Covariance Function Research Articles

Modeling Gravity Gradients from Surface Gravity Anomaly Data

Gravity gradients are useful to characterize near mass anomalies since they are much more sensitive to short wavelength anomalies than gravitational accelerations. Estimating gravity gradients from surface gravity data is based on numerical implementations of solutions to geodetic boundary value problem for determination of disturbing potential. One of methods to solve this problem is least-squares collocation which is basically based on data and a defined covariance function. This study deals with estimating gravity gradient tensor components from along track surface gravity anomaly data. The Least-Squares Collocation solution is based on a stationary local covariance function defined for the disturbing potential which allows upward continuation of the observations to a desired altitude. The modeling method is evaluated in using Earth Gravitational Model 2008(EGM2008) and real airborne gravity gradiometry data collected over Southern Texas, Oklahoma region. The results show that modeled gravity gradients estimated in both on the ground and at a certain altitude have basically good agreement with EGM08 gradients. Modeled gradients including horizontal components in the east-west direction exhibit some discrepancies in comparison to the airborne gradiometry data, which may be attributed to some measurement errors in the gradient data.

Genetic Parameter Estimates for Growth of Hāpuku (Groper, Polyprion oxygeneios) in Land-Based Aquaculture Using Random Regression Models

Hāpuku (Polyprion oxygeneios) is a promising candidate for aquaculture production in New Zealand. Methods for spawning, juvenile production, and growout to harvest entirely on land, where water quality, pathogens, environmental impacts, and genetic “pollution” can be tightly controlled, have been developed, and genetic improvement to optimise land-based production is the obvious next step. However, estimates of genetic parameters are required to design a rigorous, disciplined, and effective selective breeding program. By using existing data consisting of irregularly spaced repeated measurements of fork length and live body weight collected on wild-collected founders and two generations of captively reared progeny, we evaluated the species’ genetic potential for improvement in growth. We first tested a range of univariate random regression models to identify the best-fitting models for these data. Subsequently, using a bivariate model, we estimated variance components for growth trajectories of fork length and whole body weight. With one to six records available per fish, the best-fitting univariate models included only a fixed effect for contemporary groups and fixed and random genetic third-order Legendre polynomials. More complex models that included full-sib family and/or permanent environmental effects produced unacceptable constrained and/or non-positive-definite solutions. Both traits are moderately heritable at all stages of the growout phase (~0.4–0.5), and the genetic correlation patterns between daily breeding values estimated via the covariance function are different for length and weight. Genetic correlations for length between all pairs of age-specific breeding values are positive and strong (>0.7) and change gradually and smoothly with increasing temporal separation. For weight, these correlations deteriorate more rapidly with increasing time lags between measurements and become negative for some age pairings. We conclude that random regression analyses are a valuable tool for extracting genetic information from irregularly spaced repeated measurements of fish size, speculate that emerging technologies for high-throughput genotyping and phenotyping will add to the value of this approach in the near future, and reason that a breeding strategy that rigorously takes into account the potentially unfavourable genetic correlations between breeding values for weight at some ages will further adapt hāpuku to land-based systems and enhance the profitability commercial-scale production.

Practical non-stationary extreme value analysis of peaks over threshold using the generalised Pareto distribution: Estimating uncertainties in return values

Choice of tuning parameters influences the performance of non-stationary extreme value modelling for peaks over threshold using the generalised Pareto (GP) distribution. We examine the effect of tuning parameter choice on maximum roughness-penalised likelihood estimation of GP models, the shape and scale parameters of which are assumed to vary smoothly on a one-dimensional “directional” covariate domain, under a B-spline representation. We examine the effect of (a) extreme value model parameterisation, (b) relative roughness penalty of GP parameters as a function of covariate, (c) cross-validation strategy for roughness parameter tuning, and (d) estimator for return value, on the estimation of return values corresponding to return periods 1000× the period of a sample of size 1000. Bootstrap resampling is used for thorough uncertainty quantification. We also compare results with those from stationary inference.Results from a large simulation study of 16 cases broadly representative of North Sea conditions for significant wave height with direction, indicate that (i) multiple two-group cross-validation yields lower return value estimates that ten-group cross-validation (leading to negative bias on average, for the case studies considered), (ii) the quantile of the bootstrap predictive estimator yields larger values than the mean over bootstraps of the quantile estimate (leading to reduced omni-directional bias for the case studies considered). Further, (iii) the use of stationary models for non-stationary tails is only reasonable when a high extreme value threshold is set for the stationary analysis. However, (iv) the relative performance of different modelling strategies is sensitive to the specific characteristics of the case study.

