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At least 307 records · Page 17

Differential credibility assessment for statistical downscaling

Climate science is increasingly using (i) ensembles of climate projections from multiple models derived using different assumptions and/or scenarios and (ii) process-oriented diagnostics of model fidelity. Efforts to assign differential credibility to projections and/or models are also rapidly advancing. A framework to quantify and depict the credibility of statistically downscaled model output is presented and demonstrated. Here, the approach employs transfer functions in the form of robust and resilient generalized linear models applied to downscale daily minimum and maximum temperature anomalies at 10 locations using predictors drawn from ERA-Interim reanalysis and two global climate models (GCM; GFDL-ESM2M and MPI-ESM-LR). The downscaled time series are used to derive several impact relevant CLIMDEX temperature indices that are assigned credibility based on (1) the reproduction of relevant large-scale predictors by the GCMs (i.e. fraction of regression beta-weights derived from predictors that are well-reproduced) and (2) the degree of variance in the observations reproduced in the downscaled series following application of a new variance inflation technique. Credibility of the downscaled predictands varies across locations, between the two GCM and is generally higher for minimum temperature than maximum temperature. The differential credibility assessment framework demonstrated here is easy to use and flexible. It can be applied as is to inform decision makers regarding projection confidence, and/or extended to include other components of the transfer functions, and/or used to weight members of a statistically downscaled ensemble.

54 ENVIRONMENTAL SCIENCES↗

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Wolpert, David H.↗

Long-Term Statistical Process Monitoring of an Ultrafiltration Water Treatment Process

As water treatment technology has improved, the amount of available process data has substantially increased, making real-time, data-driven fault detection a reality. One shortcoming of the fault detection literature is that methods are usually evaluated by comparing their performance on hand-picked, short-term case studies, which yields no insight into long-term performance. In this work, we first evaluate multiple statistical and machine learning approaches for detrending process data. Then, we evaluate the performance of a PCA-based fault detection approach, applied to the detrended data, to monitor influent water quality, filtrate quality, and membrane fouling of an ultrafiltration membrane system for indirect potable reuse. Based on two short case studies, the adaptive lasso detrending method is selected, and the performance of the multivariate approach is evaluated over more than a year. The method is tested for different sets of three critical tuning parameters, and we find that for long-term, autonomous monitoring to be successful, these parameters should be carefully evaluated. However, in comparison with industry standards of simpler, univariate monitoring or daily pressure decay tests, multivariate monitoring produces substantial benefits in long-term testing.

ammonia↗

Experimental investigation of probabilistic failure of SiC/SiC composite tubes under multiaxial loading

This paper presents an experimental investigation of the failure behavior of SiC fiber-reinforced SiC matrix (SiC/SiC) composite tubes under multiaxial loading. A new testing apparatus is designed to independently apply axial stress and internal pressure to SiC/SiC tubes. Acoustic emission (AE) is used to monitor the damage growth in the specimen. Based on the measured stress–strain response, a strain-based criterion is proposed to determine the proportional limit stress (PLS). The proposed strain-based criterion is compared with the PLS determined by the AE measurement. The PLS is determined for different loading ratios to form a multiaxial failure surface. By testing multiple replicates, the statistical variations of the PLS are determined. In conclusion, based on the experimental results, a mathematical model is developed to characterize the probability distribution of the PLS of SiC/SiC composites under multiaxial loading.

36 MATERIALS SCIENCE↗

Statistical prediction of dynamic distortion of inlet flow using minimum dynamic measurement. An application to the Melick statistical method and inlet flow dynamic distortion prediction without RMS measurements

The Melick method of inlet flow dynamic distortion prediction by statistical means is outlined. A hypothetic vortex model is used as the basis for the mathematical formulations. The main variables are identified by matching the theoretical total pressure rms ratio with the measured total pressure rms ratio. Data comparisons, using the HiMAT inlet test data set, indicate satisfactory prediction of the dynamic peak distortion for cases with boundary layer control device vortex generators. A method for the dynamic probe selection was developed. Validity of the probe selection criteria is demonstrated by comparing the reduced-probe predictions with the 40-probe predictions. It is indicated that the the number of dynamic probes can be reduced to as few as two and still retain good accuracy.

