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At least 19 records

Ab initio-informed maximum entropy modeling of rovibrational relaxation and state-specific dissociation with application to the O{sub 2} + O system

Quasi-classical trajectory (QCT) calculations are used to study state-specific ro-vibrational energy exchange and dissociation in the O{sub 2} + O system. Atom-diatom collisions with energy between 0.1 and 20 eV are calculated with a double many body expansion potential energy surface by Varandas and Pais [Mol. Phys. 65, 843 (1988)]. Inelastic collisions favor mono-quantum vibrational transitions at translational energies above 1.3 eV although multi-quantum transitions are also important. Post-collision vibrational favoring decreases first exponentially and then linearly as Δv increases. Vibrationally elastic collisions (Δv = 0) favor small ΔJ transitions while vibrationally inelastic collisions have equilibrium post-collision rotational distributions. Dissociation exhibits both vibrational and rotational favoring. New vibrational-translational (VT), vibrational-rotational-translational (VRT) energy exchange, and dissociation models are developed based on QCT observations and maximum entropy considerations. Full set of parameters for state-to-state modeling of oxygen is presented. The VT energy exchange model describes 22 000 state-to-state vibrational cross sections using 11 parameters and reproduces vibrational relaxation rates within 30% in the 2500–20 000 K temperature range. The VRT model captures 80 × 10{sup 6} state-to-state ro-vibrational cross sections using 19 parameters and reproduces vibrational relaxation rates within 60% in the 5000–15 000 K temperature range. The developed dissociation model reproduces state-specific and equilibrium dissociation rates within 25% using just 48 parameters. The maximum entropy framework makes it feasible to upscale ab initio simulation to full nonequilibrium flow calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Maximum entropy modeling to identify physical drivers of shallow snowpack heterogeneity using unpiloted aerial system (UAS) lidar

Understanding the spatial variability of the snowpack is valuable for hydrologists and ecologists seeking to predict hydrological processes in a cold region. Snow distribution is a function of interactions among static variables, such as terrain, vegetation, and soil properties, and dynamic meteorological variables, such as solar radiation, wind speed and direction, and soil moisture. However, identifying the dominant physical drivers responsible for spatial patterns of the snowpack, particularly for ephemeral, shallow snowpacks, has been challenging due to the lack of the high-resolution snowpack and physical variables with high vertical accuracy as well as inherent limitations in traditional approaches. This study uses an Unpiloted Aerial System (UAS) lidar-based snow depth and static variables (1-m spatial resolution) to analyze field-scale spatial structures of snow depth and apply the Maximum Entropy (MaxEnt) model to identify primary controls over open terrain and forests at the University of New Hampshire Thompson Farm Research Observatory, New Hampshire, United States. We found that, among nine topographic and soil variables, plant functional type and terrain roughness contribute up to 80% and 76% of relative importance in the MaxEnt framework to predict locations of deeper or shallower snowpacks, respectively, across a mixed temperate forested and field landscape. Soil variables, such as organic matter and saturated hydraulic conductivity, were also important controls (up to 70% and 81%) on snow depth spatial variations for both open and forested landscapes suggesting spatial variations in soil variables under snow can control thermal transfer among soil, snowpack, and surface-atmosphere. This work contributes to improving land surface and snow models by informing parameterization of the sub-grid scale snow depths, down-scaling remotely sensed snow products, and understanding field scale snow states.

Eunsang Cho↗

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

Entropy↗

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗

Maximum entropy models of ecosystem functioning

Using organism-level traits to deduce community-level relationships is a fundamental problem in theoretical ecology. This problem parallels the physical one of using particle properties to deduce macroscopic thermodynamic laws, which was successfully achieved with the development of statistical physics. Drawing on this parallel, theoretical ecologists from Lotka onwards have attempted to construct statistical mechanistic theories of ecosystem functioning. Jaynes’ broader interpretation of statistical mechanics, which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here because the classical foundations of statistical physics do not have clear ecological analogues (e.g. phase space, dynamical invariants). However, models based on the information theoretic interpretation of MaxEnt are difficult to interpret ecologically. Here I give a broad discussion of statistical mechanical models of ecosystem functioning and the application of MaxEnt in these models. Emphasising the sample frequency interpretation of MaxEnt, I show that MaxEnt can be used to construct models of ecosystem functioning which are statistical mechanical in the traditional sense using a savanna plant ecology model as an example.

54 ENVIRONMENTAL SCIENCES↗

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗

Reconstruction of Electron and Ion Distribution Functions in a Magnetotail Reconnection Diffusion Region

In the diffusion region of magnetotail reconnection, particle distributions are highly structured, exhibiting triangular shapes and multiple striations that deviate dramatically from the Maxwellian distribution. Fully kinetic simulations have been demonstrated to be capable of producing the essential structures of the observed distribution functions, yet are computationally not feasible for 3D global simulations. The fluid models used for large-scale simulations, on the other hand, do not have the kinetic physics necessary for describing reconnection accurately. Our study aims to bridge fully kinetic and fluid simulations by quantifying the information required to capture the non-Maxwellian features in the distributions underlying the closures used in the fluid code. Here, we compare the results of fully kinetic simulations with observed electron velocity distributions in a magnetotail reconnection diffusion region and use the maximum entropy model to reconstruct electron and ion distributions using various numbers of moments obtained from the simulation. Our results indicate that using only local moments, the maximum entropy model can reproduce many of the features of the distributions: (1) the electron outflow distribution with a tilted triangular structure is reproduced with 21 or more moments in agreement with Ng et al. and (2) counterstreaming distributions can be captured with the 35-moment model when the separation in velocity space between the populations is large.

