Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Computational approaches for modelling intrinsic noise and delays in genetic regulatory networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Modelling the activation of words in human memory : the spreading activation, spooky-activation-at-a-distance and the entanglement models compared

Modelling how a word is activated in human memory is an important requirement for determining the probability of recall of a word in an extra-list cueing experiment. The spreading activation, spooky-action-at-a-distance and entanglement models have all been used to model the activation of a word. Recently a hypothesis was put forward that the mean activation levels of the respective models are as follows: Spreading � Entanglment � Spooking-action-at-a-distance This article investigates this hypothesis by means of a substantial empirical analysis of each model using the University of South Florida word association, rhyme and word norms.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

The role of idea novelty and relatedness in nascent ventures

The study of venture idea characteristics and the contextual fit between venture ideas and individuals are key research goals in entrepreneurship (Davidsson, 2004). However, to date there has been limited scholarly attention given to these phenomena. Accordingly, this study aims to help fill the gap by investigating the importance of novelty and relatedness of venture ideas in entrepreneurial firms. On the premise that new venture creation is a process and that research should be focused on the early stages of the venturing process, this study primarily focuses its attention on examining how venture idea novelty and relatedness affect the performance in the venture creation process. Different types and degrees of novelty are considered here. Relatedness is shown to be based on individuals’ prior knowledge and resource endowment. Performance in the venture creation process is evaluated according to four possible outcomes: making progress, getting operational, being terminated and achieving positive cash flow. A theoretical model is developed demonstrating the relationship between these variables along with the investment of time and money. Several hypotheses are developed to be tested. Among them, it is hypothesised that novelty hinders short term performance in the venture creation process. On the other hand knowledge and resource relatedness are hypothesised to promote performance. An experimental study was required in order to understand how different types and degrees of novelty and relatedness of venture ideas affect the attractiveness of venture ideas in the eyes of experienced entrepreneurs. Thus, the empirical work in this thesis was based on two separate studies. In the first one, a conjoint analysis experiment was conducted on 32 experienced entrepreneurs in order to ascertain attitudinal preferences regarding venture idea attractiveness based on novelty, relatedness and potential financial gains. This helped to estimate utility values for different levels of different attributes of venture ideas and their relative importance in the attractiveness. The second study was a longitudinal investigation of how venture idea novelty and relatedness affect the performance in the venture creation process. The data for this study is from the Comprehensive Australian Study for Entrepreneurial Emergence (CAUSEE) project that has been established in order to explore the new venture creation process in Australia. CAUSEE collects data from a representative sample of over 30,000 households in Australia using random digit dialling (RDD) telephone interviews. From these cases, data was collected at two points in time during a 12 month period from 493 firms, who are currently involved in the start-up process. Hypotheses were tested and inferences were derived through descriptive statistics, confirmatory factor analysis and structural equation modelling. Results of study 1 indicate that venture idea characteristics have a role in the attractiveness and entrepreneurs prefer to introduce a moderate degree of novelty across all types of venture ideas concerned. Knowledge relatedness is demonstrated to be a more significant factor in attractiveness than resource relatedness. Results of study 2 show that the novelty hinders nascent venture performance. On the other hand, resource relatedness has a positive impact on performance unlike knowledge relatedness which has none. The results of these studies have important implications for potential entrepreneurs, investors, researchers, consultants etc. by developing a better understanding in the venture creation process and its success factors in terms of both theory and practice.

Activity modelling in crowded environments : a soft decision approach

Probabilistic topic models have recently been used for activity analysis in video processing, due to their strong capacity to model both local activities and interactions in crowded scenes. In those applications, a video sequence is divided into a collection of uniform non-overlaping video clips, and the high dimensional continuous inputs are quantized into a bag of discrete visual words. The hard division of video clips, and hard assignment of visual words leads to problems when an activity is split over multiple clips, or the most appropriate visual word for quantization is unclear. In this paper, we propose a novel algorithm, which makes use of a soft histogram technique to compensate for the loss of information in the quantization process; and a soft cut technique in the temporal domain to overcome problems caused by separating an activity into two video clips. In the detection process, we also apply a soft decision strategy to detect unusual events.We show that the proposed soft decision approach outperforms its hard decision counterpart in both local and global activity modelling.

Effect of cold water immersion on repeated cycling performance and limb blood flow

The purpose of the present study was to compare the effects of cold water immersion (CWI) and active recovery (ACT) on resting limb blood flow, rectal temperature and repeated cycling performance in the heat. Ten subjects completed two testing sessions separated by 1 week; each trial consisted of an initial all-out 35-min exercise bout, one of two 15-min recovery interventions (randomised: CWI or ACT), followed by a 40-min passive recovery period before repeating the 35-min exercise bout. Performance was measured as the change in total work completed during the exercise bouts. Resting limb blood flow, heart rate, rectal temperature and blood lactate were recorded throughout the testing sessions. There was a significant decline in performance after ACT (mean (SD) −1.81% (1.05%)) compared with CWI where performance remained unchanged (0.10% (0.71%)). Rectal temperature was reduced after CWI (36.8°C (1.0°C)) compared with ACT (38.3°C (0.4°C)), as was blood flow to the arms (CWI 3.64 (1.47) ml/100 ml/min; ACT 16.85 (3.57) ml/100 ml/min) and legs (CW 4.83 (2.49) ml/100 ml/min; ACT 4.83 (2.49) ml/100 ml/min). Leg blood flow at the end of the second exercise bout was not different between the active (15.25 (4.33) ml/100 ml/min) and cold trials (14.99 (4.96) ml/100 ml/min), whereas rectal temperature (CWI 38.1°C (0.3°C); ACT 38.8°C (0.2°C)) and arm blood flow (CWI 20.55 (3.78) ml/100 ml/min; ACT 23.83 (5.32) ml/100 ml/min) remained depressed until the end of the cold trial. These findings indicate that CWI is an effective intervention for maintaining repeat cycling performance in the heat and this performance benefit is associated with alterations in core temperature and limb blood flow.