Spillover and competitive exclusion in the crustacean community following the implementation of a marine reserve

Abstract Flamanville marine protected area (MPA) located in Normandy, France, was created in 2000 to sustain the local crustacean fishery. In 1985, an annual survey targeting crustacean populations (e.g. European lobster Homarus gammarus, edible crab Cancer pagurus, and European spider crab Maja brachydactyla) that include the future MPA started. The MPA implementation effects were investigated in this study. The sampling design allowed the integration of spatial and temporal covariances to estimate the MPA effects. With respect to the initial objective, the MPA significantly improves the most economically valuable species, H. gammarus, abundance. Lobster catch per unit effort increased by 597% in the MPA, whereas outside it only increased by 156%. The MPA creation also led to an increase in lobster size inside the protected area. Furthermore, a few years after the MPA implementation, lobster catches showed a significant non-linear decline with distance from the centre of the reserve, suggesting a spillover effect. However, the edible crab catches were halved following the MPA implementation suggesting an opposite effect. Spider crab abundance seemed unaffected. Finally, the MPA implementation had no effect on edible crab and spider crab sizes. These differential responses appear to result from these species’ variable movement and competitive abilities.

Almost complete convergence of the functional local linear estimator of the expectile regression for data missing at random

In this article, the authors investigate the properties of a local linear estimator for the expectile regression function in scenarios where the scalar response variable is missing at random, and the covariate is a functional variable. The study addresses the challenge of estimating the expectile regression function when the response variable is not fully observed, a common issue in statistical analysis where missing data can significantly impact the accuracy of predictions and inferences. The key contribution of the paper lies in the establishment of the almost complete convergence of the proposed estimator. This convergence resultis derived under a set of appropriate conditions, ensuring that the estimator approaches the true expectile regression function with a probability tending to wards one as the sample size increases. The authors provide a rigorous theoretical foundation for this convergence, including assumptions about the smoothness of the functional covariate and the randomness of the missing data mechanism. To demonstrate the practical applicability of their method, the authors conduct a comprehensive simulation study. This study compares the performance of their local linear estimator with other existing methods in terms of bias, variance, and convergence speed. The simulation resultshighlight the effectiveness of the proposed approach, especially in settings where the response variable is partially missing and the covariates are functional in nature.

Single Leg Hop Performance After Anterior Cruciate Ligament Reconstruction: Ready for Landing but Cleared for Take-Off?

Understanding former professional football players engagement with health promoting behaviors (physical exercise, high quality diet, and good sleep hygiene) will be helpful for developing lifestyle interventions to improve their feelings of well-being, a relatively understudied facet of health among this population. Examine associations among health-promoting behaviors and subjective outcomes related to well-being among former National Football League (NFL) players. Cross-sectional. Online or hard-copy survey. Former NFL players. Self-reported health-promoting behaviors (exercise frequency, diet quality, sleep duration and disturbance) and factors related to well-being (PROMIS ® Meaning and Purpose [MP], Self-Efficacy [SE], Ability to Participate in Social Roles and Activities [SRA]). Multivariable linear regression models were fit for each well-being-related factor with health-promoting behaviors as explanatory variables alongside select demographic, behavioral, and functional covariates. Models were fit for the full sample and separately for individual age groups: <30 years; 30-39 years; 40-49 years; 50-59 years; 60-69 years; and 70+ years. A total of 1,784 former NFL players (aged 52.3±16.3 years) completed the survey. Lower sleep disturbance was associated with better MP (β[standard error]=-0.196[0.024]), SE (β[standard error]=-0.185[0.024]), and SRA (β[standard error]=-0.137[0.017]) in the full sample and almost all the individual age groups. More frequent moderate-to-vigorous exercise was associated with higher MP (β[standard error]=0.068[0.025]) and SRA (β[standard error]=0.151[0.065]) in the full sample, and with better MP, SE, and SRA among select middle-aged groups (between 40-69 years old). Diet quality, resistance training exercise frequency, other wellness activity frequency, and sleep duration were not associated with well-being-related factors in the full-group and sparse significant associations were observed in individual age group models. Lower sleep disturbance and more frequent moderate-to-vigorous exercise frequency may be important targets for improving overall health and well-being among former NFL players.

