non-Gaussian Models Research Articles

Prediction of machine state for non-Gaussian degradation model using Hidden Markov Model approach

Machinery health management becomes an essential issue in many sectors. The ultimate goal is to predict machinery degradation and accordingly plan maintenance actions. However, prediction becomes much harder if data is noisy. We propose a procedure for on-line prediction of the forthcoming machine state. This procedure is dedicated to the non-Gaussian (impulsive) health index (HI) data. It is based on a simplified degradation model with three machine states, i.e. healthy, warning and alarm, described in terms of a Hidden Markov Model (HMM). Using simulated trajectories we demonstrate that the α-stable HMM dedicated to time series with impulsive behaviour outperforms the classical Gaussian approach and can be an efficient alternative in such a case. In particular, the percentage errors of the predicted alarm state transition points decrease from 20%−45% to 1%−6%, if the α-stable HMM is used instead of the Gaussian one. We illustrate the proposed methodology for two datasets acquired during experiment on the VIBstand test rig and for a benchmark FEMTO dataset.

Predicting the Ki-67 proliferation index in cervical cancer: a preliminary comparative study of four non-Gaussian diffusion-weighted imaging models combined with histogram analysis.

The prognosis for patients with cervical cancer (CC) is strongly correlated with the Ki-67 proliferation index (PI). However, the Ki-67 PI obtained through biopsy has certain limitations. The non-Gaussian distribution diffusion model of magnetic resonance imaging (MRI) may play an important role in characterizing tissue heterogeneity. At present, there are limited data available concerning the prediction of Ki-67 PI using models based on histogram features of non-Gaussian diffusion distribution. This study aimed to determine whether preoperative histogram features from multiple non-Gaussian models of diffusion-weighted imaging can predict the Ki-67 PI in patients with CC. Our cross-sectional prospective study recruited a total of 53 patients suspected of having CC who underwent 3.0-T MRI at Sun Yat-sen Memorial Hospital of Sun Yat-sen University between January 2022 and January 2023. Fifteen b values (0-4,000 s/mm2) were used for diffusion-weighted imaging. A total of nine parameters from four non-Gaussian diffusion-weighted imaging models, including continuous-time random walk (CTRW), diffusion kurtosis imaging (DKI), fractional order calculus (FROC), and intravoxel incoherent motion (IVIM), were used. Whole-tumor volumetric histogram analysis of these parameters was then obtained. In logistic regression, significant histogram characteristics were statistically examined across two groups to build the final prediction model. To assess diagnostic parameters of the proposed model in the diagnosis of the Ki-67 PI, along with the sensitivity, specificity, and diagnostic accuracy of these various parameters from the four models, receiver operating feature analysis was applied. Among the 53 patients (55.3±9.6 years, ranging from 23 to 79 years) included in the study, 15 had a Ki-67 PI ≤50% and 38 had a Ki-67 PI >50%. Univariable analysis determined that 12 histogram features were statistically different between the two groups. In multivariable logistic regression, we ultimately selected 6 histogram features to construct the final prediction model, with CTRW_α_10th percentile [odds ratio (OR) =0.955; 95% confidence interval (CI): 0.92-0.99; P=0.019], CTRW_α_robust mean absolute deviation (OR =0.893; 95% CI: 0.81-0.99; P=0.028), and CTRW_α_uniformity (OR =0.000, 95% CI: 0.00-0.90, P=0.047) being the independent predictive variables. The area under the curve of the combined prediction model was 0.845 (95% CI: 0.74-0.95), with a sensitivity of 78.9% (95% CI: 0.63-0.90), a specificity of 86.7% (95% CI: 0.60-0.98), an accuracy of 81.1% (95% CI: 0.68-0.91), a positive predictive value of 93.8% (95% CI: 0.79-0.99), and a negative predictive value of 61.9% (95% CI: 0.38-0.82). The histogram features of multiple non-Gaussian diffusion-weighted imaging can help to predict the Ki-67 PI of CC, providing a new method for the noninvasive evaluation of critical biological features of CC.

