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Deep learning has been increasingly used in health management and maintenance decision-making for rotating machinery. However, some challenges must be addressed to make this technology more effective. For example, the collected data is assumed to follow the same feature distribution, and sufficient labeled training data are available. Unfortunately, domain shifts occur inevitably in real-world scenarios due to different working conditions, and acquiring sufficient labeled samples is time-consuming and expensive in complex environments. This study proposes a novel domain adaptive framework called deep Multiscale Conditional Adversarial Networks (MCAN) for machinery fault diagnosis to address these shortcomings. The MCAN model comprises two key components. Constructed by a novel multiscale module with an attention mechanism, the first component is a shared feature generator that captures rich features at different internal perceptual scales, and the attention mechanism determines the weights assigned to each scale, enhancing the model's dynamic adjustment and self-adaptation capabilities. The second component consists of two domain classifiers based on Bidirectional Long Short-Term Memory (BiLSTM) leveraging spatiotemporal features at various levels to achieve domain adaptation in the output space. The deep domain classifier also captures the cross-covariance dependencies between feature representations and classifier predictions, thereby improving the predictions' discriminability. The proposed method has been evaluated using two publicly available fault diagnosis datasets and one condition monitoring experiment. The results of cross-domain transfer tasks demonstrated that the proposed method outperformed several state-of-the-art methods in terms of transferability and stability. This result is a significant step forward in deep learning for health management and maintenance decision-making for rotating machinery, and it has the potential to revolutionize its future application. • A novel Multiscale Conditional Adversarial Networks (MCAN) is proposed. • An adaptive attention mechanism network is built to extract features from raw signals. • The cross-covariance matrix of deep features and output labels can improve domain alignment. • MCAN excels in cross-domain diagnosis and monitoring of bearings and cutting tools. [ABSTRACT FROM AUTHOR]

We derive the finite sample bias of the sample cross‐covariance estimator based on a stationary vector‐valued time series with an unknown mean. This result leads to a bias‐corrected estimator of cross‐covariances constructed from linear combinations of sample cross‐covariances, which can in theory correct for the bias introduced by the first h lags of cross‐covariance with any h not larger than the sample size minus two. Based on the bias‐corrected cross‐covariance estimator, we propose a bias‐adjusted long run covariance (LRCOV) estimator. We derive the asymptotic relations between the bias‐corrected estimators and their conventional Counterparts in both the small‐b and the fixed‐b limit. Simulation results show that: (i) our bias‐corrected cross‐covariance estimators are very effective in eliminating the finite sample bias of their conventional counterparts, with potential mean squared error reduction when the data generating process is highly persistent; and (ii) the bias‐adjusted LRCOV estimators can have superior performance to their conventional counterparts with a smaller bias and mean squared error. [ABSTRACT FROM AUTHOR]

Abstract How to capture the temporal evolution of synaptic weights from measures of dynamic functional connectivity between the activity of different simultaneously recorded neurons is an important and open problem in systems neuroscience. Here, we report methodological progress to address this issue. We first simulated recurrent neural network models of spiking neurons with spike timing-dependent plasticity mechanisms that generate time-varying synaptic and functional coupling. We then used these simulations to test analytical approaches that infer fixed and time-varying properties of synaptic connectivity from directed functional connectivity measures, such as cross-covariance and transfer entropy. We found that, while both cross-covariance and transfer entropy provide robust estimates of which synapses are present in the network and their communication delays, dynamic functional connectivity measured via cross-covariance better captures the evolution of synaptic weights over time. We also established how measures of information transmission delays from static functional connectivity computed over long recording periods (i.e., several hours) can improve shorter time-scale estimates of the temporal evolution of synaptic weights from dynamic functional connectivity. These results provide useful information about how to accurately estimate the temporal variation of synaptic strength from spiking activity measures.

