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At least 73 records · Page 4

An improved representation of the relationship between photosynthesis and stomatal conductance leads to more stable estimation of conductance parameters and improves the goodness-of-fit across diverse data sets

Stomata play a central role in surface-atmosphere exchange by controlling the flux of water and CO 2 between the leaf and the atmosphere. Representation of stomatal conductance (g sw ) is therefore an essential component of models that seek to simulate water and CO 2 exchange in plants and ecosystems. For given environmental conditions at the leaf surface (CO 2 concentration and vapor pressure deficit or relative humidity), models typically assume a linear relationship between g sw and photosynthetic CO 2 assimilation (A). However, measurement of leaf-level g sw response curves to changes in A are rare, particularly in the tropics, resulting in only limited data to evaluate this key assumption. Here, we measured the response of g sw and A to irradiance in six tropical species at different leaf phenological stages. We showed that the relationship between g sw and A was not linear, challenging the key assumption upon which optimality theory is based-that the marginal cost of water gain is constant. Our data showed that increasing A resulted in a small increase in g sw at low irradiance, but a much larger increase at high irradiance. We reformulated the popular Unified Stomatal Optimization (USO) model to account for this phenomenon and to enable consistent estimation of the key conductance parameters g 0 and g 1 . Our modification of the USO model improved the goodness-of-fit and reduced bias, enabling robust estimation of conductance parameters at any irradiance. In addition, our modification revealed previously undetectable relationships between the stomatal slope parameter g 1 and other leaf traits. We also observed nonlinear behavior between A and g sw in independent datasets that included data collected from attached and detached leaves, and from plants grown at elevated CO 2 concentration. We propose that this empirical modification of the USO model can improve the measurement of g sw parameters and the estimation of plant and ecosystem-scale water and CO 2 fluxes.

54 ENVIRONMENTAL SCIENCES↗

Performance of a dynamic single bubbler in single and two-phase immiscible liquids

Ensuring nonproliferation and safeguards of special nuclear materials (SNM) is a critical aspect of advancing the nuclear fuel cycle. Traditional bubbler systems used to estimate liquid levels and densities in nuclear recycling processes have limitations, particularly in harsh environments where dip-tube corrosion and buildup necessitate frequent maintenance and recalibration. This study explores the Dynamic Single Bubbler (DSB) method, which utilizes a single dip-tube attached to a linear actuator to estimate liquid properties dynamically. This approach is extended to estimate liquid-liquid interfaces in immiscible liquids and employs a linear regression method to reduce uncertainties and improve accuracy. The DSB method achieved density estimate uncertainties of less than 0.5% and surface level estimate uncertainties typically under 0.5%, across various fluids including water, acetone, methanol, mineral oil, glycerol, and aqueous salt solutions. Results indicate that the DSB method provides accurate and robust estimates of liquid density and surface levels with minimal maintenance and without the need for calibration. Additionally, the method's applicability to immiscible liquids and various dip-tube geometries was demonstrated, showing promise for widespread use in nuclear and other industrial applications.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗

How Universal is the Relationship Between Remotely Sensed Vegetation Indices and Crop Leaf Area Index? A Global Assessment

Leaf Area Index (LAI) is a key variable that bridges remote sensing observations to the quantification of agroecosystem processes. In this study, we assessed the universality of the relationships between crop LAI and remotely sensed Vegetation Indices (VIs). We first compiled a global dataset of 1459 in situ quality-controlled crop LAI measurements and collected Landsat satellite images to derive five different VIs including Simple Ratio (SR), Normalized Difference Vegetation Index (NDVI), two versions of the Enhanced Vegetation Index (EVI and EVI2), and Green Chlorophyll Index (CI(sub Green)). Based on this dataset, we developed global LAI-VI relationships for each crop type and VI using symbolic regression and Theil-Sen (TS) robust estimator. Results suggest that the global LAI-VI relationships are statistically significant, crop-specific, and mostly non-linear. These relationships explain more than half of the total variance in ground LAI observations (R2 greater than 0.5), and provide LAI estimates with RMSE below 1.2 m2/m2. Among the five VIs, EVI/EVI2 are the most effective, and the crop-specific LAI-EVI and LAI-EVI2 relationships constructed by TS, are robust when tested by three independent validation datasets of varied spatial scales. While the heterogeneity of agricultural landscapes leads to a diverse set of local LAI-VI relationships, the relationships provided here represent global universality on an average basis, allowing the generation of large-scale spatial-explicit LAI maps. This study contributes to the operationalization of large-area crop modeling and, by extension, has relevance to both fundamental and applied agroecosystem research.