Extension of the characterization of non-Gaussianity in gravitational wave detectors with a statistical hypothesis test

Abstract In gravitational wave (GW) astronomy, non-Gaussian noise, such as scattered light noise disturbs stable interferometer operation, limiting the interferometer’s sensitivity, and reducing the reliability of the analyses. In scattered light noise, the non-Gaussian noise dominates the sensitivity in a low frequency range of less than a few hundred Hz, which is sensitive to GWs from compact binary coalescence. This non-Gaussian noise prevents reliable parameter estimation, since several analysis methods are optimized only for Gaussian noise. Therefore, identifying data contaminated by non-Gaussian noise is important. In this work, we extended the conventional method to evaluate non-Gaussian noise, the Rayleigh statistic, by using a statistical hypothesis test to determine a threshold for non-Gaussian noise. First, we estimated the distribution of the Rayleigh statistic against Gaussian noise, called the background distribution, and validated that our extension serves as the hypothetical test. The threshold on the Rayleigh statistic is estimated at 0.73 and 1.28 when the significance level is 0.05, and the sample size is 39. Moreover, we investigated the detection efficiency by assuming two non-Gaussian noise models. For example, for the model with strong scattered light noise, the true positive rate (TPR) was always above 0.7 when the significance level was 0.05. For the demonstration, we applied our extension with the estimated thresholds to the real data. We confirmed our extension provides the binarized outputs of the statistical tests and contributes to finding the non-Gaussian noise in the real data. The results showed that our extension can contribute to an initial detection of non-Gaussian noise and lead to further investigation of the origin of the non-Gaussian noise.

A novel class of non-Gaussian system performance assessment and controller parameter tuning methods

Traditional variance-based control performance assessment (CPA) and controller parameter tuning (CPT) methods tend to ignore non-Gaussian external disturbances. To address this limitation, this study proposes a novel class of CPA and CPT methods for non-Gaussian single-input single-output systems, denoted as data Gaussianization (inverse) transformation methods. The idea of quantile transformation is used to transform the non-Gaussian data with the goal of maximizing mutual information into virtual Gaussian data. In addition, optimal system data for the virtual loop are mapped back to the actual non-Gaussian system using quantile inverse transformation. Furthermore, a CARMA model-based recursive extended least square algorithm and a CARMA model-based least absolute deviation iterative algorithm are used to identify virtual Gaussian and non-Gaussian system process models, respectively, while implementing the CPT. Finally, a unified framework is proposed for the CPA and CPT of a non-Gaussian control system. The simulation results demonstrate that the proposed strategy can provide a consistent benchmark judgment criterion (threshold) for different non-Gaussian noises, and the tuned controller parameters have good performance.

Stochastic mortality model with respect to mixed fractional Poisson process: Calibration and empirical analysis of long-range dependence in actuarial valuation

Recently, many studies have adopted the fractional stochastic mortality process in characterising the long-range dependence (LRD) feature of mortality dynamics, while there are still fewer appropriate non-Gaussian fractional models to describe it. We propose a stochastic mortality process driven by a mixture of Brownian motion and modified fractional Poisson process to capture the LRD of mortality rates. The survival probability under this new stochastic mortality model keeps flexibility and consistency with existing affine-form mortality models, which makes the model convenient in evaluating mortality-linked products under the market-consistent method. The formula of survival probability also considers the historical information from survival data, which enables the model to capture historical health records of lives. The LRD feature is reflected by our proposed model in the empirical analysis, which includes the calibration and prediction of survival curves based on recent generation data in Japan and the UK. Finally, the consequent empirical analysis of annuity pricing illustrates the difference of whether this feature is involved in actuarial valuation.

Solving the puzzle of quality of life in cancer: integrating causal inference and machine learning for data-driven insights

