Probabilistic Models to Describe the Dynamics of Migrating Microbial Communities

In all but the most sterile environments bacteria will reside in fluid being transported through conduits and some of these will attach and grow as biofilms on the conduit walls. The concentration and diversity of bacteria in the fluid at the point of delivery will be a mix of those when it entered the conduit and those that have become entrained into the flow due to seeding from biofilms. Examples include fluids through conduits such as drinking water pipe networks, endotracheal tubes, catheters and ventilation systems. Here we present two probabilistic models to describe changes in the composition of bulk fluid microbial communities as they are transported through a conduit whilst exposed to biofilm communities. The first (discrete) model simulates absolute numbers of individual cells, whereas the other (continuous) model simulates the relative abundance of taxa in the bulk fluid. The discrete model is founded on a birth-death process whereby the community changes one individual at a time and the numbers of cells in the system can vary. The continuous model is a stochastic differential equation derived from the discrete model and can also accommodate changes in the carrying capacity of the bulk fluid. These models provide a novel Lagrangian framework to investigate and predict the dynamics of migrating microbial communities. In this paper we compare the two models, discuss their merits, possible applications and present simulation results in the context of drinking water distribution systems. Our results provide novel insight into the effects of stochastic dynamics on the composition of non-stationary microbial communities that are exposed to biofilms and provides a new avenue for modelling microbial dynamics in systems where fluids are being transported.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Single-ionization of helium at Ti:sapphire wavelengths: rates and scaling laws

We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175-34) X10^14 W/ cm^2 at 390 nm, and (0.275 - 14.4) X 10^14 W /cm^2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schroedinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.

Solving the advection-dispersion equation using the discrete puff particle method

A flexible, mass-conservative numerical technique for solving the advection-dispersion equation for miscible contaminant transport is presented. The method combines features of puff transport models from air pollution studies with features from the random walk particle method used in water resources studies, providing a deterministic time-marching algorithm which is independent of the grid Peclet number and scales from one to higher dimensions simply. The concentration field is discretised into a number of particles, each of which is treated as a point release which advects and disperses over the time interval. The dispersed puff is itself discretised into a spatial distribution of particles whose masses can be pre-calculated. Concentration within the simulation domain is then calculated from the mass distribution as an average over some small volume. Comparison with analytical solutions for a one-dimensional fixed-duration concentration pulse and for two-dimensional transport in an axisymmetric flow field indicate that the algorithm performs well. For a given level of accuracy the new method has lower computation times than the random walk particle method.

Analysis of multiple aspects of a repeated signal: power and rate of rapping during shell fights in hermit crabs

Repeated activities used by animals during contests are assumed to act as signals advertising the quality of the sender. However, their exact functions are not well understood and observations fit only a limited set of the predictions made by models of signaling systems. Experimental studies of contest behavior tend to focus on analysis of the rate of signaling, but individual performances may also vary in magnitude. Both of these features can vary between outcomes and within contests. We examined changes in the rate and power of shell rapping during shell fights in hermit crabs. We show that both rate and power decline during the course of the encounter and that the duration of pauses between bouts of shell rapping increases with an index of the total effort put into each bout. This supports the idea that the vigor of shell rapping is regulated by fatigue and could therefore act as a signal of stamina. By examining different interacting components of this complex activity, we gain greater insight into its function than would be achieved by investigating a single aspect in isolation.

Reduced estimated glomerular filtration rate in Alzheimer's disease

OBJECTIVES:

Renal disease is increasingly regarded as an independent risk factor for vascular disease which in itself is believed to influence risk of AD. Alterations in amyloid homeostasis via reduced renal clearance of peripheral beta-amyloid (A|*beta*|) may represent another potential role for variation in renal function leading to increased risk of AD. We sought to examine estimates of glomerular filtration rate in AD and control groups.
METHODS:

AD patients were randomly recruited from the Memory Clinic of the Belfast City Hospital (n = 83). Genomic DNA was extracted from peripheral leucocytes and was genotyped for Apolipoprotein E using standard methods. Using creatinine values, age and gender, estimated Glomerular Filtration Rates (eGFR) were calculated using the isotope dilution mass spectrometry (IDMS)-traceable Modification of Diet in Renal Disease (MDRD) Study equation (using the United Kingdom National External Quality Assessment Scheme (UKNEQAS) correction factor). IDMS eGFR values were then compared between AD and control groups.

RESULTS:

Significant baseline differences in age, diastolic blood pressure, education level attained and APOE |*epsilon*|4 carriage were noted between cases and controls. The AD group had a significantly lower eGFR versus controls (69 vs 77 ml/min) which persisted after adjustment for possible confounders (p = 0.045).

CONCLUSIONS:

This case-control analysis suggests that using a relatively accurate estimate of renal function, patients with AD have greater renal impairment than cognitively normal controls. This may reflect impaired renal clearance of peripheral A|*beta*| or be a marker of shared vascular processes altering cerebral and renal functioning.

