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Understanding the evolutionary mechanisms underlying the maintenance of individual differences in behavior and physiology is a fundamental goal in ecology and evolution. The pace-of-life syndrome hypothesis is often invoked to explain the maintenance of such within-population variation. This hypothesis predicts that behavioral traits are part of a suite of correlated traits that collectively determine an individual's propensity to prioritize reproduction or survival. A key assumption of this hypothesis is that these traits are underpinned by genetic trade-offs among life-history traits: genetic variants that increase fertility, reproduction and growth might also reduce lifespan. We performed a systematic literature review and meta-analysis to summarize the evidence for the existence of genetic trade-offs between five key life-history traits: survival, growth rate, body size, maturation rate, and fertility. Counter to our predictions, we found an overall positive genetic correlation between survival and other life-history traits and no evidence for any genetic correlations between the non-survival life-history traits. This finding was generally consistent across pairs of life-history traits, sexes, life stages, lab vs. field studies, and narrow- vs. broad-sense correlation estimates. Our study highlights that genetic trade-offs may not be as common, or at least not as easily quantifiable, in animals as often assumed.

In this paper, a novel test for testing whether data are missing completely at random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic coincides with the well-known Little's $ d^2 $ d2 statistic in the case of a multivariate data that has only one variable susceptible to missingness. Then, the extensive simulation study is conducted to examine the performance of the test in terms of the preservation of type I error and in terms of power. Various underlying distributions, dimensions of the data, sample sizes and alternatives are used. Performance of the Little's MCAR test is used as a benchmark for the comparison. The novel test shows better performance in all of the studied scenarios, better preserving the type I error and having higher empirical powers for every studied alternative. [ABSTRACT FROM AUTHOR]

Multivariate analysis is becoming central in studies investigating high-throughput molecular data, yet, some important features of these data are seldom explored. Here, we present MANOCCA (Multivariate Analysis of Conditional CovAriance), a powerful method to test for the effect of a predictor on the covariance matrix of a multivariate outcome. The proposed test is by construction orthogonal to tests based on the mean and variance and is able to capture effects that are missed by both approaches. We first compare the performances of MANOCCA with existing correlation-based methods and show that MANOCCA is the only test correctly calibrated in simulation mimicking omics data. We then investigate the impact of reducing the dimensionality of the data using principal component analysis when the sample size is smaller than the number of pairwise covariance terms analysed. We show that, in many realistic scenarios, the maximum power can be achieved with a limited number of components. Finally, we apply MANOCCA to 1000 healthy individuals from the Milieu Interieur cohort, to assess the effect of health, lifestyle and genetic factors on the covariance of two sets of phenotypes, blood biomarkers and flow cytometry–based immune phenotypes. Our analyses identify significant associations between multiple factors and the covariance of both omics data. [ABSTRACT FROM AUTHOR]

Removing stripe noise from the GRACE (Gravity Recovery and Climate Experiment) monthly gravity field model is crucial for accurately interpreting temporal gravity variations. The conventional parameter filtering (CPF) approach expresses the signal components with a harmonic model while neglecting non-periodic and interannual signals. To address this issue, we improve the CPF approach by incorporating those ignored signals using a first-order Gauss–Markov process. The improved parameter filtering (IPF) approach is used to filter the monthly spherical harmonic coefficients (SHCs) of the Tongji-Grace2018 model from April 2002 to December 2016. Compared to the CPF approach, the IPF approach exhibits stronger signals in low-degree SHCs (i.e., degrees below 20) and lower noise in high-order SHCs (i.e., orders above 40), alongside higher signal-to-noise ratios and better agreement with CSR mascon product and NOAH model in global and basin analysis. Across the 22 largest basins worldwide, the average Nash–Sutcliffe coefficients of latitude-weighted terrestrial water storage anomalies filtered by the IPF approach relative to those derived from CSR mascon product and NOAH model are 0.90 and 0.21, significantly higher than 0.17 and − 0.71, filtered by the CPF approach. Simulation experiments further demonstrate that the IPF approach yields the filtered results closest to the actual signals, reducing root-mean-square errors by 30.1%, 25.9%, 45.3%, 30.9%, 46.6%, 32.7%, 39.6%, and 38.2% over land, and 2.8%, 54.4%, 70.1%, 15.3%, 69.2%, 46.5%, 40.4%, and 23.6% over the ocean, compared to CPF, DDK3, least square, RMS, Gaussian 300, Fan 300, Gaussian 300 with P4M6, and Fan 300 with P4M6 filtering approaches, respectively [ABSTRACT FROM AUTHOR]

