Peter J. Larcombe

On the characterization of periodic generalized Horadam sequences

The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are generated by higher order recurrences for arbitrary initial conditions. The asymptotic behaviour of generalized Horadam sequences generated by roots of unity is also examined, along with upper boundaries for the disc containing periodic orbits. Some applications are suggested, along with a number of future research directions.

Computational Objectivity in Depression Assessment for Unstructured Large Datasets

The Patient Health Questionnaire (PHQ-9) is the depression module, which provides a score correlating to each of the Depression Severity Measure (DSM-IV) criteria, whose output is a total score suggesting which category of depression a patient slots into. In this paper we propose a novel method to potentially improve the current system in place for health professionals in diagnosing depression. Thus, our objective is to propose a more computational method of measurement, similar to the PHQ-9 already in place, with a mathematical ranking system based on a large unstructured dataset consisting of abstracts available from PubMed.

COMPUTER PROOFS OF MATRIX PRODUCT IDENTITIES

We introduce in this paper a straightforward but useful method for computing indefinite rational matrix products. The method is used to prove a certain identity involving definite sums and a definite integral.

Two Case Studies Based on Large Unstructured Sets

In this chapter, we shall present two case studies based on large unstructured datasets. The former specifically considers the Patient Health Questionnaire (PHQ-9), which is the most common depression assessment tool, suggesting the severity and type of depression an individual may be suffering from. In particular, we shall assess a method which appears to enhance the current system in place for health professionals when diagnosing depression. This is based on a combination of a computational assessment method, with a mathematical ranking system defined from a large unstructured dataset consisting of abstracts available from PubMed. The latter refers to a probabilistic extraction method introduced in Trovati et al. (IEEE Trans ADD, 2015, submitted). We shall consider three different datasets introduced in Trovati et al. (IEEE Trans ADD, 2015, submitted; Extraction, identification and ranking of network structures from data sets. In: Proceedings of CISIS, Birmingham, pp 331–337, 2014) and Trovati (Int J Distrib Syst Technol, 2015, in press), whose results clearly indicate the reliability and efficiency of this type of approach when addressing large unstructured datasets. This is part of ongoing research aiming to provide a tool to extract, assess and visualise intelligence extracted from large unstructured datasets.

A Semi-automated Assessment of the Direction of Influence Relations from Semantic Networks: A Case Study in Maths Anxiety

In this paper, we introduce a novel method to identify the direction of influence relations between concepts, that is concepts whose semantic attributes are not affected by the dynamics of their neighbouring concepts. We consider an unstructured dataset provided by the abstracts and articles freely available from PubMed [8], which specifically addresses maths anxiety. This is a psychological disorder, which negatively affects the process of learning mathematics resulting in low self esteem and poor academic performance. The initial evaluation shows the potential of our approach, suggesting its applicability to a wide selection of multidisciplinary topics.