Enhancing Twitter Data Analysis with Simple Semantic Filtering: Example in Tracking Influenza-Like Illnesses

Systems that exploit publicly available user generated content such as Twitter messages have been successful in tracking seasonal influenza. We developed a novel filtering method for Influenza-Like-Illnesses (ILI)-related messages using 587 million messages from Twitter micro-blogs. We first filtered messages based on syndrome keywords from the BioCaster Ontology, an extant knowledge model of laymen's terms. We then filtered the messages according to semantic features such as negation, hashtags, emoticons, humor and geography. The data covered 36 weeks for the US 2009 influenza season from 30th August 2009 to 8th May 2010. Results showed that our system achieved the highest Pearson correlation coefficient of 98.46% (p-value<2.2e-16), an improvement of 3.98% over the previous state-of-the-art method. The results indicate that simple NLP-based enhancements to existing approaches to mine Twitter data can increase the value of this inexpensive resource.Comment: 10 pages, 5 figures, IEEE HISB 2012 conference, Sept 27-28, 2012, La Jolla, California, U

The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor

The Bohl spectrum for nonautonomous differential equations

We develop the Bohl spectrum for nonautonomous linear differential equation on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker--Sell spectrum. We prove that the Bohl spectrum is given by the union of finitely many intervals, and we show by means of an explicit example that the Bohl spectrum does not coincide with the Sacker--Sell spectrum in general. We demonstrate for this example that any higher-order nonlinear perturbation is exponentially stable, although this not evident from the Sacker--Sell spectrum. We also analyze in detail situations in which the Bohl spectrum is identical to the Sacker-Sell spectrum

Lyapunov Exponents for Random Dynamical Systems

In this thesis the Lyapunov exponents of random dynamical systems are presented and investigated. The main results are: 1. In the space of all unbounded linear cocycles satisfying a certain integrability condition, we construct an open set of linear cocycles have simple Lyapunov spectrum and no exponential separation. Thus, unlike the bounded case, the exponential separation property is nongeneric in the space of unbounded cocycles. 2. The multiplicative ergodic theorem is established for random difference equations as well as random differential equations with random delay. 3. We provide a computational method for computing an invariant measure for infinite iterated functions systems as well as the Lyapunov exponents of products of random matrices.In den vorliegenden Arbeit werden Lyapunov-Exponented für zufällige dynamische Systeme untersucht. Die Hauptresultate sind: 1. Im Raum aller unbeschränkten linearen Kozyklen, die eine gewisse Integrabilitätsbedingung erfüllen, konstruieren wir eine offene Menge linearer Kyzyklen, die einfaches Lyapunov-Spektrum besitzen und nicht exponentiell separiert sind. Im Gegensatz zum beschränkten Fall ist die Eingenschaft der exponentiellen Separiertheit nicht generisch in Raum der unbeschränkten Kozyklen. 2. Sowohl für zufällige Differenzengleichungen, als auch für zufällige Differentialgleichungen, mit zufälligem Delay wird ein multiplikatives Ergodentheorem bewiesen. 3.Eine algorithmisch implementierbare Methode wird entwickelt zur Berechnung von invarianten Maßen für unendliche iterierte Funktionensysteme und zur Berechnung von Lyapunov-Exponenten für Produkte von zufälligen Matrizen

Lyapunov Exponents for Random Dynamical Systems

In this thesis the Lyapunov exponents of random dynamical systems are presented and investigated. The main results are: 1. In the space of all unbounded linear cocycles satisfying a certain integrability condition, we construct an open set of linear cocycles have simple Lyapunov spectrum and no exponential separation. Thus, unlike the bounded case, the exponential separation property is nongeneric in the space of unbounded cocycles. 2. The multiplicative ergodic theorem is established for random difference equations as well as random differential equations with random delay. 3. We provide a computational method for computing an invariant measure for infinite iterated functions systems as well as the Lyapunov exponents of products of random matrices.In den vorliegenden Arbeit werden Lyapunov-Exponented für zufällige dynamische Systeme untersucht. Die Hauptresultate sind: 1. Im Raum aller unbeschränkten linearen Kozyklen, die eine gewisse Integrabilitätsbedingung erfüllen, konstruieren wir eine offene Menge linearer Kyzyklen, die einfaches Lyapunov-Spektrum besitzen und nicht exponentiell separiert sind. Im Gegensatz zum beschränkten Fall ist die Eingenschaft der exponentiellen Separiertheit nicht generisch in Raum der unbeschränkten Kozyklen. 2. Sowohl für zufällige Differenzengleichungen, als auch für zufällige Differentialgleichungen, mit zufälligem Delay wird ein multiplikatives Ergodentheorem bewiesen. 3.Eine algorithmisch implementierbare Methode wird entwickelt zur Berechnung von invarianten Maßen für unendliche iterierte Funktionensysteme und zur Berechnung von Lyapunov-Exponenten für Produkte von zufälligen Matrizen

Facts and Fabrications about Ebola: A Twitter Based Study

Microblogging websites like Twitter have been shown to be immensely useful for spreading information on a global scale within seconds. The detrimental effect, however, of such platforms is that misinformation and rumors are also as likely to spread on the network as credible, verified information. From a public health standpoint, the spread of misinformation creates unnecessary panic for the public. We recently witnessed several such scenarios during the outbreak of Ebola in 2014 [14, 1]. In order to effectively counter the medical misinformation in a timely manner, our goal here is to study the nature of such misinformation and rumors in the United States during fall 2014 when a handful of Ebola cases were confirmed in North America. It is a well known convention on Twitter to use hashtags to give context to a Twitter message (a tweet). In this study, we collected approximately 47M tweets from the Twitter streaming API related to Ebola. Based on hashtags, we propose a method to classify the tweets into two sets: credible and speculative. We analyze these two sets and study how they differ in terms of a number of features extracted from the Twitter API. In conclusion, we infer several interesting differences between the two sets. We outline further potential directions to using this material for monitoring and separating speculative tweets from credible ones, to enable improved public health information.Comment: Appears in SIGKDD BigCHat Workshop 201