The auditory brainstem response (ABR) is a scalp recording of potentials produced by sound stimulation, and is commonly used as an indicator of auditory function. However, the ABR threshold, which is the lowest audible sound pressure, cannot be objectively determined since it is determined visually using a measurer, and this has been a problem for several decades. Although various algorithms have been developed to objectively determine ABR thresholds, they remain lacking in terms of accuracy, efficiency, and convenience. Accordingly, we proposed an improved algorithm based on the mutual covariance at adjacent sound pressure levels. An ideal ABR waveform with clearly defined waves I–V was created; moreover, using this waveform as a standard template, the experimentally obtained ABR waveform was inspected for disturbances based on mutual covariance. The ABR testing was repeated if the value was below the established cross-covariance reference value. Our proposed method allowed more efficient objective determination of ABR thresholds and a smaller burden on experimental animals. [ABSTRACT FROM AUTHOR]

For a random sample of n iid p-dimensional vectors, each partitioned into b sub-vectors of dimensions pi, i = 1 , ... , b , tests for zero correlation of sub-vectors are presented when p i ≫ n and the distribution need not be normal. The test statistics are composed of U-statistics based estimators of the Frobenius norm measuring the distance between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for n , p i → ∞ , with their finite-sample performance demonstrated through simulations. Some related tests are discussed. A real data application is also given. [ABSTRACT FROM AUTHOR]

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile. [ABSTRACT FROM AUTHOR]

This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator of the primary variable in a bivariate collocated cokriging setup to reduce to a univariate kriging estimator. Exact optimal designs for efficient prediction for such simple and ordinary reduced cokriging models with one-dimensional inputs are determined. Designs are found by minimizing the maximum and the integrated prediction variance, where the primary variable is an Ornstein–Uhlenbeck process. For simple and ordinary cokriging models with known covariance parameters, the equispaced design is shown to be optimal for both criterion functions. The more realistic scenario of unknown covariance parameters is addressed by assuming prior distributions on the parameter vector, thus adopting a Bayesian approach to the design problem. The equispaced design is proved to be the Bayesian optimal design for both criteria. The work is motivated by designing an optimal water monitoring system for an Indian river. • A linear dependency condition for reduction of simple and ordinary cokriging model to kriging model • Introduction of the generalized Markov-type covariance • G-optimal designs for reduced bivariate cokriging models under a frequentist setup • G-optimal and I-optimal designs for reduced bivariate cokriging models under a Bayesian setup [ABSTRACT FROM AUTHOR]

Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the cross-covariances, but these assumptions are rarely tenable in practice. In this article, we introduce a new and highly exible class of nonstationary and asymmetric multivariate spatial covariance models that are constructed by modeling the simpler and more familiar stationary and symmetric multivariate covariances on a warped domain. Inspired by recent developments in the univariate case, we propose modeling the warping function as a composition of a number of simple injective warping functions in a deep-learning framework. Importantly, covariance-model validity is guaranteed by construction. We establish the types of warpings that allow for cross-covariance symmetry and asymmetry, and we use likelihood-based methods for inference that are computationally efficient. The utility of this new class of models is shown through two data illustrations: a simulation study on nonstationary data, and an application to ocean temperatures at two different depths. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the problem of temporal dependence structure of univariate stochastic processes, where the auto-codifference was used, we extend its idea and propose a cross-codifference measure for a general bidimensional vector autoregressive time series of order 1 (bidimensional VAR(1)). Next, we derive analytical results for VAR(1) model with Gaussian and α − stable sub-Gaussian innovations, that are characterized by finite and infinite variance, respectively. We emphasize that obtained expressions perfectly agree with the empirical counterparts. Moreover, we show that for the considered time series the cross-codifference simplifies to the well-established cross-covariance in the case when the innovations of time series are given by Gaussian white noise. The last part of the work is devoted to the statistical estimation of VAR(1) time series parameters based on the empirical cross-codifference. Again, we demonstrate via Monte Carlo simulations that the proposed methodology works correctly. [ABSTRACT FROM AUTHOR]