Vegetation Index↗

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

54 ENVIRONMENTAL SCIENCES↗

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↗

Multidimensional synthetic estimation filter

The synthetic estimation filter (SEF) crafts an affine variation into its response to a changing parameter (e.g. scale or rotation). Sets of such filters are used in an estimation correlator to reduce the number of filters required for a given tracking accuracy. By overspecifying the system (one more SEF than parameters to be tracked), the ratio of correlation responses between filters forms a robust estimator into the spanned domain of the parameters. Previous results dealt with a laboratory correlator which could track a single parameter. This paper explores the SEF and the estimator's extension to more dimensions. A 2D example is given in which a reduction of filters from 25 to 3 is demonstrated to span a 4-degree square portion of pose space.

Monroe, Stanley E., Jr.↗

Multiple-Beam Detection of Fast Transient Radio Sources

A method has been designed for using multiple independent stations to discriminate fast transient radio sources from local anomalies, such as antenna noise or radio frequency interference (RFI). This can improve the sensitivity of incoherent detection for geographically separated stations such as the very long baseline array (VLBA), the future square kilometer array (SKA), or any other coincident observations by multiple separated receivers. The transients are short, broadband pulses of radio energy, often just a few milliseconds long, emitted by a variety of exotic astronomical phenomena. They generally represent rare, high-energy events making them of great scientific value. For RFI-robust adaptive detection of transients, using multiple stations, a family of algorithms has been developed. The technique exploits the fact that the separated stations constitute statistically independent samples of the target. This can be used to adaptively ignore RFI events for superior sensitivity. If the antenna signals are independent and identically distributed (IID), then RFI events are simply outlier data points that can be removed through robust estimation such as a trimmed or Winsorized estimator. The alternative "trimmed" estimator is considered, which excises the strongest n signals from the list of short-beamed intensities. Because local RFI is independent at each antenna, this interference is unlikely to occur at many antennas on the same step. Trimming the strongest signals provides robustness to RFI that can theoretically outperform even the detection performance of the same number of antennas at a single site. This algorithm requires sorting the signals at each time step and dispersion measure, an operation that is computationally tractable for existing array sizes. An alternative uses the various stations to form an ensemble estimate of the conditional density function (CDF) evaluated at each time step. Both methods outperform standard detection strategies on a test sequence of VLBA data, and both are efficient enough for deployment in real-time, online transient detection applications.

Thompson, David R.↗

Quantile-dependent expressivity of serum C-reactive protein concentrations in family sets

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., C-reactive protein, CRP) is high or low relative to its distribution. We have previously shown that the heritabilities ( h 2 ) of coffee and alcohol consumption, postprandial lipemia, lipoproteins, leptin, adiponectin, adiposity, and pulmonary function are quantile-specific. Whether CRP heritability is quantile-specific is currently unknown. Methods Serum CRP concentrations from 2,036 sibships and 6,144 offspring-parent pairs were analyzed from the Framingham Heart Study. Quantile-specific heritability from full-sib (β FS , h 2 ={(1 + 8r spouse β FS ) 0.5 - 1}/(2r spouse )) and offspring-parent regression slopes (β OP , h 2 = 2β OP /(1 + r spouse )) were estimated robustly by quantile regression with nonparametric significance determined from 1,000 bootstrap samples. Results Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s age- and sex-adjusted CRP distribution when estimated from β OP ( P trend = 0.0004): 0.02 ± 0.01 at the 10th, 0.04 ± 0.01 at the 25th, 0.10 ± 0.02 at the 50th, 0.20 ± 0.05 at the 75th, and 0.33 ± 0.10 at the 90th percentile, and when estimated from β FS ( P trend = 0.0008): 0.03±0.01 at the 10th, 0.06 ± 0.02 at the 25th, 0.14 ± 0.03 at the 50th, 0.24 ± 0.05 at the 75th, and 0.53 ± 0.21 at the 90th percentile. Conclusion Heritability of serum CRP concentration is quantile-specific, which may explain or contribute to the inflated CRP differences between CRP (rs1130864, rs1205, rs1800947, rs2794521, rs3091244), FGB (rs1800787), IL-6 (rs1800795, rs1800796), IL6R (rs8192284), TNF- α (rs1800629) and APOE genotypes following CABG surgery, stroke, TIA, curative esophagectomy, intensive periodontal therapy, or acute exercise; during acute coronary syndrome or Staphylococcus aureus bacteremia; or in patients with chronic rheumatoid arthritis, diabetes, peripheral arterial disease, ankylosing spondylitis, obesity or inflammatory bowel disease or who smoke.