Aiming at the problems of low convergence accuracy and ease of trapping into local stagnation in the equilibrium optimizer, this paper proposed an improved equilibrium optimizer based on adaptive crossover and covariance learning. Firstly, this algorithm constructed an external archive to retain the historically dominant individuals and increase the population diversity for improving the global optimization ability. Secondly, it introduced an adaptive crossover probability to balance the global exploration ability and local exploitation ability of the algorithm, so as to improve the optimization accuracy and robustness of the algorithm. Finally, it applied a covariance learning strategy to make full use of the relationship between the concentration vectors to enhance the information exchange among the populations and thereby to avoid local stagnation. Through simulation experiments on the CEC2019 test functions and combining the improved algorithm with back propagation(BP) neural network to predict the runoff situation of the Manas River in Xinjiang, the experimental results show that the improved algorithm remarkably improves convergence accuracy and robustness, and significantly enhances the runoff prediction performance of the BP neural network. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Every positive multilinear map between C ∗ -algebras is separately weak ∗ -continuous. We show that the joint weak ∗ -continuity is equivalent to the joint weak ∗ -continuity of the multiplications of the C ∗ -algebras under consideration. We study the behavior of general tracial positive maps on properly infinite von Neumann algebras and by applying the Aron–Berner extension of multilinear maps, we establish that under some mild conditions every tracial positive multilinear map between general C ∗ -algebras enjoys a decomposition Φ = φ 2 ∘ φ 1 , in which φ 1 is a tracial positive linear map with the commutative range and φ 2 is a tracial completely positive map with the commutative domain. As an immediate consequence, tracial positive multilinear maps are completely positive. Furthermore, we prove that if the domain of a general tracial completely positive map Φ between C ∗ -algebra is a von Neumann algebra, then Φ has a similar decomposition. As an application, we investigate the generalized variance and covariance in quantum mechanics for arbitrary positive maps. Among others, an uncertainty relation inequality for commuting observables in a composite physical system is presented. [ABSTRACT FROM AUTHOR]

Wilfrid Sellars' denunciation of the Myth of the Given was meant to clarify, against empiricism, that perceptual episodes alone are insufficient to ground and justify perceptual knowledge. Sellars showed that in order to accomplish such epistemic tasks, more resources and capacities, such as those involved in using concepts, are needed. Perceptual knowledge belongs to the space of reasons and not to an independent realm of experience. Dan Hutto and Eric Myin have recently presented the Hard Problem of Content as an ensemble of reasons against naturalistic accounts of content. In a nutshell, it states that covariance relations—even though they are naturalistically acceptable explanatory resources—do not constitute content. The authors exploit this move in order to promote their preferred radical enactivist and anti-representationalist option, according to which, basic minds—the lower stratum of cognition—do not involve content. Although it is controversial to argue that the Hard Problem of Content effectively dismisses naturalistic theories of representation, a central aspect of it—the idea that information as covariance does not suffice to explain content—finds support among the defenders of classical cognitive representationalism, such as Marcin Miłkowski. This support—together with the acknowledgment this remark about covariance is a point already made by Sellars in his criticism of the Myth of the Given—has a number of interesting implications. Not only is it of interest for the debates about representationalism in cognitive science, where it can be understood as an anticipatory move, but it also offers some clues and insights for reconsidering some issues along Sellarsian lines—a conflation between two concepts of representation that is often assumed in cognitive science, a distinction between two types of relevant normativities, and a reconsideration of the naturalism involved in such explanations. [ABSTRACT FROM AUTHOR]

In this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators. [ABSTRACT FROM AUTHOR]

In the general setting of long‐memory multivariate time series, the long‐memory characteristics are defined by two components. The long‐memory parameters describe the autocorrelation of each time series. And the long‐run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long‐memory, long‐run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi‐analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long‐memory and brain connectivity are inferred. [ABSTRACT FROM AUTHOR]

