Structured time-dependent inverse regression (STIR).

We propose and study structured time-dependent inverse regression (STIR), a novel sufficient dimension reduction model, to analyze longitudinally measured, correlated biomarkers in relation to an outcome. The time structure is accommodated in an inverse regression model for the markers that can be applied both to equally and unequally spaced time points for each sample. The inverse regression structure also naturally accommodates retrospectively sampled markers, that is, markers measured in case-control studies. We estimate the corresponding linear combinations of the markers, the reduction, using least squares. We show that under additional distributional assumptions the reduction contains sufficient information about the outcome. In extensive simulations the STIR linear combinations perform well in predictive models based on samples of realistic size. A Wald-type test for association of a particular marker with outcome at any time point based on the STIR reduction has better power overall than assessing associations based on logistic or linear regression models that include all longitudinally measured markers as independent predictors. As illustrations we estimate the STIR reductions for a cohort study of diabetes and hyperlipidemia and a case-control study of brain cancer with multiple longitudinally measured biomarkers. We assess the STIR reductions' predictive performance and identify outcome-associated biomarkers.

Design of a High-Order Kalman Filter for State and Measurement of A Class of Nonlinear Systems Based on Kronecker Product Augmented Dimension.

A high-order Kalman filter for full-dimensional variables is proposed for a class of dynamic systems whose state model and measurement model are both nonlinear. The filter requires Taylor expansion of the system equations, and then performs Kronecker product operation on the linear part in the Taylor expansion. Finally, a linear dynamic model is achieved based on the full-dimensional vector formed by the state variables and the high-order dimension expansion variables. After designing the filter, the Kalman filter for the original state variables estimation was selected through the projection operator. The excellent performance of the novel filter is analyzed from the aspects of the information utilization of the state estimation value and the size of the state estimation error covariance matrix. The numerical verification is carried out by computer simulation.

Semi-Blind Receivers for Two-Hop MIMO Relay Systems with a Combined TSTF-MSMKron Coding.

Due to the increase in the number of mobile stations in recent years, cooperative relaying systems have emerged as a promising technique for improving the quality of fifth-generation (5G) wireless networks with an extension of the coverage area. In this paper, we propose a two-hop orthogonal frequency division multiplexing and code-division multiple-access (OFDM-CDMA) multiple-input multiple-output (MIMO) relay system, which combines, both at the source and relay nodes, a tensor space-time-frequency (TSTF) coding with a multiple symbol matrices Kronecker product (MSMKron), called TSTF-MSMKron coding, aiming to increase the diversity gain. It is first established that the signals received at the relay and the destination satisfy generalized Tucker models whose core tensors are the coding tensors. Assuming the coding tensors are known at both nodes, tensor models are exploited to derive two semi-blind receivers, composed of two steps, to jointly estimate symbol matrices and individual channels. Necessary conditions for parameter identifiability with each receiver are established. Extensive Monte Carlo simulation results are provided to show the impact of design parameters on the symbol error rate (SER) performance, using the zero-forcing (ZF) receiver. Next, Monte Carlo simulations illustrate the effectiveness of the proposed TSTF-MSMKron coding and semi-blind receivers, highlighting the benefit of exploiting the new coding to increase the diversity gain.

Design Method of High-Order Kalman Filter for Strong Nonlinear System Based on Kronecker Product Transform.

In this paper, a novel design idea of high-order Kalman filter based on Kronecker product transform is proposed for a class of strong nonlinear stochastic dynamic systems. Firstly, those augmenting systems are modeled with help of the Kronecker product without system noise. Secondly, the augmented system errors are illustratively charactered by Gaussian white noise. Thirdly, at the expanded space a creative high-order Kalman filter is delicately designed, which consists of high-order Taylor expansion, introducing magical intermediate variables, representing linear systems converted from strongly nonlinear systems, designing Kalman filter, etc. The performance of the proposed filter will be much better than one of EKF, because it uses more information than EKF. Finally, its promise is verified through commonly used digital simulation examples.

Two-dimensional P-spline smoothing for spatial analysis of plant breeding trials.

