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MORPHOLOGY OF GALAXY CLUSTERS: A COSMOLOGICAL MODEL-INDEPENDENT TEST OF THE COSMIC DISTANCE-DUALITY RELATION
Aiming at comparing different morphological models of galaxy clusters, we use two new methods to make a cosmological model-independent test of the distance-duality (DD) relation. The luminosity distances come from the Union2 compilation of Supernovae Type Ia. The angular diameter distances are given by two cluster models (De Filippis et al. and Bonamente et al.). The advantage of our methods is that they can reduce statistical errors. Concerning the morphological hypotheses for cluster models, it is mainly focused on the comparison between the elliptical {beta}-model and spherical {beta}-model. The spherical {beta}-model is divided into two groups in terms of different reduction methods of angular diameter distances, i.e., the conservative spherical {beta}-model and corrected spherical {beta}-model. Our results show that the DD relation is consistent with the elliptical {beta}-model at 1{sigma} confidence level (CL) for both methods, whereas for almost all spherical {beta}-model parameterizations, the DD relation can only be accommodated at 3{sigma} CL, particularly for the conservative spherical {beta}-model. In order to minimize systematic uncertainties, we also apply the test to the overlap sample, i.e., the same set of clusters modeled by both De Filippis et al. and Bonamente et al. It is found that the DD relation is compatible with the elliptically modeled overlap sample at 1{sigma} CL; however, for most of the parameterizations the DD relation cannot be accommodated even at 3{sigma} CL for any of the two spherical {beta}-models. Therefore, it is reasonable that the marked triaxial ellipsoidal model is a better geometrical hypothesis describing the structure of the galaxy cluster compared with the spherical {beta}-model if the DD relation is valid in cosmological observations.
Determining Reduced Order Models for Optimal Stochastic Reduced Order Models
The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.
ASSESSING THE SIGNIFICANCE OF APPARENT CORRELATIONS BETWEEN RADIO AND GAMMA-RAY BLAZAR FLUXES
Whether or not a correlation exists between the radio and gamma-ray flux densities of blazars is a long-standing question, and one that is difficult to answer confidently because of various observational biases, which may either dilute or apparently enhance any intrinsic correlation between radio and gamma-ray luminosities. We introduce a novel method of data randomization to evaluate quantitatively the effect of these biases and to assess the intrinsic significance of an apparent correlation between radio and gamma-ray flux densities of blazars. The novelty of the method lies in a combination of data randomization in luminosity space (to ensure that the randomized data are intrinsically, and not just apparently, uncorrelated) and significance assessment in flux space (to explicitly avoid Malmquist bias and automatically account for the limited dynamical range in both frequencies). The method is applicable even to small samples that are not selected with strict statistical criteria. For larger samples we describe a variation of the method in which the sample is split in redshift bins, and the randomization is applied in each bin individually; this variation is designed to yield the equivalent to luminosity-function sampling of the underlying population in the limit of very large, statistically complete samples. We show that for a smaller number of redshift bins, the method yields a worse significance, and in this way it is conservative: although it may fail to confirm an existing intrinsic correlation in a small sample that cannot be split into many redshift bins, it will not assign a stronger, artificially enhanced significance. We demonstrate how our test performs as a function of number of sources, strength of correlation, and number of redshift bins used, and we show that while our test is robust against common-distance biases and associated false positives for uncorrelated data, it retains the power of other methods in rejecting the null hypothesis of no correlation for correlated data.
Predictive Fusion of Geophysical Waveforms using Fisher's Method, under the Alternative Hypothesis
This presentation tries to understand how to combine different signatures from an event or source together in a defensible way. The objective was to build a digital detector that continuously combines detection statistics recording explosions to screen sources of interest from null sources.
Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations
Here, this work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Finally, numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.
Molecular Dynamics Simulation of Complex Reactivity with the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) Software Package
Simulating chemically reactive phenomena such as proton transport on nanosecond to microsecond and beyond time scales is a challenging task. Ab initio methods are unable to currently access these time scales routinely, and traditional molecular dynamics methods feature fixed bonding arrangements that cannot account for changes in the system’s bonding topology. The Multiscale Reactive Molecular Dynamics (MS-RMD) method, as implemented in the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) software package for the LAMMPS molecular dynamics code, offers a method to routinely sample longer time scale reactive simulation data with statistical precision. RAPTOR may also be interfaced with enhanced sampling methods to drive simulations toward the analysis of reactive rare events, and a number of collective variables (CVs) have been developed to facilitate this. Key advances to this methodology, including GPU acceleration efforts and novel CVs to model water wire formation are reviewed, along with recent applications of the method which demonstrate its versatility and robustness.