With the steadily increasing abundance of longitudinal neuroimaging studies with large sample sizes and multiple repeated measures, questions arise regarding the appropriate modeling of variance and covariance. The current study examined the influence of standard classes of variance–covariance structures in linear mixed effects (LME) modeling of fMRI data from patients with pediatric mild traumatic brain injury (pmTBI; N = 181) and healthy controls (N = 162). During two visits, participants performed a cognitive control fMRI paradigm that compared congruent and incongruent stimuli. The hemodynamic response function was parsed into peak and late peak phases. Data were analyzed with a 4‐way (GROUP×VISIT×CONGRUENCY×PHASE) LME using AFNI's 3dLME and compound symmetry (CS), autoregressive process of order 1 (AR1), and unstructured (UN) variance–covariance matrices. Voxel‐wise results dramatically varied both within the cognitive control network (UN>CS for CONGRUENCY effect) and broader brain regions (CS>UN for GROUP:VISIT) depending on the variance–covariance matrix that was selected. Additional testing indicated that both model fit and estimated standard error were superior for the UN matrix, likely as a result of the modeling of individual terms. In summary, current findings suggest that the interpretation of results from complex designs is highly dependent on the selection of the variance–covariance structure using LME modeling. [ABSTRACT FROM AUTHOR]

Copyright of Railway Investigation & Surveying is the property of Railway Investigation & Surveying Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We develop the concept of covariance for waves and show that it plays a fundamental role in understanding the evolution of a propagating pulse. The concept clarifies several issues regarding the spread of a pulse and the motion of the mean. Exact results are obtained for the time dependence of the covariance between position and wavenumber and the covariance between position and group velocity. We also derive relevant uncertainty principles for waves. [ABSTRACT FROM AUTHOR]

The covariance matrix with compound symmetry structure is used in many statistical procedures, as in repeated measures design, in mixed linear or non-linear models, as well as in genetic studies. For making inferences about the compound symmetry structure, the classic original likelihood ratio test (OLRT) is commonly used. The main limitation of this test is the difficulty of establishing an exact distribution for test statistic under the null hypothesis in addition to assuming multivariate normality of the sample data, which makes the test not very robust when this condition is violated. This work aims to propose three robust tests named LRTR, PBTR, and PBTC, which are based on robust estimators and parametric bootstrap methods. Besides that, we intended to compare the performance of the three proposed tests with the classic OLRT and robust MCPT tests that already exist in the literature. We also wanted to check if the proposed tests that are based on the Comedian robust estimators performed better than the OLRT and PBTC when considering or not outliers in the data. Finally, the performance of asymptotic tests was compared to those that are computationally intensive tests. The tests were evaluated using the type I error rate and power in Monte Carlo simulations. We concluded that the Comedian robust estimators did not add improvements to the asymptotic tests or the computationally intensive tests. The PBTC and PBTR performed better than the OLRT, LRTR, and MCTP. Therefore, the PBTC and PBTR outperformed the classic OLRT and the robust MCPT. [ABSTRACT FROM AUTHOR]

In this paper we prove some improved Caffarelli–Kohn–Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on R n , which is a further study of the results in Dang et al. (J Funct Anal 265:2239-2266, 2013). In particular, we introduce an analogue of "phase derivative" for vector-valued functions. Moreover, using the introduced "phase derivative", we extend the extra-strong uncertainty principle to cases for complex- and vector-valued functions defined on S n , n ≥ 2. [ABSTRACT FROM AUTHOR]

In this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of \(\mu\)-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures \(\mu\), and to adjoints of composition operators.

Few-shot learning continues to pose a challenge as it is inherently difficult for visual recognition models to generalize with limited labeled examples. When the training data is limited, the process of training and fine-tuning the model will be unstable and inefficient due to overfitting. In this paper, we introduce NegCosIC: Negative Cosine Similarity-Invariance-Covariance Regularization, a method that aims to improve the mean accuracy from the perspective of stabilizing the fine-tuning process and regularizing variance. NegCosIC incorporates a negative simple cosine similarity loss to stabilize the parameters of the feature extractor during fine-tuning. In addition, NegCosIC integrates invariance loss and covariance loss to regularize the embeddings in order to reduce overfitting. Experimental results demonstrate that NegCosIC is able to bring substantial improvements over the current state-of-the-art methods. An in-depth worse case analysis is also conducted and shows that NegCosIC is able to outperform state-of-the-art methods on worst case accuracy. The proposed NegCosIC achieved 2.15% and 2.13% higher accuracy on miniImageNet 1-shot and 5-shot tasks, 3.22% and 2.67% higher accuracy on CUB 1-shot and 5-shot tasks, and 2.13% and 7.74% higher accuracy on CIFAR-FS 1-shot and 5-shot tasks in terms of worst-case accuracies.