Large agricultural field trials may display irregular spatial trends that cannot be fully captured by a purely randomization-based analysis. For this reason, paralleling the development of analysis-of-variance procedures for randomized field trials, there is a long history of spatial modeling for field trials, starting with the early work of Papadakis on nearest neighbor analysis, which can be cast in terms of first or second differences among neighboring plot values. This kind of spatial modeling is amenable to a natural extension using splines, as has been demonstrated in recent publications in the field. Here, we consider the P-spline framework, focusing on model options that are easy to implement in linear mixed model packages. Two examples serve to illustrate and evaluate the methods. A key conclusion is that first differences are rather competitive with second differences. A further key observation is that second differences require special attention regarding the representation of the null space of the smooth terms for spatial interaction, and that an unstructured variance-covariance structure is required to ensure invariance to translation and rotation of eigenvectors associated with that null space. We develop a strategy that permits fitting this model with ease, but the approach is more demanding than that needed for fitting models using first differences. Hence, even though in other areas, second differences are very commonly used in the application of P-splines, our conclusion is that with field trials, first differences have advantages for routine use.

Scalable proximal methods for cause-specific hazard modeling with time-varying coefficients.

Survival modeling with time-varying coefficients has proven useful in analyzing time-to-event data with one or more distinct failure types. When studying the cause-specific etiology of breast and prostate cancers using the large-scale data from the Surveillance, Epidemiology, and End Results (SEER) Program, we encountered two major challenges that existing methods for estimating time-varying coefficients cannot tackle. First, these methods, dependent on expanding the original data in a repeated measurement format, result in formidable time and memory consumption as the sample size escalates to over one million. In this case, even a well-configured workstation cannot accommodate their implementations. Second, when the large-scale data under analysis include binary predictors with near-zero variance (e.g., only 0.6% of patients in our SEER prostate cancer data had tumors regional to the lymph nodes), existing methods suffer from numerical instability due to ill-conditioned second-order information. The estimation accuracy deteriorates further with multiple competing risks. To address these issues, we propose a proximal Newton algorithm with a shared-memory parallelization scheme and tests of significance and nonproportionality for the time-varying effects. A simulation study shows that our scalable approach reduces the time and memory costs by orders of magnitude and enjoys improved estimation accuracy compared with alternative approaches. Applications to the SEER cancer data demonstrate the real-world performance of the proximal Newton algorithm.

Generalized Solution of Inverse Problem for Ising Connection Matrix on d-Dimensional Hypercubic Lattice.

We analyze a connection matrix of a d-dimensional Ising system and solve the inverse problem, restoring the constants of interaction between spins, based on the known spectrum of its eigenvalues. When the boundary conditions are periodic, we can account for interactions between spins that are arbitrarily far. In the case of the free boundary conditions, we have to restrict ourselves with interactions between the given spin and the spins of the first d coordination spheres.

The Analysis of Multivariate Longitudinal Data: An Instructive Application of the Longitudinal Three-Mode Model.

Structural equation modeling is a common technique to assess change in longitudinal designs. However, these models can become of unmanageable size with many measurement occasions. One solution is the imposition of Kronecker product restrictions to model the multivariate longitudinal structure of the data. The resulting longitudinal three-mode models (L3MMs) are very parsimonious and have attractive interpretation. This paper provides an instructive description of L3MMs. The models are applied to health-related quality of life (HRQL) data obtained from 682 patients with painful bone metastasis, with eight measurements at 13 occasions; before and every week after treatment with radiotherapy. We explain (1) how the imposition of Kronecker product restrictions can be used to model the multivariate longitudinal structure of the data, (2) how to interpret the Kronecker product restrictions and the resulting L3MM parameters, and (3) how to test substantive hypotheses in L3MMs. In addition, we discuss the challenges for the evaluation of (differences in) fit of these complex and parsimonious models. The L3MM restrictions lead to parsimonious models and provide insight in the change patterns of relationships between variables in addition to the general patterns of change. The L3MM thus provides a convenient model for multivariate longitudinal data, as it not only facilitates the analysis of complex longitudinal data but also the substantive interpretation of the dynamics of change.

Simultaneous Robot⁻World and Hand⁻Eye Calibration without a Calibration Object.

