Bayesian inference for multivariate probit model with latent envelope.

The response envelope model proposed by Cook et al. (2010) is an efficient method to estimate the regression coefficient under the context of the multivariate linear regression model. It improves estimation efficiency by identifying material and immaterial parts of responses and removing the immaterial variation. The response envelope model has been investigated only for continuous response variables. In this paper, we propose the multivariate probit model with latent envelope, in short, the probit envelope model, as a response envelope model for multivariate binary response variables. The probit envelope model takes into account relations between Gaussian latent variables of the multivariate probit model by using the idea of the response envelope model. We address the identifiability of the probit envelope model by employing the essential identifiability concept and suggest a Bayesian method for the parameter estimation. We illustrate the probit envelope model via simulation studies and real-data analysis. The simulation studies show that the probit envelope model has the potential to gain efficiency in estimation compared to the multivariate probit model. The real data analysis shows that the probit envelope model is useful for multi-label classification.

Detection of invasive ductal carcinoma in quadrant breast areas by electrical impedance tomography implemented with gaussian relaxation-time distribution (EIT-GRTD).

Invasive ductal carcinoma (IDC) in breast specimens has been detected in the quadrant breast area: (I) upper outer, (II) upper inner, (III) lower inner, and (IV) lower outer areas by electrical impedance tomography implemented with Gaussian relaxation-time distribution (EIT-GRTD). The EIT-GRTD consists of two steps which are (1) the optimum frequencyfoptselection and (2) the time constant enhancement of breast imaging reconstruction.foptis characterized by a peak in the majority measurement pair of the relaxation-time distribution functionγ,which indicates the presence of IDC.γrepresents the inverse of conductivity and indicates the response of breast tissues to electrical currents across varying frequencies based on the Voigt circuit model. The EIT-GRTD is quantitatively evaluated by multi-physics simulations using a hemisphere container of mimic breast, consisting of IDC and adipose tissues as normal breast tissue under one condition with known IDC in quadrant breast area II. The simulation results show that EIT-GRTD is able to detect the IDC in four layers atfopt= 30, 170 Hz. EIT-GRTD is applied in the real breast by employed six mastectomy specimens from IDC patients. The placement of the mastectomy specimens in a hemisphere container is an important factor in the success of quadrant breast area reconstruction. In order to perform the evaluation, EIT-GRTD reconstruction images are compared to the CT scan images. The experimental results demonstrate that EIS-GRTD exhibits proficiency in the detection of the IDC in quadrant breast areas while compared qualitatively to CT scan images.

Extended Poisson Gaussian-Process Latent Variable Model for Unsupervised Neural Decoding.

Dimension reduction on neural activity paves a way for unsupervised neural decoding by dissociating the measurement of internal neural pattern reactivation from the measurement of external variable tuning. With assumptions only on the smoothness of latent dynamics and of internal tuning curves, the Poisson gaussian-process latent variable model (P-GPLVM; Wu et al., 2017) is a powerful tool to discover the low-dimensional latent structure for high-dimensional spike trains. However, when given novel neural data, the original model lacks a method to infer their latent trajectories in the learned latent space, limiting its ability for estimating the neural reactivation. Here, we extend the P-GPLVM to enable the latent variable inference of new data constrained by previously learned smoothness and mapping information. We also describe a principled approach for the constrained latent variable inference for temporally compressed patterns of activity, such as those found in population burst events during hippocampal sharp-wave ripples, as well as metrics for assessing the validity of neural pattern reactivation and inferring the encoded experience. Applying these approaches to hippocampal ensemble recordings during active maze exploration, we replicate the result that P-GPLVM learns a latent space encoding the animal's position. We further demonstrate that this latent space can differentiate one maze context from another. By inferring the latent variables of new neural data during running, certain neural patterns are observed to reactivate, in accordance with the similarity of experiences encoded by its nearby neural trajectories in the training data manifold. Finally, reactivation of neural patterns can be estimated for neural activity during population burst events as well, allowing the identification for replay events of versatile behaviors and more general experiences. Thus, our extension of the P-GPLVM framework for unsupervised analysis of neural activity can be used to answer critical questions related to scientific discovery.

