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At least 37 records · Page 2

Unveiling the gamma-ray source count distribution below the Fermi detection limit with photon statistics

The source-count distribution as a function of their flux, dN/dS, is one of the main quantities characterizing gamma-ray source populations. We employ statistical properties of the Fermi Large Area Telescope (LAT) photon counts map to measure the composition of the extragalactic gamma-ray sky at high latitudes (|b|⩾30°) between 1 and 10 GeV. We present a new method, generalizing the use of standard pixel-count statistics, to decompose the total observed gamma-ray emission into (a) point-source contributions, (b) the Galactic foreground contribution, and (c) a truly diffuse isotropic background contribution. Using the 6 yr Fermi-LAT data set (P7REP), we show that the dN/dS distribution in the regime of so far undetected point sources can be consistently described with a power law with an index between 1.9 and 2.0. We measure dN/dS down to an integral flux of ∼2×10{sup −11} cm{sup −2} s{sup −1}, improving beyond the 3FGL catalog detection limit by about one order of magnitude. The overall dN/dS distribution is consistent with a broken power law, with a break at 2.1{sub −1.3}{sup +1.0}×10{sup −8} cm{sup −2} s{sup −1}. The power-law index n{sub 1}=3.1{sub −0.5}{sup +0.7} for bright sources above the break hardens to n{sub 2}=1.97±0.03 for fainter sources below the break. A possible second break of the dN/dS distribution is constrained to be at fluxes below 6.4×10{sup −11} cm{sup −2} s{sup −1} at 95% confidence level. The high-latitude gamma-ray sky between 1 and 10 GeV is shown to be composed of ∼25% point sources, ∼69.3% diffuse Galactic foreground emission, and ∼6% isotropic diffuse background.

79 ASTRONOMY AND ASTROPHYSICS↗

Research Update: Spatially resolved mapping of electronic structure on atomic level by multivariate statistical analysis

Atomic level spatial variability of electronic structure in Fe-based superconductor FeTe0.55Se0.45 (Tc = 15 K) is explored using current-imaging tunneling-spectroscopy. Multivariate statistical analysis of the data differentiates regions of dissimilar electronic behavior that can be identified with the segregation of chalcogen atoms, as well as boundaries between terminations and near neighbor interactions. Subsequent clustering analysis allows identification of the spatial localization of these dissimilar regions. Similar statistical analysis of modeled calculated density of states of chemically inhomogeneous FeTe1 x Sex structures further confirms that the two types of chalcogens, i.e., Te and Se, can be identified by their electronic signature and differentiated by their local chemical environment. This approach allows detailed chemical discrimination of the scanning tunneling microscopy data including separation of atomic identities, proximity, and local configuration effects and can be universally applicable to chemically and electronically inhomogeneous surfaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

MASKED AREAS IN SHEAR PEAK STATISTICS: A FORWARD MODELING APPROACH

The statistics of shear peaks have been shown to provide valuable cosmological information beyond the power spectrum, and will be an important constraint of models of cosmology in forthcoming astronomical surveys. Surveys include masked areas due to bright stars, bad pixels etc., which must be accounted for in producing constraints on cosmology from shear maps. We advocate a forward-modeling approach, where the impacts of masking and other survey artifacts are accounted for in the theoretical prediction of cosmological parameters, rather than correcting survey data to remove them. We use masks based on the Deep Lens Survey, and explore the impact of up to 37% of the survey area being masked on LSST and DES-scale surveys. By reconstructing maps of aperture mass the masking effect is smoothed out, resulting in up to 14% smaller statistical uncertainties compared to simply reducing the survey area by the masked area. We show that, even in the presence of large survey masks, the bias in cosmological parameter estimation produced in the forward-modeling process is ≈1%, dominated by bias caused by limited simulation volume. We also explore how this potential bias scales with survey area and evaluate how much small survey areas are impacted by the differences in cosmological structure in the data and simulated volumes, due to cosmic variance.