BackgroundUnderstanding the determinants of global quality of life in cancer patients is crucial for improving their overall well-being. While correlations between various factors and quality of life have been established, the causal relationships remain largely unexplored. This study aimed to identify the causal factors influencing global quality of life in cancer patients and compare them with known correlative factors.MethodsWe conducted a retrospective analysis of European Organization for Research and Treatment of Cancer Quality of Life Questionnaire data, alongside demographic and disease-related features, collected from new cancer patients during their initial visit to an oncology outpatient clinic. Correlations with global quality of life were identified using univariate and multivariate regression analyses. Causal inference analysis was performed using two approaches. First, we employed the Dowhy Python library for causal analysis, incorporating prior information and manual characterization of an acyclic graph. Second, we utilized the Linear Non-Gaussian Acyclic Model (LiNGAM) machine learning algorithm from the Lingam Python library, which automatically generated an acyclic graph without prior information. The significance level was set at p < 0.05.ResultsMultivariate analysis of 469 new admissions revealed that disease stage, role functioning, emotional functioning, social functioning, fatigue, pain and diarrhea were linked with global quality of life. The most influential direct causal factors were emotional functioning, social functioning, and physical functioning, while the most influential indirect factors were physical functioning, emotional functioning, and fatigue. Additionally, the most prominent total causal factors were identified as type of cancer (diagnosis), cancer stage, and sex, with total causal effect ratios of -9.47, -4.67, and − 1.48, respectively. The LiNGAM algorithm identified type of cancer (diagnosis), nausea and vomiting and social functioning as significant, with total causal effect ratios of -9.47, -0.42, and 0.42, respectively.ConclusionsThis study identified that causal factors for global quality of life in new cancer patients are distinct from correlative factors. Understanding these causal relationships could provide valuable insights into the complex dynamics of quality of life in cancer patients and guide targeted interventions to improve their well-being.

A Bayesian incorporated linear non-Gaussian acyclic model for multiple directed graph estimation to study brain emotion circuit development in adolescence.

Emotion perception is essential to affective and cognitive development which involves distributed brain circuits. Emotion identification skills emerge in infancy and continue to develop throughout childhood and adolescence. Understanding the development of the brain's emotion circuitry may help us explain the emotional changes during adolescence. In this work, we aim to deepen our understanding of emotion-related functional connectivity (FC) from association to causation. We proposed a Bayesian incorporated linear non-Gaussian acyclic model (BiLiNGAM), which incorporated association model into the estimation pipeline. Simulation results indicated stable and accurate performance over various settings, especially when the sample size was small. We used fMRI data from the Philadelphia Neurodevelopmental Cohort (PNC) to validate the approach. It included 855 individuals aged 8-22 years who were divided into five different adolescent stages. Our network analysis revealed the development of emotion-related intra- and intermodular connectivity and pinpointed several emotion-related hubs. We further categorized the hubs into two types: in-hubs and out-hubs, as the center of receiving and distributing information, respectively. In addition, several unique developmental hub structures and group-specific patterns were discovered. Our findings help provide a directed FC template of brain network organization underlying emotion processing during adolescence.

Whole-tumor histogram analysis of multiple non-Gaussian diffusion models at high b values for assessing cervical cancer.

To assess the diagnostic potential of whole-tumor histogram analysis of multiple non-Gaussian diffusion models for differentiating cervical cancer (CC) aggressive status regarding of pathological types, differentiation degree, stage, and p16 expression. Patients were enrolled in this prospective single-center study from March 2022 to July 2023. Diffusion-weighted images (DWI) were obtained including 15 b-values (0 ~ 4000s/mm2). Diffusion parameters derived from four non-Gaussian diffusion models including continuous-time random-walk (CTRW), diffusion-kurtosis imaging (DKI), fractional order calculus (FROC), and intravoxel incoherent motion (IVIM) were calculated, and their histogram features were analyzed. To select the most significant features and establish predictive models, univariate analysis and multivariate logistic regression were performed. Finally, we evaluated the diagnostic performance of our models by using receiver operating characteristic (ROC) analyses. 89 women (mean age, 55 ± 11 years) with CC were enrolled in our study. The combined model, which incorporated the CTRW, DKI, FROC, and IVIM diffusion models, offered a significantly higher AUC than that from any individual models (0.836 vs. 0.664, 0.642, 0.651, 0.649, respectively; p < 0.05) in distinguishing cervical squamous cell cancer from cervical adenocarcinoma. To distinguish tumor differentiation degree, except the combined model showed a better predictive performance compared to the DKI model (AUC, 0.839 vs. 0.697, respectively; p < 0.05), no significant differences in AUCs were found among other individual models and combined model. To predict the International Federation of Gynecology and Obstetrics (FIGO) stage, only DKI and FROC model were established and there was no significant difference in predictive performance among different models. In terms of predicting p16 expression, the predictive ability of DKI model is significantly lower than that of FROC and combined model (AUC, 0.693 vs. 0.850, 0.859, respectively; p < 0.05). Multiple non-Gaussian diffusion models with whole-tumor histogram analysis show great promise to assess the aggressive status of CC.

