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Sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition has been utilized in many multivariate regression methods. The appeal of this factorization is owing to its power in discovering a highly-interpretable latent association network. However, many existing methods are either ad hoc without a general performance guarantee, or are computationally intensive. We formulate the statistical problem as a sparse factor regression and tackle it with a two-stage "deation + stagewise learning" approach. In the first stage, we consider both sequential and parallel approaches for simplifying the task into a set of co-sparse unit-rank estimation (CURE) problems, and establish the statistical underpinnings of these commonly-adopted and yet poorly understood deation methods. In the second stage, we innovate a contended stagewise learning technique, consisting of a sequence of simple incremental updates, to efficiently trace out the whole solution paths of CURE. Our algorithm achieves a much lower computational complexity than alternating convex search, and it enables a exible and principled tradeoff between statistical accuracy and computational efficiency. Our work is among the first to enable stagewise learning for non-convex problems, and the idea can be applicable in many multi-convex problems. Extensive simulation studies and an application in genetics demonstrate the effectiveness and scalability of our approach. [ABSTRACT FROM AUTHOR]

Modelling the covariance matrix of multiple responses in longitudinal data plays a vital role. It is more challenging than its univariate counterpart due to the presence of correlations among multiple responses. Using the modified Cholesky block decomposition, we impose an adaptive block‐banded structure on the Cholesky factor and sparsity on the innovation variance matrices via a novel convex hierarchical penalty and lasso penalty, respectively. The resulting adaptive block‐banding regularized estimator is fully data‐driven and has more flexibility than regular banding estimators. We develop an efficient alternative convex optimization algorithm using the Alternating Direction Method of Multipliers (ADMM) algorithm. The resulting estimators converge optimally in the Frobenius norm. We establish row‐specific support recovery for the precision matrix. Simulations and real data analysis show that the proposed estimator is better able to reveal banding sparsity patterns in data. [ABSTRACT FROM AUTHOR]

Abstract Background Ewing’s sarcoma family of tumors consists of small round cell neoplasms, inclusive of primitive neuroectodermal tumor (PNET), Askin’s tumor, and PNET of the bone. Extraosseous Ewing’s sarcoma occurs commonly at bones of lower extremities and paravertebral region of the spine. It rarely presents as a primary intracranial lesion. When intracranial, it can be misdiagnosed as central PNET (e.g., medulloblastoma, pinealoblastoma, or supratentorial PNET), other intracranial lesions, or even as an epidural hematoma. Case presentation We report the case of a 20-year-old patient who presented to the emergency department with complaints of drowsiness, headache, and fever for 1 day. On initial computed tomography (CT) scan of the brain, a right temporal biconvex epidural lesion involving squamous-temporal bone with periosteal reaction was noted. The patient underwent urgent craniotomy, and a tumor was found and excised. Biopsy report confirmed Ewing’s sarcoma. Conclusion Ewing’s sarcoma is a rare intracranial malignancy with only a few cases reported in literature. In a young patient with a biconvex epidural lesion, in the absence of trauma or ongoing infection, the possibility of Ewing’s sarcoma should be considered as well.

Because of variability of the force vs. penetration relationship (FPR) from one blow to another in percussive drilling, and difficulty to predict FPRs under such conditions, use is commonly made of simple FPR models, such as the bilinear one defined by its loading/unloading slopes. Here a biconvex model with an added parameter representing convexity is considered. One aim is to study the effect of convexity on maximal penetration, maximal force and efficiency. Another is to assess, with the biconvex FPR as an example, how well a bilinear FPR can be used to approximate one that is nonlinear. A simple percussive top-hammer drill model is considered, comprising a hammer, a drill rod and a bit with the same characteristic impedance. The maximal penetration is found to decrease and the maximal force to increase with increasing convexity. The efficiency has a maximum for a finite hammer length (incident wave duration), and the highest maximal efficiency is obtained for a linear FPR. With increasing convexity, the maximal efficiency decreases and occurs for shorter hammers (incident waves). The bilinear approximation of a biconvex FPR accurately predicts the position of the maximum in efficiency, even for large convexity, but somewhat overestimates its height and width. [ABSTRACT FROM AUTHOR]

