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A stochastic control model of the NASA/MSFC Ground Facility for Large Space Structures (LSS) control verification through Maximum Entropy (ME) principle adopted in Hyland's method was presented. Using ORACLS, a computer program was implemented for this purpose. Four models were then tested and the results presented.
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.
We have made deconvolved maps of M101 in each of the 4 IRAS bands using a new maximum-entropy based model for reconstructing distributions with correlated structure on multiple scales. This new deconvolution procedure, developed by Weir (1992, J.Opt.Soc.Am., submitted), is superior to other maximum entropy-based techniques for several reasons. For our purposes, an important advantage is that it has less artifacts and greatly reduced systematic biases compared with the 'HiRes' maps of M101 produced by Aumann, Fowler, and Melnyk (1990, AJ, 99, 1674), thus it is accurate enough to perform aperture photometry. The deconvolved maps have a maximum resolution of approximately 30 sec, sufficient to resolve the brightest HII complexes and much of the spiral structure. The new maps and our comparison of the far-infrared, gas, and optical distributions are being written up in Kenney, Weir & Scoville (1992, in preparation). The quality of the reconstructed far-infrared maps is good enough for us to carry out most of the analyses outlined in the original proposal. From a ratio of the 60 micron and 100 micron maps, we have found that the ultraluminous HII complexes in the outer galaxy have the hottest dust temperatures with T approximately 50-60 K, which is twice as hot as most of the disk. Their extraordinary luminosity in the far-infrared is due to a relatively small amount of dust being heated to high temperatures, rather than a large concentration of dust and gas. A map of the dust opacity at 60 microns shows good overall agreement with a map of cold gas (HI+H2), indicating that throughout most of the galaxy only approximately 20 percent of the dust is warm enough to be detected by IRAS. The ultraluminous HII complexes have a high luminosity-to-gas mass ratio, independent of whether the far-infrared or the H-alpha emission line is used to measure the luminosity, which implies that gas is being converted into high mass stars more rapidly in these complexes compared to other locations in the disk.
A stochastic structural control model is described. In contrast to the customary deterministic model, the stochastic minimum data/maximum entropy model directly incorporates the least possible a priori parameter information. The approach is to adopt this model as the basic design model, thus incorporating the effects of parameter uncertainty at a fundamental level, and design mean-square optimal controls (that is, choose the control law to minimize the average of a quadratic performance index over the parameter ensemble).
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.
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.
Estimates of ground-level ozone concentrations are necessary to determine the human health burden of ozone. To support the Global Burden of Disease Study, we produce yearly fine resolution global surface ozone estimates from 1990 to 2017 through a data fusion of observations and models. As ozone observations are sparse in many populated regions, we use a novel combination of the M3Fusion and Bayesian Maximum Entropy (BME) methods. With M3Fusion, we create a multi-model composite by bias-correcting and weighting nine global atmospheric chemistry models based on their ability to predict observations (8,834 sites globally)in each region and year. BME is then used to integrate observations, such that estimates match observations at each monitoring site with the observational influence decreasing smoothly across space and time until the output matches the multi-model composite. After estimating at 0.5° resolution using BME, we add fine spatial detail from an additional model, yielding estimates at 0.1° resolution. Observed ozone is predicted more accurately (R2=0.81 at test point, 0.63 at 0.1°,0.62 at 0.5°) than the multi-model mean (R2=0.28 at 0.5°). Global ozone exposure is estimated to be increasing, driven by highly populated regions of Asia and Africa, despite decreases in the United States and Russia.
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.
A family of self-consistent maximum entropy dynamical models is presented for the triaxial 'perfect ellipsoids'. These models are projected in different viewing geometries to explore the possible morphologies of the 2D radial-velocity fields of elliptical galaxies. It is found that, typically, about half the time an 'ordinary' velocity field is seen with a mixture of major- and minor-axis rotation. For other lines of sight, the velocity fields are more complicated, showing multiple peaks, steep gradients, strongly twisted contours, or kinematically distinct or counter-rotating cores. The origin of each of these velocity field morphologies is explained in terms of competing contributions from the major families of tube orbits.
The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family— the total number of sequences in that family—can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occurring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of *30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of frustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family and suggests new strategies for protein design.
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
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.
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.
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.
