APPROXIMATE GAUSS-MARKOV REALISATION OF MULTIVARIATE STOCHASTIC PROCESSES.

Given a spectral density matrix or, equivalently, a real autocovariance sequence, the author seeks to determine a finite-dimensional linear time-invariant system which, when driven by white noise, will produce an output whose spectral density is approximately PHI ( omega ), and an approximate spectral factor of PHI ( omega ). The author employs the Anderson-Faurre theory in his analysis.

Evaluating the impacts of iteration on PD processes by transforming task network models into System Dynamics models

Iteration is unavoidable in the design process and should be incorporated when planning and managing projects in order to minimize surprises and reduce schedule distortions. However, planning and managing iteration is challenging because the relationships between its causes and effects are complex. Most approaches which use mathematical models to analyze the impact of iteration on the design process focus on a relatively small number of its causes and effects. Therefore, insights derived from these analytical models may not be robust under a broader consideration of potential influencing factors. In this article, we synthesize an explanatory framework which describes the network of causes and effects of iteration identified from the literature, and introduce an analytic approach which combines a task network modeling approach with System Dynamics simulation. Our approach models the network of causes and effects of iteration alongside the process architecture which is required to analyze the impact of iteration on design process performance. We show how this allows managers to assess the impact of changes to process architecture and to management levers which influence iterative behavior, accounting for the fact that these changes can occur simultaneously and can accumulate in non-linear ways. We also discuss how the insights resulting from this analysis can be visualized for easier consumption by project participants not familiar with simulation methods. Copyright © 2010 by ASME.

Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Campylobacter jejuni colonization and transmission in broiler chickens: a modelling perspective.

Campylobacter jejuni is one of the most common causes of acute enteritis in the developed world. The consumption of contaminated poultry, where C. jejuni is believed to be a commensal organism, is a major risk factor. However, the dynamics of this colonization process in commercially reared chickens is still poorly understood. Quantification of these dynamics of infection at an individual level is vital to understand transmission within populations and formulate new control strategies. There are multiple potential routes of introduction of C. jejuni into a commercial flock. Introduction is followed by a rapid increase in environmental levels of C. jejuni and the level of colonization of individual broilers. Recent experimental and epidemiological evidence suggest that the celerity of this process could be masking a complex pattern of colonization and extinction of bacterial strains within individual hosts. Despite the rapidity of colonization, experimental transmission studies exhibit a highly variable and unexplained delay time in the initial stages of the process. We review past models of transmission of C. jejuni in broilers and consider simple modifications, motivated by the plausible biological mechanisms of clearance and latency, which could account for this delay. We show how simple mathematical models can be used to guide the focus of experimental studies by providing testable predictions based on our hypotheses. We conclude by suggesting that competition experiments could be used to further understand the dynamics and mechanisms underlying the colonization process. The population models for such competition processes have been extensively studied in other ecological and evolutionary contexts. However, C. jejuni can potentially adapt phenotypically through phase variation in gene expression, leading to unification of ecological and evolutionary time-scales. For a theoretician, the colonization dynamics of C. jejuni offer an experimental system to explore these 'phylodynamics', the synthesis of population dynamics and evolutionary biology.

A dynamic view of the spread and intracellular distribution of Salmonella enterica.

The events that determine the dynamics of proliferation, spread and distribution of microbial pathogens within their hosts are surprisingly heterogeneous and poorly understood. We contend that understanding these phenomena at a sophisticated level with the help of mathematical models is a prerequisite for the development of truly novel, targeted preventative measures and drug regimes. We describe here recent studies of Salmonella enterica infections in mice which suggest that bacteria resist the antimicrobial environment inside host cells and spread to new sites, where infection foci develop, and thus avoid local escalation of the adaptive immune response. We further describe implications for our understanding of the pathogenic mechanism inside the host.

Bacterial growth rate and host factors as determinants of intracellular bacterial distributions in systemic Salmonella enterica infections.

Bacteria of the species Salmonella enterica cause a range of life-threatening diseases in humans and animals worldwide. The within-host quantitative, spatial, and temporal dynamics of S. enterica interactions are key to understanding how immunity acts on these infections and how bacteria evade immune surveillance. In this study, we test hypotheses generated from mathematical models of in vivo dynamics of Salmonella infections with experimental observation of bacteria at the single-cell level in infected mouse organs to improve our understanding of the dynamic interactions between host and bacterial mechanisms that determine net growth rates of S. enterica within the host. We show that both bacterial and host factors determine the numerical distributions of bacteria within host cells and thus the level of dispersiveness of the infection.

Stability of flow through multistage axial compressors

This paper describes measurements of the performance of a research stage operating in isolation and as part of a multistage compressor. It is shown that the stall point and the stalled performance of the stage are properties of the system in which it operates rather than a property of the stage itself. The consequences of this for the estimation of the stall point for compressors and compression systems are discussed. The support that the measurements give to assumptions made by mathematical models which use the concept of an 'underlying axisymmetric' characteristic, are highlighted.

Passive suspensions incorporating inerters for railway vehicles

This paper investigates the possibility of improving the performance of railway vehicle suspensions by incorporating a newly developed mechanical device known as the inerter. A comparative study of several low-complexity passive suspension layouts is made. Improved performance for the lateral and vertical ride comfort, as well as lateral body movement when curving are demonstrated in comparison with the conventional suspension layout. The constraints imposed are to maintain the same level of other performance metrics. The calculations and optimisations are based on linearised plan-view and side-view high-speed train mathematical models. © 2012 Copyright Taylor and Francis Group, LLC.