Stereological Modelling of Random Particles

Stochastic models for three-dimensional particles have many applications in applied sciences. Lévy–based particle models are a flexible approach to particle modelling. The structure of the random particles is given by a kernel smoothing of a Lévy basis. The models are easy to simulate but statistical inference procedures have not yet received much attention in the literature. The kernel is not always identifiable and we suggest one approach to remedy this problem. We propose a method to draw inference about the kernel from data often used in local stereology and study the performance of our approach in a simulation study.

Agent-based modelling for cement hydration

The Agent-Based Modelling and simulation (ABM) is a rather new approach for studying complex systems withinteracting autonomous agents that has lately undergone great growth in various fields such as biology, physics, social science, economics and business. Efforts to model and simulate the highly complex cement hydration process have been made over the past 40 years, with the aim of predicting the performance of concrete and designing innovative and enhanced cementitious materials. The ABM presented here - based on previous work - focuses on the early stages of cement hydration by modelling the physical-chemical processes at the particle level. The model considers the cement hydration process as a time and 3D space system, involving multiple diffusing and reacting species of spherical particles. Chemical reactions are simulated by adaptively selecting discrete stochastic simulation for the appropriate reaction, whenever that is necessary. Interactions between particles are also considered. The model has been inspired by reported cellular automata?s approach which provides detailed predictions of cement microstructure at the expense of significant computational difficulty. The ABM approach herein seeks to bring about an optimal balance between accuracy and computational efficiency.

Modelling Pinus pinea forest management to attain natural regeneration under present and future climatic scenarios

Natural regeneration-based silviculture has been increasingly regarded as a reliable option in sustainable forest management. However, successful natural regeneration is not always easy to achieve. Recently, new concerns have arisen because of changing future climate. To date, regeneration models have proved helpful in decision-making concerning natural regeneration. The implementation of such models into optimization routines is a promising approach in providing forest managers with accurate tools for forest planning. In the present study, we present a stochastic multistage regeneration model for Pinus pinea L. managed woodlands in Central Spain, where regeneration has been historically unsuccessful. The model is able to quantify recruitment under different silviculture alternatives and varying climatic scenarios, with further application to optimize management scheduling. The regeneration process in the species showed high between-year variation, with all subprocesses (seed production, dispersal, germination, predation, and seedling survival) having the potential to become bottlenecks. However, model simulations demonstrate that current intensive management is responsible for regeneration failure in the long term. Specifically, stand densities at rotation age are too low to guarantee adequate dispersal, the optimal density of seed-producing trees being around 150 stems·ha−1. In addition, rotation length needs to be extended up to 120 years to benefit from the higher seed production of older trees. Stochastic optimization confirms these results. Regeneration does not appear to worsen under climate change conditions; the species exhibiting resilience worthy of broader consideration in Mediterranean silviculture.

Multisensor data fusion for accurate modelling of mobile objects

In the last decade, multi-sensor data fusion has become a broadly demanded discipline to achieve advanced solutions that can be applied in many real world situations, either civil or military. In Defence,accurate detection of all target objects is fundamental to maintaining situational awareness, to locating threats in the battlefield and to identifying and protecting strategically own forces. Civil applications, such as traffic monitoring, have similar requirements in terms of object detection and reliable identification of incidents in order to ensure safety of road users. Thanks to the appropriate data fusion technique, we can give these systems the power to exploit automatically all relevant information from multiple sources to face for instance mission needs or assess daily supervision operations. This paper focuses on its application to active vehicle monitoring in a particular area of high density traffic, and how it is redirecting the research activities being carried out in the computer vision, signal processing and machine learning fields for improving the effectiveness of detection and tracking in ground surveillance scenarios in general. Specifically, our system proposes fusion of data at a feature level which is extracted from a video camera and a laser scanner. In addition, a stochastic-based tracking which introduces some particle filters into the model to deal with uncertainty due to occlusions and improve the previous detection output is presented in this paper. It has been shown that this computer vision tracker contributes to detect objects even under poor visual information. Finally, in the same way that humans are able to analyze both temporal and spatial relations among items in the scene to associate them a meaning, once the targets objects have been correctly detected and tracked, it is desired that machines can provide a trustworthy description of what is happening in the scene under surveillance. Accomplishing so ambitious task requires a machine learning-based hierarchic architecture able to extract and analyse behaviours at different abstraction levels. A real experimental testbed has been implemented for the evaluation of the proposed modular system. Such scenario is a closed circuit where real traffic situations can be simulated. First results have shown the strength of the proposed system.

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Forest-based supply chain modelling using the SimPy simulation framework

Proper management of supply chains is fundamental in the overall system performance of forestbased activities. Usually, efficient management techniques rely on a decision support software, which needs to be able to generate fast and effective outputs from the set of possibilities. In order to do this, it is necessary to provide accurate models representative of the dynamic interactions of systems. Due to forest-based supply chains’ nature, event-based models are more suited to describe their behaviours. This work proposes the modelling and simulation of a forestbased supply chain, in particular the biomass supply chain, through the SimPy framework. This Python based tool allows the modelling of discrete-event systems using operations such as events, processes and resources. The developed model was used to access the impact of changes in the daily working plan in three situations. First, as a control case, the deterministic behaviour was simulated. As a second approach, a machine delay was introduced and its implications in the plan accomplishment were analysed. Finally, to better address real operating conditions, stochastic behaviours of processing and driving times were simulated. The obtained results validate the SimPy simulation environment as a framework for modelling supply chains in general and for the biomass problem in particular.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.