An extended robot⁻world and hand⁻eye calibration method is proposed in this paper to evaluate the transformation relationship between the camera and robot device. This approach could be performed for mobile or medical robotics applications, where precise, expensive, or unsterile calibration objects, or enough movement space, cannot be made available at the work site. Firstly, a mathematical model is established to formulate the robot-gripper-to-camera rigid transformation and robot-base-to-world rigid transformation using the Kronecker product. Subsequently, a sparse bundle adjustment is introduced for the optimization of robot⁻world and hand⁻eye calibration, as well as reconstruction results. Finally, a validation experiment including two kinds of real data sets is designed to demonstrate the effectiveness and accuracy of the proposed approach. The translation relative error of rigid transformation is less than 8/10,000 by a Denso robot in a movement range of 1.3 m × 1.3 m × 1.2 m. The distance measurement mean error after three-dimensional reconstruction is 0.13 mm.

On a Matrix Inequality Related to the Distillability Problem.

We investigate the distillability problem in quantum information in ℂ d ⊗ ℂ d . One case of the problem has been reduced to proving a matrix inequality when d = 4 . We investigate the inequality for three families of non-normal matrices. We prove the inequality for the first two families with d = 4 and for the third family with d ≥ 5 . We also present a sufficient condition for the fulfillment of the inequality with d = 4 .

Spatio-Temporal EEG Models for Brain Interfaces.

Multichannel electroencephalography (EEG) is widely used in non-invasive brain computer interfaces (BCIs) for user intent inference. EEG can be assumed to be a Gaussian process with unknown mean and autocovariance, and the estimation of parameters is required for BCI inference. However, the relatively high dimensionality of the EEG feature vectors with respect to the number of labeled observations lead to rank deficient covariance matrix estimates. In this manuscript, to overcome ill-conditioned covariance estimation, we propose a structure for the covariance matrices of the multichannel EEG signals. Specifically, we assume that these covariances can be modeled as a Kronecker product of temporal and spatial covariances. Our results over the experimental data collected from the users of a letter-by-letter typing BCI show that with less number of parameter estimations, the system can achieve higher classification accuracies compared to a method that uses full unstructured covariance estimation. Moreover, in order to illustrate that the proposed Kronecker product structure could enable shortening the BCI calibration data collection sessions, using Cramer-Rao bound analysis on simulated data, we demonstrate that a model with structured covariance matrices will achieve the same estimation error as a model with no covariance structure using fewer labeled EEG observations.

CS²-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing.

In this paper, we consider the problem of reconstructing the temporal and spatial profile of some physical phenomena monitored by large-scale Wireless Sensor Networks (WSNs) in an energy efficient manner. Compressive sensing is one of the popular choices to reduce the energy consumption of the data collection in WSNs. The existing solutions only consider sparsity of sensors' data from either temporal or spatial dimensions. In this paper, we propose a novel data collection strategy, CS²-collector, for WSNs based on the theory of Two Dimensional Compressive Sensing (2DCS). It exploits both temporal and spatial sparsity, i.e., 2D-sparsity of WSNs and achieves significant gain on the tradeoff between the compression ratio and reconstruction accuracy as the numerical simulations and evaluations on different types of sensors' data. More intuitively, with the same given energy budget, CS²-collector provides significantly more accurate reconstruction of the profile of the physical phenomena that are temporal-spatially sparse.

A three domain covariance framework for EEG/MEG data.

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets.

A generalized mechanistic codon model.

Models of codon evolution have attracted particular interest because of their unique capabilities to detect selection forces and their high fit when applied to sequence evolution. We described here a novel approach for modeling codon evolution, which is based on Kronecker product of matrices. The 61 × 61 codon substitution rate matrix is created using Kronecker product of three 4 × 4 nucleotide substitution matrices, the equilibrium frequency of codons, and the selection rate parameter. The entities of the nucleotide substitution matrices and selection rate are considered as parameters of the model, which are optimized by maximum likelihood. Our fully mechanistic model allows the instantaneous substitution matrix between codons to be fully estimated with only 19 parameters instead of 3,721, by using the biological interdependence existing between positions within codons. We illustrate the properties of our models using computer simulations and assessed its relevance by comparing the AICc measures of our model and other models of codon evolution on simulations and a large range of empirical data sets. We show that our model fits most biological data better compared with the current codon models. Furthermore, the parameters in our model can be interpreted in a similar way as the exchangeability rates found in empirical codon models.

Flexible marginalized models for bivariate longitudinal ordinal data.

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.

A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to electrocardiographic imaging.

This paper presents a method to solve a linear regression problem subject to grouplassoand ridge penalisation when the model has a Kronecker structure. This model was developed to solve the inverse problem of electrocardiography using sparse signal representation over a redundant dictionary or frame. The optimisation algorithm was performed using the block coordinate descent and proximal gradient descent methods. The explicit computation of the underlying Kronecker structure in the regression was avoided, reducing space and temporal complexity. We developed an algorithm that supports the use of arbitrary dictionaries to obtain solutions and allows a flexible group distribution.

A Novel COVID-19-Related Drug Discovery Approach Based on Non-Equidimensional Data Clustering.

The novel coronavirus disease (COVID-19) caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has spread all over the world. Since currently no effective antiviral treatment is available and those original inhibitors have no significant effect, the demand for the discovery of potential novel SARS-CoV-2 inhibitors has become more and more urgent. In view of the availability of the inhibitor-bound SARS-CoV-2 Mpro and PLpro crystal structure and a large amount of proteomics knowledge, we attempted using the existing coronavirus inhibitors to synthesize new ones, which combined the advantages of similar effective substructures for COVID-19 treatment. To achieve this, we first formulated this issue as a non-equidimensional inhibitor clustering and a following cluster center generating problem, where three essential challenges were carefully addressed, which are 1) how to define the distance between pairwise inhibitors with non-equidimensional molecular structure; 2) how to group inhibitors into clusters when the dimension is different; 3) how to generate the cluster center under this non-equidimensional condition. To be more specific, a novel matrix Kronecker product (p, m)-norm ⋅ p m ⊗ was first defined to induce the distance D p (A, B) between two inhibitors. Then, the hierarchical clustering approach was conducted to find similar inhibitors, and a novel iterative algorithm-based Kronecker product (p, m)-norm was designed to generate individual cluster centers as the drug candidates. Numerical experiments showed that the proposed methods can find novel drug candidates efficiently for COVID-19, which has provided valuable predictions for further biological evaluations.

Lightweight network study of leather defect segmentation with Kronecker product multipath decoding.

In the leather production process, defects on the leather surface are a key factor in the quality of the finished leather. Leather defect detection is an important step in the leather production process, especially for wet blue leather. To improve the efficiency and accuracy of detection, we propose a leather segmentation network using the Kronecker product for multi-path decoding and named KMDNet. The network uses Kronecker products to construct a new semantic information extraction layer named KPCL layer. The KPCL layer is added to the decoding network to form new decoding paths, and these different decoding paths are combined that segment the defective part of the leather image. We collaborate with leather companies to collect relevant leather defect images; use Tensorflow for training, validation, and testing experiments; and compare the detection results with non-machine learning algorithms and semantic segmentation algorithms. The experimental results show that KMDNet has a 1.99% improvement in F1 score compared to UNet for leather and a nearly three times improvement in detection speed.

Variance partitioning in spatio-temporal disease mapping models.

Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that we name the variance partitioning model. The variance partitioning model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a penalized complexity prior on the mixing parameter aids in coding prior information in an intuitive way. We illustrate the advantages of the variance partitioning model using two case studies.

Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control.

This paper investigates state estimation for complex dynamical networks (CDNs) with time-varying delays by using sampled-data control. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling state estimator is transformed into a continuous time-delay system with stochastic parameters in the system matrices, where the purpose is to design a state estimator to estimate the network states through available output measurements. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) containing triple and fourth integral terms and applying Wirtinger-based single and double integral inequality, Jenson integral inequality technique, delay-dependent stability conditions are established. The obtained conditions can be readily solved by using the LMI tool box in MATLAB. Finally, a numerical example is provided to demonstrate the validity of the proposed scheme.