axisymmetric Reflection Nebulosities

We report the results from an optical imaging survey of proto-planetary nebula candidates using the HST. We exploited the high resolving power and wide dynamic range of HST and detected nebulosities in 21 of 27 sources. All detected reflection nebulosities show elongation, and the nebula morphology bifurcates depending on the degree of the central star obscuration. The Star-Obvious Low-level-Elongated (SOLE) nebulae show a bright central star embedded in a faint, extended nebulosity, whereas the DUst-Prominent Longitudinally-EXtended (DUPLEX) nebulae have remarkable bipolar structure with a completely or partially obscured central star. The intrinsic axisymmetry of these proto-planetary nebula reflection nebulosities demonstrates that the axisymmetry frequently found in planetary nebulae predates the proto-planetary nebula phase, confirming previous independent results. We suggest that axisymmetry in proto-planetary nebulae is created by an equatorially enhanced superwind at the end of the asymptotic giant branch phase. We discuss that the apparent morphological dichotomy is caused by a difference in the optical thickness of the circumstellar dust/gas shell with a differing equator-to-pole density contrast. Moreover, we show that SOLE and DUPLEX nebulae are physically distinct types of proto-planetary nebulae, with a suggestion that higher mass progenitor AGB stars are more likely to become DUPLEX proto-planetary nebulae.Comment: 27 pages (w/ aaspp4.sty), 6 e/ps figures, 4 tables (w/ apjpt4.sty). Data images are available via ADIL (http://imagelib.ncsa.uiuc.edu/document/99.TU.01) To be published in Ap

A Mid-Infrared Imaging Survey of Proto-Planetary Nebula Candidates

We present the data from a mid-infrared imaging survey of 66 proto-planetary nebula candidates using two mid-IR cameras (MIRAC2 and Berkcam) at the NASA Infrared Telescope Facility and the United Kingdom Infrared Telescope. The goal of this survey is to determine the size, flux, and morphology of the mid-IR emission regions, which sample the inner regions of the circumstellar dust shells of proto-planetary nebulae. We imaged these proto-planetary nebulae with narrow-band filters ($\Delta\lambda / \lambda \sim 10$) at wavelengths of notable dust features. With our typical angular resolution of 1\arcsec, we resolve 17 sources, find 48 objects unresolved, and do not detect 1 source. For several sources, we checked optical and infrared associations and positions of the sources. In table format, we list the size and flux measurements for all the detected objects and show figures of all the resolved sources. Images for all the detected objects are available on line in FITS format from the Astronomy Digital Image Library at the National Center for Supercomputing Application. The proto-planetary nebula candidate sample includes, in addition to the predominant proto-planetary nebulae, extreme asymptotic giant branch stars, young planetary nebulae, a supergiant, and a luminous blue variable. We find that dust shells which are cooler ($\rm T \sim 150$ K) and brighter in the infrared are more easily resolved. Eleven of the seventeen resolved sources are extended and fall into one of two types of mid-IR morphological classes: core/elliptical or toroidal. Core/elliptical structures show unresolved cores with lower surface brightness elliptical nebulae. Toroidal structures show limb-brightened peaks suggesting equatorial density enhancements. We argue that core/ellipticals have denser dust shells than toroidals.Comment: 32 pages, 5 tables, 2 e/ps figures (fig3 is available through ADIL [see text]), to be published in ApJS May 1999 issu

A hierarchical key pre-distribution scheme for fog networks

Security in fog computing is multi-faceted, and one particular challenge is establishing a secure communication channel between fog nodes and end devices. This emphasizes the importance of designing efficient and secret key distribution scheme to facilitate fog nodes and end devices to establish secure communication channels. Existing secure key distribution schemes designed for hierarchical networks may be deployable in fog computing, but they incur high computational and communication overheads and thus consume significant memory. In this paper, we propose a novel hierarchical key pre-distribution scheme based on “Residual Design” for fog networks. The proposed key distribution scheme is designed to minimize storage overhead and memory consumption, while increasing network scalability. The scheme is also designed to be secure against node capture attacks. We demonstrate that in an equal-size network, our scheme achieves around 84% improvement in terms of node storage overhead, and around 96% improvement in terms of network scalability. Our research paves the way for building an efficient key management framework for secure communication within the hierarchical network of fog nodes and end devices. KEYWORDS: Fog Computing, Key distribution, Hierarchical Networks

Interpretation of heart rate variability via detrended fluctuation analysis and alpha-beta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alpha-beta filter to DFA to determine patterns in the power-law behaviour that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behaviour, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.Comment: 18 pages, 14 figure

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Magnetic Field Effects in the Pseudogap Phase: A Competing Energy Gap Scenario for Precursor Superconductivity

We study the sensitivity of T_c and T^* to low fields, H, within the pseudogap state using a BCS-based approach extended to arbitrary coupling. We find that T^* and T_c, which are of the same superconducting origin, have very different H dependences. This is due to the pseudogap, \Delta_{pg}, which is present at the latter, but not former temperature. Our results for the coherence length \xi fit well with existing experiments.We predict that very near the insulator \xi will rapidly increase.Comment: 4 pages, 4 figures, RevTe