A one-dimensional echo map of the broad H-beta emission-line region in the Seyfert 1 galaxy NGC 5548 is reconstructed by using a maximum entropy technique to model the variable optical continuum and integrated H-beta emission-line fluxes observed during the 1989-1990 monitoring campaign as reported by Peterson et al. (1991). The echo map has a strong peak at a time delay of 20 lt-days which has an unresolved full width of 20 days at half-maximum. The H-beta response at time delay zero is less than one-third of that at 20 days, implying a deficit of H-beta-emitting gas near the line of sight to the continuum source. This rules out spherically symmetric and edge-on disk geometries for isotropically emitting H-beta clouds.
Intermetallic γ' precipitates typically strengthen nickel-based superalloys. The shape, size and spatial distribution of strengthening precipitates critically influence alloy strength, while their temporal evolution characteristics determine the high-temperature alloy stability. Combined ultra-small-, small- and wide-angle X-ray scattering (USAXS–SAXS–WAXS) analysis can be used to evaluate the temporal evolution of an alloy's precipitate size distribution (PSD) and phase structure during in situ heat treatment. Analysis of PSDs from USAXS–SAXS data employs either least-squares fitting of a preordained PSD model or a maximum entropy (MaxEnt) approach, the latter avoiding a priori definition of a functional form of the PSD. However, strong low- q scattering from grain boundaries and/or structure factor effects inhibit MaxEnt analysis of typical alloys. Lastly, this work describes the extension of Bayesian–MaxEnt analysis methods to data exhibiting structure factor effects and low- q power law slopes and demonstrates their use in an in situ study of precipitate size evolution during heat treatment of a model Ni–Al–Si alloy.
The WMAP team subtracted template-based foreground models to produce foreground-reduced maps, and masked point sources and uncertain sky regions directly; however, whether foreground residuals exist in the WMAP foreground-reduced maps is still an open question. Here, we use Pearson correlation coefficient analysis with AS-γ TeV cosmic ray (CR) data to probe possible foreground residuals in the WMAP nine-year data. The correlation results between the CR and foreground-contained maps (WMAP foreground-unreduced maps, WMAP template-based, and Maximum Entropy Method foreground models) suggest that: (1) CRs can trace foregrounds in the WMAP data; (2) at least some TeV CRs originate from the Milky Way; (3) foregrounds may be related to the existence of CR anisotropy (loss-cone and tail-in structures); (4) there exist differences among different types of foregrounds in the decl. range of <15°. Then, we generate 10,000 mock cosmic microwave background (CMB) sky maps to describe the cosmic variance, which is used to measure the effect of the fluctuations of all possible CMB maps to the correlations between CR and CMB maps. Finally, we do correlation analysis between the CR and WMAP foreground-reduced maps, and find that: (1) there are significant anticorrelations; and (2) the WMAP foreground-reduced maps are credible. However, the significant anticorrelations may be accidental, and the higher signal-to-noise ratio Planck SMICA map cannot reject the hypothesis of accidental correlations. We therefore can only conclude that the foreground residuals exist with ∼95% probability.
Ambient pressure stable perovskite oxides with all Bi3+ on the A-site are rare, with only four examples known. Due to the lone pair on Bi 3+ , these materials are seen as the best alternative to Pb-based piezoelectrics, which are used widely in society. The industry standard piezoelectric, Pb (Zr 1 – x Ti x )O 3 , relies on the [001] polarization of PbTiO 3 , but there are currently no ambient pressure stable Bi-based perovskites with this polarization vector, preventing the creation of an analogous system. We present the full structural analysis of the orthorhombic phase of (1 – x)Bi (Ti 3/8 Fe 2/8 Mg 3/8 )O 3 – x CaTiO 3 , which crystallizes in Pna2 1 symmetry with [001] polarization. This symmetry is rare and has only been reported twice for perovskites at ambient conditions. Analysis of maximum entropy method (MEM) models using synchrotron radiation powder X-ray diffraction reveals a disordered A-site configuration, and the MEM/Rietveld technique generates a structural model of this extreme disorder. Combined Rietveld analysis of X-ray and neutron diffraction data yields an accurate description of the local A-site configuration, which we use to understand our dielectric, ferroelectric, and piezoelectric measurements. These results give insight into how to stabilize this unique symmetry and inspire new design principles for Bi-based piezoelectrics.