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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Tomography and weak lensing statistics

We provide generic predictions for the lower order cumulants of weak lensing maps, and their correlators for tomographic bins as well as in three dimensions (3D). Using small-angle approximation, we derive the corresponding one- and two-point probability distribution function for the tomographic maps from different bins and for 3D convergence maps. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast that involves hierarchal ansatz and lognormal distribution. We study the dependence of our results on cosmological parameters and source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our results. We also show how topological properties of convergence maps can be quantified using our results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Distinguishing dark matter from unresolved point sources in the Inner Galaxy with photon statistics

Data from the Fermi Large Area Telescope suggests that there is an extended excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential astrophysical sources that contribute to this excess is an important step in verifying whether the signal originates from annihilating dark matter. In this paper, we focus on the potential contribution of unresolved point sources, such as millisecond pulsars (MSPs). We propose that the statistics of the photons—in particular, the flux probability density function (PDF) of the photon counts below the point-source detection threshold—can potentially distinguish between the dark-matter and point-source interpretations. We calculate the flux PDF via the method of generating functions for these two models of the excess. Working in the framework of Bayesian model comparison, we then demonstrate that the flux PDF can potentially provide evidence for an unresolved MSP-like point-source population.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Vacuum statistics and stability in axionic landscapes

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. On the other hand, the probability P(B) for a vacuum to have a tunneling action B greater than a given value declines as a slow power law in B. This is in sharp contrast with the studies of random quartic potentials, which found a fast exponential decline of P(B). Our results suggest that the total number of relatively stable vacua (say, with B>100) grows exponentially with the number of fields N and can get extremely large for N∼> 100. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Statistics of the charge spectrum of photo-multipliers and methods for absolute calibration

We derive the full expression for the shape of the charge spectrum that results from the illumination of a photo-multiplier tube. The derivation is for low intensity illumination with constant gain, a common condition for most nuclear and particle physics applications. Under these conditions, it is shown that an analytic expression can be formulated that describes details of the spectrum including the pedestal and dark noise with excellent fidelity to allow statistical fits to data. The derivation and full formula using either Gaussian or Poisson models for gain, and its limiting forms under various simplifying assumptions are presented with strategies on their use. The analytic description can be used to formulate data acquisition strategies to perform precise absolute calibration of photo-multipliers, the digitizers, and the data acquisition system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Self-calibrating the look-elsewhere effect: fast evaluation of the statistical significance using peak heights

In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. Here, this paper introduces a method to calibrate the false alarm probability (FAP), or p-value, for a given dataset by considering the heights of the highest peaks in the likelihood. Specifically, we derive an equation relating the global p-value to the rank and height of local maxima. In the simplest form of self-calibration, the look-elsewhere-corrected $\chi^2$ of a physical peak is approximated by the $\chi^2$ of the peak minus the $\chi^2$ of the highest noise-induced peak, with accuracy improved by considering lower peaks. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Statistical theory of deformation distributions in nuclear spectra

The dependence of the nuclear level density on intrinsic deformation is an important input to dynamical nuclear processes such as fission. The auxiliary-field Monte Carlo (AFMC) method is a powerful method for computing state densities. However, the statistical distribution of intrinsic shapes is not readily accessible due to the formulation of the AFMC method in a spherical configuration-interaction shell-model approach. Instead, the theory of deformation has largely relied on a mean-field approximation which breaks rotational symmetry. We show here how the distributions of the intrinsic quadrupole deformation parameters can be calculated within the AFMC method and present results for a chain of even-mass samarium nuclei ( 148 Sm, 150 Sm, 152 Sm, 154 Sm) which includes spherical, transitional, and strongly deformed isotopes. The method relies on a Landau-like expansion of the Helmholtz free energy in invariant polynomials of the quadrupole tensor. Here we find that an expansion to fourth order provides an excellent description of the AFMC results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Solidarity of signal of measures for the liquid-gas phase transition in the statistical multifragmentation model

