Polynomial calculus space and resolution width

We show that if a k-CNF requires width w to refute in resolution, then it requires space square root of √ω to refute in polynomial calculus, where the space of a polynomial calculus refutation is the number of monomials that must be kept in memory when working through the proof. This is the first analogue, in polynomial calculus, of Atserias and Dalmau's result lower-bounding clause space in resolution by resolution width. As a by-product of our new approach to space lower bounds we give a simple proof of Bonacina's recent result that total space in resolution (the total number of variable occurrences that must be kept in memory) is lower-bounded by the width squared. As corollaries of the main result we obtain some new lower bounds on the PCR space needed to refute specific formulas, as well as partial answers to some open problems about relations between space, size, and degree for polynomial calculus

Real-time processing of social media with SENTINEL: a syndromic surveillance system incorporating deep learning for health classification

Interest in real-time syndromic surveillance based on social media data has greatly increased in recent years. The ability to detect disease outbreaks earlier than traditional methods would be highly useful for public health officials. This paper describes a software system which is built upon recent developments in machine learning and data processing to achieve this goal. The system is built from reusable modules integrated into data processing pipelines that are easily deployable and configurable. It applies deep learning to the problem of classifying health-related tweets and is able to do so with high accuracy. It has the capability to detect illness outbreaks from Twitter data and then to build up and display information about these outbreaks, including relevant news articles, to provide situational awareness. It also provides nowcasting functionality of current disease levels from previous clinical data combined with Twitter data. The preliminary results are promising, with the system being able to detect outbreaks of influenza-like illness symptoms which could then be confirmed by existing official sources. The Nowcasting module shows that using social media data can improve prediction for multiple diseases over simply using traditional data sources

Formation of molecular oxygen in ultracold O + OH reaction

We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic and reactive cross sections as well as the vibrational and rotational populations of the product O2 molecules are reported. A J-shifting approximation is used to compute the rate coefficients. At temperatures T = 10 - 100 mK for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, T < 1 mK, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at T=0.3 K, at higher temperatures, the quantum calculations predict a larger rate coefficient than the classical model, in agreement with experimental data for the O + OH reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about 6.10^{-12} cm^3 molecule^{-1} s^{-1}, a value comparable to that of barrierless alkali-metal atom - dimer systems and about a factor of five larger than that of the tunneling dominated F + H2 reaction.Comment: 9 pages, 8 figure

The Complexity of Treelike Systems over lamdda-Local Formulae

21-24 June 2004, Amherst, MA, USA. IEEE Computer Society 2004

DEFENDER: Detecting and Forecasting Epidemics Using Novel Data-Analytics for Enhanced Response

In recent years social and news media have increasingly been used to explain patterns in disease activity and progression. Social media data, principally from the Twitter network, has been shown to correlate well with official disease case counts. This fact has been exploited to provide advance warning of outbreak detection, forecasting of disease levels and the ability to predict the likelihood of individuals developing symptoms. In this paper we introduce DEFENDER, a software system that integrates data from social and news media and incorporates algorithms for outbreak detection, situational awareness and forecasting. As part of this system we have developed a technique for creating a location network for any country or region based purely on Twitter data. We also present a disease nowcasting (forecasting the current but still unknown level) approach which leverages counts from multiple symptoms, which was found to improve the nowcasting accuracy by 37 percent over a model that used only previous case data. Finally we attempt to forecast future levels of symptom activity based on observed user movement on Twitter, finding a moderate gain of 5 percent over a time series forecasting model