Abstract Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin's theorem. [ABSTRACT FROM AUTHOR]

When we treat behavior within an evolutionary framework and as temporally extended flow, two fundamental questions arise: (a) What is an organism? and (b) What is behavior? An organism is a process that stays intact by constantly exchanging energy with the environment. It takes in resources and puts out waste. The behavior of an organism consists of those process parts of the organism process that make up the exchange. These activities serve the function of reproducing, which generally depends on surviving. Surviving and reproducing depend on responding to phylogenetically important events (PIEs). A PIE induces activities that enhance or mitigate the PIE. Organisms respond not only to a PIE but also to events that covary with the PIE. Both activities and environmental features may covary with a PIE. When either type of covariance is introduced to an organism, behavior adapts over time. The early stages of adaptation constitute what researchers call "goal direction," and the later stages constitute what researchers call "habit." Behavior and environment constitute a dynamic system, and manipulations of the covariances and environmental features of the system allow many experimental interventions. This molar approach allows experiments on goal direction and habit to be understood without appeal to everyday mentalistic terms. [ABSTRACT FROM AUTHOR]

Principal Component Analysis (PCA) is a powerful statistical technique for reducing the complexity of data and making patterns and relationships within the data more easily understandable. By using PCA, students can learn to identify the most important features of a data set, visualize relationships between variables, and make informed decisions based on the data. As such, PCA can be an effective tool to increase students data literacy by providing a visual and intuitive way to understand and work with data. This article outlines a teaching strategy to introduce and explain PCA using basic mathematics and statistics together with visual demonstrations. [ABSTRACT FROM AUTHOR]

Complex systems often produce multifractal signals defined by stationary increments that exhibit power-law scaling properties. The Legendre transform of the domain-dependent scaling function that defines the power law is known as the multifractal spectrum. The multifractal spectrum can also be defined by a power-series expansion of the scaling function and in practice the first two leading coefficients of that series are estimated from the discrete wavelet transform of the signal. To quantify, validate, and compare simulations of complex systems with data collected empirically from the actual system, practitioners require methods for approximating the variance associated with estimates of these coefficients. In this work, we generalize a previously developed semi-parametric statistical model for the values extracted from a discrete multi-scale wavelet transform to include both within-scale and between-scale covariance dependencies. We employ multiplicative cascades to simulate multifractals with known parameters to illustrate the necessity for this generalization and to test the precision of our improved model. The combined within- and between-scale model of covariance results in a more accurate estimate of the expected variance of the coefficients extracted from an empirical data set. [ABSTRACT FROM AUTHOR]

We look at a mechanical dissipation inequality differing from the standard one by what we call a relative power, a notion that is appropriate in the presence of material mutations. We prove that a requirement of structural invariance for such an inequality under the action of diffeomorphism-based changes of observers (covariance) implies (i) the representation of contact actions in terms of the first Piola–Kirchhoff stress, (ii) local balances of standard and configurational actions, (iii) a priori constitutive restrictions in terms of free energy, and (iv) a representation of viscous-type stress components. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'. [ABSTRACT FROM AUTHOR]

Hyperspectral target detection (HTD) aims to identifying targets within a hyperspectral image (HSI) based on provided target spectra. In the current HTD field, representation-based detectors have attracted much attention. However, there are two prominent challenges that are particularly noteworthy. First, the background class encompasses diverse land covers, making its accurate representation challenging. Second, the detection ability can be significantly influenced by the abnormalities and noise in HSI. To tackle these concerns, we propose a novel background covariance discriminative dictionary learning (BCDDL) model for HTD. To enhance the background representation ability and overcome the sparse noise, we combine the dictionary learning with spectral covariance descriptors and undertake background reconstruction in regional scale. Specifically, the input HSI is pre-processed into superpixels, the spectral covariance of each superpixel is used to provide a compact and flexible description of local regional statistical properties. Further, a novel spatial clustering-based dictionary learning method is proposed to learn the background discriminative covariances dictionary. The collaborative representation model within symmetric positive definite (SPD) manifold is utilized to reconstruct background region and get the residual. By merging the background residual with pixel-wise target reconstruction residual, we derive final detection output. Comprehensive experiments on two public hyperspectral datasets and two novel GaoFen-5 datasets demonstrate the superiority of our BCDDL approach over 10 state-of-the-art methods, especially in terms of suppressing background.

