Extrapolation of a discrete collocation-type method of Hammerstein equations

AbstractIn recent papers, Kumar and Sloan introduced a new collocation-type method for numerical solution of Hammerstein integral equations. Kumar studied a discretized version of this method and obtained superconvergence rate for the discrete approximation to the exact solution. In this paper, the asymptotic error expansion of a discrete collocation-type method for Hammerstein integral equations is obtained. We show that when piecewise polynomials of degree p − 1 are used and numerical quadrature is used to approximate the definite integrals occurring in this method, the approximation solution admits an error expansion in powers of the step-size h. For a special choice of collocation points and numerical quadrature rule, the leading terms in the error expansion for the collocation solution contain only even powers of the step-size h, beginning with a term h2p. Thus Richardson's extrapolation can be performed on the solution, and this will increase the accuracy of numerical solution greatly. Some numerical results are given to illustrate this theory

A New Cell Association Scheme In Heterogeneous Networks

Cell association scheme determines which base station (BS) and mobile user (MU) should be associated with and also plays a significant role in determining the average data rate a MU can achieve in heterogeneous networks. However, the explosion of digital devices and the scarcity of spectra collectively force us to carefully re-design cell association scheme which was kind of taken for granted before. To address this, we develop a new cell association scheme in heterogeneous networks based on joint consideration of the signal-to-interference-plus-noise ratio (SINR) which a MU experiences and the traffic load of candidate BSs1. MUs and BSs in each tier are modeled as several independent Poisson point processes (PPPs) and all channels experience independently and identically distributed ( i.i.d.) Rayleigh fading. Data rate ratio and traffic load ratio distributions are derived to obtain the tier association probability and the average ergodic MU data rate. Through numerical results, We find that our proposed cell association scheme outperforms cell range expansion (CRE) association scheme. Moreover, results indicate that allocating small sized and high-density BSs will improve spectral efficiency if using our proposed cell association scheme in heterogeneous networks.Comment: Accepted by IEEE ICC 2015 - Next Generation Networking Symposiu

Spatial spectrum and energy efficiency of random cellular networks

It is a great challenge to evaluate the network performance of cellular mobile communication systems. In this paper, we propose new spatial spectrum and energy efficiency models for Poisson-Voronoi tessellation (PVT) random cellular networks. To evaluate the user access the network, a Markov chain based wireless channel access model is first proposed for PVT random cellular networks. On that basis, the outage probability and blocking probability of PVT random cellular networks are derived, which can be computed numerically. Furthermore, taking into account the call arrival rate, the path loss exponent and the base station (BS) density in random cellular networks, spatial spectrum and energy efficiency models are proposed and analyzed for PVT random cellular networks. Numerical simulations are conducted to evaluate the network spectrum and energy efficiency in PVT random cellular networks.Comment: appears in IEEE Transactions on Communications, April, 201

Context-aware and Scale-insensitive Temporal Repetition Counting

Temporal repetition counting aims to estimate the number of cycles of a given repetitive action. Existing deep learning methods assume repetitive actions are performed in a fixed time-scale, which is invalid for the complex repetitive actions in real life. In this paper, we tailor a context-aware and scale-insensitive framework, to tackle the challenges in repetition counting caused by the unknown and diverse cycle-lengths. Our approach combines two key insights: (1) Cycle lengths from different actions are unpredictable that require large-scale searching, but, once a coarse cycle length is determined, the variety between repetitions can be overcome by regression. (2) Determining the cycle length cannot only rely on a short fragment of video but a contextual understanding. The first point is implemented by a coarse-to-fine cycle refinement method. It avoids the heavy computation of exhaustively searching all the cycle lengths in the video, and, instead, it propagates the coarse prediction for further refinement in a hierarchical manner. We secondly propose a bidirectional cycle length estimation method for a context-aware prediction. It is a regression network that takes two consecutive coarse cycles as input, and predicts the locations of the previous and next repetitive cycles. To benefit the training and evaluation of temporal repetition counting area, we construct a new and largest benchmark, which contains 526 videos with diverse repetitive actions. Extensive experiments show that the proposed network trained on a single dataset outperforms state-of-the-art methods on several benchmarks, indicating that the proposed framework is general enough to capture repetition patterns across domains.Comment: Accepted by CVPR202

Cell contraction induces long-ranged stress stiffening in the extracellular matrix

Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells

Advances in Resting State Neuroimaging of Mild Cognitive Impairment

The rapidly increasing number of patients with Alzheimer's disease (AD) worldwide has become a major public concern. Mild cognitive impairment (MCI), characterized with accelerated memory decline than normal aging, is a stage between cognitively unimpaired and dementia. Identification of MCI in the Alzheimer's continuum from normal aging, is important for early diagnosis and improved intervention of AD. The imaging technique has been extensively used for diagnose and understanding the mechanisms of MCI. Firstly, we review the recent progresses in the research framework of MCI depending on the clinical and/or biomarker findings. Secondly, we cover studies that use of rs-fMRI (resting state functional magnetic resonance imaging) for the brain activities and functional connectivity between normal aging and MCI. Other methodologies and multi-modal studies for investigating the mechanism and early diagnosis of MCI are also discussed. Finally, we discuss how genetic and environmental factors such as education could interact with in MCI. Overall, MCI is a heterogeneous state and employing resting state neuroimaging with other AD biomarker approaches will be able to target in the more precise population and AD-related pathology process