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators.

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

A Gaussian-plume based Monte Carlo method for calculating radiation dose in the near field of buildings.

A Monte Carlo (MC) programme was written using the dose point kernel method to calculate doses in the roof zone of a building from nearby releases of radioactive gases. A Gaussian Plume Model (GPM) was parameterised to account for near-field building effects on plume spread and reflection from the roof. Rooftop recirculation zones and building-generated plume spread effects were accounted in a novel Dual Gaussian Plume (DGP) formulation used with the MC model, which allowed for the selection of angle of approach flow, plume release height in relation to the building and position of the release point in relation to the leading edge of the building. Three-dimensional wind tunnel concentration field data were used for the parameterisation. The MC code used the parameterised concentration field to calculate the contributions to effective dose from inhalation, cloud immersion from positron/beta particles, and gamma-ray dose for a wide range of receptor dose positions in the roof zone, including receptor positions at different heights above the roof. Broad trends in predicted radiation dose with angle of approach flow, release position in relation to the building and release height are shown. Alternative approaches for the derivation of the concentration field are discussed.

The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche.

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a "mixed" situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an "inverse" Allee effect, in which low density populations may access additional benefits.

Adaptive design of experiments to fit surrogate Gaussian process regression models allows fast sensitivity analysis of the input waveform for patient-specific 3D CFD models of liver radioembolization.

BACKGROUND AND OBJECTIVE: Patient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. METHODS: We extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75 %-125 % of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. RESULTS: We tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. CONCLUSIONS: Although the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

Unveiling Conformational States of CDK6 Caused by Binding of Vcyclin Protein and Inhibitor by Combining Gaussian Accelerated Molecular Dynamics and Deep Learning.

CDK6 plays a key role in the regulation of the cell cycle and is considered a crucial target for cancer therapy. In this work, conformational transitions of CDK6 were identified by using Gaussian accelerated molecular dynamics (GaMD), deep learning (DL), and free energy landscapes (FELs). DL finds that the binding pocket as well as the T-loop binding to the Vcyclin protein are involved in obvious differences of conformation contacts. This result suggests that the binding pocket of inhibitors (LQQ and AP9) and the binding interface of CDK6 to the Vcyclin protein play a key role in the function of CDK6. The analyses of FELs reveal that the binding pocket and the T-loop of CDK6 have disordered states. The results from principal component analysis (PCA) indicate that the binding of the Vcyclin protein affects the fluctuation behavior of the T-loop in CDK6. Our QM/MM-GBSA calculations suggest that the binding ability of LQQ to CDK6 is stronger than AP9 with or without the binding of the Vcyclin protein. Interaction networks of inhibitors with CDK6 were analyzed and the results reveal that LQQ contributes more hydrogen binding interactions (HBIs) and hot interaction spots with CDK6. In addition, the binding pocket endures flexibility changes from opening to closing states and the Vcyclin protein plays an important role in the stabilizing conformation of the T-loop. We anticipate that this work could provide useful information for further understanding the function of CDK6 and developing new promising inhibitors targeting CDK6.

Gaussian process regression coupled with mRMR to predict adulterant concentration in cocaine.

Street cocaine is often mixed with various substances that intensify its harmful effects. This paper proposes a framework to identify attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) intervals that best predict the concentration of adulterants in cocaine samples. Wavelengths are ranked according to their relevance through ReliefF and mRMR feature selection approaches, and an iterative process removes less relevant wavelengths based on the ranking suggested by each approach. Gaussian Process (GP) regression models are constructed after each wavelength removal and the prediction performance is evaluated using RMSE. The subset balancing a low RMSE value and a small percentage of retained wavelengths is chosen. The proposed framework was validated using a dataset consisting of 345 samples of cocaine with different amounts of levamisole, caffeine, phenacetin, and lidocaine. Averaged over the four adulterants, the GP regression coupled with the mRMR retained 1.07 % of the 662 original wavelengths, outperforming PLS and SVR regarding prediction performance.