79 ASTRONOMY AND ASTROPHYSICS↗

Event detection and sub-state discovery from biomolecular simulations using higher-order statistics: Application to enzyme adenylate kinase

Biomolecular simulations at millisecond and longer time-scales can provide vital insights into functional mechanisms. Because post-simulation analyses of such large trajectory datasets can be a limiting factor in obtaining biological insights, there is an emerging need to identify key dynamical events and relating these events to the biological function online, that is, as simulations are progressing. Recently, we have introduced a novel computational technique, quasi-anharmonic analysis (QAA) (Ramanathan et al., PLoS One 2011;6:e15827), for partitioning the conformational landscape into a hierarchy of functionally relevant sub-states. The unique capabilities of QAA are enabled by exploiting anharmonicity in the form of fourth-order statistics for characterizing atomic fluctuations. In this article, we extend QAA for analyzing long time-scale simulations online. In particular, we present HOST4MD—a higher-order statistical toolbox for molecular dynamics simulations, which (1) identifies key dynamical events as simulations are in progress, (2) explores potential sub-states, and (3) identifies conformational transitions that enable the protein to access those sub-states. We demonstrate HOST4MD on microsecond timescale simulations of the enzyme adenylate kinase in its apo state. HOST4MD identifies several conformational events in these simulations, revealing how the intrinsic coupling between the three subdomains (LID, CORE, and NMP) changes during the simulations. Further, it also identifies an inherent asymmetry in the opening/closing of the two binding sites. We anticipate that HOST4MD will provide a powerful and extensible framework for detecting biophysically relevant conformational coordinates from long time-scale simulations.

Ramanathan, Arvind↗

Uncertainties in turbulent statistics and fluxes of CO2 associated with density effect corrections

Density effect corrections (DEC) are applied to adjust raw CO2 fluxes measured by eddy covariance (EC) systems with open-path gas analyzers. DEC is also required for adjusting the measured CO2 concentration fluctuations to obtain the adjusted CO2 for analyzing turbulent statistics or quantifying fluxes. However, our data show that the power spectra of the DEC-adjusted CO2 are distorted in the high frequency range, as compared with the corresponding spectra of temperature and water vapor density. This contradicts the similarity behavior of scalars, as suggested by Monin-Obukhov similarity theory. It is demonstrated that such a distortion is caused by the DEC-induced spikes in the DEC-adjusted CO2, altering turbulent statistics of CO2 and scalar similarity between CO2 and other scalars. Our results suggest that CO2 fluxes are overestimated by applying DEC especially under high Bowen ratio conditions, potentially leading to substantial uncertainties in long-term ecosystem carbon exchange in dry regions.

Gao, Zhongming↗

In silico environmental chemical science: properties and processes from statistical and computational modelling

Quantitative structure–activity relationships (QSARs) have long been used in the environmental sciences. More recently, molecular modeling and chemoinformatic methods have become widespread. These methods have the potential to expand and accelerate advances in environmental chemistry because they complement observational and experimental data with “in silico” results and analysis. The opportunities and challenges that arise at the intersection between statistical and theoretical in silico methods are most apparent in the context of properties that determine the environmental fate and effects of chemical contaminants (degradation rate constants, partition coefficients, toxicities, etc.). The main example of this is the calibration of QSARs using descriptor variable data calculated from molecular modeling, which can make QSARs more useful for predicting property data that are unavailable, but also can make them more powerful tools for diagnosis of fate determining pathways and mechanisms. Emerging opportunities for “in silico environmental chemical science” are to move beyond the calculation of specific chemical properties using statistical models and toward more fully in silico models, prediction of transformation pathways and products, incorporation of environmental factors into model predictions, integration of databases and predictive models into more comprehensive and efficient tools for exposure assessment, and extending the applicability of all the above from chemicals to biologicals and materials.

