The low-rank matrix completion problem is a fundamental problem with many important applications. Recently, [4],[13] and [5] obtained the first non-trivial theoretical results for the problem assuming that the observed entries are sampled uniformly at random. Unfortunately, most real-world datasets do not satisfy this assumption, but instead exhibit power-law distributed samples. In this paper,...

Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametr...

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination with no pivoting as well as block Gaussian elimination, approximation of the leading and trailing singular spaces of an ill conditioned matrix, associated wit...

Power grid vulnerability to targeted attack has been a focus of research after the robust yet fragile nature of complex systems was discovered. Various measures has been proposed to analyze the topological fragility since then. This paper focuses on providing a matrix which is able to find out critical elements within the system. A step by step method for building the matrix is shown. Various v...

This survey paper contains recent results for power matrix means and related inequalities for convex functions, Hadamard product of matrices as well as some inequalities involving exponential function of matrices.

Power packet is a unit of electric power transferred by a power pulse with an information tag. In Shannon’s information theory, messages are represented by symbol sequences in a digitized manner. Referring to this formulation, we define symbols in power packetization as a minimum unit of power transferred by a tagged pulse. Here, power is digitized and quantized. In this paper, we consider pack...

Harmonics have become an important issue in modern power systems. The widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs an Extended Harmonic Domain (EHD) based framework for dynamic analysis of long term analysis over voltages during the tra...