Pulsed Laser Links Simulation for Small Satellite Clock Model Estimation

The expansion of satellite constellation applications brings attention to the need for responsive, reliable satellite communication. For preflight technology assessment of missions, a simulation of two spacecraft in low Earth orbit has been created to estimate clock synchronization and precision orbit determination based on measured instrumentation performance. A novel MATLAB-based numerical simulator was developed to model spacecraft-to-spacecraft laser time-transfer and estimate the offset between the spacecraft clocks over time. This simulation includes timing errors associated with laser pulse detection, as well as non-Gaussian clock drift models. Two on-board clocks are modeled: a cesium-based chip-scale atomic clock and a rubidium-based miniature atomic clock. The positions and velocities of the spacecraft at a reference epoch and the constant coefficients of a polynomial clock model are estimated. Results compare the estimated clock model of a mission operation that only uses GPS measurements and one that uses both GPS and laser pulse time-of-flight measurements between spacecraft referenced to their on-board clocks. Including lasing measurements reduces the root-mean-square clock model error to approximately 80% of the RMS of the cases with only GPS measurements. This simulation tool can be used to optimize the lasing operations schedule based on mission timing performance objectives.

Non-Gaussian diffusion metrics with whole-tumor histogram analysis for bladder cancer diagnosis: muscle invasion and histological grade

PurposeTo investigate the performance of histogram features of non-Gaussian diffusion metrics for diagnosing muscle invasion and histological grade in bladder cancer (BCa).MethodsPatients were prospectively allocated to MR scanner1 (training cohort) or MR2 (testing cohort) for conventional diffusion-weighted imaging (DWIconv) and multi-b-value DWI. Metrics of continuous time random walk (CTRW), diffusion kurtosis imaging (DKI), fractional-order calculus (FROC), intravoxel incoherent motion (IVIM), and stretched exponential model (SEM) were simultaneously calculated using multi-b-value DWI. Whole-tumor histogram features were extracted from DWIconv and non-Gaussian diffusion metrics for logistic regression analysis to develop diffusion models diagnosing muscle invasion and histological grade. The models’ performances were quantified by area under the receiver operating characteristic curve (AUC).ResultsMR1 included 267 pathologically-confirmed BCa patients (median age, 67 years [IQR, 46–82], 222 men) and MR2 included 83 (median age, 65 years [IQR, 31–82], 73 men). For discriminating muscle invasion, CTRW achieved the highest testing AUC of 0.915, higher than DWIconv’s 0.805 (p = 0.014), and similar to the combined diffusion model’s AUC of 0.885 (p = 0.076). For differentiating histological grade of non-muscle-invasion bladder cancer, IVIM outperformed a testing AUC of 0.897, higher than DWIconv’s 0.694 (p = 0.020), and similar to the combined diffusion model’s AUC of 0.917 (p = 0.650). In both tasks, DKI, FROC, and SEM failed to show diagnostic superiority over DWIconv (p > 0.05).ConclusionCTRW and IVIM are two potential non-Gaussian diffusion models to improve the MRI application in assessing muscle invasion and histological grade of BCa, respectively.Critical relevance statementOur study validates non-Gaussian diffusion imaging as a reliable, non-invasive technique for early assessment of muscle invasion and histological grade in BCa, enhancing accuracy in diagnosis and improving MRI application in BCa diagnostic procedures.Key PointsMuscular invasion largely determines bladder salvageability in bladder cancer patients.Evaluated non-Gaussian diffusion metrics surpassed DWIconv in BCa muscle invasion and histological grade diagnosis.Non-Gaussian diffusion imaging improved MRI application in preoperative diagnosis of BCa.Graphical

Bayesian Estimation of Inverted Beta Mixture Models With Extended Stochastic Variational Inference for Positive Vector Classification.