Large-Scale Low-Rank Gaussian Process Prediction with Support Points

Low-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified.

A Geostatistics‐Based Tool to Characterize Spatio‐Temporal Patterns of Remotely Sensed Land Surface Temperature Fields Over the Contiguous United States

AbstractSurface fluxes and states can recur and remain consistent across various spatial and temporal scales, forming space‐time patterns. Quantifying and understanding the observed patterns is desirable, as they provide information about the dynamics of the processes involved. This study introduces the empirical spatio‐temporal covariance function and a corresponding parametric covariance function as tools to identify and characterize spatio‐temporal patterns in remotely sensed fields. The method is demonstrated using 2 km hourly GOES‐16/17 land surface temperature (LST) data over the Contiguous United States by splitting the area into 1.0° × 1.0° domains. The summer day‐time LST ESTCFs for 2018 to 2022 are derived for each domain, and a parametric covariance model is fitted. Clustering analysis is applied to detect areas with similar spatio‐temporal LST patterns. Six main zones within CONUS are identified and characterized based on their variance and temporal and spatial characteristic length scales (i.e., scales for which the temperature variations are temporally and spatially related), respectively: (a) Eastern plains with 3 K2, ∼6 hr, and 0.15°, (b) Gulf of California with 60 K2, ∼8 hr, and 0.34°, (c) mountains and coasts transition 1 with 16 K2, ∼11 hr, and 0.25°, (d) central US, Midwest, and South cities with 5.5 K2, ∼8 hr, and ∼0.2°, (e) mountains and coasts transition 2 with ∼10 K2, ∼8 hr, and 0.2°, and (f) largest mountains and coastlines with ∼19 K2, ∼13 hr, and 0.3°. The tools introduced provide a pathway to formally identify and summarize the spatio‐temporal patterns observed in remotely sensed fields and relate those to more complex processes within the Soil‐Vegetation‐Atmosphere System.

501 The effect of dietary camelina, flaxseed, and canola oil supplementation on skin fatty acid profile, inflammation and immune responses in healthy adult horses

Abstract As n-6 and n-3 fatty acids (FA) have pro- and anti-inflammatory effects, respectively, supplemental oils have the potential to impact inflammation, the immune response, and skin and coat health. This study aimed to evaluate the effects of camelina (CAM), in comparison to canola (OLA) and flaxseed (FLX) oil on the skin FA profile, inflammation, and the immune response in horses. Horses [n = 24; 14.2 ± 4.8 yr; 518 ± 63 kg body weight (BW)] were acclimated to sunflower oil over 4 wk. Groups were balanced by location, age, weight, sex, and breed and randomly assigned one of the three treatments (CAM, OLA, FLX). Horses were fed their assigned oil at a dose of 0.37 g/kg BW for 16 wk. Skin samples were collected on wk 16, and the skin FA composition was analyzed by gas chromatography. On wk 10 and 12, keyhole limpet hemocyanin (KLH) was administered intramuscularly to each horse to stimulate a systemic immune response. Blood was collected on wk 14 and 16 for the evaluation of plasma KLH immunoglobulin G (IgG) concentrations using a modified ELISA protocol and results were presented as optical density units. On wk 12, after the first KLH injection, a delayed-type hypersensitivity (DTH) test was performed by intradermally injecting KLH and the area of swelling was measured using the software ImageJ at 0.5-, 1-, 8-, 24-, 48-, 72-, and 96-h post-injection. Data were analyzed using the GLIMMIX procedure of SAS considering the effects of treatment, time, and their interaction as fixed, and the effects of horse and location as random. Repeated measures on horses were modelled using a spatial power covariance structure. Significance was declared at P ≤ 0.05 and when fixed effects were significant, means were separated using Tukey-Kramer adjustments. Immune and inflammatory responses were produced by the KLH injections; however, there were no differences among treatment groups regarding KLH antibody and DTH response (P &amp;gt; 0.44). The percentages of palmitic (P = 0.02) and stearic acid (P = 0.03) in the skin at wk 16 were greater in FLX as compared with CAM but neither differed from the OLA. The percentage of linoleic acid (P = 0.01) was greater in CAM than OLA but neither differed from FLX at wk 16. The percentage of all other FA was similar among treatment groups (P &amp;gt; 0.06). These results suggest that CAM is comparable to FLX and OLA regarding support of an immune and inflammatory response, and the oil FA composition was not reflected in the skin FA profile after feeding for 16 wk as hypothesized. In conclusion, at the dose provided, CAM supports a similar immune and inflammatory response to KLH as FLX and OLA; however, the lack of incorporation of FA from the diet into the skin should be further explored.