Oxygen delivery through high-flow nasal cannulae increase end-expiratory lung volume and reduce respiratory rate in post-cardiac surgical patients

Background: High-flow nasal cannulae (HFNC) create positive oropharyngeal airway pressure but it is unclear how their use affects lung volume. Electrical impedance tomography (EIT) allows assessment of changes in lung volume by measuring changes in lung impedance. Primary objectives were to investigate the effects of HFNC on airway pressure (Paw) and end-expiratory lung volume (EELV), and to identify any correlation between the two. Secondary objectives were to investigate the effects of HFNC on respiratory rate (RR), dyspnoea, tidal volume and oxygenation; and the interaction between body mass index (BMI) and EELV. Methods: Twenty patients prescribed HFNC post-cardiac surgery were investigated. Impedance measures, Paw, PaO2/FiO2 ratio, RR and modified Borg scores were recorded first on low flow oxygen (nasal cannula or Hudson face mask) and then on HFNC. Results: A strong and significant correlation existed between Paw and end-expiratory lung impedance (EELI) (r=0.7, p<0.001). Compared with low flow oxygen, HFNC significantly increased EELI by 25.6% (95% CI 24.3, 26.9) and Paw by 3.0 cmH2O (95% CI 2.4, 3.7). RR reduced by 3.4 breaths per minute (95% CI 1.7, 5.2) with HFNC use, tidal impedance variation increased by 10.5% (95% CI 6.1, 18.3) and PaO2/FiO2 ratio improved by 30.6 mmHg (95% CI 17.9, 43.3). HFNC improved subjective dyspnoea scoring (p=0.023). Increases in EELI were significantly influenced by BMI, with larger increases associated with higher BMIs (p<0.001). Conclusions: This study suggests that HFNC improve dyspnoea and oxygenation by increasing both EELV and tidal volume, and are most beneficial in patients with higher BMIs.

Modelling word meaning using efficient tensor representations

Models of word meaning, built from a corpus of text, have demonstrated success in emulating human performance on a number of cognitive tasks. Many of these models use geometric representations of words to store semantic associations between words. Often word order information is not captured in these models. The lack of structural information used by these models has been raised as a weakness when performing cognitive tasks. This paper presents an efficient tensor based approach to modelling word meaning that builds on recent attempts to encode word order information, while providing flexible methods for extracting task specific semantic information.

The geometric modelling of social frames and contexts

How do humans respond to their social context? This question is becoming increasingly urgent in a society where democracy requires that the citizens of a country help to decide upon its policy directions, and yet those citizens frequently have very little knowledge of the complex issues that these policies seek to address. Frequently, we find that humans make their decisions more with reference to their social setting, than to the arguments of scientists, academics, and policy makers. It is broadly anticipated that the agent based modelling (ABM) of human behaviour will make it possible to treat such social effects, but we take the position here that a more sophisticated treatment of context will be required in many such models. While notions such as historical context (where the past history of an agent might affect its later actions) and situational context (where the agent will choose a different action in a different situation) abound in ABM scenarios, we will discuss a case of a potentially changing context, where social effects can have a strong influence upon the perceptions of a group of subjects. In particular, we shall discuss a recently reported case where a biased worm in an election debate led to significant distortions in the reports given by participants as to who won the debate (Davis et al 2011). Thus, participants in a different social context drew different conclusions about the perceived winner of the same debate, with associated significant differences among the two groups as to who they would vote for in the coming election. We extend this example to the problem of modelling the likely electoral responses of agents in the context of the climate change debate, and discuss the notion of interference between related questions that might be asked of an agent in a social simulation that was intended to simulate their likely responses. A modelling technology which could account for such strong social contextual effects would benefit regulatory bodies which need to navigate between multiple interests and concerns, and we shall present one viable avenue for constructing such a technology. A geometric approach will be presented, where the internal state of an agent is represented in a vector space, and their social context is naturally modelled as a set of basis states that are chosen with reference to the problem space.

Modelling and performance evaluation of the IEEE 802.11 DCF for real-time control

Popular wireless networks, such as IEEE 802.11/15/16, are not designed for real-time applications. Thus, supporting real-time quality of service (QoS) in wireless real-time control is challenging. This paper adopts the widely used IEEE 802.11, with the focus on its distributed coordination function (DCF), for soft-real-time control systems. The concept of the critical real-time traffic condition is introduced to characterize the marginal satisfaction of real-time requirements. Then, mathematical models are developed to describe the dynamics of DCF based real-time control networks with periodic traffic, a unique feature of control systems. Performance indices such as throughput and packet delay are evaluated using the developed models, particularly under the critical real-time traffic condition. Finally, the proposed modelling is applied to traffic rate control for cross-layer networked control system design.

Periodically forced natural convection through the roof of an attic-shaped building

In this study, numerical simulations of natural convection in an attic space subject to diurnal temperature condition on the sloping wall have been carried out. An explanation of choosing the period of periodic thermal effect has been given with help of the scaling analysis which is available in the literature. Moreover, the effects of the aspect ratio and Rayleigh number on the fluid flow and heat transfer have been discussed in details as well as the formation of a pitchfork bifurcation of the flow at the symmetric line of the enclosure.