54 ENVIRONMENTAL SCIENCES↗

Wind power curve modeling in complex terrain using statistical models

The simplest power curves model wind power only as a function of the wind speed at the turbine hub height. While the latter is an essential predictor of power output, wind speed information in other parts of the vertical profile, as well as additional atmospheric variables, are also important determinants of power. The goal of this work was to determine the gain in predictive ability afforded by adding wind speed information at other heights, as well as other atmospheric variables, to the power prediction model. Using data from a wind farm with a moderately complex terrain in the Altamont Pass region in California, we trained three statistical models—a neural network, a random forest and a Gaussian process model—to predict power output from various sets of aforementioned predictors. The comparison of these predictions to the observed power data revealed that considerable improvements in prediction accuracy can be achieved both through the addition of predictors other than the hub-height wind speed and the use of statistical models. To our knowledge, the use of the Gaussian process model in this context is new, in contrast to neural networks and random forests. The advantage of this model over the other two models is that it provides a much more natural way to estimate the uncertainty associated with its predictions. In addition, this study presents one of the most comprehensive analyses to date of the relative importance of various wind power curve inputs.

Bulaevskaya, V.↗

TRANSIT TIMING OBSERVATIONS FROM KEPLER. VI. POTENTIALLY INTERESTING CANDIDATE SYSTEMS FROM FOURIER-BASED STATISTICAL TESTS

We analyze the deviations of transit times from a linear ephemeris for the Kepler Objects of Interest (KOI) through quarter six of science data. We conduct two statistical tests for all KOIs and a related statistical test for all pairs of KOIs in multi-transiting systems. These tests identify several systems which show potentially interesting transit timing variations (TTVs). Strong TTV systems have been valuable for the confirmation of planets and their mass measurements. Many of the systems identified in this study should prove fruitful for detailed TTV studies.

79 ASTRONOMY AND ASTROPHYSICS↗

Inference of reaction rate parameters based on summary statistics from experiments

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2 /O 2 -mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

97 MATHEMATICS AND COMPUTING↗

A Unified Statistical Rain-Attenuation Model for Communication Link Fade Predictions and Optimal Stochastic Fade Control Design Using a Location-Dependent Rain-Statistic Database

A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.

Manning, Robert M.↗

Poincaré recurrence statistics as an indicator of chaos synchronization

The dynamics of the autonomous and non-autonomous Rössler system is studied using the Poincaré recurrence time statistics. It is shown that the probability distribution density of Poincaré recurrences represents a set of equidistant peaks with the distance that is equal to the oscillation period and the envelope obeys an exponential distribution. The dimension of the spatially uniform Rössler attractor is estimated using Poincaré recurrence times. The mean Poincaré recurrence time in the non-autonomous Rössler system is locked by the external frequency, and this enables us to detect the effect of phase-frequency synchronization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-extensive statistics to the cosmological lithium problem

Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, 3 He, 4 He, and 7 Li produced in the early universe. The primordial abundances of D and 4 He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial 7 Li abundance by about a factor of three. This is the so-called "cosmological lithium problem." Solutions to this problem using conventional astrophysics and nuclear physics have not been successful over the past few decades, probably indicating the presence of new physics during the era of BBN. We have investigated the impact on BBN predictions of adopting a generalized distribution to describe the velocities of nucleons in the framework of Tsallis non-extensive statistics. This generalized velocity distribution is characterized by a parameter q, and reduces to the usually assumed Maxwell–Boltzmann distribution for q = 1. We find excellent agreement between predicted and observed primordial abundances of D, 4 He, and 7 Li for 1.069 ≤ q ≤ 1.082, suggesting a possible new solution to the cosmological lithium problem.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical measurement of the gamma-ray source-count distribution as a function of energy

Statistical properties of photon count maps have recently been proven as a new tool to study the composition of the gamma-ray sky with high precision. We employ the 1-point probability distribution function of six years of Fermi-LAT data to measure the source-count distribution dN/dS and the diffuse components of the high-latitude gamma-ray sky as a function of energy. To that aim, we analyze the gamma-ray emission in five adjacent energy bands between 1 and 171 GeV. It is demonstrated that the source-count distribution as a function of flux is compatible with a broken power law up to energies of ∼50 GeV. The index below the break is between 1.95 and 2.0. For higher energies, a simple power-law fits the data, with an index of 2.2{sub −0.3}{sup +0.7} in the energy band between 50 and 171 GeV. Upper limits on further possible breaks as well as the angular power of unresolved sources are derived. We find that point-source populations probed by this method can explain 83{sub −13}{sup +7}% (81{sub −19}{sup +52}%) of the extragalactic gamma-ray background between 1.04 and 1.99 GeV (50 and 171 GeV). The method has excellent capabilities for constraining the gamma-ray luminosity function and the spectra of unresolved blazars.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical scattering of waves in disordered waveguides: The limiting macroscopic statistics in the ballistic regime

