Lower bounds on the rank and symmetric rank of real tensors

We lower bound the rank of a tensor by a linear combination of the ranks of three of its unfoldings, using Sylvester's rank inequality. In a similar way, we lower bound the symmetric rank by a linear combination of the symmetric ranks of three unfoldings. Lower bounds on the rank and symmetric rank of tensors are important for finding counterexamples to Comon's conjecture. A real counterexample to Comon's conjecture is a tensor whose real rank and real symmetric rank differ. Previously, only one real counterexample was known. We divide the construction into three steps. The first step involves linear spaces of binary tensors. The second step considers a linear space of larger decomposable tensors. The third step is to verify a conjecture that lower bounds the symmetric rank, on a tensor of interest. We use the construction to build an order six real tensor whose real rank and real symmetric rank differ.Comment: 26 pages, 3 figures, v2: updated to match published versio

Identifiability of overcomplete independent component analysis

Independent component analysis (ICA) studies mixtures of independent latent sources. An ICA model is identifiable if the mixing can be recovered uniquely. It is well-known that ICA is identifiable if and only if at most one source is Gaussian. However, this applies only to the setting where the number of sources is at most the number of observations. In this paper, we generalize the identifiability of ICA to the overcomplete setting, where the number of sources exceeds the number of observations. We give an if and only if characterization of the identifiability of overcomplete ICA. The proof studies linear spaces of rank one symmetric matrices. For generic mixing, we present an identifiability condition in terms of the number of sources and the number of observations. We use our identifiability results to design an algorithm to recover the mixing matrix from data and apply it to synthetic data and two real datasets.Comment: 28 pages, 7 figure

DiGiME: An Interactive Experience to Ease the Education of Social Information Sharing

Ever since digital and social media activities made their way into our day-to-day lives, things have become very different. People are continuously glued to their mobile devices, including children. Besides the tv screen time, mobile media time for 0-to-8 year-olds has tripled between 2013 and 2017, from an average of 15 minutes per day to 48 minutes per day1. As digital exposure is increasing at earlier ages, the danger of social information sharing increases as well. Children do not often realize that they are giving out a vast quantity of their personal information, and even their parents\u27 to the internet while being online. They are a particular vulnerable population when speaking of digital marketing and advertising - they could be easily manipulated and persuaded towards sharing their personal information and using the services or products. This thesis project intends to raise awareness about the impact of online safety among children and their parents, and also seeks to explore the possible communicational ways of helping parents helping their kids better protect their online user data in the meantime. The goal is to find an easy tool to serve as an easy-to-learn life lesson for both the kids and their parents, with parents leading the way. And the project should communicate the idea of safety does not happen by accident and people should help their loved ones better manage and protect their online data

Carbothermal Synthesis of Spherical AlN Fillers

Micro-sized spherical AlN particles have presented great commercial potential as thermally conductive fillers for high-performance thermal interface materials, benefiting from their high thermal conductivity and good fluidity in the polymers. In this chapter, recent research progress in the carbothermal synthesis of spherical AlN fillers is highlighted. The influences of various synthetic parameters, including N2 gas pressure, additive content, additive particle size, reaction temperature, reaction time, carbon content, and additive types, on the nitridation rate and the particle size and morphology of final AlN powders are summarized. More importantly, the growth mechanism of micro-sized spherical AlN granules is deeply discussed as well