International order flows: Explaining equity and exchange rate returns

Macroeconomic models of equity and exchange rate returns perform poorly at high frequencies. The proportion of daily returns that these models explain is essentially zero. Instead of relying on macroeconomic determinants, we model equity price and exchange rate behavior based on a concept from microstructure – order flow. The international order flows are derived from belief changes of different investor groups in a two-country setting. We obtain a structural relationship between equity returns, exchange rate returns and their relationship to home and foreign equity market order flow. To test the model we construct daily aggregate order flow data from 800 million equity trades in the U.S. and France from 1999 to 2003. Almost 60% of the daily returns in the S&P100 index are explained jointly by exchange rate returns and aggregate order flows in both markets. As predicted by the model, daily exchange rate returns and order flow into the French market have significant incremental explanatory power for the daily S&P returns. The model implications are also validated for intraday returns.

Comparisons, mental models, and the action effect in judgments of regret

People tend to attribute more regret to a character who has decided to take action and experienced a negative outcome than to one who has decided not to act and experienced a negative outcome. For some decisions, however, this finding is not observed in a between-participants design and thus appears to rely on comparisons between people's representations of action and their representations of inaction. In this article, we outline a mental models account that explains findings from studies that have used within- and between-participants designs, and we suggest that, for decisions with uncertain counterfactual outcomes, information about the consequences of a decision to act causes people to flesh out their representation of the counterfactual states of affairs for inaction. In three experiments, we confirm our predictions about participants' fleshing out of representations, demonstrating that an action effect occurs only when information about the consequences of action is available to participants as they rate the nonactor and when this information about action is informative with respect to judgments about inaction. It is important to note that the action effect always occurs when the decision scenario specifies certain counterfactual outcomes. These results suggest that people sometimes base their attributions of regret on comparisons among different sets of mental models.

The finding of reduced estimated glomerular filtration rate is associated with increased mortality in a large UK population

BACKGROUND: CKD as defined by KDIGO/KDOQI has been shown to affect ~ 8.5% of the UK population. The prevalence of CKD in the UK is similar to that in the USA, yet incident dialysis rates are dramatically different. This retrospective cohort study investigates the association between reduced kidney function and mortality in a large UK population. METHODS: All serum creatinine results covering Northern Ireland's 1.7 million population were collected between 1 January 2001 and 31 December 2002. Estimated glomerular filtration rates (eGFR) were calculated for all serum creatinine measurements using four-variable MDRD equation (IDMS aligned). Patients were followed up for both all-cause and cardiovascular mortality data until the end of December 2006. Patients on renal replacement therapy were excluded. Subgroup analysis in the 75 345 subjects enrolled within a parallel primary care study permitted additional survival analysis with adjustment for traditional cardiovascular risk factors. RESULTS: A total of 1 967 827 serum creatinine results from 533 798 patients were collected. During the period of follow-up, 59 980 deaths occurred. In multivariate survival analysis, using eGFR as a time-varying covariate, a graded association between CKD (defined by eGFR) and all-cause mortality was identified. Compared with participants with an eGFR of > 60 mL/min/1.73 m(2), the adjusted hazard ratios (and 95% confidence intervals) for participants with an eGFR of 45-59 mL/min/1.73 m(2) was 1.02 (0.99-1.04), an eGFR of 30-44 mL/min/1.73 m(2) was 1.44 (1.40-1.47), an eGFR of 15-29 mL/min/1.73 m(2) was 2.12 (2.05-2.20) and an eGFR of

Analysis of Degradation Data of Poly(L-lactide-co-L,D-lactic actide) and Poly(L-lactide) Obtained at Elevated and Physiological Temperatures Using Mathematical Models

The degradation of resorbable polymeric devices often takes months to years. Accelerated testing at elevated temperatures is an attractive but controversial technique. The purposes of this paper include: (a) to provide a summary of the mathematical models required to analyse accelerated degradation data and to indicate the pitfalls of using these models; (b) to improve the model previously developed by Han and Pan; (c) to provide a simple version of the model of Han and Pan with an analytical solution that is convenient to use; (d) to demonstrate the application of the improved model in two different poly(lactic acid) systems. It is shown that the simple analytical relations between molecular weight and degradation time widely used in the literature can lead to inadequate conclusions. In more general situations the rate equations are only part of a complete degradation model. Together with previous works in the literature, our study calls for care in using the accelerated testing technique.