A Gaussian process approach for rapid evaluation of skin tension.

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations, and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension. STATEMENT OF SIGNIFICANCE: To prevent unfavourable patient outcomes from reconstructive surgery, it is necessary to determine relevant subject-specific skin properties. For example, during a skin graft, it is necessary to estimate the pre-stretch of the skin to account for shrinkage upon excision. Existing methods are invasive or rely on the experience of the clinician. Our work aims to present an innovative framework to non-invasively determine in vivo material properties using the speed of a surface wave travelling through the skin. Our findings have implications for the planning of surgical procedures and provides further motivation for the use of elastic wave measurements to determine in vivo material properties.

Estimated greenhouse gas emissions in the Mbalmayo thermal power plant between 2016-2020 using the genetic-Gaussian algorithm coupling.

The greenhouse gas (GHG) emissions inventories in our context result from the production of electricity from fuel oil at the Mbalmayo thermal power plant between 2016 and 2020. Our study area is located in the Central Cameroon region. The empirical method of the second level of industrialisation was applied to estimate GHG emissions and the application of the genetic algorithm-Gaussian (GA-Gaussian) coupling method was used to optimise the estimation of GHG emissions. Our work is of an experimental nature and aims to estimate the quantities of GHG produced by the Mbalmayo thermal power plant during its operation. The search for the best objective function using genetic algorithms is designed to bring us closer to the best concentration, and the Gaussian model is used to estimate the concentration level. The results obtained show that the average monthly emissions in kilograms (kg) of GHGs from the Mbalmayo thermal power plant are: 526 kg for carbon dioxide (CO2), 971.41 kg for methane (CH4) and 309.41 kg for nitrous oxide (N2O), for an average monthly production of 6058.12 kWh of energy. Evaluation of the stack height shows that increasing the stack height helps to reduce local GHG concentrations. According to the Cameroonian standards published in 2021, the limit concentrations of GHGs remain below 30 mg/m3 for CO2 and 200 µg/m3 for N2O, while for CH4 we reach the limit value of 60 µg/m3. These results will enable the authorities to take appropriate measures to reduce GHG concentrations.

Learning active subspaces and discovering important features with Gaussian radial basis functions neural networks.

Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the radial basis function neural network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link.1.

GABA-edited MEGA-PRESS at 3 T: Does a measured macromolecule background improve linear combination modeling?

PURPOSE: The J-difference edited γ-aminobutyric acid (GABA) signal is contaminated by other co-edited signals-the largest of which originates from co-edited macromolecules (MMs)-and is consequently often reported as "GABA+." MM signals are broader and less well-characterized than the metabolites, and are commonly approximated using a Gaussian model parameterization. Experimentally measured MM signals are a consensus-recommended alternative to parameterized modeling; however, they are relatively under-studied in the context of edited MRS. METHODS: To address this limitation in the literature, we have acquired GABA-edited MEGA-PRESS data with pre-inversion to null metabolite signals in 13 healthy controls. An experimental MM basis function was derived from the mean across subjects. We further derived a new parameterization of the MM signals from the experimental data, using multiple Gaussians to accurately represent their observed asymmetry. The previous single-Gaussian parameterization, mean experimental MM spectrum and new multi-Gaussian parameterization were compared in a three-way analysis of a public MEGA-PRESS dataset of 61 healthy participants. RESULTS: Both the experimental MMs and the multi-Gaussian parameterization exhibited reduced fit residuals compared to the single-Gaussian approach (p = 0.034 and p = 0.031, respectively), suggesting they better represent the underlying data than the single-Gaussian parameterization. Furthermore, both experimentally derived models estimated larger MM fractional contribution to the GABA+ signal for the experimental MMs (58%) and multi-Gaussian parameterization (58%), compared to the single-Gaussian approach (50%). CONCLUSIONS: Our results indicate that single-Gaussian parameterization of edited MM signals is insufficient and that both experimentally derived GABA+ spectra and their parameterized replicas improve the modeling of GABA+ spectra.