The finite inverted beta mixture model (IBMM) has been proven to be efficient in modeling positive vectors. Under the traditional variational inference framework, the critical challenge in Bayesian estimation of the IBMM is that the computational cost of performing inference with large datasets is prohibitively expensive, which often limits the use of Bayesian approaches to small datasets. An efficient alternative provided by the recently proposed stochastic variational inference (SVI) framework allows for efficient inference on large datasets. Nevertheless, when using the SVI framework to address the non-Gaussian statistical models, the evidence lower bound (ELBO) cannot be explicitly calculated due to the intractable moment computation. Therefore, the algorithm under the SVI framework cannot directly use stochastic optimization to optimize the ELBO, and an analytically tractable solution cannot be derived. To address this problem, we propose an extended version of the SVI framework with more flexibility, namely, the extended SVI (ESVI) framework. This framework can be used in many non-Gaussian statistical models. First, some approximation strategies are applied to further lower the ELBO to avoid intractable moment calculations. Then, stochastic optimization with noisy natural gradients is used to optimize the lower bound. The excellent performance and effectiveness of the proposed method are verified in real data evaluation.

Prediction and causal inference of hyperuricemia using gut microbiota.

Hyperuricemia (HUA) is a symptom of high blood uric acid (UA) levels, which causes disorders such as gout and renal urinary calculus. Prolonged HUA is often associated with hypertension, atherosclerosis, diabetes mellitus, and chronic kidney disease. Studies have shown that gut microbiota (GM) affect these chronic diseases. This study aimed to determine the relationship between HUA and GM. The microbiome of 224 men and 254 women aged 40years was analyzed through next-generation sequencing and machine learning. We obtained GM data through 16S rRNA-based sequencing of the fecal samples, finding that alpha-diversity by Shannon index was significantly low in the HUA group. Linear discriminant effect size analysis detected a high abundance of the genera Collinsella and Faecalibacterium in the HUA and non-HUA groups. Based on light gradient boosting machine learning, we propose that HUA can be predicted with high AUC using four clinical characteristics and the relative abundance of nine bacterial genera, including Collinsella and Dorea. In addition, analysis of causal relationships using a direct linear non-Gaussian acyclic model indicated a positive effect of the relative abundance of the genus Collinsella on blood UA levels. Our results suggest abundant Collinsella in the gut can increase blood UA levels.

Performance assessment of corroded stiffened steel plates considering non-Gaussian spatial correlated corrosion random field

This paper investigates the effect of corrosion randomness on the compression performance of stiffened steel plates. An anisotropic non-Gaussian random filed model is proposed to characterize the corrosion depth of the corroded steel plate surface. The specimens of corroded steel plate were obtained utilizing the artificial climate environment method. Corrosion characteristics were measured through 3D-scanning and reverse modeling. Statistical methods are utilized to analyze corrosion depth, including probability distribution and correlation coefficient. Two models are proposed for steel plate placing flatly and inclinedly, respectively. It is found that for both models corrosion depth follows truncated GEV distribution, and the correlation coefficient follows a bidirectional exponential function. To investigate the effect of non-Gaussian and correlation characteristics on bearing capacity, the proposed model is used for generating anisotropic non-Gaussian corrosion random fields for stiffened steel plates. Generated samples were used for finite element analysis. It is found the ignorance of non-Gaussian or correlation of the corrosion depth field will underestimate the deterioration of bearing capacity of stiffened steel plates. Finally, a parametric study on the correlation coefficients of the corrosion field indicates that correlation length will affect the residual bearing capacity of corroded steel plate. The proposed random field for corrosion depth of steel plate could be used for potential application on the safety assessment of corroded steel structures.

Problematic social media use and psychological symptoms in adolescents

PurposeThis study examined time trends in significant child and adolescent psychological symptoms and explored the association of frequent and problematic social media use with these symptoms.MethodsTime trends in psychological symptoms were assessed using data from five waves of the international survey of Health Behavior in School-aged Children (HBSC), conducted between 2001 and 2018 (N = 1,036,869). The associations of frequent and problematic social media use with significant psychological symptoms were assessed by hierarchical multinomial logistic regression using data from 2001–2002 and the 2017–2018 survey waves. The direction of effect between social media use variables and psychological symptoms was explored using Linear Non-Gaussian Acyclic Models (LiNGAM).ResultsPrevalence of more severe psychological symptoms increased from 6.7% in 2001–2002 to 10.4% in the 2017–2018 survey waves. The increase was especially large among 15-year old and older girls: from 10.9 to 19.1%. The higher prevalence of more severe psychological symptoms in 2017–2018 compared with 2001–2002 was eliminated after adjusting the model for problematic social media use. LiNGAM analysis supported the direction of effect going from social media use and problematic social media use to psychological symptoms.ConclusionsThe findings suggest that frequent and problematic use of social media contribute to the increasing trend of psychological symptoms in adolescents in recent years.