Schweikhard, W. G.↗

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

Yijun, Huang↗

Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds

Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.

97 MATHEMATICS AND COMPUTING↗

Probabilistic measures for biological adaptation and resilience

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

60 APPLIED LIFE SCIENCES↗

MIDAS: Modeling Individual Differences using Advanced Statistics

This research explores novel methods for extracting relevant information from EEG data to characterize individual differences in cognitive processing. Our approach combines expertise in machine learning, statistics, and cognitive science, advancing the state-of-the art in all three domains. Specifically, by using cognitive science expertise to interpret results and inform algorithm development, we have developed a generalizable and interpretable machine learning method that can accurately predict individual differences in cognition. The output of the machine learning method revealed surprising features of the EEG data that, when interpreted by the cognitive science experts, provided novel insights to the underlying cognitive task. Additionally, the outputs of the statistical methods show promise as a principled approach to quickly find regions within the EEG data where individual differences lie, thereby supporting cognitive science analysis and informing machine learning models. This work lays methodological ground work for applying the large body of cognitive science literature on individual differences to high consequence mission applications.

97 MATHEMATICS AND COMPUTING↗

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗

Using data-science approaches to unravel insights for enhanced transport of lithium ions in single-ion conducting polymer electrolyte

Solid polymer electrolytes have yet to achieve the an ionic conductivity > 1 mS/cm at room temperature for realistic applications. This target implies the need to reduce the effective energy barriers of ion transport in polymer electrolytes to around 20 kJ/mol. In this work, we combine information extracted from existing experimental results with theoretical calculations to provide insights into ion transport in single-ion conductors (SICs) with a focus on lithium ion SICs. Through the analysis of temperature-dependent ionic conductivity data obtained from the literature, we evaluate different methods of extracting energy barriers for lithium transport. The traditional Arrhenius fit to the temperature-dependent ionic conductivity data indicates that the Meyer-Neldel rule holds for SICs. However, the values of the fitting parameters remain unphysical. Our modified approach based on recent work (Macromolecules, 56, 15, 6051(2023)), which incorporates a fixed pre-exponential factor, reveals that the energy barriers exhibit temperature dependence over a wide range of temperatures. Using this approach, we identify a series of anions leading to the energy barriers less than 30 kJ/mol, which include trifluoromethane sulfonimide (TFSI), fluoromethane sulfonimide (FSI), and boron-based organic anions. In our efforts to design the next generation of anions, which can exhibit the energy barriers less than 20 kJ/mol, we focused on boron-containing SICs, and performed density functional theory (DFT) based calculations to connect the chemical structures via the binding energy of cation (lithium)-anion pairs with the experimentally derived effective energy barriers for ion transport. Not only have we identified a correlation between the binding energy and the energy barriers, but we also propose a strategy to design new boron-based anions by using the correlation. This combined approach involving experiments and theoretical calculations is capable of facilitating the identification of promising new anions, which can exhibit ionic conductivity $> 1$ mS/cm near room temperature, thereby expediting the development of novel superionic single-ion conducting polymer electrolytes. The published datasets include all the temperature-dependent ionic conductivity collected from the literature with literature DOIs, DFT calculated binding energies, and python scripts to analyze data, construct statistical models, and generate plots.