502 Cat and mouse: The effect of consuming four different diet formants (intact mice, raw, canned wet and kibble) on energy expended to consume a meal and immediately post-prandial in domestic cats

Abstract Cats are obligate carnivores; however, we feed them a variety of different diet formats without a clear understanding of feeding behavior and metabolism among diet formats. Whole-prey or raw diets may mimic a more natural diet and require more energy to consume. However, there is currently a dearth of literature examining feline energy expenditure (EE) during the consumption of and immediate post-prandial period when fed different diet formats. The present study aimed to investigate differences in the energetics of adult cats consuming four different diet formats in isocaloric offerings: raw intact mice, commercial raw, canned wet, and kibble diets. Adult neutered male cats [n = 12; body weight (BW) = 4.82 ± 0.164 kg) were used in a 4 x 4 replicated Latin square design and adapted to consuming each diet format before the initiation of the study. Following a 2-d adaptation period, cats were fed 25% of their daily caloric requirement (50.77 ± 1.549 kcal) in indirect calorimetry chambers in which VO2 and VCO2 exchange were measured. Energy expenditure (kcal/BW0.67 kg) was calculated for the consumption period, 15 min immediately post-prandial and 2 h post-prandial. Respiratory gases were measured for one fasted reading, followed by the first feeding. During each feeding, measurements were taken during the consumption period and 15 min post-prandial. For the following 2 h, respiratory gases were measured every 25 min for an additional 4 measures of respiratory gases. All data were analyzed using a generalized linear mixed model considering the effects of treatment, time and their interaction as fixed, and the effects of cat and period as random. A spatial power covariance structure was used to model repeated measures. Significance was considered at P &amp;lt; 0.05 and Tukey’s post-hoc test was performed to separate means. Energy expenditure during consumption and 15 min post-prandial was similar among treatments, and EE for 15 min post-prandial was greater than EE during consumption (P &amp;lt; 0.001). During the 2 h post-prandial, EE for the mice diet was greater than the kibble and canned wet diets (P &amp;lt; 0.001), while EE for the raw diet was only greater than the kibble diet (P &amp;lt; 0.001). Energy expenditure was similar between the kibble and canned wet diets (P = 0.919) and between the mice and raw diets (P = 0.598). Among all treatments and time periods, the mouse diet had the greatest mean EE. An increase in EE during the feeding period and post-prandial could benefit sedentary indoor cats who may be in positive energy balance. Feeding cats a naturalistic diet, such as intact mice or a raw diet, may increase activity levels and EE, but the longer-term effects of these feeding formats on energy balance need to be explored.

Predicting cognitive load with EEG using Riemannian geometry-based features

Objective. We show that electroencephalography (EEG)-based cognitive load (CL) prediction using Riemannian geometry features outperforms existing models. The performance is estimated using Riemannian Procrustes Analysis (RPA) with a test set of subjects unseen during training.Approach. Performance is evaluated by using the Minimum Distance to Riemannian Mean model trained on CL classification. The baseline performance is established using spatial covariance matrices of the signal as features. Various novel features are explored and analyzed in depth, including spatial covariance and correlation matrices computed on the EEG signal and its first-order derivative. Furthermore, each RPA step effect on the performance is investigated, and the generalization performance of RPA is compared against a few different generalization methods.Main results. Performances are greatly improved by using the spatial covariance matrix of the first-order derivative of the signal as features. Furthermore, this work highlights both the importance and efficiency of RPA for CL prediction: it achieves good generalizability with little amounts of calibration data and largely outperforms all the comparison methods.Significance. CL prediction using RPA for generalizability across subjects is an approach worth exploring further, especially for real-world applications where calibration time is limited. Furthermore, the feature exploration uncovers new, promising features that can be used and further experimented within any Riemannian geometry setting.

Higher-order correction of persistent batch effects in correlation networks.