Determination of proton PDF uncertainties with Markov chain Monte Carlo
We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.
An investigation of Newton-Sketch and subsampled Newton methods
Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.
Statistical scaling of geometric characteristics in stochastically generated pore microstructures
In this study, we analyze the statistical scaling of structural attributes of virtual porous microstructures that are stochastically generated by thresholding Gaussian random fields. Characterization of the extent at which randomly generated pore spaces can be considered as representative of a particular rock sample depends on the metrics employed to compare the virtual sample against its physical counterpart. Typically, comparisons against features and/patterns of geometric observables, e.g., porosity and specific surface area, flow-related macroscopic parameters, e.g., permeability, or autocorrelation functions are used to assess the representativeness of a virtual sample, and thereby the quality of the generation method. Here, we rely on manifestations of statistical scaling of geometric observables which were recently observed in real millimeter scale rock samples [13] as additional relevant metrics by which to characterize a virtual sample. We explore the statistical scaling of two geometric observables, namely porosity (Φ) and specific surface area (SSA), of porous microstructures generated using the method of Smolarkiewicz and Winter [42] and Hyman and Winter [22]. Our results suggest that the method can produce virtual pore space samples displaying the symptoms of statistical scaling observed in real rock samples. Order q sample structure functions (statistical moments of absolute increments) of Φ and SSA scale as a power of the separation distance (lag) over a range of lags, and extended self-similarity (linear relationship between log structure functions of successive orders) appears to be an intrinsic property of the generated media. The width of the range of lags where power-law scaling is observed and the Hurst coefficient associated with the variables we consider can be controlled by the generation parameters of the method.
A new method for imaging nuclear threats using cosmic ray muons
Muon tomography is a technique that uses cosmic ray muons to generate three-dimensional images of volumes using information contained in the Coulomb scattering of the muons. Advantages of this technique are the ability of cosmic rays to penetrate significant overburden and the absence of any additional dose delivered to subjects under study beyond the natural cosmic ray flux. Disadvantages include the relatively long exposure times and poor position resolution and complex algorithms needed for reconstruction. Furthermore, we demonstrate a new method for obtaining improved position resolution and statistical precision for objects with spherical symmetry.
Multinomial diffusion equation
We describe a new, microscopic model for diffusion that captures diffusion induced uctuations at scales where the concept of concentration gives way to discrete par- ticles. We show that in the limit as the number of particles N ! 1, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
An empirical method that separates irreversible stem radial growth from bark water content changes in trees: theory and case studies
Substantial uncertainty surrounds our knowledge of tree stem growth, with some of the most basic questions, such as when stem radial growth occurs through the daily cycle, still unanswered. Here, we employed high-resolution point dendrometers, sap flow sensors, and developed theory and statistical approaches, to devise a novel method separating irreversible radial growth from elastic tension-driven and elastic osmotically driven changes in bark water content. We tested this method using data from five case study species. Experimental manipulations, namely a field irrigation experiment on Scots pine and a stem girdling experiment on red forest gum trees, were used to validate the theory. Time courses of stem radial growth following irrigation and stem girdling were consistent with a-priori predictions. Patterns of stem radial growth varied across case studies, with growth occurring during the day and/or night, consistent with the available literature. Importantly, our approach provides a valuable alternative to existing methods, as it can be approximated by a simple empirical interpolation routine that derives irreversible radial growth using standard regression techniques. In conclusion, our novel method provides an improved understanding of the relative source–sink carbon dynamics of tree stems at a sub-daily time scale.
PROPERTIES OF SATELLITE GALAXIES IN THE SDSS PHOTOMETRIC SURVEY: LUMINOSITIES, COLORS, AND PROJECTED NUMBER DENSITY PROFILES
We analyze photometric data in the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7) to infer statistical properties of faint satellites associated with isolated bright galaxies (M{sub r} < -20.5) in the redshift range 0.03 < z < 0.1. The mean projected radial number density profile shows an excess of companions in the photometric sample around the primaries, with approximately a power-law shape that extends up to {approx_equal} 700 kpc. Given this overdensity signal, a suitable background subtraction method is used to study the statistical properties of the population of bound satellites, down to magnitude M{sub r} = -14.5, in the projected radial distance range 100 < r{sub p} /kpc < 3(R{sub vir}). The maximum projected distance corresponds to the range 470-660 kpc for the different samples. We have also considered a color cut consistent with the observed colors of spectroscopic satellites in nearby galaxies so that distant redshifted galaxies do not dominate the statistics. We have tested the implementation of this background subtraction procedure using a mock catalog derived from the Millennium simulation semianalytic galaxy catalog based on a {Lambda} cold dark matter model. We find that the method is effective in reproducing the true projected radial satellite number density profile and luminosity distributions, providing confidence in the results derived from SDSS data. We find that the spatial extent of satellite systems is larger for bright, red primaries. Also, we find a larger spatial distribution of blue satellites. For the different samples analyzed, we derive the average number of satellites and their luminosity distributions down to M{sub r} = -14.5. The mean number of satellites depends very strongly on host luminosity. Bright primaries (M{sub r} < -21.5) host on average {approx}6 satellites with M{sub r} < -14.5. This number is reduced for primaries with lower luminosities (-21.5 < M{sub r} < -20.5) which have less than one satellite per host. We provide Schechter function fits to the luminosity distributions of satellite galaxies where the resulting faint-end slopes equal to 1.3 {+-} 0.2, consistent with the universal value. This shows that satellites of bright primaries lack an excess population of faint objects, in agreement with the results in the Milky Way and nearby galaxies.
