Vector-exponential time-series modeling for polynomial J-spectral factorization

An iterative algorithm to perform the J-spectral factorization of a para-Hermitian matrix is presented. The algorithm proceeds by computing a special kernel representation of an interpolant for a sequence of points and associated directions determined from the spectral zeroes of the to-be factored matrix

A behavioral view of Nevanlinna-Pick interpolation

The classical Nevanlinna-Pick (NP) interpolation problem is about finding a rational function that satisfies given interpolation conditions, along with a norm condition. In this paper we address the NP problem using concepts from behavioral systems theory and quadratic differential forms (QDFs). The NP problem is solved using a certain “dualization of data”. We address system theoretic motivations for this dualization and the advantages gained in this process. Finally, we address the problem of constructing interpolating functions that satisfy a “frequency dependent” norm condition

Interpolation with bilinear differential forms

We present a recursive algorithm for modeling with bilinear differential forms. We discuss applications of this algorithm for interpolation with symmetric bivariate polynomials, and for computing storage functions for autonomous systems

Optimal Moments on Redundancies in Noisy Parallel Computing Setup

We consider the problem of job assignment where a master server aims to compute some tasks and is provided a few child servers to compute under a uniform straggling pattern where each server is equally likely to straggle. We distribute tasks to the servers so that the master is able to receive most of the tasks even if a significant number of child servers fail to communicate. We first show that all \textit{balanced} assignment schemes have the same expectation on the number of distinct tasks received and then study the variance. The variance or the second moment is a useful metric to study as there could be a high \textit{variation} in the number of distinct tasks received. We show constructions using a generalization of ``Balanced Incomplete Block Design'' [11,40] minimizes the variance, and constructions based on repetition coding schemes attain the largest variance. Both minimum variance and maximum variance attaining designs have their own use cases depending on whether the master aims for a heavy-tailed or light-tailed distribution on the number of distinct jobs. We further show the equivalence between job and server-based assignment schemes when the number of jobs and child servers are equal

The Variable Limits

Fitness Trackers (FTs) have enabled users with new affordance in health management. However, users report low retention rates of FTs for long term usage. The objective of this thesis is to explore a design paradigm for FTs using principles of self-modeling and neurophenomenology in the design of FT visualizations. It is aimed to foster long term use of FTs by employing art-design aesthetics and analytical visualization by integrating user’s actions with the intent of providing users a better experience, motivating them to curate data visualization over a long term period. Research methodology in process and design of Art Graph (AG) utilized archetype, persona and usability test. The design of interaction is experienced as personal examination through data analytics that functions as a visual data language of mind-body synergy. Three types of persona were employed to demonstrate the AG visualization values with classic somatotype body classification ectomorph, endomorph and mesomorph