How to capture the temporal evolution of synaptic weights from measures of dynamic functional connectivity between the activity of different simultaneously recorded neurons is an important and open problem in systems neuroscience. Here, we report methodological progress to address this issue. We first simulated recurrent neural network models of spiking neurons with spike timing-dependent plasticity mechanisms that generate time-varying synaptic and functional coupling. We then used these simulations to test analytical approaches that infer fixed and time-varying properties of synaptic connectivity from directed functional connectivity measures, such as cross-covariance and transfer entropy. We found that, while both cross-covariance and transfer entropy provide robust estimates of which synapses are present in the network and their communication delays, dynamic functional connectivity measured via cross-covariance better captures the evolution of synaptic weights over time. We also established how measures of information transmission delays from static functional connectivity computed over long recording periods (i.e., several hours) can improve shorter time-scale estimates of the temporal evolution of synaptic weights from dynamic functional connectivity. These results provide useful information about how to accurately estimate the temporal variation of synaptic strength from spiking activity measures. [ABSTRACT FROM AUTHOR]

The use of location weights on the formation of the spatio-temporal model contributes to the accuracy of the model formed. The location weights that are often used include uniform location weight, inverse distance, and cross-correlation normalization. The weight of the location considers the proximity between locations. For data that has a high level of variability, the use of the location weights mentioned above is less relevant. This research was conducted with the aim of obtaining a weighting method that is more suitable for data with high variability. This research was conducted using secondary data derived from 10 daily rainfall data obtained from BMKG Karangploso. The data period used was January 2008 to December 2018. The points of the rain posts studied included the rain post of the Blimbing, Karangploso, Singosari, Dau, and Wagir regions. Based on the results of the research forecasting model obtained is the GSTAR ((1), 1,2,3,12,36) -SUR model. The cross-covariance model produces a better level of accuracy in terms of lower RMSE values and higher R2 values, especially for Karangploso, Dau, and Wagir areas.

We compare strongly coupled data assimilation (SCDA) and weakly coupled data assimilation (WCDA) by analyzing the assimilation effect on the estimation of the ocean and the atmosphere variables. The AWI climate model (AWI‐CM‐1.1) is coupled with the parallel data assimilation framework (PDAF). Only satellite sea surface temperature data are assimilated. For WCDA, only the ocean variables are directly updated by the assimilation. For SCDA, both the ocean and the atmosphere variables are directly updated by the assimilation. Both WCDA and SCDA improve ocean state and yield similar errors. In the atmosphere, WCDA gives slightly smaller errors for the near‐surface temperature and wind velocity than SCDA. In the free atmosphere, SCDA yields smaller errors for the temperature, wind velocity, and specific humidity than WCDA in the Arctic region, while in the tropical region, the errors are generally larger. Plain Language Summary: Satellite sea surface temperature observations are combined with a coupled ocean‐atmosphere model to improve the estimation of the ocean as well as the atmosphere variables. This is done by the so‐called strongly coupled data assimilation, which updates not only the ocean state but uses the cross‐covariance to update the atmosphere variables directly through the assimilation algorithm. The results are compared with the weakly coupled data assimilation, which only updates the ocean state directly. Both of the two assimilation algorithms improve the estimation of the ocean temperature. In the atmosphere, the strongly coupled data assimilation outperforms the weakly coupled data assimilation only in the Arctic region while in the low latitudes the strongly coupled data assimilation deteriorates the results. Key Points: Strongly coupled data assimilation is implemented for a coupled ocean atmosphere modelSatellite sea surface temperatures are the only observations for assimilationStrongly coupled data assimilation performs better in the Arctic region than the weakly coupled data assimilation [ABSTRACT FROM AUTHOR]

Domain adversarial learning is a mainstream approach of domain adaptation, which learns discriminative domain-invariant feature representation through classifier and domain discriminator. However, existing adversarial domain adaptation methods often use first-order features to learn domain-invariant feature representation, ignoring the second-order features with more powerful representative ability. This paper proposed conditional adversarial domain adaptation networks based on second-order representation, which modeled the second-order moments of features and the cross-covariance between features and classifier predictions for more effectively learning discriminative domain-invariant features. Moreover,it introduced entropy conditioning to guarantee the transferability. The proposed method was evaluated on two commonly used datasets Office-31 and ImageCLEF-DA. Experiments show that the proposed method outperforms its counterpart. [ABSTRACT FROM AUTHOR]