The multi-species coalescent (MSC) provides a theoretical foundation for modern phylogenetics and comparative population genetics. Its theoretical properties have been heavily studied but there are still aspects of the MSC that are largely unknown, including the covariances in pairwise coalescence times, which are fundamental for understanding the properties of statistics that combine data from multiple species, such as the fixation index (FST). The major contribution of this study is the derivation and implementation of exact expressions for the covariances of pairwise coalescence times under phylogenetic models with piecewise constant changes in population size, assuming no gene flow after species divergence. We use these expressions to derive the variance in average pairwise differences within and between populations. We then derive approximations for the expectation and bias of a sequence-based estimator of FST, a commonly used genetic measurement of population differentiation, when it is applied to a non-recombining region of the genome. We show that the estimator of FST is generally biased downward. A freely available software package is provided, STCov, to calculate the mean, variances and covariances in coalescence times presented here under user-defined piecewise-constant species trees. This article is part of the theme issue 'Celebrating 50 years since Lewontin's apportionment of human diversity'.

Aims: To map the Oxford Knee Score (OKS) and High Activity Arthroplasty Score (HAAS) items to a common scale, and to investigate the psychometric properties of this new scale for the measurement of knee health. Methods: Patient-reported outcome measure (PROM) data measuring knee health were obtained from the NHS PROMs dataset and Total or Partial Knee Arthroplasty Trial (TOPKAT). Assumptions for common scale modelling were tested. A graded response model (fitted to OKS item responses in the NHS PROMs dataset) was used as an anchor to calibrate paired HAAS items from the TOPKAT dataset. Information curves for the combined OKS-HAAS model were plotted. Bland-Altman analysis was used to compare common scale scores derived from OKS and HAAS items. A conversion table was developed to map between HAAS, OKS, and the common scale. Results: We included 3,329 response sets from 528 patients undergoing knee arthroplasty. These generally met the assumptions of unidimensionality, monotonicity, local independence, and measurement invariance. The HAAS items provided more information than OKS items at high levels of knee health. Combining both instruments resulted in higher test-level information than either instrument alone. The mean error between common scale scores derived from the OKS and HAAS was 0.29 logits. Conclusion: The common scale allowed more precise measurement of knee health than use of either the OKS or HAAS individually. These techniques for mapping PROM instruments may be useful for the standardization of outcome reporting, and pooling results across studies that use either PROM in individual-patient meta-analysis. Cite this article: Bone Joint Res 2023;12(10):624–635.

Abstract It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algorithms for fitting such models face issues in scaling up to high dimensions due to the intractability of the likelihood, involving an integral over a multivariate normal distribution having no analytic form. Although a variety of algorithms have been proposed to approximate this intractable integral, these approaches are difficult to implement and/or inaccurate in high dimensions. Our main focus is in accommodating high-dimensional binary response data with a small-to-moderate number of covariates. We propose a two-stage approach for inference on model parameters while taking care of uncertainty propagation between the stages. We use the special structure of latent Gaussian models to reduce the highly expensive computation involved in joint parameter estimation to focus inference on marginal distributions of model parameters. This essentially makes the method embarrassingly parallel for both stages. We illustrate performance in simulations and applications to joint species distribution modeling in ecology. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The inverse square root of a covariance matrix is often desirable for performing data whitening in the process of applying many common multivariate data analysis methods. Direct calculation of the inverse square root is not available when the covariance matrix is either singular or nearly singular, as often occurs in high dimensions. We develop new methods, which we broadly call polynomial whitening, to construct a low-degree polynomial in the empirical covariance matrix which has similar properties to the true inverse square root of the covariance matrix (should it exist). Our method does not suffer in singular or near-singular settings, and is computationally tractable in high dimensions. We demonstrate that our construction of low-degree polynomials provides a good substitute for high-dimensional inverse square root covariance matrices, in both d < N and d ≥ N cases. We offer examples on data whitening, outlier detection and principal component analysis to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This study considers a robust quadratic covariance‐constrained filtering problem for discrete time‐varying linear and non‐linear dynamic systems with non‐Gaussian noises. Non‐Gaussian noises are presumed to be unknown, bounded, and limited in a specified ellipsoidal set. In this approach, first, a general standard linear form of the filter is introduced for state estimation in linear dynamic systems. The filter gain is obtained by minimizing the upper bound of the estimation error's covariance matrix. The Lyapunov theory demonstrates the stability of this filter. Second, we extend the proposed filtering approach to non‐linear dynamic systems that are considered as a combination of linear and non‐linear terms. The Lipschitz‐like condition is assumed for the non‐linear part. A new filter structure is proposed in this case and the filter gain is obtained by the same idea to minimize the upper bound of the error's covariance matrix. Finally, four numerical examples are presented to signify the effectiveness and performance of the proposed filters for linear and non‐linear systems. [ABSTRACT FROM AUTHOR]