58 GEOSCIENCES↗

Automatic Labeling for Entity Extraction in Cyber Security

Timely analysis of cyber-security information necessitates automated information extraction from unstructured text. While state-of-the-art extraction methods produce extremely accurate results, they require ample training data, which is generally unavailable for specialized applications, such as detecting security related entities; moreover, manual annotation of corpora is very costly and often not a viable solution. In response, we develop a very precise method to automatically label text from several data sources by leveraging related, domain-specific, structured data and provide public access to a corpus annotated with cyber-security entities. Next, we implement a Maximum Entropy Model trained with the average perceptron on a portion of our corpus (~750,000 words) and achieve near perfect precision, recall, and accuracy, with training times under 17 seconds.

Automatic Labeling↗

Does the air pollution model influence the evidence of socio-economic disparities in exposure and susceptibility?

Highlights: • Daily exposure to ozone may vary across air pollution models, considerably. • The exposure model influenced disparity of exposure across socio-economic strata. • The air pollution model does not affect disparity of susceptibility. • Multiple air pollution models should be used to assess socio-economic disparities. Studies assessing socio-economic disparities in air pollution exposure and susceptibility are usually based on a single air pollution model. A time stratified case-crossover study was designed to assess the impact of the type of model on differential exposure and on the differential susceptibility in the relationship between ozone exposure and daily mortality by socio-economic strata (SES) in Montreal. Non-accidental deaths along with deaths from cardiovascular and respiratory causes on the island of Montreal for the period 1991–2002 were included as cases. Daily ozone concentration estimates at partictaipants’ residence were obtained from the five following air pollution models: Average value (AV), Nearest station model (NS), Inverse-distance weighting interpolation (IDW), Land-use regression model with back-extrapolation (LUR-BE) and Bayesian maximum entropy model combined with a land-use regression (BME-LUR). The prevalence of a low household income (< 20,000/year) was used as socio-economic variable, divided into two categories as a proxy for deprivation. Multivariable conditional logistic regressions were used considering 3-day average concentrations. Multiplicative and additive interactions (using Relative Excess Risk due to Interaction) as well as Cochran's tests were calculated and results were compared across the different air pollution models. Heterogeneity of susceptibility and exposure according to socio-economic status (SES) were found. Ratio of exposure across SES groups means ranged from 0.75 [0.74–0.76] to 1.01 [1.00–1.02], respectively for the LUR-BE and the BME-LUR models. Ratio of mortality odds ratios ranged from 1.01 [0.96–1.05] to 1.02 [0.97–1.08], respectively for the IDW and LUR-BE models. Cochran's test of heterogeneity between the air pollution models showed important heterogeneity regarding the differential exposure by SES, but the air pollution model was not found to influence heterogeneity regarding the differential susceptibility. The study showed air pollution models can influence the assessment of disparities in exposure according to SES in Montreal but not that of disparities in susceptibility.

54 ENVIRONMENTAL SCIENCES↗

Crystallization Mechanism in Spark Plasma Sintered Bulk Metallic Glass Analyzed using Small Angle Neutron Scattering

Understanding the thermal stability of metallic glasses is critical to determining their safe temperatures of service. In this paper, the crystallization mechanism in spark plasma sintered Fe 48 Cr 15 Mo 14 Y 2 C15B6 metallic glass is established by analyzing the crystal size distribution using x-ray diffraction, transmission electron microscopy and in-situ small angle neutron scattering. Isothermal annealing at 700 °C and 725 °C for 100 min resulted in the formation of (Fe,Cr) 23 C 6 crystals, measured from transmission electron micrographs, to be from 10 to 30 nm. The small angle neutron scattering intensity measured in-situ, over a Q-range of 0.02 to 0.3 Å -1 , during isothermal annealing of the sintered samples, confirmed the presence of (Fe,Cr) 23 C 6 crystals. The measured scattering intensity, fitted by the maximum entropy model, over the Q-range of 0.02 to 0.06 Å -1 , revealed that the crystals had radii ranging from 3 to 18 nm. The total volume fraction of crystals were estimated to be 0.13 and 0.22 upon isothermal annealing at 700 °C and 725 °C for 100 min respectively. The mechanism of crystallization in this spark plasma sintered iron based metallic glass was established to be from pre-existing nuclei as confirmed by Avrami exponents of 0.25 ± 0.01 and 0.39 ± 0.01 at the aforesaid temperatures.

42 ENGINEERING↗

Characterization of Root Zone Soil Moisture and Herpetofaunal Biodiversity in the Southern Great Plains

(1) Goal: The scientific objective to the proposed research is to develop a proto-type downscaled (<1 km) version of the root-zone soil moisture product called SoilMERGE or SMERGE. This objective is linked as root zone soil moisture is a critical climate variable that has a more direct influence on plant growth than precipitation. Therefore, the developed downscaled version of SMERGE can be used as input into biodiversity informatic techniques (i.e., maximum entropy modeling) Development of downscaled SMERGE will be facilitated by Department of Energy (DOE) resources specifically data from the DOE Atmospheric Radiation Measurement (ARM) facility and modeling platforms such as the Energy Exascale Earth System Model (E3SM).

54 ENVIRONMENTAL SCIENCES↗

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy Data Fusion to Map Global Surface Ozone Concentration and Associated Uncertainty

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R 2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m −3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Ozone↗

Bounding Species Distribution Models

Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].

Stohlgren, Thomas J.↗