Lie algebra solution of population models based on time-inhomogeneous Markov chains

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical and social applications. This paper presents the Lie algebraic method, and applies it to three biologically well motivated examples. The result of this is a solution form that is often highly computationally advantageous.Comment: 10 pages; 1 figure; 2 tables. To appear in Applied Probabilit

Demographic characteristics and opportunistic diseases associated with attrition during preparation for antiretroviral therapy in primary health centres in Kibera, Kenya.

Using routine data from HIV-positive adult patients eligible for antiretroviral therapy (ART), we report on routinely collected demographic characteristics and opportunistic diseases associated with pre-ART attrition (deaths and loss to follow-up). Among 2471 ART eligible patients, enrolled between January 2005 and November 2008, 446 (18%) were lost to attrition pre-ART. Adjusted risk factors significantly associated with pre-ART attrition included age <35 years (Odds Ratio, OR 1.4, 95% Confidence Interval, CI 1.1-1.8), severe malnutrition (OR 1.5, 95% CI 1.1-2.0), active pulmonary tuberculosis (OR 1.6, 95% CI 1.1-2.4), severe bacterial infections including severe bacterial pneumonia (OR 1.9, 95% CI 1.2-2.8) and prolonged unexplained fever (>1 month), (OR 2.6, 95% CI 1.3-5.2). This study highlights a number of clinical markers associated with pre-ART attrition that could serve as 'pointers' or screening tools to identify patients who merit fast-tracking onto ART and/or closer clinical attention and follow-up

On the stability and ergodicity of adaptive scaling Metropolis algorithms

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.Comment: 24 pages, 1 figure; major revisio

Crosslinking of Styrene Homopolymers and Copolymers by p-Di(chloromethyl) Benzene

This thesis is principally concerned with the kinetics of the crosslinking of polystyrene using p-di(chloromethyl)benzene (DCMB), in the presence of a Friedel-Crafts catalyst, and the effect of this crosslinking on the thermal properties of polystyrene. As the polymerisation of styrene and the condensation of DCMB with aromatic nuclei can both be initiated by Friedel-Crafts catalysts, an attempt was made to produce crosslinked polystyrene by mixing styrene DCMB and stannic chloride in 1,2-dichloroethane (DCE) at 3

Alien Registration- Gilks, Leonard (Bridgewater, Aroostook County)

https://digitalmaine.com/alien_docs/26283/thumbnail.jp

Catching Super Massive Black Hole Binaries Without a Net

The gravitational wave signals from coalescing Supermassive Black Hole Binaries are prime targets for the Laser Interferometer Space Antenna (LISA). With optimal data processing techniques, the LISA observatory should be able to detect black hole mergers anywhere in the Universe. The challenge is to find ways to dig the signals out of a combination of instrument noise and the large foreground from stellar mass binaries in our own galaxy. The standard procedure of matched filtering against a grid of templates can be computationally prohibitive, especially when the black holes are spinning or the mass ratio is large. Here we develop an alternative approach based on Metropolis-Hastings sampling and simulated annealing that is orders of magnitude cheaper than a grid search. We demonstrate our approach on simulated LISA data streams that contain the signals from binary systems of Schwarzschild Black Holes, embedded in instrument noise and a foreground containing 26 million galactic binaries. The search algorithm is able to accurately recover the 9 parameters that describe the black hole binary without first having to remove any of the bright foreground sources, even when the black hole system has low signal-to-noise.Comment: 4 pages, 3 figures, Refined search algorithm, added low SNR exampl

Mining Frequent Graph Patterns with Differential Privacy

Discovering frequent graph patterns in a graph database offers valuable information in a variety of applications. However, if the graph dataset contains sensitive data of individuals such as mobile phone-call graphs and web-click graphs, releasing discovered frequent patterns may present a threat to the privacy of individuals. {\em Differential privacy} has recently emerged as the {\em de facto} standard for private data analysis due to its provable privacy guarantee. In this paper we propose the first differentially private algorithm for mining frequent graph patterns. We first show that previous techniques on differentially private discovery of frequent {\em itemsets} cannot apply in mining frequent graph patterns due to the inherent complexity of handling structural information in graphs. We then address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling based algorithm. Unlike previous work on frequent itemset mining, our techniques do not rely on the output of a non-private mining algorithm. Instead, we observe that both frequent graph pattern mining and the guarantee of differential privacy can be unified into an MCMC sampling framework. In addition, we establish the privacy and utility guarantee of our algorithm and propose an efficient neighboring pattern counting technique as well. Experimental results show that the proposed algorithm is able to output frequent patterns with good precision

Estimating population cardinal health state valuation models from individual ordinal (rank) health state preference data

Ranking exercises have routinely been used as warm-up exercises within health state valuation surveys. Very little use has been made of the information obtained in this process. Instead, research has focussed upon the analysis of health state valuation data obtained using the visual analogue scale, standard gamble and time trade off methods. Thurstone’s law of comparative judgement postulates a stable relationship between ordinal and cardinal preferences, based upon the information provided by pairwise choices. McFadden proposed that this relationship could be modelled by estimating conditional logistic regression models where alternatives had been ranked. In this paper we report the estimation of such models for the Health Utilities Index Mark 2 and the SF-6D. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations. For both the HUI2 and the SF-6D, the models estimated using rank data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that rank data has the potential to provide useful insights into community health state preferences. However, important questions remain

Markov Chain Monte Carlo Method without Detailed Balance

We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.Comment: 5 pages, 5 figure