Centres and limit cycles for an extended Kukles system

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Centres and limit cycles for an extended Kukles system', Electronic Journal of Differential Equations, Vol. 2007(2007), No. 119, pp. 1-23.

Limit cycles of a predator-prey model with intratrophic predation

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Limit cycles of a predator-prey model with intratrophic predation', Journal of Mathematical Analysis and Applications Volume 349, Issue 2, 15 January 2009, Pages 544-555

A model for the simulation of macroalgal population dynamics and productivity

A mathematical model to simulate the population dynamics and productivity of macroalgae is described. The model calculates the biomass variation of a population divided into size-classes. Biomass variation in each class is estimated from the mass balance of carbon fixation, carbon release and demographic processes such as mortality and frond breakage. The transitions between the different classes are calculated in biomass and density units as a function of algal growth. Growth is computed from biomass variations using an allometric relationship between weight and length. Gross and net primary productivity is calculated from biomass production and losses over the period of simulation. The model allows the simulation of different harvesting strategies of commercially important species. The cutting size and harvesting period may be changed in order to optimise the calculated yields. The model was used with the agarophyte Gelidium sesquipedale (Clem.) Born. et Thur. This species was chosen because of its economic importance as a the main raw material for the agar industry. Net primary productivity calculated with it and from biomass variations over a yearly period, gave similar results. The results obtained suggest that biomass dynamics and productivity are more sensitive to the light extinction coefficient than to the initial biomass conditions for the model. Model results also suggest that biomass losses due to respiration and exudation are comparable to those resulting from mortality and frond breakage. During winter, a significant part of the simulated population has a negative net productivity. The importance of considering different parameters in the productivity light relationships in order to account for their seasonal variability is demonstrated with the model results. The model was implemented following an object oriented programming approach. The programming methodology allows a fast adaptation of the model to other species without major software development.

Retrieval by Shape Population: An Index Tree Approach

Based on our previous work in deformable shape model-based object detection, a new method is proposed that uses index trees for organizing shape features to support content-based retrieval applications. In the proposed strategy, different shape feature sets can be used in index trees constructed for object detection and shape similarity comparison respectively. There is a direct correspondence between the two shape feature sets. As a result, application-specific features can be obtained efficiently for shape-based retrieval after object detection. A novel approach is proposed that allows retrieval of images based on the population distribution of deformed shapes in each image. Experiments testing these new approaches have been conducted using an image database that contains blood cell micrographs. The precision vs. recall performance measure shows that our method is superior to previous methods.