We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results. [ABSTRACT FROM AUTHOR]

Modeling a mineral microstructure accurately in three dimensions can render realistic mineralogical patterns which can be used for three-dimensional processing simulations and calculation of three-dimensional mineral quantities. The present study introduces a flexible approach to model the microstructure of mineral material composed of a large number of facies. The common plurigaussian method, a valuable approach in geostatistics, can account for correlations within each facies and in principle be extended to correlations between the facies. Assuming stationarity and isotropy, founded on a new description of this model, formulas for first- and second-order characteristics, such as volume fraction, correlation function and cross-correlation function can be given by a multivariate normal distribution. In this particular situation, based on first- and second-order statistics, a fitting procedure can be developed which requires only numerical inversion of several one-dimensional monotone functions. The paper describes the whole workflow. The covariance structure is quickly obtained from two-dimensional particle pixel images using Fourier transform. Followed by model fitting and sampling, where the resulting three-dimensional microstructure is then efficiently represented by tessellations. The applicability is demonstrated for the three-dimensional case by modeling the microstructure from a Mineral Liberation Analyzer image data set of an andesitic basalt breccia. [ABSTRACT FROM AUTHOR]

The accuracy of graph based learning techniques relies on the underlying topological structure and affinity between data points, which are assumed to lie on a smooth Riemannian manifold. However, the assumption of local linearity in a neighborhood does not always hold true. Hence, the Euclidean distance based affinity that determines the graph edges may fail to represent the true connectivity strength between data points. Moreover, the affinity between data points is influenced by the distribution of the data around them and must be considered in the affinity measure. In this paper, we propose two techniques, CCGAL and CCGAN that use cross-covariance based graph affinity (CCGA) to represent the relation between data points in a local region. CCGAL also explores the additional connectivity between data points which share a common local neighborhood. CCGAN considers the influence of respective neighborhoods of the two immediately connected data points, which further enhance the affinity measure. Experimental results of manifold learning on synthetic datasets show that CCGA is able to represent the affinity measure between data points more accurately. This results in better low dimensional representation. Manifold regularization experiments on standard image dataset further indicate that the proposed CCGA based affinity is able to accurately identify and include the influence of the data points and its common neighborhood that increase the classification accuracy. The proposed method outperforms the existing state-of-the-art manifold regularization methods by a significant margin. [ABSTRACT FROM AUTHOR]

In this article, we propose a simple estimator of cross‐covariance matrices for a multi‐variate time series with an unknown mean based on a linear combination of the circular sample cross‐covariance estimator. Our estimator is exactly unbiased when the data generating process follows a vector moving average (VMA) model with an order less than one half of the sampling period, and is nearly unbiased if such VMA model can approximate the data generating process well. In addition, our estimator is shown to be asymptotically equivalent to the conventional sample cross‐covariance estimator. Via simulation, we show that the proposed estimator can to a large extent eliminate the finite sample bias of cross‐covariance estimates, while not necessarily increase the mean squared error. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the distributed fusion estimation problem for multisensor nonlinear systems. Based on the Kalman filtering framework and the spherical cubature rule, a general method for calculating the cross‐covariance matrices between any two local estimators is presented for multisensor nonlinear systems. In the linear unbiased minimum variance sense, based on the cross‐covariance matrices, a distributed fusion cubature Kalman filter weighted by matrices (MW‐CKF) is presented. The proposed MW‐CKF has better accuracy and robustness. An example verifies the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The direction of arrival （DOA）estimation for L-shaped uniform antenna array is limited by low resolution, number of incident signals and signal-to-noise ratio. A two-dimensional DOA estimation algorithm for L-shaped nested array based on cross-covariance matrix is proposed to solve this problem. In the proposed algorithm, the cross-covariance matrixes of different sub-arrays are used to generate longer virtual arrays without redundant elements, which eliminate the noise. To cope with the coherent signals of virtual arrays, several equivalent covariance matrixes are constructed by using the signal of virtual arrays and its conjugate signal. The rotational invariance technique is used to deal with the equivalent covariance matrixes to obtain the angle of incident signals, and the angles are matched by using the uniqueness of equivalent signal vectors of virtual arrays. The effectiveness of the proposed algorithm for DOA estimation was verified. The simulated results show that the proposed algorithm can achieve better DOA estimation performance in low SNR environment and identify more spatial sources compared to the L-shaped uniform array with the same number of array elements. [ABSTRACT FROM AUTHOR]

