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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↗

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↗

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↗

Modeling of dissociation and energy transfer in shock-heated nitrogen flows

This work addresses the modeling of dissociation and energy transfer processes in shock heated nitrogen flows by means of the maximum entropy linear model and a newly proposed hybrid bin vibrational collisional model. Both models aim at overcoming two of the main limitations of the state of the art non-equilibrium models: (i) the assumption of equilibrium between rotational and translational energy modes of the molecules and (ii) the reliance on the quasi-steady-state distribution for the description of the population of the internal levels. The formulation of the coarse-grained models is based on grouping the energy levels into bins, where the population is assumed to follow a Maxwell-Boltzmann distribution at its own temperature. Different grouping strategies are investigated. Following the maximum entropy principle, the governing equations are obtained by taking the zeroth and first-order moments of the rovibrational master equations. The accuracy of the proposed models is tested against the rovibrational master equation solution for both flow quantities and population distributions. Calculations performed for free-stream velocities ranging from 5 km/s to 10 km/s demonstrate that dissociation can be accurately predicted by using only 2-3 bins. It is also shown that a multi-temperature approach leads to an under-prediction of dissociation, due to the inability of the former to account for the faster excitation of high-lying vibrational states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A MaxEnt Model for Mineral Prospectivity Mapping

Mineral prospectivity mapping is an important preliminary step for mineral resource exploration. It has been widely applied to distinguish areas of high potential to host mineral deposits and to minimize the financial risks associated with decision making in mineral industry. In the present study, a maximum entropy (MaxEnt) model was applied to investigate its potential for mineral prospectivity analysis. A case study from the Nanling tungsten polymetallic metallogenic belt, South China, was used to evaluate its performance. In order to deal with model over-fitting, varying levels of β j -regularization were set to determine suitable β value based on response curves and receiver operating characteristic (ROC) curves, as well as via visual inspections of prospectivity maps. The area under the ROC curve (AUC = 0.863) suggests good performance of the MaxEnt model under the condition of balancing model complexity and generality. The relative importance of ore-controlling factors and their relationships with known deposits were examined by jackknife analysis and response curves. Prediction–area (P–A) curves were used to determine threshold values for demarcating high probability of tungsten polymetallic deposit occurrence within small exploration area. The final predictive map showed that high favorability zones occupy 14.5% of the study area and contain 85.5% of the known tungsten polymetallic deposits. Our study suggests that the MaxEnt model can be efficiently used to integrate multisource geo-spatial information for mineral prospectivity analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spatial modeling of daily concentrations of ground-level ozone in Montreal, Canada: A comparison of geostatistical approaches

Highlights: • The KED model with road and vegetation density as covariates showed good performance for all six synoptic classes. • The model using KED demonstrated the best results (R{sup 2} = 0.92; RMSE = 3.14 ppb). • The model using OK demonstrated a R{sup 2} = 0.85 and RMSE = 4 ppb. • Our results showed that errors appear to be substantially reduced with the KED model. • When measurements at numerous monitoring stations in a region are available, it may be better to use KED. • The BME may be more useful for prediction when data is not available. Ground-level ozone (O{sub 3}) is a powerful oxidizing agent and a harmful pollutant affecting human health, forests and crops. Estimating O{sub 3} exposure is a challenge because it exhibits complex spatiotemporal patterns. The aim in this study was to provide high-resolution maps (100 × 100 m) of O{sub 3} for the metropolitan area of Montreal, Canada. We assessed the kriging with external drift (KED) model to estimate O{sub 3} concentration by synoptic weather classes for 2010. We compared these results with ordinary kriging (OK), and a simple average of 12 monitoring stations. We also compared the estimates obtained for the 2010 summer with those from a Bayesian maximum entropy (BME) model reported in the literature (Adam-Poupart et al., 2014). The KED model with road and vegetation density as covariates showed good performance for all six synoptic classes (daily R{sup 2} estimates ranging from 0.77 to 0.92 and RMSE from 2.79 to 3.37 ppb). For the summer of 2010, the model using KED demonstrated the best results (R{sup 2} = 0.92; RMSE = 3.14 ppb), followed by the OK model (R{sup 2} = 0.85, RMSE = 4 ppb). Our results showed that errors appear to be substantially reduced with the KED model. This may increase our capacity of linking O{sub 3} levels to health problems by means of improved assessments of ambient exposures. However, future work integrating the temporal dependency in the data is needed to not overstate the performance of the KED model.