59 BASIC BIOLOGICAL SCIENCES↗

Online Bayesian State Estimation for Real-Time Monitoring of Growth Kinetics in Thin Film Synthesis

Rapid validation of newly predicted materials through autonomous synthesis requires real-time adaptive control methods that exploit physics knowledge, a capability that is lacking in most systems. Here, in this study, we demonstrate an approach to enable real-time control of thin film synthesis by combining in situ optical diagnostics with a Bayesian state estimation method. We developed a physical model for film growth and applied the direct filter (DF) method for real-time estimation of nucleation and growth rates during pulsed laser deposition (PLD). We validated the approach using simulated and experimental reflectivity data for WSe 2 growth and ultimately deployed the algorithm on an autonomous PLD system during the growth of 1T'-MoTe 2 . The DF robustly estimates growth parameters in real time at early stages of growth, down to 15% monolayer area coverage. This fusion of in situ diagnostics, data assimilation, and physical modeling opens new opportunities in adaptive control of synthesis trajectories toward desired material states.

36 MATERIALS SCIENCE↗

Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional Theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. Here, in this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

Quiton, Stephen Jon [University of California, Ber↗

Controlling extrapolations of nuclear properties with feature selection

Predictions of nuclear properties far from measured data are inherently inaccurate because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model bias can be directly calculated when experimental data is available, only an estimate can be made in the absence of such measurements. Current approaches to compute the estimated bias quickly lose predictive power when their input variables are taken far from the training region, resulting in uncontrolled uncertainties in applications such as nucleosynthesis simulations. In this letter, we present a novel technique to identify the input variables of machine learning algorithms that can provide robust estimates of model bias. Our process is based on selecting input variables, or features, based on their probability distribution functions across the entire nuclear chart. We illustrate our approach on the problem of quantifying the model bias in nuclear binding energies calculated with Density Functional Theory (DFT). We prove that building model biases with only Z and N as features leads to highly unreliable extrapolations. Conversely, we show that proper feature selection can systematically improve theoretical predictions without increasing uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantifying Climate Change Effects of Bioenergy and BECCS: Critical Considerations and Guidance on Methodology

Bioenergy is a critical element in many national and international climate change mitigation efforts, including as a carbon dioxide removal strategy combined with the capture and durable geological storage of flue gas emissions (BECCS). However, divergent results on the effectiveness of bioenergy as a climate change mitigation measure are reported in the scientific literature. Climate impacts of bioenergy depend on case-specific factors, primarily biophysical features of the biomass production system, and the design and efficiency of conversion and capture processes. Estimates of climate impacts are also strongly affected by methodological choices and assumptions, and much of the divergence between studies derives from differences in the assumed alternate use of the land or feedstock, the alternate energy source and the system boundaries applied. We present a methodology to support robust estimates of the climate change effects of bioenergy systems, updating the standard methodology developed by the International Energy Agency's Technology Collaboration Program on Bioenergy. We provide guidance on the key choices including the reference land use and energy system that bioenergy is assumed to displace, spatial and temporal system boundaries, co-product handling, climate forcers considered, metrics applied and time horizon of impact assessment. Researchers should consider the whole bioenergy system including all life cycle stages, and choose system boundaries, reference systems and treatment of co-products that are consistent with the intended application of the results. The assessment should be normalised to a functional unit that can be compared with other systems delivering an equivalent quantity of the same function. All significant climate forcers should be included, and climate effects should be quantified using appropriate impact assessment methods that distinguish the impact of time. Consistency in methodology and interpretation will facilitate comparison between studies of different bioenergy systems.

09 BIOMASS FUELS↗

Evaluation of a methodology for model identification in the time domain

A model identification methodology for structural dynamics has been applied to simulated vibrational data as a first step in evaluating its accuracy. The evaluation has taken into account a wide variety of factors which affect the accuracy of the procedure. The effects of each of these factors were observed in both the response time histories and the estimates of the parameters of the model by comparing them with the exact values of the system. Each factor was varied independently but combinations of these have also been considered in an effort to simulate real situations. The results of the tests have shown that for the chain model, the procedure yields robust estimates of the stiffness parameters under the conditions studied whenever uniqueness is ensured. When inaccuracies occur in the results, they are intimately related to non-uniqueness conditions inherent in the inverse problem and not to shortcomings in the methodology.