Abstract We propose a new feature representation algorithm using cross-covariance in the context of deep learning. Existing feature representation algorithms based on the sparse autoencoder and nonnegativity-constrained autoencoder tend to produce duplicative encoding and decoding receptive fields, which leads to feature redundancy and overfitting. We propose using the cross-covariance to regularize the feature weight vector to construct a new objective function to eliminate feature redundancy and reduce overfitting. The results from the MNIST handwritten digits dataset, the NORB normalized-uniform dataset and the Yale face dataset indicate that relative to other algorithms based on the conventional sparse autoencoder and nonnegativity-constrained autoencoder, our method can effectively eliminate feature redundancy, extract more distinctive features, and improve sparsity and reconstruction quality. Furthermore, this method improves the image classification performance and reduces the overfitting of conventional networks without adding more computational time. [ABSTRACT FROM AUTHOR]

We conduct statistical analysis of correlations for pre-alert system of the infection in population by wastewater screening of SARS-CoV-2 genomic fragments using qRT-PCR. We analyze data on surveillance of SARS-CoV-2 in wastewater as an epidemiological tool to anticipate outbreaks in Chile and Peru. We found there exists a positive relationship between genomic copies in wastewater and reported cases, and the relationship is of probabilistic nature. • We statistically relate reported Covid-19 cases with observed genomic copies in wastewater in Chile and Peru. • We show that there exists a statistical relationship. • The heterogeneity of collecting sites/plants are outlined and discussed. [ABSTRACT FROM AUTHOR]

The Hoffmann reflex (H-wave) is produced by alpha-motoneuron activation in the spinal cord. A feature of this electromyography response is that it exhibits fluctuations in amplitude even during repetitive stimulation with the same intensity of current. We herein explore the hypothesis that physical training induces plastic changes in the motor system. Such changes are evaluated with the fractal dimension (FD) analysis of the H-wave amplitude-fluctuations (H-wave FD) and the cross-covariance (CCV) between the bilateral H-wave amplitudes. The aim of this study was to compare the H-wave FD as well as the CCV before and after track training in sedentary individuals and athletes. The training modality in all subjects consisted of running three times per week (for 13 weeks) in a concrete road of 5 km. Given the different physical condition of sedentary vs. athletes, the running time between sedentary and athletes was different. After training, the FD was significantly increased in sedentary individuals but significantly reduced in athletes, although there were no changes in spinal excitability in either group of subjects. Moreover, the CCV between bilateral H-waves exhibited a significant increase in athletes but not in sedentary individuals. These differential changes in the FD and CCV indicate that the plastic changes in the complexity of the H-wave amplitude fluctuations as well as the synaptic inputs to the Ia-motoneuron systems of both legs were correlated to the previous fitness history of the subjects. Furthermore, these findings demonstrate that the FD and CCV can be employed as indexes to study plastic changes in the human motor system.

