Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

History-aware, real-time risk detection in business processes (Extended Version)

This paper proposes a novel approach for identifying risks in executable business processes and detecting them at run time. The approach considers risks in all phases of the business process management lifecycle, and is realized via a distributed, sensor-based architecture. At design-time, sensors are defined to specify risk conditions which when fulfilled, are a likely indicator of faults to occur. Both historical and current execution data can be used to compose such conditions. At run-time, each sensor independently notifies a sensor manager when a risk is detected. In turn, the sensor manager interacts with the monitoring component of a process automation suite to prompt the results to the user who may take remedial actions. The proposed architecture has been implemented in the YAWL system and its performance has been evaluated in practice.

Information sharing in Onesocialweb using a multiple profile manager to better informed medical decision making processes

The study shows an alternative solution to existing efforts at solving the problem of how to centrally manage and synchronise users’ Multiple Profiles (MP) across multiple discrete social networks. Most social network users hold more than one social network account and utilise them in different ways depending on the digital context (Iannella, 2009a). They may, for example, enjoy friendly chat on Facebook1, professional discussion on LinkedIn2, and health information exchange on PatientsLikeMe3 In this thesis the researcher proposes a framework for the management of a user’s multiple online social network profiles. A demonstrator, called Multiple Profile Manager (MPM), will be showcased to illustrate how effective the framework will be. The MPM will achieve the required profile management and synchronisation using a free, open, decentralized social networking platform (OSW) that was proposed by the Vodafone Group in 2010. The proposed MPM will enable a user to create and manage an integrated profile (IP) and share/synchronise this profile with all their social networks. The necessary protocols to support the prototype are also proposed by the researcher. The MPM protocol specification defines an Extensible Messaging and Presence Protocol (XMPP) extension for sharing vCard and social network accounts information between the MPM Server, MPM Client, and social network sites (SNSs). . Therefore many web users need to manage disparate profiles across many distributed online sources. Maintaining these profiles is cumbersome, time-consuming, inefficient, and may lead to lost opportunity. The writer of this thesis adopted a research approach and a number of use cases for the implementation of the project. The use cases were created to capture the functional requirements of the MPM and to describe the interactions between users and the MPM. In the research a development process was followed in establishing the prototype and related protocols. The use cases were subsequently used to illustrate the prototype via the screenshots taken of the MPM client interfaces. The use cases also played a role in evaluating the outcomes of the research such as the framework, prototype, and the related protocols. An innovative application of this project is in the area of public health informatics. The researcher utilised the prototype to examine how the framework might benefit patients and physicians. The framework can greatly enhance health information management for patients and more importantly offer a more comprehensive personal health overview of patients to physicians. This will give a more complete picture of the patient’s background than is currently available and will prove helpful in providing the right treatment. The MPM prototype and related protocols have a high application value as they can be integrated into the real OSW platform and so serve users in the modern digital world. They also provide online users with a real platform for centrally storing their complete profile data, efficiently managing their personal information, and moreover, synchronising the overall complete profile with each of their discrete profiles stored in their different social network sites.

Moments of action provide insight into critical times for advection–diffusion–reaction processes

In 2010 Berezhkovskii and coworkers introduced the concept of local accumulation time (LAT) as a finite measure of the time required for the transient solution of a reaction diffusion equation to effectively reach steady state(Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Berezhkovskii’s approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb (IMA J Appl Math. 47, 193 (1991)). Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time; the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one–dimensional linear advection–diffusion–reaction partial differential equation(PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Real-time risk monitoring in business processes : a sensor-based approach

This article proposes an approach for real-time monitoring of risks in executable business process models. The approach considers risks in all phases of the business process management lifecycle, from process design, where risks are defined on top of process models, through to process diagnosis, where risks are detected during process execution. The approach has been realized via a distributed, sensor-based architecture. At design-time, sensors are defined to specify risk conditions which when fulfilled, are a likely indicator of negative process states (faults) to eventuate. Both historical and current process execution data can be used to compose such conditions. At run-time, each sensor independently notifies a sensor manager when a risk is detected. In turn, the sensor manager interacts with the monitoring component of a business process management system to prompt the results to process administrators who may take remedial actions. The proposed architecture has been implemented on top of the YAWL system, and evaluated through performance measurements and usability tests with students. The results show that risk conditions can be computed efficiently and that the approach is perceived as useful by the participants in the tests.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Event interval analysis: Why do processes take time?

Through the application of process mining, valuable evidence-based insights can be obtained about business processes in organisations. As a result the field has seen an increased uptake in recent years as evidenced by success stories and increased tool support. However, despite this impact, current performance analysis capabilities remain somewhat limited in the context of information-poor event logs. For example, natural daily and weekly patterns are not considered. In this paper a new framework for analysing event logs is defined which is based on the concept of event gap. The framework allows for a systematic approach to sophisticated performance-related analysis of event logs containing varying degrees of information. The paper formalises a range of event gap types and then presents an implementation as well as an evaluation of the proposed approach.

Real-time decision making by driverless city vehicles : a discrete event driven approach

This thesis addresses the topic of real-time decision making by driverless (autonomous) city vehicles, i.e. their ability to make appropriate driving decisions in non-simplified urban traffic conditions. After addressing the state of research, and explaining the research question, the thesis presents solutions for the subcomponents which are relevant for decision making with respect to information input (World Model), information output (Driving Maneuvers), and the real-time decision making process. TheWorld Model is a software component developed to fulfill the purpose of collecting information from perception and communication subsystems, maintaining an up-to-date view of the vehicle’s environment, and providing the required input information to the Real-Time Decision Making subsystem in a well-defined, and structured way. The real-time decision making process consists of two consecutive stages. While the first decision making stage uses a Petri net to model the safetycritical selection of feasible driving maneuvers, the second stage uses Multiple Criteria Decision Making (MCDM) methods to select the most appropriate driving maneuver, focusing on fulfilling objectives related to efficiency and comfort. The complex task of autonomous driving is subdivided into subtasks, called driving maneuvers, which represent the output (i.e. decision alternatives) of the real-time decision making process. Driving maneuvers are considered as implementations of closed-loop control algorithms, each capable of maneuvering the autonomous vehicle in a specific traffic situation. Experimental tests in both a 3D simulation and real-world experiments attest that the developed approach is suitable to deal with the complexity of real-world urban traffic situations.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.

Communication Architecture Design for Real-Time Networked Control Systems

Networked control over data networks has received increasing attention in recent years. Among many problems in networked control systems (NCSs) is the need to reduce control latency and jitter and to deal with packet dropouts. This paper introduces our recent progress on a queuing communication architecture for real-time NCS applications, and simple strategies for dealing with packet dropouts. Case studies for a middle-scale process or multiple small-scale processes are presented for TCP/IP based real-time NCSs. Variations of network architecture design are modelled, simulated, and analysed for evaluation of control latency and jitter performance. It is shown that a simple bandwidth upgrade or adding hierarchy does not necessarily bring benefits for performance improvement of control latency and jitter. A co-design of network and control is necessary to maximise the real-time control performance of NCSs