Systems biology analyses often use correlations in gene expression profiles to infer co-expression networks that are then used as input for gene regulatory network inference or to identify functional modules of co-expressed or putatively co-regulated genes. While systematic biases, including batch effects, are known to induce spurious associations and confound differential gene expression analyses (DE), the impact of batch effects on gene co-expression has not been fully explored. Methods have been developed to adjust expression values, ensuring conditional independence of mean and variance from batch or other covariates for each gene, resulting in improved fidelity of DE analysis. However, such adjustments do not address the potential for spurious differential co-expression (DC) between groups. Consequently, uncorrected, artifactual DC can skew the correlation structure, leading to the identification of false, non-biological associations, even when the input data are corrected using standard batch correction. In this work, we demonstrate the persistence of confounders in covariance after standard batch correction using synthetic and real-world gene expression data examples. We then introduce Co-expression Batch Reduction Adjustment (COBRA), a method for computing a batch-corrected gene co-expression matrix based on estimating a conditional covariance matrix. COBRA estimates a reduced set of parameters expressing the co-expression matrix as a function of the sample covariates, allowing control for continuous and categorical covariates. COBRA is computationally efficient, leveraging the inherently modular structure of genomic data to estimate accurate gene regulatory associations and facilitate functional analysis for high-dimensional genomic data. COBRA is available under the GLP3 open source license in R and Python in netZoo (https://netzoo.github.io).

Concurrent Functional Linear Regression Via Plug-in Empirical Likelihood

AbstractFunctional data with non-smooth features (e.g., discontinuities in the functional mean and/or covariance) and monotonicity arise frequently in practice. This paper develops simultaneous inference for concurrent functional linear regression in this setting. We construct a simultaneous confidence band for a functional covariate effect of interest. Along with a Wald-type formulation, our approach is based on a powerful nonparametric likelihood ratio method. Our procedures are flexible enough to allow discontinuities in the coefficient functions and the covariance structure, while accounting for discretization of the observed trajectories under a fixed dense design. A simulation study shows that the proposed likelihood ratio-based procedure outperforms the Wald-type procedure in moderate sample sizes. We apply the proposed methods to studying the effect of age on the occupation time curve derived from wearable device data obtained in an NHANES study.

Weighing massive neutrinos with Lyman-α observations

The presence of massive neutrinos has still not been revealedby the cosmological data. We considera novel method based on the two-point line-of-sight correlation function ofhigh-resolution Lyman-α data to achieve this end in the paper.We adopt semi-analytic models of Lyman-αclouds for the study. We employ Fisher matrix technique to show thatit is possible to achieve a scenario in whichthe covariance of the two-point function nearly vanishes for both the spectroscopic noise and the signal.We analyze this near `zero noise' outcome in detail to argue it might be possible to detect neutrinosof mass range m ν ≃ 0.05–0.1 eV with signal-to-noise of unity witha single QSO line of sight. We show that this estimate can be improved to SNR ≃ 3–6 with data along multiple line of sightswithin the redshift range z ≃ 2–2.5.Such data sets already exist in the literature.We further carry outprincipal component analysis of the Fisher matrix to study the degeneraciesof the neutrino mass with otherparameters. We show that Planck priors lift the degeneracies betweenthe neutrino mass and other cosmological parameters.However, the prospects of the detection of neutrino mass are driven by the poorly-determined parameters characterizing the ionization and thermal state of Lyman-α clouds. We have also mentioned the possible limitations andobservational challenges posed in measuring the neutrino mass using our method.

Optimizing Gaussian process regression (GPR) hyperparameters with three metaheuristic algorithms for viscosity prediction of suspensions containing microencapsulated PCMs

Suspensions containing microencapsulated phase change materials (MPCMs) play a crucial role in thermal energy storage (TES) systems and have applications in building materials, textiles, and cooling systems. This study focuses on accurately predicting the dynamic viscosity, a critical thermophysical property, of suspensions containing MPCMs and MXene particles using Gaussian process regression (GPR). Twelve hyperparameters (HPs) of GPR are analyzed separately and classified into three groups based on their importance. Three metaheuristic algorithms, namely genetic algorithm (GA), particle swarm optimization (PSO), and marine predators algorithm (MPA), are employed to optimize HPs. Optimizing the four most significant hyperparameters (covariance function, basis function, standardization, and sigma) within the first group using any of the three metaheuristic algorithms resulted in excellent outcomes. All algorithms achieved a reasonable R-value (0.9983), demonstrating their effectiveness in this context. The second group explored the impact of including additional, moderate-significant HPs, such as the fit method, predict method and optimizer. While the resulting models showed some improvement over the first group, the PSO-based model within this group exhibited the most noteworthy enhancement, achieving a higher R-value (0.99834). Finally, the third group was analyzed to examine the potential interactions between all twelve HPs. This comprehensive approach, employing the GA, yielded an optimized GPR model with the highest level of target compliance, reflected by an impressive R-value of 0.999224. The developed models are a cost-effective and efficient solution to reduce laboratory costs for various systems, from TES to thermal management.