The modulation of spinal cord excitability during rhythmic limb movement reflects the neuronal coordination underlying actions of the arms and legs. Integration of network activity in the spinal cord can be assessed by reflex variability between the limbs, an approach so far very little studied. The present work addresses this question by eliciting Hoffmann (H-) reflexes in both limbs to assess if common drive onto bilateral pools of motoneurons influence spinal cord excitability simultaneously or with a delay between sides. A cross-covariance (CCV) sequence between reflexes in both arms or legs was evaluated under conditions providing common drive bilaterally through voluntary muscle contraction and/or rhythmic movement of the remote limbs. For H-reflexes in the flexor carpi radialis (FCR) muscle, either contraction of the FCR or leg cycling induced significant reduction in the amplitude of the peak at the zero lag in the CCV sequence, indicating independent variations in spinal excitability between both sides. In contrast, for H-reflexes in the soleus (SO) muscle, arm cycling revealed no reduction in the amplitude of the peak in the CCV sequence at the zero lag. This suggests a more independent control of the arms compared with the legs. These results provide new insights into the organization of human limb control in rhythmic activity and the behavior of bilateral reflex fluctuations under different motor tasks. From a functional standpoint, changes in the co-variability might reflect dynamic adjustments in reflex excitability that are subsumed under more global control features during locomotion.

Numerical representations of a target reservoir can help to assess the potential of different development plans. To be as predictive as possible, these representations or models must reproduce the data (static, dynamic) collected on the field. However, constraining reservoir models to dynamic data - the history-matching process - can be very time consuming. Many uncertain parameters need to be taken into account, such as the spatial distribution of petrophysical properties. This distribution is mostly unknown and usually represented by millions of values populating the reservoir grid. Dedicated parameterization techniques make it possible to investigate many spatial distributions from a small number of parameters. The efficiency of the matching process can be improved from the perturbation of specific regions of the reservoir. Distinct approaches can be considered to define such regions. For instance, one can refer to streamlines. The leading idea is to identify areas that influence the production behavior where the data are poorly reproduced. Here, we propose alternative methods based on connectivity analysis to easily provide approximate influence areas for any fluid-flow simulation. The reservoir is viewed as a set of nodes connected by weighted links that characterize the distance between two nodes. The path between nodes (or grid blocks) with the lowest cumulative weight yields an approximate flow path used to define influence areas. The potential of the approach is demonstrated on the basis of 2D synthetic cases for the joint integration of production and 4D saturation data, considering several formulations for the weights attributed to the links. [ABSTRACT FROM AUTHOR]

The Hoffmann reflex (H-wave) is produced by alpha-motoneuron activation in the spinal cord. A feature of this electromyography response is that it exhibits fluctuations in amplitude even during repetitive stimulation with the same intensity of current. We herein explore the hypothesis that physical training induces plastic changes in themotor system. Such changes are evaluated with the fractal dimension (FD) analysis of the H-wave amplitude-fluctuations (H-wave FD) and the cross-covariance (CCV) between the bilateral H-wave amplitudes. The aim of this study was to compare the H-wave FD as well as the CCV before and after track training in sedentary individuals and athletes. The training modality in all subjects consisted of running three times per week (for 13 weeks) in a concrete road of 5 km. Given the different physical condition of sedentary vs. athletes, the running time between sedentary and athletes was different. After training, the FD was significantly increased in sedentary individuals but significantly reduced in athletes, although there were no changes in spinal excitability in either group of subjects.Moreover, the CCV between bilateral H-waves exhibited a significant increase in athletes but not in sedentary individuals. These differential changes in the FD and CCV indicate that the plastic changes in the complexity of the H-wave amplitude fluctuations as well as the synaptic inputs to the Ia-motoneuron systems of both legs were correlated to the previous fitness history of the subjects. Furthermore, these findings demonstrate that the FD and CCV can be employed as indexes to study plastic changes in the human motor system. [ABSTRACT FROM AUTHOR]

The modulation of spinal cord excitability during rhythmic limb movement reflects the neuronal coordination underlying actions of the arms and legs. Integration of network activity in the spinal cord can be assessed by reflex variability between the limbs, an approach so far very little studied. The present work addresses this question by eliciting Hoffmann (H-) reflexes in both limbs to assess if common drive onto bilateral pools of motoneurons influence spinal cord excitability simultaneously or with a delay between sides. A cross-covariance (CCV) sequence between reflexes in both arms or legs was evaluated under conditions providing common drive bilaterally through voluntary muscle contraction and/or rhythmic movement of the remote limbs. For H-reflexes in the flexor carpi radialis (FCR) muscle, either contraction of the FCR or leg cycling induced significant reduction in the amplitude of the peak at the zero lag in the CCV sequence, indicating independent variations in spinal excitability between both sides. In contrast, for H-reflexes in the soleus (SO) muscle, arm cycling revealed no reduction in the amplitude of the peak in the CCV sequence at the zero lag. This suggests a more independent control of the arms compared with the legs. These results provide new insights into the organization of human limb control in rhythmic activity and the behavior of bilateral reflex fluctuations under different motor tasks. From a functional standpoint, changes in the co-variability might reflect dynamic adjustments in reflex excitability that are subsumed under more global control features during locomotion. [ABSTRACT FROM AUTHOR]

Different types of sensors in a structural health monitoring (SHM) system installed in a structure enable various types of structural responses to be measured. However, their distinct properties and limitations considerably complicate multisensing structural condition assessment. As a result, the information from these sensors is often used separately, and the potential advantage of multisensing information has not been used effectively. This paper first proposes a covariance-based multisensing (CBMS) damage detection method in the time domain in terms of a CBMS vector as a new damage index and a sensitivity study for damage detection. The proposed method has the merit of assimilating heterogeneous data and reducing the adverse effect of measurement noise. The CBMS damage detection method is then used in two stages for detecting damage location and severity consecutively. Numerical studies are finally performed to investigate the feasibility and accuracy of the proposed framework using an overhanging beam with two damage scenarios. The results show that the two-stage CBMS damage detection method improves the accuracy of damage detection and that the proposed method can be effectively used to combine multisensing information for better damage detection. [ABSTRACT FROM AUTHOR]

We present a general coregionalization framework for developing coregionalized multivariate Gaussian conditional autoregressive (cMCAR) models for Bayesian analysis of multivariate lattice data in general and multivariate disease mapping data in particular. This framework is inclusive of cMCARs that facilitate flexible modelling of spatially structured symmetric or asymmetric cross-variable local interactions, allowing a wide range of separable or non-separable covariance structures, and symmetric or asymmetric cross-covariances, to be modelled. We present a brief overview of established univariate Gaussian conditional autoregressive (CAR) models for univariate lattice data and develop coregionalized multivariate extensions. Classes of cMCARs are presented by formulating precision structures. The resulting conditional properties of the multivariate spatial models are established, which cast new light on cMCARs with richly structured covariances and cross-covariances of different spatial ranges. The related methods are illustrated via an in-depth Bayesian analysis of a Minnesota county-level cancer data set. We also bring a new dimension to the traditional enterprize of Bayesian disease mapping: estimating and mapping covariances and cross-covariances of the underlying disease risks. Maps of covariances and cross-covariances bring to light spatial characterizations of the cMCARs and inform on spatial risk associations between areas and diseases. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the recent years, there has been a growing interest in proposing covariance models for multivariate Gaussian random fields. Some of these covariance models are very flexible and can capture both the marginal and the cross-spatial dependence of the components of the associated multivariate Gaussian random field. However, effective estimation methods for these models are somehow unexplored. Maximum likelihood is certainly a useful tool, but it is impractical in all the circumstances where the number of observations is very large. In this work, we consider two possible approaches based on composite likelihood for multivariate covariance model estimation. We illustrate, through simulation experiments, that our methods offer a good balance between statistical efficiency and computational complexity. Asymptotic properties of the proposed estimators are assessed under increasing domain asymptotics. Finally, we apply the method for the analysis of a bivariate dataset on chlorophyll concentration and sea surface temperature in the Chilean coast. [ABSTRACT FROM AUTHOR]