Sample size determination for prediction models via learning-type curves.

This article is concerned with sample size determination methodology for prediction models. We propose to combine the individual calculations via learning-type curves. We suggest two distinct ways of doing so, a deterministic skeleton of a learning curve and a Gaussian process centered upon its deterministic counterpart. We employ several learning algorithms for modeling the primary endpoint and distinct measures for trial efficacy. We find that the performance may vary with the sample size, but borrowing information across sample size universally improves the performance of such calculations. The Gaussian process-based learning curve appears more robust and statistically efficient, while computational efficiency is comparable. We suggest that anchoring against historical evidence when extrapolating sample sizes should be adopted when such data are available. The methods are illustrated on binary and survival endpoints.

Novel gene-specific Bayesian Gaussian mixture model to predict the missense variants pathogenicity of Sanfilippo syndrome.

MPS III is an autosomal recessive lysosomal storage disease caused mainly by missense variants in the NAGLU, GNS, HGSNAT, and SGSH genes. The pathogenicity interpretation of missense variants is still challenging. We aimed to develop unsupervised clustering-based pathogenicity predictor scores using extracted features from eight in silico predictors to predict the impact of novel missense variants of Sanfilippo syndrome. The model was trained on a dataset consisting of 415 uncertain significant (VUS) missense NAGLU variants. Performance The SanfilippoPred tool was evaluated by validation and test datasets consisting of 197-labelled NAGLU missense variants, and its performance was compared versus individual pathogenicity predictors using receiver operating characteristic (ROC) analysis. Moreover, we tested the SanfilippoPred tool using extra-labelled 427 missense variants to assess its specificity and sensitivity threshold. Application of the trained machine learning (ML) model on the test dataset of labelled NAGLU missense variants showed that SanfilippoPred has an accuracy of 0.93 (0.86-0.97 at CI 95%), sensitivity of 0.93, and specificity of 0.92. The comparative performance of the SanfilippoPred showed better performance (AUC = 0.908) than the individual predictors SIFT (AUC = 0.756), Polyphen-2 (AUC = 0.788), CADD (AUC = 0.568), REVEL (AUC = 0.548), MetaLR (AUC = 0.751), and AlphMissense (AUC = 0.885). Using high-confidence labelled NAGLU variants, showed that SanfilippoPred has an 85.7% sensitivity threshold. The poor correlation between the Sanfilippo syndrome phenotype and genotype represents a demand for a new tool to classify its missense variants. This study provides a significant tool for preventing the misinterpretation of missense variants of the Sanfilippo syndrome-relevant genes. Finally, it seems that ML-based pathogenicity predictors and Sanfilippo syndrome-specific prediction tools could be feasible and efficient pathogenicity predictors in the future.

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components.

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

SAN: Mitigating spatial covariance heterogeneity in cortical thickness data collected from multiple scanners or sites.