In this paper, a wireless energy harvesting and information transfer protocol in cognitive relay networks is investigated, where an energy harvesting secondary network shares the spectrum as well as harvests energy by assisting the primary transmission. Specifically, a secondary transmitter scavenges energy from the received primary signal and then employs the harvested energy to forward the resulting signals along with the secondary signal. The secondary receiver can also harvest the ambient energy, and use the remaining signal to cancel the primary interference. We analytically derive the exact expressions of the outage probabilities for both primary and secondary networks. The rate-energy tradeoff between the ergodic capacity and harvested energy in the secondary network is also discussed. Furthermore, to quantify the energy consumption, we investigate the system energy efficiency. Moreover, we address the optimization power allocation strategy under three performance criteria and theoretically prove that the resulting nonconvex optimization problems can be converted into biconvex problems. The corresponding effective algorithms are then developed to solve the optimization problems. Numerical results show that the proposed protocol not only achieves both the primary and secondary transmissions but also harvests the ambient energy. [ABSTRACT FROM PUBLISHER]

This paper considers the allocation of time slots in a frame, as well as power and rate to multiple receivers on an energy harvesting downlink. Energy arrival times that will occur within the frame are known at the beginning of the frame. The goal is to optimize throughput in a proportionally fair way, taking into account the inherent differences of channel quality among users. Analysis of structural characteristics of the problem reveals that it can be formulated as a biconvex optimization problem, and that it has multiple optima. Due to the biconvex nature of the problem, a Block Coordinate Descent (BCD) based optimization algorithm that converges to an optimal solution is presented. However, finding the optimal allocation with BCD entails a computational complexity that increases sharply in terms of the number of users or slots. Therefore, certain structural characteristics of the optimal power-time allocation policy are derived. Building on those, two simple and computationally scalable heuristics, PTF and ProNTO are proposed. Simulation results suggest that PTF and ProNTO can closely track the performance of BCD which achieves a good balance between total throughput and fairness. [ABSTRACT FROM PUBLISHER]

Cognitive radio networks require fast and reliable spectrum sensing to achieve high network utilization by secondary users. Optimization approaches to spectrum sensing to-date have largely focused on maximizing throughput for secondary users while considering only a single parameter variable pertinent to sensing - notably the threshold or duration, but not both. In this work, we investigate the impact of true joint minimization under two performance criteria: a) minimization of the average time to detection of a spectrum hole and b) joint maximization of the aggregate opportunistic throughput. We show that the resulting non-convex problem is actually biconvex under practical conditions for which effective algorithms can be developed that yields reliable numerical procedures to solve the resulting optimization problem. The results show that the proposed approach can considerably improve system performance (in terms of the mean time to detect a spectrum hole and also the aggregate opportunistic throughput of both primary and secondary users), relative to the scenarios with only a single sensing variable or a sub-optimal ad-hoc optimization approach used for two variable case. [ABSTRACT FROM PUBLISHER]

Estimating covariance matrix is one of the most important analytical tasks in analyzing multivariate longitudinal data, which provides a unique opportunity in studying the joint evolution of multiple response variables over time. This paper introduces a BiConvex Blockwise Regularization (BCBR) sparse estimator for the precision matrix (inverse of the covariance matrix) of high dimensional multivariate longitudinal responses. Using the modified Cholesky block decomposition, we impose a block banded structure on the Cholesky factor and sparsity on the innovation variance matrices via a novel convex hierarchical penalty and lasso penalty, respectively. The blockwise banding structure is a generalization of the existing banding structure for univariate longitudinal data. An efficient alternative convex optimization algorithm is developed by using ADMM algorithm. The resulting estimators are shown to converge in an optimal rate of Frobenius norm, and the exact bandwidth recovery is established for the precision matrix. Simulations and real-life data analysis show that the proposed estimator outperforms its competitors. [ABSTRACT FROM AUTHOR]