Delivery of a telephone-based intervention appears feasible. All family caregivers who began the program completed the four education modules. Future studies evaluating the effectiveness of the educational program should include a control group.

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In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is illustrated by an interesting example of remote sensing data. Also, we develop an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.

This paper develops a method for simultaneous estimation of This paper develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed method was used to estimate neighbor-dependent distributions of protein backbone dihedral angles (i.e., Ramachandran distributions). The estimated distributions were applied to protein loop modeling, one of the most challenging open problems in protein structure prediction, by feeding them into an angular-sampling-based loop structure prediction framework. Our estimated distributions compared favorably to the Ramachandran distributions estimated by fitting a hierarchical Dirichlet process model; and in particular, our distributions showed significant improvements on the hard cases where existing methods do not work well.

Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered on p−dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the loglikelihood function involves an infinite sum of indices in Z p , where p is the dimension of the data. To overcome this problem, for moderate dimension p, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction.

Coarctation of the aorta (CoA; constriction of the proximal descending thoracic aorta) is among the most common congenital cardiovascular defects. Coarctation-induced mechanical perturbations trigger a cycle of mechano-transduction events leading to irreversible precursors of hypertension including arterial thickening, stiffening, and vasoactive dysfunction in proximal conduit arteries. This study sought to identify kinetics of the stress-mediated compensatory response leading to these alterations using a preclinical rabbit model of CoA. Methods: A prior growth and remodeling (G&R) framework was reformulated and fit to empirical measurements from CoA rabbits classified into one control and nine CoA groups of various severities and durations (n = 63, 5–11/group). Empirical measurements included Doppler ultrasound imaging, uniaxial extension testing, catheter-based blood pressure, and wire myography, yielding the time evolution of arterial thickening, stiffening, and vasoactive dysfunction required to fit G&R constitutive parameters. Results: Excellent agreement was observed between model predictions and observed patterns of arterial thickening, stiffening, and dysfunction among all CoA groups. For example, predicted vascular impairment was not significantly different from empirical observations via wire myography (p-value > 0.13). Specifically, 48% and 45% impairment was observed in smooth muscle contraction and endothelial-dependent relaxation, respectively, which were accurately predicted using the G&R model. Conclusions: The resulting G&R model, for the first time, allows for prediction of hypertension precursors at neonatal ages that is currently challenging to examine in preclinical models. These findings provide a validated computational tool for prediction of persistent arterial dysfunction and identification of revised severity–duration thresholds that may ultimately avoid hypertension from CoA.

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence-structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations.