Nigel Bean

An analysis of the interactions between individual comorbidities and their treatments--implications for guidelines and polypharmacy.

BACKGROUND With aging there is an increase in frailty and chronic disease leading to a potential increase in medication use. Most clinical trials have excluded old, frail individuals and have failed to take into account the effects of outcome interaction. METHODS AND RESULTS In this article we provide a mathematical model demonstrating that comorbidities, including old age, interact with therapies, reducing their effectiveness. CONCLUSION These findings question the validity of single disease guidelines in old persons or in persons with multiple chronic diseases.

The Cross-Entropy Method for Network Reliability Estimation

Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network—expressed as the probability that certain nodes in the network are connected—is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability estimation procedures. Three techniques of estimation are considered: Crude Monte Carlo and the more sophisticated Permutation Monte Carlo and Merge Process. We show that the Cross-Entropy method yields a speed-up over all three techniques.

Characterization of Matrix-Exponential Distributions

The class of matrix-exponential distributions can be equivalently defined as the class of all distributions with rational Laplace–Stieltjes transform. An immediate question that arises is: when does a rational Laplace–Stieltjes transform correspond to a matrix-exponential distribution? For a rational Laplace–Stieltjes transform that has a pole of maximal real part that is real and negative, we give a geometric description of all admissible numerator polynomials that give rise to matrix-exponential distributions. Using this approach we give a complete characterization for all matrix-exponential distributions of order three.

ALGORITHMS FOR RETURN PROBABILITIES FOR STOCHASTIC FLUID FLOWS

Abstract We consider several known algorithms and introduce some new algorithms that can be used to calculate the probability of return to the initial level in the Markov stochastic fluid flow model. We give the physical interpretations of these algorithms within the fluid flow environment. The rates of convergence are explained in terms of the physical properties of the fluid flow processes. We compare these algorithms with respect to the number of iterations required and their complexity. The performance of the algorithms depends on the nature of the process considered in the analysis. We illustrate this with examples and give appropriate recommendations.

Performance measures of a multi-layer Markovian fluid model

Abstract Our goal is to model the behaviour of the fluid in a buffer with threshold controls with a wide range of behaviour possible at the boundaries. To model this, we consider a class of Markovian fluid flow models with several layers, each with their own parameters, separated by boundaries. The behaviour of the fluid at each boundary is modelled by parameters unique to that boundary. We derive the Laplace-Stieltjes transforms of time-related performance measures of this model. This is illustrated with numerical examples. All results are obtained via techniques within the fluid flow environment, and useful physical interpretations are presented.

Aboriginal mitogenomes reveal 50,000 years of regionalism in Australia

Aboriginal Australians represent one of the longest continuous cultural complexes known. Archaeological evidence indicates that Australia and New Guinea were initially settled approximately 50 thousand years ago (ka); however, little is known about the processes underlying the enormous linguistic and phenotypic diversity within Australia. Here we report 111 mitochondrial genomes (mitogenomes) from historical Aboriginal Australian hair samples, whose origins enable us to reconstruct Australian phylogeographic history before European settlement. Marked geographic patterns and deep splits across the major mitochondrial haplogroups imply that the settlement of Australia comprised a single, rapid migration along the east and west coasts that reached southern Australia by 49–45 ka. After continent-wide colonization, strong regional patterns developed and these have survived despite substantial climatic and cultural change during the late Pleistocene and Holocene epochs. Remarkably, we find evidence for the continuous presence of populations in discrete geographic areas dating back to around 50 ka, in agreement with the notable Aboriginal Australian cultural attachment to their country.

Quasi-Birth-and-Death Processes with Rational Arrival Process Components

This paper introduces the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process (RAP) components. We use the physical interpretation of the prediction process of the RAP, developed by Asmussen and Bladt, and develop an analysis that parallels the analysis of a traditional QBD. Further, we present an algorithm for the numerical evaluation of the matrix G. As an example, we consider two queues where the arrival process and the sequence of service times are taken from two dependent RAPs, that are not Markovian Arrival Processes.

THE TREE CUT AND MERGE ALGORITHM FOR ESTIMATION OF NETWORK RELIABILITY

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Hitting probabilities and hitting times for stochastic fluid flows: The bounded model

We consider a Markovian stochastic fluid flow model in which the fluid level has a lower bound zero and a positive upper bound. The behavior of the process at the boundaries is modeled by parameters that are different than those in the interior and allow for modeling a range of desired behaviors at the boundaries. We illustrate this with examples. We establish formulas for several time-dependent performance measures of significance to a number of applied probability models. These results are achieved with techniques applied within the fluid flow model directly. This leads to useful physical interpretations, which are presented.

Where’s Waldo? practical searches for stability in iBGP

What does a childpsilas search of a large, complex cartoon for the eponymous character (Waldo) have to do with Internet routing? Network operators also search complex datasets, but Waldo is the least of their worries. Routing oscillation is a much greater concern. Networks can be designed to avoid routing oscillation, but the approaches so far proposed unnecessarily reduce the configuration flexibility. More importantly, apparently minor changes to a configuration can lead to instability. Verification of network stability is therefore an important task, but unlike the childpsilas search, this problem is NP hard. Until now, no practical method was available for large networks. In this paper, we present an efficient algorithm for proving stability of iBGP, or finding the potential oscillatory modes, and demonstrate its efficacy by applying it to the iBGP configuration of a large Tier-2 AS.