We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are crucial in applications, such as DNA microarrays and sensor networks, where dense measurements are not practically feasible. One possible construction uses ...

Large data sets are ubiquitous today with the advent of high speed computers and connectivity. Being able to gainfully use these data sets, however, is a challenge, especially when they are used to answer online queries which are generated rapidly. Even linear time algorithms are too slow in this context, and therefore sublinear time algorithms become critical. In many applications, queries to ...

The primary objective of the study is to compare insertion loss in an expansion chamber muffler using white and pink noise. White noise has equal power per hertz over entire range frequencies, while decreases with increasing frequency. Nonetheless, as width successive octaves increases, renders octave. sound pressure level at output port recorded acoustic analyzer, maintaining a constant input ...

X iv :1 00 8. 50 35 v1 [ m at h. N T ] 3 0 A ug 2 01 0 RECOVERING FOURIER COEFFICIENTS OF MODULAR FORMS AND FACTORING OF INTEGERS Sergei N. Preobrazhenskĭi It is shown that if a function defined on the segment [−1, 1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function’s Fourier coefficients cn for some subset of n ∈ [n1, n2], one c...

In this article, we develop new closed-form asymptotic approximations for the average symbol error rate (ASER) and the outage probability performance metrics of digital communication systems impaired by additive white Gaussian noise and fading. Specifically, our expressions generalize some of the known asymptotic results to a wide range of fading environments and digital modulation schemes. We ...

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

Stochastic differential equations (SDE) are a natural tool for modelling systems that are inherently noisy or contain uncertainties that can be modelled as stochastic processes. Crucial to the process of using SDE to build mathematical models is the ability to estimate parameters of those models from observed data. Over the past few decades, significant progress has been made on this problem, b...