Beck, R. T.↗

A Measurement-Based Adaptive Voltage Regulation Method Considering Topology Changes

This paper proposes an online adaptive data-driven distributed energy resource (DER) dispatch optimization method for voltage control considering topology changes. By using a local sensitivity factor (LSF)-enabled voltage control, traditional DER control can be reformulated into a linear programming (LP) problem, leading to faster computation speeds. Power injection alteration and topology changes are two common operational changes in the distribution network that can affect the LSF and voltage control performance. To address this issue, a robust estimation method is developed to adjust the sensitivity matrix at each time step for the time-varying power injection changes. When topology changes occur, only the allocated predominant LSF submatrices are updated based on measurement data, allowing for a fast adaptation to the system reconfiguration. Results obtained from a real distribution feeder in Southern California demonstrate its robustness as compared to traditional volt-var control and constant LSF matrix dispatch control methods.

DERs↗

Applications of MODIS Fluorescent Line Height Measurements to Monitor Water Quality Trends and Algal Bloom Activity

Recent advances in satellite and airborne remote sensing, such as improvements in sensor and algorithm calibrations, processing techniques and atmospheric correction procedures have provided for increased coverage of remote-sensing, ocean-color products for coastal regions. In particular, for the Moderate Resolution Imaging Spectrometer (MODIS) sensor calibration updates, improved aerosol retrievals and new aerosol models has led to improved atmospheric correction algorithms for turbid waters and have improved the retrieval of ocean color in coastal waters. This has opened the way for studying ocean phenomena and processes at finer spatial scales, such as the interactions at the land-sea interface, trends in coastal water quality and algal blooms. Human population growth and changes in coastal management practices have brought about significant changes in the concentrations of organic and inorganic, particulate and dissolved substances entering the coastal ocean. There is increasing concern that these inputs have led to declines in water quality and have increase local concentrations of phytoplankton, which cause harmful algal blooms. In two case studies we present MODIS observations of fluorescence line height (FLH) to 1) assess trends in water quality for Tampa Bay, Florida and 2) illustrate seasonal and annual variability of algal bloom activity in Monterey Bay, California as well as document estuarine/riverine plume induced red tide events. In a comprehensive analysis of long term (2003-2011) in situ monitoring data and satellite imagery from Tampa Bay we assess the validity of the MODIS FLH product against chlorophyll-a and a suite of water quality parameters taken in a variety of conditions throughout a large optically complex estuarine system. A systematic analysis of sampling sites throughout the bay is undertaken to understand how the relationship between FLH and in situ chlorophyll-a responds to varying conditions and to develop a near decadal trend in water quality changes. In situ monitoring locations that correlated well with satellite imagery were in depths greater than seven meters and were located over five kilometers from shore. Water quality parameter of total nitrogen, phosphorous, turbidity and biological oxygen demand had high correlations with these sites, as well. Satellite FLH estimates show improving water quality from 2003-2007 with a slight decline up through 2011. Dinoflagellate blooms in Monterey Bay, California (USA) have recently increased in frequency and intensity. Nine years of MODIS FLH observations are used to describe the annual and seasonal variability of bloom activity within the Bay. Three classes of MODIS algorithms were correlated against in situ chlorophyll measurements. The FLH algorithm provided the most robust estimate of bloom activity. Elevated concentrations of phytoplankton were evident during the months of August-November, a period during which increased occurrences of dinoflagellate blooms have been observed in situ. Seasonal patterns of FLH show the on- and offshore movement of areas of high phytoplankton biomass between oceanographic seasons. Higher concentrations of phytoplankton are also evident in the vicinity of the land-based nutrient sources and outflows, and the cyclonic bay-wide circulation can transport these nutrients to the northern Bay bloom incubation region. Both of these case studies illustrate the utility MODIS FLH observations in supporting management decisions in coastal and estuarine waters.

