Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

Building energy simulation and parallel computing : opportunities and challenges

Increased focus on energy cost savings and carbon footprint reduction efforts improved the visibility of building energy simulation, which became a mandatory requirement of several building rating systems. Despite developments in building energy simulation algorithms and user interfaces, there are some major challenges associated with building energy simulation; an important one is the computational demands and processing time. In this paper, we analyze the opportunities and challenges associated with this topic while executing a set of 275 parametric energy models simultaneously in EnergyPlus using a High Performance Computing (HPC) cluster. Successful parallel computing implementation of building energy simulations will not only improve the time necessary to get the results and enable scenario development for different design considerations, but also might enable Dynamic-Building Information Modeling (BIM) integration and near real-time decision-making. This paper concludes with the discussions on future directions and opportunities associated with building energy modeling simulations.

Pre-processing for approximate Bayesian computation in image analysis

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.

Large Scale Simulations of Hippocampal-Neocortical Interactions in a Parallel Version of Genesis

A hippocampal-CA3 memory model was constructed with PGENESIS, a recently developed version of GENESIS that allows for distributed processing of a neural network simulation. A number of neural models of the human memory system have identified the CA3 region of the hippocampus as storing the declarative memory trace. However, computational models designed to assess the viability of the putative mechanisms of storage and retrieval have generally been too abstract to allow comparison with empirical data. Recent experimental evidence has shown that selective knock-out of NMDA receptors in the CA1 of mice leads to reduced stability of firing specificity in place cells. Here a similar reduction of stability of input specificity is demonstrated in a biologically plausible neural network model of the CA3 region, under conditions of Hebbian synaptic plasticity versus an absence of plasticity. The CA3 region is also commonly associated with seizure activity. Further simulations of the same model tested the response to continuously repeating versus randomized nonrepeating input patterns. Each paradigm delivered input of equal intensity and duration. Non-repeating input patterns elicited a greater pyramidal cell spike count. This suggests that repetitive versus non-repeating neocortical inpus has a quantitatively different effect on the hippocampus. This may be relevant to the production of independent epileptogenic zones and the process of encoding new memories.

A subexponential construction of graph coloring for multiparty computation

We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non-Abelian groups which is both optimal (secure against an adversary who possesses any t

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.

In silico biology : making the most of parallel computing

Biological systems are typically complex and adaptive, involving large numbers of entities, or organisms, and many-layered interactions between these. System behaviour evolves over time, and typically benefits from previous experience by retaining memory of previous events. Given the dynamic nature of these phenomena, it is non-trivial to provide a comprehensive description of complex adaptive systems and, in particular, to define the importance and contribution of low-level unsupervised interactions to the overall evolution process. In this chapter, the authors focus on the application of the agent-based paradigm in the context of the immune response to HIV. Explicit implementation of lymph nodes and the associated lymph network, including lymphatic chain structure, is a key objective, and requires parallelisation of the model. Steps taken towards an optimal communication strategy are detailed.

A parallel approach to social network generation and agent-based epidemic simulation

Understanding the dynamics of disease spread is essential in contexts such as estimating load on medical services, as well as risk assessment and interven- tion policies against large-scale epidemic outbreaks. However, most of the information is available after the outbreak itself, and preemptive assessment is far from trivial. Here, we report on an agent-based model developed to investigate such epidemic events in a stylised urban environment. For most diseases, infection of a new individual may occur from casual contact in crowds as well as from repeated interactions with social partners such as work colleagues or family members. Our model therefore accounts for these two phenomena. Given the scale of the system, efficient parallel computing is required. In this presentation, we focus on aspects related to paralllelisation for large networks generation and massively multi-agent simulations.

Parallel attentive visual tracking

The research reported here addresses the problem of detecting and tracking independently moving objects from a moving observer in real-time, using corners as object tokens. Corners are detected using the Harris corner detector, and local image-plane constraints are employed to solve the correspondence problem. The approach relaxes the restrictive static-world assumption conventionally made, and is therefore capable of tracking independently moving and deformable objects. Tracking is performed without the use of any 3-dimensional motion model. The technique is novel in that, unlike traditional feature-tracking algorithms where feature detection and tracking is carried out over the entire image-plane, here it is restricted to those areas most likely to contain-meaningful image structure. Two distinct types of instantiation regions are identified, these being the “focus-of-expansion” region and “border” regions of the image-plane. The size and location of these regions are defined from a combination of odometry information and a limited knowledge of the operating scenario. The algorithms developed have been tested on real image sequences taken from typical driving scenarios. Implementation of the algorithm using T800 Transputers has shown that near-linear speedups are achievable, and that real-time operation is possible (half-video rate has been achieved using 30 processing elements).

Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.