Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group $G$. If $f \in L^1(G)$ has lacunary Fourier series, and vanishes on a non empty open set, then we prove that $f$ vanishes identically. This may be viewed as a qualitative uncertainty principle

What Trends in Chinese Social Media

There has been a tremendous rise in the growth of online social networks all over the world in recent times. While some networks like Twitter and Facebook have been well documented, the popular Chinese microblogging social network Sina Weibo has not been studied. In this work, we examine the key topics that trend on Sina Weibo and contrast them with our observations on Twitter. We find that there is a vast difference in the content shared in China, when compared to a global social network such as Twitter. In China, the trends are created almost entirely due to retweets of media content such as jokes, images and videos, whereas on Twitter, the trends tend to have more to do with current global events and news stories

The Pulse of News in Social Media: Forecasting Popularity

News articles are extremely time sensitive by nature. There is also intense competition among news items to propagate as widely as possible. Hence, the task of predicting the popularity of news items on the social web is both interesting and challenging. Prior research has dealt with predicting eventual online popularity based on early popularity. It is most desirable, however, to predict the popularity of items prior to their release, fostering the possibility of appropriate decision making to modify an article and the manner of its publication. In this paper, we construct a multi-dimensional feature space derived from properties of an article and evaluate the efficacy of these features to serve as predictors of online popularity. We examine both regression and classification algorithms and demonstrate that despite randomness in human behavior, it is possible to predict ranges of popularity on twitter with an overall 84% accuracy. Our study also serves to illustrate the differences between traditionally prominent sources and those immensely popular on the social web

Trends in Social Media : Persistence and Decay

Social media generates a prodigious wealth of real-time content at an incessant rate. From all the content that people create and share, only a few topics manage to attract enough attention to rise to the top and become temporal trends which are displayed to users. The question of what factors cause the formation and persistence of trends is an important one that has not been answered yet. In this paper, we conduct an intensive study of trending topics on Twitter and provide a theoretical basis for the formation, persistence and decay of trends. We also demonstrate empirically how factors such as user activity and number of followers do not contribute strongly to trend creation and its propagation. In fact, we find that the resonance of the content with the users of the social network plays a major role in causing trends

An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups

We generalise a result of Hardy, which asserts the impossibility of a function and its Fourier transform to be simultaneously “very rapidly decreasing” to: (i) all noncompact, semi-simple Lie groups with one conjugacy class of Cartan subgroups; (ii) SL(2, R); and (iii) all symmetric spaces of the noncompact type

Hardy's uncertainty principle on semisimple groups

A theorem of Hardy states that, if f is a function on R such that |f(x)|≤ C e−α|x|2 for all x in R and |f(ξ)|≤ C e−β|ξ|2 for all ξ in R, where α > 0, β > 0, and αβ > 1∕4, then f = 0. Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We extend the theorem to all semisimple groups

Free Tools for Teaching & Researching Wireless Networking Concepts

As wireless networking and security become more prevalent in the market, more and more computer science programs are incorporating courses in wireless networks or at the least, devoting a significant percentage of the advanced networking courses to wireless topics. As a result, in addition to industry practitioners, there is a growing interest among university researchers and faculty regarding tools used for teaching and researching in wireless networking concepts.This tutorial will demonstrate two free tools, Network Stumbler and ITGuru\u27s wireless module (academic version is free)