Fischer, Andrew↗

Fractional Snowcover Estimates from Earth Observing System (EOS) Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)

The Moderate Resolution Imaging Spectroradiometer (MODIS) on the NASA Earth Observing System (EOS) Terra and Aqua missions has shown considerable capability for mapping snowcover. The typical approach that has used, along with other criteria, the Normalized Snow Difference Index (NDSI) that takes the difference between 500 meter observations at 1.64 micrometers (MODIS band 6) and 0.555 micrometers (MODIS band 4) over the sum of these observations to determine whether MODIS pixels are snowcovered or not in mapping the extent of snowcover. For many hydrological and climate studies using remote sensing of snowcover, it is desirable to assess if the MODIS snowcover observations could not be enhanced by providing the fraction of snowcover in each MODIS observation (pixel). Pursuant to this objective studies have been conducted to assess whether there is sufficient "signal%o in the NDSI parameter to provide useful estimates of fractional snowcover in each MODIS 500 meter pixel. To accomplish this objective high spatial resolution (30 meter) Landsat snowcover observations were used and co-registered with MODIS 500 meter pixels. The NDSI approach was used to assess whether a Landsat pixel was or was not snowcovered. Then the number of snowcovered Landsat pixels within a MODIS pixel was used to determine the fraction of snowcover within each MODIS pixel. The e results were then used to develop statistical relationships between the NDSI value for each 500 meter MODIS pixel and the fraction of snowcover in the MODIS pixel. Such studies were conducted for three widely different areas covered by Landsat scenes in Alaska, Russia, and the Quebec Province in Canada. The statistical relationships indicate that a 10 percent accuracy can be attained. The variability in the statistical relationship for the three areas was found to be remarkably similar (-0.02 for mean error and less than 0.01 for mean absolute error and standard deviation). Independent tests of the relationships were accomplished by taking the relationship of fractional snow-cover to NDSI from one area (e.g., Alaska) and testing it on the other two areas (e.g. Russia and Quebec). Again the results showed that fractional snow-cover can be estimated to 10 percent. The results have been shown to have advantages over other published fractional snowcover algorithms applied to MODIS data. Most recently the fractional snow-cover algorithm has been applied using 500-meter observations over the state of Colorado for a period spanning 25 days. The results exhibit good behavior in mapping the spatial and temporal variability in snowcover over that 25-day period. Overall these studies indicate that robust estimates of fractional snow-cover can be attained using the NDSI parameter over areas extending in size from watersheds relatively large compared to MODIS pixels to global land cover. Other refinements to this approach as well as different approaches are being examined for mapping fractional snow-cover using MODIS observations.

Salomonson, Vincent V.↗

Satellite-based aerosol optical depth estimates over the continental U.S. during the 2020 wildfire season: Roles of smoke and land cover

Wildfires produce smoke that can affect an area >1000 times the burn extent, with far-reaching human health, ecologic, and economic impacts. Accurately estimating aerosol load within smoke plumes is therefore crucial for understanding and mitigating these impacts. We evaluated the effectiveness of the latest Collection 6.1 MODIS Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm in estimating aerosol optical depth (AOD) across the U.S. during the historic 2020 wildfire season. We compared satellite-based MAIAC AOD to ground-based AERONET AOD measurements during no-, light-, medium-, and heavy-smoke conditions identified using the Hazard Mapping System Fire and Smoke Product. This smoke product consists of maximum extent smoke polygons digitized by analysts using visible band imagery and classified according to smoke density. We also examined the strength of the correlations between satellite- and ground-based AOD for major land cover types under various smoke density levels. MAIAC performed well in estimating AOD during smoke-affected conditions. Correlations between MAIAC and AERONET AOD were strong for medium- (r = 0.91) and heavy-smoke (r = 0.90) density, and MAIAC estimates of AOD showed little bias relative to ground-based AERONET measurements (normalized mean bias = 3 % for medium, 5 % for heavy smoke). During two high AOD, heavy smoke episodes, MAIAC underestimated ground-based AERONET AOD under mixed aerosol (i.e., smoke and dust; median bias = −0.08) and overestimated AOD under smoke-dominated (median bias = 0.02) aerosol. MAIAC most overestimated ground-based AERONET AOD over barren land (mean NMB = 48 %). Our findings indicate that MODIS MAIAC can provide robust estimates of AOD as smoke density increases in coming years. Increased frequency of mixed aerosol and expansion of developed land could affect the performance of the MAIAC algorithm in the future, however, with implications for evaluating wildfire-associated health and welfare effects and air quality standards.

54 ENVIRONMENTAL SCIENCES↗

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