A systematic study of system size, N / Z asymmetry, and fragmenting volume effects as well as the Coulomb effect on experimental measures for the nuclear liquid-gas phase transition and the mechanism of phase transition are carried out in the framework of the statistical multifragmentation model (SMM). The measures examined here are the caloric curve, the specific heat capacity ( C v ), the multiplicity derivative (dM / dT), the moment parameters (M2 and γ2), the fluctuation of maximum fragment charge number (NVZ), the Fisher exponent (τ), and the Zipf's law parameter (ξ). A signal for the first-order phase transition for all the measures is observed. A stronger signal is observed in the system with smaller sizes or with more neutron rich or in smaller fragmenting volumes for the caloric curve, Cv, and dM/dT. The phase-transition temperatures are independent of the system size, N / Z asymmetry, fragmenting volume, and Coulomb force, which indicates these measures give a solid signal for the liquid-gas phase transition in SMM. On the other hand, the phase transition temperature and its behavior of the others slightly depend on the size, the N / Z asymmetry and the volume of the system. A negative heat capacity is observed for systems with A s ≥ 100 without the Coulomb force but disappears with the Coulomb. An instructive picture is given in the charge distributions for the observed first-order phase transition.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Many-Body Level Statistics of Single-Particle Quantum Chaos

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q = 2 complex Sachdev-Ye-Kitaev model)—a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Thermodynamically informed priors for uncertainty propagation in first-principles statistical mechanics

Here, this work demonstrates how first-principles statistical mechanics approaches within a Bayesian framework can quantify and propagate uncertainties to downstream thermodynamic calculations. To address the issue of Bayesian prior selection, knowledge of 0 K ground states in the material system of interest is incorporated into the prior. The effectiveness of this framework is shown by creating a phase diagram for the fcc zirconium nitride system, including confidence intervals on order-disorder transition temperatures.

Bayesian methods↗
DOE OSTI2025

Temporal Forecasting of Distributed Temperature Sensing in a Thermal Hydraulic System With Machine Learning and Statistical Models

We benchmark performance of long-short term memory (LSTM) network machine learning model and autoregressive integrated moving average (ARIMA) statistical model in temporal forecasting of distributed temperature sensing (DTS). Data in this study consists of fluid temperature transient measured with two co-located Rayleigh scattering fiber optic sensors (FOS) in a forced convection mixing zone of a thermal tee. We treat each gauge of a FOS as an independent temperature sensor. We first study prediction of DTS time series using Vanilla LSTM and ARIMA models trained on prior history of the same FOS that is used for testing. The results yield maximum absolute percentage error (MaxAPE) and root mean squared percentage error (RMSPE) of 1.58% and 0.06% for ARIMA, and 3.14% and 0.44% for LSTM, respectively. Next, we investigate zero-shot forecasting (ZSF) with LSTM and ARIMA trained on history of the co-located FOS only, which is advantageous when limited training data is available. The ZSF MaxAPE and RMSPE values for ARIMA are comparable to those of the Vanilla use case, while the error values for LSTM increase. We show that in ZSF, performance of LSTM network can be improved by training on most correlated gauges between the two FOS, which are identified by calculating the Pearson correlation coefficient. The improved ZSF MaxAPE and RMSPE for LSTM are 4.4% and 0.33%, respectively. Performance of ZSF LSTM can be further enhanced through transfer learning (TL), where LSTM is re-trained on a subset of the FOS that is the target of forecasting. We show that LSTM pre-trained on correlated dataset and re-trained on 30% of testing target dataset achieves MaxAPE and RMSPE values of 2.32% and 0.28%, respectively.

ARIMA↗
DOE OSTI2017

Representative Day Selection Using Statistical Bootstrapping for Accelerating Annual Distribution Simulations

Capturing technical and economic impacts of solar photovoltaics (PV) and other distributed energy resources (DERs) on electric distribution systems can require high-time resolution (e.g. 1 minute), long-duration (e.g. 1 year) simulations. However, such simulations can be computationally prohibitive, particularly when including complex control schemes in quasi-steady-state time series (QSTS) simulation. Various approaches have been used in the literature to down select representative time segments (e.g. days), but typically these are best suited for lower time resolutions or consider only a single data stream (e.g. PV production) for selection. We present a statistical approach that combines stratified sampling and bootstrapping to select representative days while also providing a simple method to reassemble annual results. We describe the approach in the context of a recent study with a utility partner. This approach enables much faster QSTS analysis by simulating only a subset of days, while maintaining accurate annual estimates.