This paper concerns with multivariate conditional autoregressive models defined by linear combination of independent or correlated underlying spatial processes. Known as linear models of coregionalization, the method offers a systematic and unified approach for formulating multivariate extensions to a broad range of univariate conditional autoregressive models. The resulting multivariate spatial models represent classes of coregionalized multivariate conditional autoregressive models that enable flexible modelling of multivariate spatial interactions, yielding coregionalization models with symmetric or asymmetric cross-covariances of different spatial variation and smoothness. In the context of multivariate disease mapping, for example, they facilitate borrowing strength both over space and cross variables, allowing for more flexible multivariate spatial smoothing. Specifically, we present a broadened coregionalization framework to include order-dependent, order-free, and order-robust multivariate models; a new class of order-free coregionalized multivariate conditional autoregressives is introduced. We tackle computational challenges and present solutions that are integral for Bayesian analysis of these models. We also discuss two ways of computing deviance information criterion for comparison among competing hierarchical models with or without unidentifiable prior parameters. The models and related methodology are developed in the broad context of modelling multivariate data on spatial lattice and illustrated in the context of multivariate disease mapping. The coregionalization framework and related methods also present a general approach for building spatially structured cross-covariance functions for multivariate geostatistics. [ABSTRACT FROM AUTHOR]

Grouping strategy exactly specifies the form of covariance matrix, therefore it is very essential. Most 2DPCA methods use the original 2D image matrices to form the covariance matrix which actually means that the strategy is to group the random variables by row or column of the input image. Because of their grouping strategies these methods have two main drawbacks. Firstly, 2DPCA and some of its variants such as A2DPCA, DiaPCA and MatPCA preserve only the covariance information between the elements of these groups. This directly implies that 2DPCA and these variants eliminate some covariance information while PCA preserves such information that can be useful for recognition. Secondly, all the existing methods suffer from the relatively high intra-group correlation, since the random variables in a row, column, or a block are closely located and highly correlated. To overcome such drawbacks we propose a novel grouping strategy named cross grouping strategy. The algorithm focuses on reducing the redundancy among the row and the column vectors of the image matrix. While doing this the algorithm completely preserves the covariance information of PCA between local geometric structures in the image matrix which is partially maintained in 2DPCA and its variants. And also in the proposed study intra-group correlation is weak according to the 2DPCA and its variants because the random variables spread over the whole face image. These make the proposed algorithm superior to 2DPCA and its variants. In order to achieve this, image cross-covariance matrix is calculated from the summation of the outer products of the column and the row vectors of all images. The singular value decomposition (SVD) is then applied to the image cross-covariance matrix. The right and the left singular vectors of SVD of the image cross-covariance matrix are used as the optimal projective vectors. Further in order to reduce the dimension LDA is applied on the feature space of the proposed method that is proposed method + LDA. The exhaustive experimental results demonstrate that proposed grouping strategy for 2DPCA is superior to 2DPCA, its specified variants and PCA, and proposed method outperforms bi-directional PCA + LDA. [ABSTRACT FROM AUTHOR]

The present manuscript aims at identifying patterns of electrical activity recorded from neurons of the leech nervous system, characterizing specific behaviors. When leeches are at rest, the electrical activity of neurons and motoneurons is poorly correlated. When leeches move their head and/or tail, in contrast, action potential (AP) firing becomes highly correlated. When the head or tail suckers detach, specific patterns of electrical activity are detected. During elongation and contraction the electrical activity of motoneurons in the Medial Anterior and Dorsal Posterior nerves increase respectively and several motoneurons are activated both during elongation and contraction. During crawling, swimming and pseudo-swimming patterns of electrical activity are better described by the dendrograms of cross-correlations of motoneurons pairs. Dendrograms obtained from different animals exhibiting the same behavior are similar and by averaging these dendrograms we obtained a template underlying a given behavior. By using this template, the corresponding behavior is reliably identified from the recorded electrical activity. The analysis of dendrograms during different leech behavior reveals the fine orchestration of motoneurons firing specific to each stereotyped behavior. Therefore, dendrograms capture the subtle changes in the correlation pattern of neuronal networks when they become involved in different tasks or functions.