Framework for Establishing Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of the Euler equations for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Maneuvers for the AGARD Standard Dynamics Model sharp leading-edge wind-tunnel geometry are considered as a test case. Wind-tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low to moderate angles of attack. Then the generation of aerodynamic tables is described based on a data fusion approach. Time-optimal maneuvers are generated based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degrees turns. The maneuver definition includes the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the maneuvers. This is done by replaying them, including the control surface motions, through the time accurate computational fluid dynamics code. The resulting forces and moments are compared with the tabular values to assess the presence of inadequately modeled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow maneuvers. Increasing rate maneuvers show discrepancies which are ascribed to vortical flow hysteresis at the higher rate motions. The framework is suitable for application to more complex viscous flow models, and is powerful for the assessment of the validity of aerodynamics models of the type currently used for studies of flight dynamics.

GAS-PHASE REACTIONS AND RATE COEFFICIENTS FOR USE IN ASTROCHEMISTRY - THE UMIST RATEFILE

We present the rate coefficients of 2880 gas-phase reactions among 313 species involving 12 elements for use in astrochemical models. We describe the motivation behind this work and the caveats which attach to the data in general as well as to specific reactions. We give the permanent electric dipole moments of nearly all the 112 neutral molecules contained in the data set, so that rate coefficients can be calculated at the low temperatures of dark interstellar dust clouds. We have used the data to calculate the pseudo-time-dependent chemical evolution of a dark, dense interstellar cloud and present both early time and steady-state abundances for all 313 species.

Response characteristics of optical sensors for oxygen: models based on a distribution in tau(o) or kappa(q)

The features of two popular models used to describe the observed response characteristics of typical oxygen optical sensors based on luminescence quenching are examined critically. The models are the 'two-site' and 'Gaussian distribution in natural lifetime, tau(o),' models. These models are used to characterise the response features of typical optical oxygen sensors; features which include: downward curving Stern-Volmer plots and increasingly non-first order luminescence decay kinetics with increasing partial pressures of oxygen, pO(2). Neither model appears able to unite these latter features, let alone the observed disparate array of response features exhibited by the myriad optical oxygen sensors reported in the literature, and still maintain any level of physical plausibility. A model based on a Gaussian distribution in quenching rate constant, k(q), is developed and, although flawed by a limited breadth in distribution, rho, does produce Stern-Volmer plots which would cover the range in curvature seen with real optical oxygen sensors. A new 'log-Gaussian distribution in tau(o) or k(q)' model is introduced which has the advantage over a Gaussian distribution model of placing no limitation on the value of rho. Work on a 'log-Gaussian distribution in tau(o)' model reveals that the Stern-Volmer quenching plots would show little degree in curvature, even at large rho values and the luminescence decays would become increasingly first order with increasing pO(2). In fact, with real optical oxygen sensors, the opposite is observed and thus the model appears of little value. In contrast, a 'log-Gaussian distribution in k(o)' model does produce the trends observed with real optical oxygen sensors; although it is technically restricted in use to those in which the kinetics of luminescence decay are good first order in the absence of oxygen. The latter model gives a good fit to the major response features of sensors which show the latter feature, most notably the [Ru(dpp)(3)(2+)(Ph4B-)(2)] in cellulose optical oxygen sensors. The scope of a log-Gaussian model for further expansion and, therefore, application to optical oxygen sensors, by combining both a log-Gaussian distribution in k(o) with one in tau(o) is briefly discussed.

How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks

A conceptual model is described for generating distributions of grazing animals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behaviors ranging from random diffusion, through taxis and cognitively aided navigation (i.e., using memory), to the optimization extreme of the Ideal Free Distribution. These behaviors are generated from simulation of biased diffusion that operates at multiple scales simultaneously, formalizing ideas of multiple-scale foraging behavior. It uses probabilistic bias to represent decisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bias to arise at multiple scales within the environment, each weighted relative to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows different constraints to be applied to the animal's ability (e.g., applying food-patch accessibility and information limits). Simulations show that foraging-decision randomness and spatial scale of decision bias have potentially profound effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can differentially change the spatial pattern of resource abundance in the environment to one characteristic of the foraging strategy.</

Beyond the ideal free distribution: More general models of predator distribution

The ideal free distribution model which relates the spatial distribution of mobile consumers to that of their resource is shown to be a limiting case of a more general model which we develop using simple concepts of diffusion. We show how the ideal free distribution model can be derived from a more general model and extended by incorporating simple models of social influences on predator spacing. First, a free distribution model based on patch switching rules, with a power-law interference term, which represents instantaneous biased diffusion is derived. A social bias term is then introduced to represent the effect of predator aggregation on predator fitness, separate from any effects which act through intake rate. The social bias term is expanded to express an optimum spacing for predators and example solutions of the resulting biased diffusion models are shown. The model demonstrates how an empirical interference coefficient, derived from measurements of predator and prey densities, may include factors expressing the impact of social spacing behaviour on fitness. We conclude that empirical values of log predator/log prey ratio may contain information about more than the relationship between consumer and resource densities. Unlike many previous models, the model shown here applies to conditions without continual input. (C) 1997 Academic Press Limited.</p>