Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Models of protein linear molecular motors for dynamic nanodevices

Protein molecular motors are natural nano-machines that convert the chemical energy from the hydrolysis of adenosine triphosphate into mechanical work. These efficient machines are central to many biological processes, including cellular motion, muscle contraction and cell division. The remarkable energetic efficiency of the protein molecular motors coupled with their nano-scale has prompted an increasing number of studies focusing on their integration in hybrid micro- and nanodevices, in particular using linear molecular motors. The translation of these tentative devices into technologically and economically feasible ones requires an engineering, design-orientated approach based on a structured formalism, preferably mathematical. This contribution reviews the present state of the art in the modelling of protein linear molecular motors, as relevant to the future design-orientated development of hybrid dynamic nanodevices. © 2009 The Royal Society of Chemistry.

Multi-action recognition via stochastic modelling of optical flow and gradients

In this paper we propose a novel approach to multi-action recognition that performs joint segmentation and classification. This approach models each action using a Gaussian mixture using robust low-dimensional action features. Segmentation is achieved by performing classification on overlapping temporal windows, which are then merged to produce the final result. This approach is considerably less complicated than previous methods which use dynamic programming or computationally expensive hidden Markov models (HMMs). Initial experiments on a stitched version of the KTH dataset show that the proposed approach achieves an accuracy of 78.3%, outperforming a recent HMM-based approach which obtained 71.2%.

Managing and learning with multiple models: Objectives and optimization algorithms

The quality of environmental decisions should be gauged according to managers' objectives. Management objectives generally seek to maximize quantifiable measures of system benefit, for instance population growth rate. Reaching these goals often requires a certain degree of learning about the system. Learning can occur by using management action in combination with a monitoring system. Furthermore, actions can be chosen strategically to obtain specific kinds of information. Formal decision making tools can choose actions to favor such learning in two ways: implicitly via the optimization algorithm that is used when there is a management objective (for instance, when using adaptive management), or explicitly by quantifying knowledge and using it as the fundamental project objective, an approach new to conservation.This paper outlines three conservation project objectives - a pure management objective, a pure learning objective, and an objective that is a weighted mixture of these two. We use eight optimization algorithms to choose actions that meet project objectives and illustrate them in a simulated conservation project. The algorithms provide a taxonomy of decision making tools in conservation management when there is uncertainty surrounding competing models of system function. The algorithms build upon each other such that their differences are highlighted and practitioners may see where their decision making tools can be improved. © 2010 Elsevier Ltd.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Dynamic agent composition for large-scale agent-based models

PURPOSE: This paper describes dynamic agent composition, used to support the development of flexible and extensible large-scale agent-based models (ABMs). This approach was motivated by a need to extend and modify, with ease, an ABM with an underlying networked structure as more information becomes available. Flexibility was also sought after so that simulations are set up with ease, without the need to program. METHODS: The dynamic agent composition approach consists in having agents, whose implementation has been broken into atomic units, come together at runtime to form the complex system representation on which simulations are run. These components capture information at a fine level of detail and provide a vast range of combinations and options for a modeller to create ABMs. RESULTS: A description of the dynamic agent composition is given in this paper, as well as details about its implementation within MODAM (MODular Agent-based Model), a software framework which is applied to the planning of the electricity distribution network. Illustrations of the implementation of the dynamic agent composition are consequently given for that domain throughout the paper. It is however expected that this approach will be beneficial to other problem domains, especially those with a networked structure, such as water or gas networks. CONCLUSIONS: Dynamic agent composition has many advantages over the way agent-based models are traditionally built for the users, the developers, as well as for agent-based modelling as a scientific approach. Developers can extend the model without the need to access or modify previously written code; they can develop groups of entities independently and add them to those already defined to extend the model. Users can mix-and-match already implemented components to form large-scales ABMs, allowing them to quickly setup simulations and easily compare scenarios without the need to program. The dynamic agent composition provides a natural simulation space over which ABMs of networked structures are represented, facilitating their implementation; and verification and validation of models is facilitated by quickly setting up alternative simulations.

Estimating the parameters of stochastic volatility models using option price data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.

Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

Net radiation dynamics: performance of 20 daily net radiation models as related to model structure and intricacy in two climates.

