Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas

In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles.Comment: Final version, to appear in Nonlinearity. Corrected some minor typos from previous versio

Studies of childhood tuberculosis

Includes abstract. Includes bibliographical references (leaves 200-218)

A randomised trial of the safety and immunogenicity of low dose haemophilus conjugate vaccine in healthy infants at 6,10, and 14 weeks of age

A Research Report submitted to the Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Medicine in the branch of Medical MicrobiologyBackground Despite their proven efficacy, Haemophilus influenzae type b (Hib) conjugate vaccines are not given to most children in the developing world in the face of an estimated global Hib disease burden of nearly 2 million cases per annum. A major barrier to the introduction of the vaccine would be overcome by diluting the vaccine tenfold in DTP. We report a randomised trial comparing the use of Hib conjugate vaccine diluted tenfold in a multidose vial of DTP, with that of the full Hib dose.IT201

Extremal dichotomy for uniformly hyperbolic systems

We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is strictly maximized at $\zeta$ then the corresponding time series $\{\phi\circ T^i\}$ exhibits extreme value statistics corresponding to an iid sequence of random variables with the same distribution function as $\phi$ and with extremal index one. If however $\phi$ is strictly maximized at a periodic point $q$ then the corresponding time-series exhibits extreme value statistics corresponding to an iid sequence of random variables with the same distribution function as $\phi$ but with extremal index not equal to one. We give a formula for the extremal index (which depends upon the metric used and the period of $q$). These results imply that return times are Poisson to small balls centered at non-periodic points and compound Poisson for small balls centered at periodic points.Comment: 21 pages, 4 figure

Investigating error injection to enhance the effectiveness of mobile text entry studies of error behaviour

During lab studies of text entry methods it is typical to observer very few errors in participants' typing - users tend to type very carefully in labs. This is a problem when investigating methods to support error awareness or correction as support mechanisms are not tested. We designed a novel evaluation method based around injection of errors into the users' typing stream and report two user studies on the effectiveness of this technique. Injection allowed us to observe a larger number of instances and more diverse types of error correction behaviour than would normally be possible in a single study, without having a significant impact on key input behaviour characteristics. Qualitative feedback from both studies suggests that our injection algorithm was successful in creating errors that appeared realistic to participants. The use of error injection shows promise for the investigation of error correction behaviour in text entry studies

Almost sure convergence of maxima for chaotic dynamical systems

ArticleSuppose (f,X,ν) is a measure preserving dynamical system and ϕ:X→R is an observable with some degree of regularity. We investigate the maximum process M n :=max{X 1 ,…,X n } , where X i =ϕ∘f i is a time series of observations on the system. When M n →∞ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence u n →∞ such that M n /u n →1 almost surely. The observables we consider will be functions of the distance to a distinguished point x ~ ∈X . Our results are based on the interplay between shrinking target problem estimates at x ~ and the form of the observable (in particular polynomial or logarithmic) near x ~ . We determine where such an almost sure limit exists and give examples where it does not. Our results apply to a wide class of non-uniformly hyperbolic dynamical systems, under mild assumptions on the rate of mixing, and on regularity of the invariant measure

Designed with older adults to support better error correction in smartphone text entry : the MaxieKeyboard

Through our participatory design with older adults a need for improved error support for texting on smartphones emerged. Here we present the MaxieKeyboard based on the outcomes from this process. The keyboard highlights errors, auto-corrections and suggestion bar usage in the composition area and gives feedback on the keyboard on typing correctness. Our older adult groups have shown strong support for the keyboard