This paper analyzes the practical strategy and significance of integrating form training in yoga training teaching and constructs an evaluation index system for yoga training teaching based on it. Secondly, a principal component analysis was used to introduce the covariance to calculate the comprehensive score of the indexes. Finally, an empirical analysis was conducted to verify the specific effects of yoga training on body shape. The research revealed that yoga asana teaching and breathing control method introduction were the primary components of yoga training, with factor loadings of 0.845 and 0.623, respectively. Yoga training significantly affected cardiorespiratory function, body fat and circumference, and flexibility, p

Epilepsy is a common and serious neurological disorder, with many different constituent conditions characterized by their electro clinical, imaging, and genetic features. MRI has been fundamental in advancing our understanding of brain processes in the epilepsies. Smaller-scale studies have identified many interesting imaging phenomena, with implications both for understanding pathophysiology and improving clinical care. Through the infrastructure and concepts now well-established by the ENIGMA Consortium, ENIGMA-Epilepsy was established to strengthen epilepsy neuroscience by greatly increasing sample sizes, leveraging ideas and methods established in other ENIGMA projects, and generating a body of collaborating scientists and clinicians to drive forward robust research. Here we review published, current, and future projects, that include structural MRI, diffusion tensor imaging (DTI), and resting state functional MRI (rsfMRI), and that employ advanced methods including structural covariance, and event-based modeling analysis. We explore age of onset- and duration-related features, as well as phenomena-specific work focusing on particular epilepsy syndromes or phenotypes, multimodal analyses focused on understanding the biology of disease progression, and deep learning approaches. We encourage groups who may be interested in participating to make contact to further grow and develop ENIGMA-Epilepsy.

We describe and apply novel methodology for whole-brain analysis of resting state fMRI functional connectivity data, combining conventional multi-channel Pearson correlation with covariance analysis. Unlike correlation, covariance analysis preserves signal amplitude information, which feature of fMRI time series may carry physiological significance. Additionally, we demonstrate that dimensionality reduction of the fMRI data offers several computational advantages including projection onto a space of manageable dimension, enabling linear operations on functional connectivity measures and exclusion of variance unrelated to resting state network structure. We show that group-averaged, dimensionality reduced, covariance and correlation matrices are related, to reasonable approximation, by a single scalar factor. We apply this methodology to the analysis of a large, resting state fMRI data set acquired in a prospective, controlled study of mindfulness training and exercise in older, sedentary participants at risk for developing cognitive decline. Results show marginally significant effects of both mindfulness training and exercise in both covariance and correlation measures of functional connectivity.

It is shown, with two sets of indicators that separately load on two distinct factors, independent of one another conditional on the past, that if it is the case that at least one of the factors causally affects the other, then, in many settings, the process will converge to a factor model in which a single factor will suffice to capture the covariance structure among the indicators. Factor analysis with one wave of data then cannot distinguish between factor models with a single factor vs those with two factors that are causally related. Therefore, unless causal relations between factors can be ruled out a priori, alleged empirical evidence from one-wave factor analysis for a single factor still leaves open the possibilities of a single factor or of two factors that causally affect one another. The implications for interpreting the factor structure of psychological scales, such as self-report scales for anxiety and depression, or for happiness and purpose, are discussed. The results are further illustrated through simulations to gain insight into the practical implications of the results in more realistic settings prior to the convergence of the processes. Some further generalizations to an arbitrary number of underlying factors are noted. Factor analyses with one wave of data should themselves be interpreted as characterizing associations among indicators that may be present either due to conceptual relations or due to causal relations concerning the underlying construct phenomena.

We develop the concept of covariance for waves and show that it plays a fundamental role in understanding the evolution of a propagating pulse. The concept clarifies several issues regarding the spread of a pulse and the motion of the mean. Exact results are obtained for the time dependence of the covariance between position and wavenumber and the covariance between position and group velocity. We also derive relevant uncertainty principles for waves.