Determining causality in travel mode choice

This article presents one of the pioneering studies on causal modeling in travel mode choice decision-making using causal discovery algorithms. These models are a major advancement from conventional correlation-based techniques. We propose a novel methodology that combines causal discovery with structural equation modeling (SEM). This modeling approach overcomes some of the limitations of SEM by combining the strengths of both causal discovery and SEM. Causal discovery algorithms determine causal graphs from observational data and domain knowledge, and SEMs estimate direct causal effects and test the performance of causal discovery algorithms. In this study, we test four causal discovery algorithms: Peter-Clark (PC), Fast Causal Inference (FCI), Fast Greedy Equivalence Search (FGES), and Direct Linear Non-Gaussian Acyclic Models (DirectLiNGAM). The results show that DirectLiNGAM based SEM model best captures causality in mode choice behavior. It passes several goodness-of-fit tests, including Root Mean Square Error of Approximation (RMSEA) and Goodness-of-Fit Index (GFI), and it achieves the lowest Bayesian Information Criterion (BIC) value. The analyses are conducted on data collected from the 2017 National Household Travel Survey in the New York Metropolitan area.

Efficient Algorithms for Non-gaussian Single Index Models with Generative Priors

In this work, we focus on high-dimensional single index models with non-Gaussian sensing vectors and generative priors. More specifically, our goal is to estimate the underlying signal from i.i.d. realizations of the semi-parameterized single index model, where the underlying signal is contained in (up to a constant scaling) the range of a Lipschitz continuous generative model with bounded low-dimensional inputs, the sensing vector follows a non-Gaussian distribution, the noise is a random variable that is independent of the sensing vector, and the unknown non-linear link function is differentiable. Using the first- and second-order Stein's identity, we introduce efficient algorithms to obtain estimated vectors that achieve the near-optimal statistical rate. Experimental results on image datasets are provided to support our theory.

Elastic instabilities of soft laminates with stiffening behavior

This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications.

Functional linear non-Gaussian acyclic model for causal discovery

Functional linear non-Gaussian acyclic model for causal discovery

Direct lingam and visibility graphs for analyzing brain connectivity in BCI.

The brain-computer interface (BCI) is a direct pathway of communication between the electrical activity of the brain and an external device. The present paper was aimed to investigate directed connectivity between different areas of the brain during motor imagery (MI)-based BCI. For this purpose, two methods were implemented including, Limited Penetrable Horizontal Visibility Graph (LPHVG) and Direct Lingam. The visibility graph (VG) is a robust algorithm for analyzing complex systems such as the brain. Direct Lingam uses a non-Gaussian model to extract causal links which is appropriate for analyzing large-scale connectivity. First, LPHVG map MI-EEG (electroencephalogram) signals into networks. After extracting the topological features of the networks, a support vector machine classifier was applied to categorize multi-classes MI. The network of all classes was found to be different from one another, and the kappa value of classification was 0.68. The degree sequence of LPHVG was calculated for each channel in order to obtain the direction of brain information flow. Transfer entropy (TE) is used to compute the relations of the channel degree sequence. Therefore, the directed graph between channels was formed. This method is called LPHVG_TE directed graph. The Bayesian network, also known as the Direct LiNGAM model, was implemented for the second method. Finally, images of the LPHVG and Direct Lingam were classified by convolutional neural network (CNN). In this study, Data sets 2a of BCI competition IV was used. The outcomes reveal that the brain network developed by LPHVG (92.7%) might be more effective to distinguish 4 classes of MI than the Direct Lingam (90.6%) and it was shown that graph theory has the potential to get better efficiency of BCI.

Large effects and the infinitesimal model

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring’s genetic trait component and the average of their two parents’ genetic trait components is Normally distributed and independent of the parents’ values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent α<2, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a “stable distribution”, for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.