14 SOLAR ENERGY↗
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems: Experimental assessment of noise performance

Purpose: To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system. Methods: Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods. Results: (1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a “redder” NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose){sup −β} with the component β ≈ 0.25, which violated the classical σ ∝ (dose){sup −0.5} power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2. Conclusions: The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance

Purpose: Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks. Methods: The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDI{sub vol} =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d′. Results: (1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels. Conclusions: Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-FG-CAMPUS-JeP3-01: A Statistical Model for Analyzing the Rotational Error of Single Iso-Center Technique

Purpose: To develop a generalized statistical model that incorporates the treatment uncertainty from the rotational error of single iso-center technique, and calculate the additional PTV (planning target volume) margin required to compensate for this error. Methods: The random vectors for setup and additional rotation errors in the three-dimensional (3D) patient coordinate system were assumed to follow the 3D independent normal distribution with zero mean, and standard deviations σx, σy, σz, for setup error and a uniform σR for rotational error. Both random vectors were summed, normalized and transformed to the spherical coordinates to derive the chi distribution with 3 degrees of freedom for the radical distance ρ. PTV margin was determined using the critical value of this distribution for 0.05 significant level so that 95% of the time the treatment target would be covered by ρ. The additional PTV margin required to compensate for the rotational error was calculated as a function of σx, σy, σz and σR. Results: The effect of the rotational error is more pronounced for treatments that requires high accuracy/precision like stereotactic radiosurgery (SRS) or stereotactic body radiotherapy (SBRT). With a uniform 2mm PTV margin (or σx =σy=σz=0.7mm), a σR=0.32mm will decrease the PTV coverage from 95% to 90% of the time, or an additional 0.2mm PTV margin is needed to prevent this loss of coverage. If we choose 0.2 mm as the threshold, any σR>0.3mm will lead to an additional PTV margin that cannot be ignored, and the maximal σR that can be ignored is 0.0064 rad (or 0.37°) for iso-to-target distance=5cm, or 0.0032 rad (or 0.18°) for iso-to-target distance=10cm. Conclusions: The rotational error cannot be ignored for high-accuracy/-precision treatments like SRS/SBRT, particularly when the distance between the iso-center and target is large.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

New method of automated statistical analysis of polymer-stabilized metal nanoparticles in electron microscopy images

The efficiency of the synthesis and application of metal/nonmetal particles several nanometers in size, prepared in solutions and stabilized with polymers, can be increased by applying a reliable statistical analysis and determining particle-size distributions for different systems. A new method for processing electron microscopy images of nanoparticles ≤10 nm in size and the program Analyzer of Nanoparticles designed for rapid recognition and measurements are presented. The program combines two approaches: threshold image processing for particle recognition and fitting the model of the particles with neighborhood background to the real experimental images.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics

We study the effect of anisotropy in elastic properties on the electron–phonon drag and thermoelectric phenomena in gapless semiconductors with degenerate charge-carrier statistics. It is shown that phonon focusing leads to a number of new effects in the drag thermopower at low temperatures, when diffusive phonon scattering from the boundaries is the predominant relaxation mechanism. We analyze the effect of phonon focusing on the dependences of the thermoelectromotive force (thermopower) in HgSe:Fe crystals on geometric parameters and the heat-flow directions relative to the crystal axes in the Knudsen regime of the phonon gas flow. The crystallographic directions that ensure the maximum and minimum values of the thermopower are determined and the role of quasi-longitudinal and quasi-transverse phonons in the drag thermopower in HgSe:Fe crystals at low temperatures is analyzed. It is shown that the main contribution to the drag thermopower comes from slow quasi-transverse phonons in the directions of focusing in long samples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

On a simple molecular–statistical model of a liquid-crystal suspension of anisometric particles

A molecular–statistical mean-field theory is constructed for suspensions of anisometric particles in nematic liquid crystals (NLCs). The spherical approximation, well known in the physics of ferromagnetic materials, is considered that allows one to obtain an analytic expression for the free energy and simple equations for the orientational state of a suspension that describe the temperature dependence of the order parameters of the suspension components. The transition temperature from ordered to isotropic state and the jumps in the order parameters at the phase-transition point are studied as a function of the anchoring energy of dispersed particles to the matrix, the concentration of the impurity phase, and the size of particles. The proposed approach allows one to generalize the model to the case of biaxial ordering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

A Quantum Random Number Generator Based on the 100-Mbit/s Poisson Photocount Statistics

A quantum random number generator is experimentally realized. The initial randomness source is a sequence of photocounts from quasi-single-photon radiation detected with a SiPM (Silicon Photo Multiplier) silicon avalanche detector array. The use of a SiPM provides a reliable control of the quantum nature of the Poisson photocount statistics. A special algorithm with nonexponential complexity allows one to extract from the Poisson process all the randomness contained in it, namely, a random uniform sequence of 0 and 1.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