In neuroimaging studies, combining data collected from multiple study sites or scanners is becoming common to increase the reproducibility of scientific discoveries. At the same time, unwanted variations arise by using different scanners (inter-scanner biases), which need to be corrected before downstream analyses to facilitate replicable research and prevent spurious findings. While statistical harmonization methods such as ComBat have become popular in mitigating inter-scanner biases in neuroimaging, recent methodological advances have shown that harmonizing heterogeneous covariances results in higher data quality. In vertex-level cortical thickness data, heterogeneity in spatial autocorrelation is a critical factor that affects covariance heterogeneity. Our work proposes a new statistical harmonization method called spatial autocorrelation normalization (SAN) that preserves homogeneous covariance vertex-level cortical thickness data across different scanners. We use an explicit Gaussian process to characterize scanner-invariant and scanner-specific variations to reconstruct spatially homogeneous data across scanners. SAN is computationally feasible, and it easily allows the integration of existing harmonization methods. We demonstrate the utility of the proposed method using cortical thickness data from the Social Processes Initiative in the Neurobiology of the Schizophrenia(s) (SPINS) study. SAN is publicly available as an R package.

Neurovascular Coupling Analysis Based on Multivariate Variational Gaussian Process Convergent Cross-Mapping.

Neurovascular coupling (NVC) provides important insights into the intricate activity of brain functioning and may aid in the early diagnosis of brain diseases. Emerging evidences have shown that NVC could be assessed by the coupling between electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS). However, this endeavor presents significant challenges due to the absence of standardized methodologies and reliable techniques for coupling analysis of these two modalities. In this study, we introduced a novel method, i.e., the collaborative multi-output variational Gaussian process convergent cross-mapping (CMVGP-CCM) approach to advance coupling analysis of EEG and fNIRS. To validate the robustness and reliability of the CMVGP-CCM method, we conducted extensive experiments using chaotic time series models with varying noise levels, sequence lengths, and causal driving strengths. In addition, we employed the CMVGP-CCM method to explore the NVC between EEG and fNIRS signals collected from 26 healthy participants using a working memory (WM) task. Results revealed a significant causal effect of EEG signals, particularly the delta, theta, and alpha frequency bands, on the fNIRS signals during WM. This influence was notably observed in the frontal lobe, and its strength exhibited a decline as cognitive demands increased. This study illuminates the complex connections between brain electrical activity and cerebral blood flow, offering new insights into the underlying NVC mechanisms of WM.

Morphological Features Among Gaussian, Sagittal, and Tangential Curvature Maps in Normal and Keratoconus Eyes Using Anterior Segment Optical Coherence Tomography.

PURPOSE: To investigate and compare the morphological features and differences among Gaussian, Sagittal, and Tangential anterior corneal curvature maps obtained with an anterior segment optical coherence tomographer combined with a Placido disc MS-39 device in keratoconus (KC) and normal eyes. METHODS: Prospective, cross-sectional study including 37 KC and 51 healthy eyes. The pattern of astigmatism and maximum keratometry (Kmax), keratometry at the thinnest point (Ktp) and 2 mm diameter (K 2mm ), and inferior-superior dioptric asymmetry values were obtained and calculated from Gaussian, Tangential, and Sagittal curvature maps using the MS-39 (CSO). RESULTS: In KC eyes, an asymmetric bowtie pattern was observed in 64.86% (24/37), 64.86% (24/37), and 0% in the Sagittal, Tangential, and Gaussian maps, respectively. In normal eyes, 51.0% (26/51), 51.0% (26/51), and 0% showed a symmetric bowtie pattern in the Sagittal, Tangential, and Gaussian maps, respectively. There was a significant difference for the variables Kmax, Ktp, and K 2mm inferior among the Gaussian, Tangential, and Sagittal maps in both normal and KC groups. Sensitivity discriminating between normal and KC eyes was 100%, 97.3%, and 90.9% and specificity was 94.1%, 100%, and 100% for Kmax coming from the Tangential, Gaussian, and Sagittal maps, respectively. CONCLUSIONS: Gaussian maps displayed significantly different morphological features when compared with Sagittal and Tangential maps in normal and KC eyes. Anterior curvature maps from Gaussian maps do not show the morphological pattern of symmetric bowtie in normal eyes nor asymmetric bowtie in KC eyes. Kmax from Gaussian maps are more specific, however less sensitive than Tangential maps in discriminating KC from normal eyes.