The good, the bad, and the ugly: Data-driven load profile discord identification in a large building portfolio
Reducing the overall energy consumption and associated greenhouse gas emissions in the building sector is essential for meeting our future sustainability goals. Recently, smart energy metering facilities have been deployed to enable monitoring of energy consumption data with hourly or subhourly temporal resolution. This unprecedented data collection has created various opportunities for advanced data analytics involving load profiles (e.g., building energy benchmarking programs, building-to-grid integration, and calibration of urban-scale energy models). These applications often need preprocessing steps to detect daily load profile discords, such as: 1) outliers due to system malfunctions (the bad) and 2) irregular energy consumption patterns, such as those resulting from holidays (the ugly) compared to normal consumption patterns (the good). However, current preprocessing methods predominantly focus on filtering using statistical threshold values, which fail to capture the contextual discords of daily profiles. In addition, discord detection algorithms in building research are often aimed at finding individual building-level discords, which are not suitable at a large scale. Thus, here, we develop a method for automated load profile discord identification (ALDI) in a large portfolio of buildings (more than 100 buildings). Specifically, ALDI 1) uses the matrix profile (MP) method to quantify the similarities of daily subsequences in time series meter data, 2) compares daily MP values with typical-day MP distributions using the Kolmogorov-Smirnov test, and 3) identifies daily load profile discords in a large building portfolio. We evaluate ALDI using the metering data of both an academic campus and a residential neighborhood. Our results demonstrate that ALDI efficiently discovers measurement errors by system malfunctions and low energy consumption days in the academic campus portfolio, and it detects unique load shape patterns likely driven by occupant behavior and extreme weather conditions in the residential neighborhood.
Photometric redshift estimation with convolutional neural networks and galaxy images: Case study of resolving biases in data-driven methods
Deep-learning models have been increasingly exploited in astrophysical studies, but these data-driven algorithms are prone to producing biased outputs that are detrimental for subsequent analyses. In this work, we investigate two main forms of biases: class-dependent residuals, and mode collapse. We do this in a case study, in which we estimate photometric redshift as a classification problem using convolutional neural networks (CNNs) trained with galaxy images and associated spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multichannel outputs, balancing the training data, and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshift or photometric redshift, and the biases with respect to these two definitions are incompatible and should be treated individually. We suggest that a prerequisite for resolving biases in photometric space is resolving biases in spectroscopic space. Experiments show that our methods can better control biases than benchmark methods, and they are robust in various implementing and training conditions with high-quality data. Our methods hold promises for future cosmological surveys that require a good constraint of biases, and they may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance tradeoff and the requirement of sufficient statistics suggest that we need better methods and optimized data usage strategies.
3D Reconstruction of Carbon Nanotube Composite Microstructure Using Correlation Functions
Reconstruction of simulated microstructure from statistical microstructure descriptors attracts strong research interest due to its importance in materials design. A new methodology is presented in this paper to reconstruct robust microstructure with large number of representative volume elements which may acts as a stable input for deterministic method to simulate performance and effective properties. It is applied in carbon nanotube composite to demonstrate the capability of this method to generate robust microstructure while incorporating more statistical information on geometry, shape, anisotropy and spatial arrangement. Not only one point based statistical information, such as size, volume fraction, is taken into consideration, but correlation function is incorporated to cover information from geometry, shape and spatial correlation. Monte Carlo method was applied in reconstruction. Instead of using discrete image matrix, the information of geometric distribution of the nanotube composite is stored with the information of location of nanotubes. In this way, robust micrographs with large number of representative volume elements were generated for the future evaluation using finite element methods.