Energy harvesting holds great potential to achieve long-lifespan self-powered operations of wireless sensor networks, wearable devices, and medical implants, and thus has attracted substantial interest from both academia and industry. This paper presents a comprehensive review of piezoelectric energyharvesting techniques developed in the last decade. The piezoelectric effect has been widely adopted to convert mechanical energy to electricity, due to its high energy conversion efficiency, ease of implementation, and miniaturization. From the viewpoint of applications, we are most concerned about whether an energy harvester can generate sufficient power under a variable excitation. Therefore, here we concentrate on methodologies leading to high power output and broad operational bandwidth. Different designs, nonlinear methods, optimization techniques, and harvesting materials are reviewed and discussed in depth. Furthermore, we identify four promising applications: shoes, pacemakers, tire pressure monitoring systems, and bridge and building monitoring. We review new high-performance energy harvesters proposed for each application.

One goal of statistical privacy research is to construct a data release mechanism that protects individual privacy while preserving information content. An example is a random mechanism that takes an input database X and outputs a random database Z according to a distribution Q n (·|X). Differential privacy is a particular privacy requirement developed by computer scientists in which Q n (·|X) is required to be insensitive to changes in one data point in X. This makes it difficult to infer from Z whether a given individual is in the original database X. We consider differential privacy from a statistical perspective. We consider several data-release mechanisms that satisfy the differential privacy requirement. We show that it is useful to compare these schemes by computing the rate of convergence of distributions and densities constructed from the released data. We study a general privacy method, called the exponential mechanism, introduced by McSherry and Talwar (2007). We show that the accuracy of this method is intimately linked to the rate at which the probability that the empirical distribution concentrates in a small ball around the true distribution.

Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is among the most general assumptions on the matrix, guaranteeing recovery. We prove a reduction principle showing that the RE condition can be guaranteed by checking the restricted isometry on a certain family of low-dimensional subspaces. This principle allows us to establish the RE condition for several broad classes of random matrices with dependent entries, including random matrices with subgaussian rows and non-trivial covariance structure, as well as matrices with independent rows, and uniformly bounded entries.Here X is an n × p design matrix, Y is a vector of noisy observations, and ǫ is the noise term. Even in the noiseless case, recovering β (or its support) from (X, Y ) seems impossible when n ≪ p, given that we have more variables than observations.A line of recent research shows that when β is sparse, that is, when it has a relatively small number of nonzero coefficients, it is possible to recover β from an underdetermined system of equations. In order to * Keywords. ℓ1 minimization, Sparsity, Restricted Eigenvalue conditions, Subgaussian random matrices, Design matrices with uniformly bounded entries.

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using 1 penalization methods. However, current methods assume that the data are independent and identically distributed. If the distribution, and hence the graph, evolves over time then the data are not longer identically distributed. In this paper we develop a nonparametric method for estimating time varying graphical structure for multivariate Gaussian distributions using an 1 regularization method, and show that, as long as the covariances change smoothly over time, we can estimate the covariance matrix well (in predictive risk) even when p is large.

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