In this work, we present a theoretical study of the statistical properties of wave scattering in a disordered ballistic waveguide of length L; we have called this system the ''building block''. The building block is interesting as a physical system because its statistical properties could be studied experimentally in the laboratory.In order to study the building block, as a physical system in itself, we have developed a perturbative method based on Born series. This method is valid only in the ballistic regime, when the length of the system L is smaller than the mean free path l, and in the short-wave-length approximation, when the the wave number k and the mean free path l satisfy kl>>1. This method has allowed to find, analytically, the behavior of quantities of interest that we have not been able to find from the diffusion equation. In contrast with the diffusion equation method, which takes into account approximately the contribution of closed channels, this method takes them explicitly. In earlier works numerical evidence was found that the expectation values of some interesting quantities are insensitive to the number of closed channels that were used on the calculations; with this method, we could show that closed channels are relevant for the expectation values of amplitudes but irrelevant for the intensities and conductance expectation values. The results of this method show a good agreement with numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Statistical mechanical models for dissociative adsorption of O{sub 2} on metal(100) surfaces with blocking, steering, and funneling

We develop statistical mechanical models amenable to analytic treatment for the dissociative adsorption of O{sub 2} at hollow sites on fcc(100) metal surfaces. The models incorporate exclusion of nearest-neighbor pairs of adsorbed O. However, corresponding simple site-blocking models, where adsorption requires a large ensemble of available sites, exhibit an anomalously fast initial decrease in sticking. Thus, in addition to blocking, our models also incorporate more facile adsorption via orientational steering and funneling dynamics (features supported by ab initio Molecular Dynamics studies). Behavior for equilibrated adlayers is distinct from those with finite adspecies mobility. We focus on the low-temperature limited-mobility regime where analysis of the associated master equations readily produces exact results for both short- and long-time behavior. Kinetic Monte Carlo simulation is also utilized to provide a more complete picture of behavior. These models capture both the initial decrease and the saturation of the experimentally observed sticking versus coverage, as well as features of non-equilibrium adlayer ordering as assessed by surface-sensitive diffraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The joint space-time statistics of macroweather precipitation, space-time statistical factorization and macroweather models

Over the range of time scales from about 10 days to 30–100 years, in addition to the familiar weather and climate regimes, there is an intermediate “macroweather” regime characterized by negative temporal fluctuation exponents: implying that fluctuations tend to cancel each other out so that averages tend to converge. We show theoretically and numerically that macroweather precipitation can be modeled by a stochastic weather-climate model (the Climate Extended Fractionally Integrated Flux, model, CEFIF) first proposed for macroweather temperatures and we show numerically that a four parameter space-time CEFIF model can approximately reproduce eight or so empirical space-time exponents. In spite of this success, CEFIF is theoretically and numerically difficult to manage. We therefore propose a simplified stochastic model in which the temporal behavior is modeled as a fractional Gaussian noise but the spatial behaviour as a multifractal (climate) cascade: a spatial extension of the recently introduced ScaLIng Macroweather Model, SLIMM. Both the CEFIF and this spatial SLIMM model have a property often implicitly assumed by climatologists that climate statistics can be “homogenized” by normalizing them with the standard deviation of the anomalies. Physically, it means that the spatial macroweather variability corresponds to different climate zones that multiplicatively modulate the local, temporal statistics. This simplified macroweather model provides a framework for macroweather forecasting that exploits the system's long range memory and spatial correlations; for it, the forecasting problem has been solved. We test this factorization property and the model with the help of three centennial, global scale precipitation products that we analyze jointly in space and in time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