54 ENVIRONMENTAL SCIENCES↗

Implications of Climate Change for Bird Conservation in the Southwestern U.S. under Three Alternative Futures

Future expected changes in climate and human activity threaten many riparian habitats, particularly in the southwestern U.S. Using Maximum Entropy (MaxEnt3.3.3) modeling, we characterized habitat relationships and generated spatial predictions of habitat suitability for the Lucy’s warbler (Oreothlypis luciae), the Southwestern willow flycatcher (Empidonax traillii extimus) and the Western yellow-billed cuckoo (Coccyzus americanus). Our goal was to provide site- and species-specific information that can be used by managers to identify areas for habitat conservation and/or restoration along the Rio Grande in New Mexico. We created models of suitable habitat for each species based on collection and survey samples and climate, biophysical, and vegetation data. We projected habitat suitability under future climates by applying these models to conditions generated from three climate models for 2030, 2060 and 2090. By comparing current and future distributions, we identified how habitats are likely to change as a result of changing climate and the consequences of those changes for these bird species. We also examined whether land ownership of high value sites shifts under changing climate conditions. Habitat suitability models performed well. Biophysical characteristics were more important that climate conditions for predicting habitat suitability with distance to water being the single most important predictor. Climate, though less important, was still influential and led to declines of suitable habitat of more than 60% by 2090. For all species, suitable habitat tended to shrink over time within the study area leaving a few core areas of high importance. Overall, climate changes will increase habitat fragmentation and reduce breeding habitat patch size. The best strategy for conserving bird species within the Rio Grande will include measures to maintain and restore critical habitat refugia. This study provides an example of a presence-only habitat model that can be used to inform the management of species at intermediate scales.

54 ENVIRONMENTAL SCIENCES↗

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Integrating Maximum Entropy Production Theory and Machine Learning to Improve Global Evapotranspiration Modeling

Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding global water and energy cycles. However, current global ET estimations are not well constrained. This study introduces an integrated framework combining the Maximum Entropy Production (MEP) theory with Random Forest (RF) model to improve global ET estimation. Specifically, in contrast to direct ET estimation by the RF model, the integrated framework (MEP‐RF) trains to predict error of MEP‐simulated ET. MEP‐RF outperforms RF in spatiotemporal extrapolation. Attribution analysis with in situ observations reveals that the inputs of MEP are the most critical variables for the ET process, including net radiation, vegetated area, soil moisture, and surface temperature. We further drive MEP‐RF with global reanalysis and satellite data sets of these four inputs, yielding a global mean terrestrial ET of 548 mm/year, with 77% attributed to transpiration. The global ET increased at a rate of 0.85 mm/year per year during 2003–2021, primarily due to vegetation greening rather than rising temperature, while decreasing soil moisture led to decreasing regional ET. The integrated framework provides a novel approach for the estimation of global ET without the need for hard‐to‐obtain and thus uncertain inputs, such as wind speed, surface roughness, aerodynamic and canopy stomatal resistance. Therefore, MEP‐RF offers an independent method on existing global ET products. It represents a promising physically based approach that can be incorporated into Earth System Models to enhance water and energy cycle simulations.

54 ENVIRONMENTAL SCIENCES↗

Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ordinary differential equation (ODE) based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution; (2) the predicted metabolite concentrations are compared to those generally expected from experiments using a loss function from which post-translational regulation of enzymes is inferred; (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrations and reaction fluxes; and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1,6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.

Cannon, William R.↗

Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems

Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

97 MATHEMATICS AND COMPUTING↗