A flexible and interpretable spatial covariance model for data on graphs

A flexible and interpretable spatial covariance model for data on graphs

Dissecting glial scar formation by spatial point pattern and topological data analysis

Glial scar formation represents a fundamental response to central nervous system (CNS) injuries. It is mainly characterized by a well-defined spatial rearrangement of reactive astrocytes and microglia. The mechanisms underlying glial scar formation have been extensively studied, yet quantitative descriptors of the spatial arrangement of reactive glial cells remain limited. Here, we present a novel approach using point pattern analysis (PPA) and topological data analysis (TDA) to quantify spatial patterns of reactive glial cells after experimental ischemic stroke in mice. We provide open and reproducible tools using R and Julia to quantify spatial intensity, cell covariance and conditional distribution, cell-to-cell interactions, and short/long-scale arrangement, which collectively disentangle the arrangement patterns of the glial scar. This approach unravels a substantial divergence in the distribution of GFAP+ and IBA1+ cells after injury that conventional analysis methods cannot fully characterize. PPA and TDA are valuable tools for studying the complex spatial arrangement of reactive glia and other nervous cells following CNS injuries and have potential applications for evaluating glial-targeted restorative therapies.

Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo.

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations, we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We further demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics in covariance.

A canonical polyadic tensor basis for fast Bayesian estimation of multi-subject brain activation patterns.

Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and language processing. A fast Bayesian function-on-scalar model is proposed for estimating population-level activation maps linked to the working memory task. The model is based on the canonical polyadic (CP) tensor decomposition of coefficient maps obtained for each subject. This decomposition effectively yields a tensor basis capable of extracting both common features and subject-specific features from the coefficient maps. These subject-specific features, in turn, are modeled as a function of covariates of interest using a Bayesian model that accounts for the correlation of the CP-extracted features. The dimensionality reduction achieved with the tensor basis allows for a fast MCMC estimation of population-level activation maps. This model is applied to one hundred unrelated subjects from the HCP dataset, yielding significant insights into brain signatures associated with working memory.

Gaussian process regression to predict dryout incipience quality of saturated flow boiling in mini/micro-channels

In the present study, a Gaussian process regression (GPR) model is developed to predict the dryout incipience quality for flow boiling in mini / micro – channels based on a consolidated database obtained from Purdue University Boiling and Two – Phase Flow Laboratory (PU – BTPFL) consisting of 997 points from 26 sources. The database includes 13 different working fluids over a wide range of operating conditions: hydraulic diameter (0.51 – 6.0 mm), mass velocities (29 – 2303 kg/ m2 s), liquid – only Reynolds number (125 – 53,770), boiling number (0.31 – 44.3 × 10-4), and reduced pressure (0.005 – 0.78). The inputs to the model were liquid – only Weber number (Wefo), reduced pressure (PR), boiling number (Bo), heated to frictional perimeter ratio(PH/PF), capillary number (Ca) and density ratio (ρg/ρf), and the output was dryout incipience quality. The database was randomly divided into training data to learn GPR kernel (covariance) parameters using maximum likelihood estimation, and test data to evaluate the prediction accuracy of the outputs based on mean absolute error (MAE). Six – different types of covariance functions were tested, and GPR model with automatic relevance detection (ARD) rational quadratic covariance function showed the best overall performance. A performance comparison of approved GPR model was made with an existing highly reliable universal correlation to predict dryout incipience quality for mini / micro – channels. Results show that the developed GPR model exhibits superior generalization ability with an overall MAE of 6.03 %, and a significant reduction of 51.76 % in MAE compared with the universal correlation. Overall, the GPR model was found to be a data efficient machine learning technique for predicting dryout incipience quality for flow boiling in mini / micro – channels based on a consolidated database.