A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows

This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes. Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques. The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic system’ components serves as a knowledge base. The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete. After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system. A real-life case (from the King’s College hospital accident and emergency (A&E) department’s trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling

A literature review on the use of expert opinion in probabilistic risk analysis

Risk assessment is part of the decision making process in many fields of discipline, such as engineering, public health, environment, program management, regulatory policy, and finance. There has been considerable debate over the philosophical and methodological treatment of risk in the past few decades, ranging from its definition and classification to methods of its assessment. Probabilistic risk analysis (PRA) specifically deals with events represented by low probabilities of occurring with high levels of unfavorable consequences. Expert judgment is often a critical source of information in PRA, since empirical data on the variables of interest are rarely available. The author reviews the literature on the use of expert opinion in PRA, in particular on the approaches to eliciting and aggregating experts'assessments. The literature suggests that the methods by which expert opinions are collected and combined have a significant effect on the resulting estimates. The author discusses two types of approaches to eliciting and aggregating expert judgments-behavioral and mathematical approaches, with the emphasis on the latter. It is generally agreed that mathematical approaches tend to yield more accurate estimates than behavioral approaches. After a short description of behavioral approaches, the author discusses mathematical approaches in detail, presenting three aggregation models: non-Bayesian axiomatic models, Bayesian models, andpsychological scaling models. She also discusses issues of stochastic dependence.Health Monitoring&Evaluation,ICT Policy and Strategies,Public Health Promotion,Enterprise Development&Reform,Statistical&Mathematical Sciences,ICT Policy and Strategies,Health Monitoring&Evaluation,Statistical&Mathematical Sciences,Science Education,Scientific Research&Science Parks

Is nature OO?

What exists "out there"? What does "doing physics" mean? What are the axiomatic ideas for microphysics? What is a particle? What is an apparatus made of? We show that Quantum Mechanics textbooks cannot truly answer this kind of question whereas they should. By adopting a pure "hitological" point of view for microphysics, we introduce the Hit in Apparatuses Theory (HAT) and the Vacuum of Apparatuses (VA) that restore, through Object Orientation (OO), an intuitive ontology to deal with this kind of physics. Through a review of what it means to "observe" and what relativism means in Special and General Relativities (SR and GR), we address the problem of finding common maths for GR and QM. Finally, with our new HAT, we address the measurement problem in QM and propose two possible approaches.Comment: 26 page

An optimal-control based integrated model of supply chain

Problems of supply chain scheduling are challenged by high complexity, combination of continuous and discrete processes, integrated production and transportation operations as well as dynamics and resulting requirements for adaptability and stability analysis. A possibility to address the above-named issues opens modern control theory and optimal program control in particular. Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of complexity, dynamics, uncertainty, and adaptivity. Supply chain schedule generation is represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. With the developed model, important categories of supply chain analysis such as stability and adaptability can be taken into consideration. Besides, the dimensionality of operations research-based problems can be relieved with the help of distributing model elements between an operations research (static aspects) and a control (dynamic aspects) model. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes.supply chain, model of supply chain scheduling, optimal program control theory, Pontryagin’s maximum principle, operations research model,

The Thayer Method: Student Active Learning with Positive Results

Graduation from West Point requires successful completion of four courses in the mathematical sciences. These core mathematics courses include topics in discrete dynamical systems, differential and integral calculus (single variable and multivariable), differential equations, linear algebra, probability, and statistics. The instructional system employed throughout the core is the Thayer Method, named for Colonel Sylvanus Thayer, the Father of the Military Academy. In the Thayer Method, traces of cooperative education and discovery learning are evident. It is quintessential active learning. The West Point catalyst is the fundamental principle that cadets are responsible for their own education