Clare E. Martin

Disciplined, efficient, generalised folds for nested datatypes

Abstract.Nested (or non-uniform, or non-regular) datatypes have recursive definitions in which the type parameter changes. Their folds are restricted in power due to type constraints. Bird and Paterson introduced generalised folds for extra power, but at the cost of a loss of efficiency: folds may take more than linear time to evaluate. Hinze introduced efficient generalised folds to counter this inefficiency, but did so in a pragmatic way: he did not provide categorical or equivalent underpinnings, so did not get the associated universal properties for manipulating folds. We combine the efficiency of Hinze’s construction with the powerful reasoning tools of Bird and Paterson’s.

Modelling angelic and demonic nondeterminism with multirelations

This paper presents an introduction to a calculus of binary multirelations, which can model both angelic and demonic kinds of non-determinism. The isomorphism between up-closed multirelations and monotonic predicate transformers allows a different view of program transformation, and program transformation calculations using multirelations are easier to perform in some circumstances. Multirelations are illustrated by modelling both kinds of nondeterministic behaviour in games and resource-sharing protocols.

Systematic analysis of mobile diabetes management applications on different platforms

There are a number of mobile applications available to help patients suffering from Type 1 diabetes to manage their condition, but the quality of these applications varies greatly. This paper details the findings from a systematic analysis of these applications on three mobile platforms (Android, iOS, and Blackberry) that was conducted to establish the state of the art in mobile applications for diabetes management. The findings from this analysis will help to inform the future development of more effective mobile applications to help patients suffering from Type 1 diabetes who wish to manage their condition with a mobile application.

A systematic evaluation of mobile applications for diabetes management

This short paper contains a summary of work that is currently in progress towards the development of an intelligent, personalised tool for diabetes management. A preliminary part of the development process has consisted of a systematic evaluation of existing applications for mobile phones.

On the semantics of nested datatypes

Regular datatypes can be given a semantics as initial algebras in the category Set of sets and total functions [7], but it was shown in [1] that this theory is inadequate to describe nested datatypes. Instead, one solution proposed there was to define them as initial algebras in the functor category Nat(Set), where Nat(C) is the category with objects all endofunctors on C and arrows all natural transformations between them. It was observed, however, that this approach had not been validated, in the sense of ensuring that such initial algebras always exist. Blampied’s recent thesis [3] has only a weak result about existence in certain special cases. We show here that initial algebras are not guaranteed to exist in the functor category itself, but that they do exist in some other categories, and in particular the subcategory of all cocontinuous endofunctors and natural transformations between them. This category is then a semantic domain for nested datatypes, both first order as in [1, 2] and higher-order as in [4, 5].

Temporal case-based reasoning for type 1 diabetes mellitus bolus insulin decision support

Individuals with type 1 diabetes have to monitor their blood glucose levels, determine the quantity of insulin required to achieve optimal glycaemic control and administer it themselves subcutaneously, multiple times per day. To help with this process bolus calculators have been developed that suggest the appropriate dose. However these calculators do not automatically adapt to the specific circumstances of an individual and require fine-tuning of parameters, a process that often requires the input of an expert. To overcome the limitations of the traditional methods this paper proposes the use of an artificial intelligence technique, case-based reasoning, to personalise the bolus calculation. A novel aspect of our approach is the use of temporal sequences to take into account preceding events when recommending the bolus insulin doses rather than looking at events in isolation. The in silico results described in this paper show that given the initial conditions of the patient, the temporal retrieval algorithm identifies the most suitable case for reuse. Additionally through insulin-on-board adaptation and postprandial revision, the approach is able to learn and improve bolus predictions, reducing the blood glucose risk index by up to 27% after three revisions of a bolus solution.

An ontology of diabetes self management

This work is part of a planned larger project to develop an intelligent mobile personalised guidance service for the management of diabetes by harnessing the power of the new generation of smart phones. Existing mobile applications enable diabetic patients to record blood glucose readings, carbohydrates consumed, insulin dosage, physical activity undertaken, and other activities and observations. Our aim is to develop a lightweight ontology that captures the kinds of information recorded by such applications, and which would facilitate interoperation. In order to establish a list of terms that must be captured by the ontology, we have undertaken a systematic review of applications (limited, for the moment to the iOS platform). We use this list to establish suitable classes and properties for the ontology, and then investigate how it can be mapped on to existing standards such as HL7 RIM and OpenEHR.

Monadic maps and folds for multirelations in an allegory

This paper contributes to the unification of semantic models and program development techniques by making a link from multirelations and predicate transformer semantics to algebraic semantics and the derivation of programs by calculation, as used in functional programming and relational program development. Two common ways to characterise iteration, namely the functional programming operators map and fold, are extended to multirelations, using concepts from category theory, power allegories and monads.

Nondeterministic folds

The map and fold operators are both key elements of every functional programmers toolkit. In this paper we examine the corresponding concepts in the domain of multirelations, which can be used to model both angelic and demonic nondeterminism.

Developing a mobile case-based reasoning application to assist type 1 diabetes management

Effective management of diabetes is crucial for patient wellbeing and the prevention of low blood sugar levels (Hypoglycemia) and high blood sugar levels (Hyperglycemia) both of which can be potentially dangerous. Traditionally log books are maintained by patients to record information such as insulin usage and their meals. The ever increasing popularity of smart phones has resulted in various applications being developed to allow patients to log data and help manage their condition. However these applications are often developed simply for the logging of data and only occasionally provide basic calculations to suggest insulin doses following a meal. The goal of this research is to use case-based reasoning techniques to suggest an insulin dosage for the patient as opposed to using a one calculation fits all approach. This is to be achieved by building a knowledge base of the patients history that is then used to obtain a solution which best fits the current circumstances. The proposed case-based reasoning system is described alongside the development of the system to date and discussion into further research and development. The final implementation will be tested and validated using a diabetic patient simulator to create a knowledge base and observe system behavior and accuracy.