We compared daily net radiation (Rn) estimates from 19 methods with the ASCE-EWRI Rn estimates in two climates: Clay Center, Nebraska (sub-humid) and Davis, California (semi-arid) for the calendar year. The performances of all 20 methods, including the ASCE-EWRI Rn method, were then evaluated against Rn data measured over a non-stressed maize canopy during two growing seasons in 2005 and 2006 at Clay Center. Methods differ in terms of inputs, structure, and equation intricacy. Most methods differ in estimating the cloudiness factor, emissivity (e), and calculating net longwave radiation (Rnl). All methods use albedo (a) of 0.23 for a reference grass/alfalfa surface. When comparing the performance of all 20 Rn methods with measured Rn, we hypothesized that the a values for grass/alfalfa and non-stressed maize canopy were similar enough to only cause minor differences in Rn and grass- and alfalfa-reference evapotranspiration (ETo and ETr) estimates. The measured seasonal average a for the maize canopy was 0.19 in both years. Using a = 0.19 instead of a = 0.23 resulted in 6% overestimation of Rn. Using a = 0.19 instead of a = 0.23 for ETo and ETr estimations, the 6% difference in Rn translated to only 4% and 3% differences in ETo and ETr, respectively, supporting the validity of our hypothesis. Most methods had good correlations with the ASCE-EWRI Rn (r2 > 0.95). The root mean square difference (RMSD) was less than 2 MJ m-2 d-1 between 12 methods and the ASCE-EWRI Rn at Clay Center and between 14 methods and the ASCE-EWRI Rn at Davis. The performance of some methods showed variations between the two climates. In general, r2 values were higher for the semi-arid climate than for the sub-humid climate. Methods that use dynamic e as a function of mean air temperature performed better in both climates than those that calculate e using actual vapor pressure. The ASCE-EWRI-estimated Rn values had one of the best agreements with the measured Rn (r2 = 0.93, RMSD = 1.44 MJ m-2 d-1), and estimates were within 7% of the measured Rn. The Rn estimates from six methods, including the ASCE-EWRI, were not significantly different from measured Rn. Most methods underestimated measured Rn by 6% to 23%. Some of the differences between measured and estimated Rn were attributed to the poor estimation of Rnl. We conducted sensitivity analyses to evaluate the effect of Rnl on Rn, ETo, and ETr. The Rnl effect on Rn was linear and strong, but its effect on ETo and ETr was subsidiary. Results suggest that the Rn data measured over green vegetation (e.g., irrigated maize canopy) can be an alternative Rn data source for ET estimations when measured Rn data over the reference surface are not available. In the absence of measured Rn, another alternative would be using one of the Rn models that we analyzed when all the input variables are not available to solve the ASCE-EWRI Rn equation. Our results can be used to provide practical information on which method to select based on data availability for reliable estimates of daily Rn in climates similar to Clay Center and Davis.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Predicting the temporal response of seagrass meadows to dredging using Dynamic Bayesian Networks

Predicting temporal responses of ecosystems to disturbances associated with industrial activities is critical for their management and conservation. However, prediction of ecosystem responses is challenging due to the complexity and potential non-linearities stemming from interactions between system components and multiple environmental drivers. Prediction is particularly difficult for marine ecosystems due to their often highly variable and complex natures and large uncertainties surrounding their dynamic responses. Consequently, current management of such systems often rely on expert judgement and/or complex quantitative models that consider only a subset of the relevant ecological processes. Hence there exists an urgent need for the development of whole-of-systems predictive models to support decision and policy makers in managing complex marine systems in the context of industry based disturbances. This paper presents Dynamic Bayesian Networks (DBNs) for predicting the temporal response of a marine ecosystem to anthropogenic disturbances. The DBN provides a visual representation of the problem domain in terms of factors (parts of the ecosystem) and their relationships. These relationships are quantified via Conditional Probability Tables (CPTs), which estimate the variability and uncertainty in the distribution of each factor. The combination of qualitative visual and quantitative elements in a DBN facilitates the integration of a wide array of data, published and expert knowledge and other models. Such multiple sources are often essential as one single source of information is rarely sufficient to cover the diverse range of factors relevant to a management task. Here, a DBN model is developed for tropical, annual Halophila and temperate, persistent Amphibolis seagrass meadows to inform dredging management and help meet environmental guidelines. Specifically, the impacts of capital (e.g. new port development) and maintenance (e.g. maintaining channel depths in established ports) dredging is evaluated with respect to the risk of permanent loss, defined as no recovery within 5 years (Environmental Protection Agency guidelines). The model is developed using expert knowledge, existing literature, statistical models of environmental light, and experimental data. The model is then demonstrated in a case study through the analysis of a variety of dredging, environmental and seagrass ecosystem recovery scenarios. In spatial zones significantly affected by dredging, such as the zone of moderate impact, shoot density has a very high probability of being driven to zero by capital dredging due to the duration of such dredging. Here, fast growing Halophila species can recover, however, the probability of recovery depends on the presence of seed banks. On the other hand, slow growing Amphibolis meadows have a high probability of suffering permanent loss. However, in the maintenance dredging scenario, due to the shorter duration of dredging, Amphibolis is better able to resist the impacts of dredging. For both types of seagrass meadows, the probability of loss was strongly dependent on the biological and ecological status of the meadow, as well as environmental conditions post-dredging. The ability to predict the ecosystem response under cumulative, non-linear interactions across a complex ecosystem highlights the utility of DBNs for decision support and environmental management.