36 MATERIALS SCIENCE↗

Comparative Study of Differentially Private Data Synthesis Methods

When sharing data among researchers or releasing data for public use, there is a risk of exposing sensitive information of individuals in the data set. Data synthesis is a statistical disclosure limitation technique for releasing synthetic data sets with pseudo individual records. Traditional data synthesis techniques often rely on strong assumptions of a data intruder’s behaviors and background knowledge to assess disclosure risk. Differential privacy (DP) formulates a theoretical approach for a strong and robust privacy guarantee in data release without having to model intruders’ behaviors. Efforts have been made aiming to incorporate the DP concept in the data synthesis process. Here, we examine current DIfferentially Private Data Synthesis (DIPS) techniques for releasing individual-level surrogate data for the original data, compare the techniques conceptually and evaluate the statistical utility and inferential properties of the synthetic data via each DIPS technique through extensive simulation studies. Our work sheds light on the practical feasibility and utility of the various DIPS approaches, and suggests future research directions for DIPS.

97 MATHEMATICS AND COMPUTING↗

Management of SSME hardware life utilization

Statistical and probabilistic reliability methodologies were developed for the determination of hardware life limits for the Space Shuttle Main Engine (SSME). Both methodologies require that a mathematical reliability model of the engine (system) performance be developed as a function of the reliabilities of the components and parts. The system reliability model should be developed from the Failute Modes and Effects Analysis/Critical Items List. The statistical reliability methodology establishes hardware life limits directly from the failure distributions of the components and parts obtained from statistically-designed testing. The probabilistic reliability methodology establishes hardware life limits from a decision analysis methodology which incorporates the component/part reliabilities obtained from a probabilistic structural analysis, a calibrated maintenance program, inspection techniques, and fabrication procedures. Probilistic structural analysis is recommended as a tool to prioritize upgrading of the components and parts. The Weibull probability distribution is presently being investigated by NASA/MSFC to characterize the failure distribution of the SSME hardware from a limited data base of failures.

Pauschke, J. M.↗

Federal Automotive Statistical Tool: FY 2022 Data Call Status & Review Tools [Slides]

This presentation presents an overview of current federal vehicle fleet current data collection efforts covering required information submissions about the motor vehicles, fueling centers, and electric vehicle supply equipment (EVSE) inventory through the Federal Automotive Statistical Tool (FAST). The presentation also provides an overview of the capabilities within FAST to assist federal agency users with reviewing and improving the quality of their fleet data submissions. This presentation is intended for delivery via WebEx at the November 9, 2022 meeting of the DOE-sponsored INTERFUEL working group. FAST is a web-based information management tool developed by INL and funded by GSA's Office of Government-wide Policy and DOE's Federal Energy Management Program.

33 ADVANCED PROPULSION SYSTEMS↗

Cryo-EM model validation recommendations based on outcomes of the 2019 EMDataResource challenge

This paper describes outcomes of the 2019 Cryo-EM Model Challenge. The goals were to (1) assess the quality of models that can be produced from cryogenic electron microscopy (cryo-EM) maps using current modeling software, (2) evaluate reproducibility of modeling results from different software developers and users and (3) compare performance of current metrics used for model evaluation, particularly Fit-to-Map metrics, with focus on near-atomic resolution. Our findings demonstrate the relatively high accuracy and reproducibility of cryo-EM models derived by 13 participating teams from four benchmark maps, including three forming a resolution series (1.8 to 3.1 Å). The results permit specific recommendations to be made about validating near-atomic cryo-EM structures both in the context of individual experiments and structure data archives such as the Protein Data Bank. We recommend the adoption of multiple scoring parameters to provide full and objective annotation and assessment of the model, reflective of the observed cryo-EM map density.

59 BASIC BIOLOGICAL SCIENCES↗

Low-temperature breakdown of many-body perturbation theory for thermodynamics

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as T → 0. Contrary to earlier suggestions of renormalizability by the chemical potential μ, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e –E/k e T at T = 0, also plaguing the canonical ensemble, which does not involve chemical potential. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

74 ATOMIC AND MOLECULAR PHYSICS↗

Neural units with time-dependent functionality

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of n oscillators, observed at different times, can perform an arbitrary number of analog-to-n-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

97 MATHEMATICS AND COMPUTING↗

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