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.

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.

3D ellipsoid fitting for multi-view gait recognition

Gait recognition approaches continue to struggle with challenges including view-invariance, low-resolution data, robustness to unconstrained environments, and fluctuating gait patterns due to subjects carrying goods or wearing different clothes. Although computationally expensive, model based techniques offer promise over appearance based techniques for these challenges as they gather gait features and interpret gait dynamics in skeleton form. In this paper, we propose a fast 3D ellipsoidal-based gait recognition algorithm using a 3D voxel model derived from multi-view silhouette images. This approach directly solves the limitations of view dependency and self-occlusion in existing ellipse fitting model-based approaches. Voxel models are segmented into four components (left and right legs, above and below the knee), and ellipsoids are fitted to each region using eigenvalue decomposition. Features derived from the ellipsoid parameters are modeled using a Fourier representation to retain the temporal dynamic pattern for classification. We demonstrate the proposed approach using the CMU MoBo database and show that an improvement of 15-20% can be achieved over a 2D ellipse fitting baseline.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

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.

Error analysis and attitude observability of a monocular GPS/visual odometry integrated navigation filter

In this paper, we present a method for the recovery of position and absolute attitude (including pitch, roll and yaw) using a novel fusion of monocular Visual Odometry and GPS measurements in a similar manner to a classic loosely-coupled GPS/INS error state navigation filter. The proposed filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. An observability analysis of the proposed filter is performed, showing that the scale factor, position and attitude errors are fully observable under acceleration that is non-parallel to velocity vector in the navigation frame. The observability properties of the proposed filter are demonstrated using numerical simulations. We conclude the article with an implementation of the proposed filter using real flight data collected from a Cessna 172 equipped with a downwards-looking camera and GPS, showing the feasibility of the algorithm in real-world conditions.

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.

Modelling contractor's and subcontractor's trust : a system dynamics approach

A general mistrust within the contactor and subcontractor companies has identified one of the significant barriers to derive benefits from true downstream supply chain integration. Using the general theory of trust in inter-organizational relations and conducting interviews, this research discusses factors that influence development of trust and cooperation in contractor– subcontractor relationships in construction projects. System dynamics is the simulation method is selected in this theory-building effort, based on qualitative data collected from two projects of a construction company in Thailand. Performance, permeability and system based trust are found to make significant contributions toward parties’ trust level. Three strategic policies such as best value contracting, management of subcontractors as internal team and semi project partnering approach are recommended to stimulate the trust factors as well as cooperative long term relationship.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

The flammability of metallic materials in normal and reduced gravity

Metallic materials exposed to oxygen-enriched atmospheres – as commonly used in the medical, aerospace, aviation and numerous chemical processing industries – represent a significant fire hazard which must be addressed during design, maintenance and operation. Hence, accurate knowledge of metallic materials flammability is required. Reduced gravity (i.e. space-based) operations present additional unique concerns, where the absence of gravity must also be taken into account. The flammability of metallic materials has historically been quantified using three standardised test methods developed by NASA, ASTM and ISO. These tests typically involve the forceful (promoted) ignition of a test sample (typically a 3.2 mm diameter cylindrical rod) in pressurised oxygen. A test sample is defined as flammable when it undergoes burning that is independent of the ignition process utilised. In the standardised tests, this is indicated by the propagation of burning further than a defined amount, or „burn criterion.. The burn criterion in use at the onset of this project was arbitrarily selected, and did not accurately reflect the length a sample must burn in order to be burning independent of the ignition event and, in some cases, required complete consumption of the test sample for a metallic material to be considered flammable. It has been demonstrated that a) a metallic material.s propensity to support burning is altered by any increase in test sample temperature greater than ~250-300 oC and b) promoted ignition causes an increase in temperature of the test sample in the region closest to the igniter, a region referred to as the Heat Affected Zone (HAZ). If a test sample continues to burn past the HAZ (where the HAZ is defined as the region of the test sample above the igniter that undergoes an increase in temperature of greater than or equal to 250 oC by the end of the ignition event), it is burning independent of the igniter, and should be considered flammable. The extent of the HAZ, therefore, can be used to justify the selection of the burn criterion. A two dimensional mathematical model was developed in order to predict the extent of the HAZ created in a standard test sample by a typical igniter. The model was validated against previous theoretical and experimental work performed in collaboration with NASA, and then used to predict the extent of the HAZ for different metallic materials in several configurations. The extent of HAZ predicted varied significantly, ranging from ~2-27 mm depending on the test sample thermal properties and test conditions (i.e. pressure). The magnitude of the HAZ was found to increase with increasing thermal diffusivity, and decreasing pressure (due to slower ignition times). Based upon the findings of this work, a new burn criterion requiring 30 mm of the test sample to be consumed (from the top of the ignition promoter) was recommended and validated. This new burn criterion was subsequently included in the latest revision of the ASTM G124 and NASA 6001B international test standards that are used to evaluate metallic material flammability in oxygen. These revisions also have the added benefit of enabling the conduct of reduced gravity metallic material flammability testing in strict accordance with the ASTM G124 standard, allowing measurement and comparison of the relative flammability (i.e. Lowest Burn Pressure (LBP), Highest No-Burn Pressure (HNBP) and average Regression Rate of the Melting Interface(RRMI)) of metallic materials in normal and reduced gravity, as well as determination of the applicability of normal gravity test results to reduced gravity use environments. This is important, as currently most space-based applications will typically use normal gravity information in order to qualify systems and/or components for reduced gravity use. This is shown here to be non-conservative for metallic materials which are more flammable in reduced gravity. The flammability of two metallic materials, Inconel® 718 and 316 stainless steel (both commonly used to manufacture components for oxygen service in both terrestrial and space-based systems) was evaluated in normal and reduced gravity using the new ASTM G124-10 test standard. This allowed direct comparison of the flammability of the two metallic materials in normal gravity and reduced gravity respectively. The results of this work clearly show, for the first time, that metallic materials are more flammable in reduced gravity than in normal gravity when testing is conducted as described in the ASTM G124-10 test standard. This was shown to be the case in terms of both higher regression rates (i.e. faster consumption of the test sample – fuel), and burning at lower pressures in reduced gravity. Specifically, it was found that the LBP for 3.2 mm diameter Inconel® 718 and 316 stainless steel test samples decreased by 50% from 3.45 MPa (500 psia) in normal gravity to 1.72 MPa (250 psia) in reduced gravity for the Inconel® 718, and 25% from 3.45 MPa (500 psia) in normal gravity to 2.76 MPa (400 psia) in reduced gravity for the 316 stainless steel. The average RRMI increased by factors of 2.2 (27.2 mm/s in 2.24 MPa (325 psia) oxygen in reduced gravity compared to 12.8 mm/s in 4.48 MPa (650 psia) oxygen in normal gravity) for the Inconel® 718 and 1.6 (15.0 mm/s in 2.76 MPa (400 psia) oxygen in reduced gravity compared to 9.5 mm/s in 5.17 MPa (750 psia) oxygen in normal gravity) for the 316 stainless steel. Reasons for the increased flammability of metallic materials in reduced gravity compared to normal gravity are discussed, based upon the observations made during reduced gravity testing and previous work. Finally, the implications (for fire safety and engineering applications) of these results are presented and discussed, in particular, examining methods for mitigating the risk of a fire in reduced gravity.

Virtual world process perspective visualization

Product Lifecycle Management has been developed as an approach to providing timely engineering information. However, the number of domain specializations within manufacturing makes such information communication disjointed, inefficient and error-prone. In this paper we propose an immersive 3D visualization of linked domain- specific information views for improving and accelerating communication processes in Product Lifecycle Management. With a common and yet understandable visualization of several domain views, interconnections and dependencies become obvious. The conceptual framework presented here links domain-specific information extracts from Product Lifecycle Management systems with each other and displays them via an integrated 3D representation scheme. We expect that this visualization framework should support holistic tactical decision making processes between domain-experts in operational and tactical manufacturing scenarios.

Data modelling in the beginning school years

This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling. Some of the core components of data modelling are addressed. A selection of results from the first data modelling activity implemented during the second year (2010; second grade) of a current longitudinal study are reported. Data modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Reported here are children's abilities to identify diverse and complex attributes, sort and classify data in different ways, and create and interpret models to represent their data.

Closing the loop of design and analysis : Parametric modelling tools for early decision support

There is a growing need for parametric design software that communicates building performance feedback in early architectural exploration to support decision-making. This paper examines how the circuit of design and analysis process can be closed to provide active and concurrent feedback between architecture and services engineering domains. It presents the structure for an openly customisable design system that couples parametric modelling and energy analysis software to allow designers to assess the performance of early design iterations quickly. Finally, it discusses how user interactions with the system foster information exchanges that facilitate the sharing of design intelligence across disciplines.