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Regulation of the human menstrual cycle is a frequency dependent process controlled in part by the pulsatile release of gonadotropin releasing hormone (GnRH) from the hypothalamus. The binding of GnRH to gonadotroph cells in the pituitary stimulates inositol 1,4,5-trisphosphate (IP3) mediated release of calcium from the endoplasmic reticulum, resulting in(More)
This thesis concerns parameter estimation for bursting neural models. Parameter estimation for differential equations is a difficult task due to complicated objective function landscapes and numerical challenges. These difficulties are particularly salient in bursting models and other multiple time scale systems. Here we make use of the geometry underlying(More)
Social aggregations of fish are extremely common in nature. Pitcher (1983) defines a social aggregation of fish as a shoal, with a highly polarized shoal constituting a school. The ultimate causes of fish shoaling have been extensively studied and are well established, with the main causes being protection from predators and enhanced foraging ability. The(More)
This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the(More)
Ovulation in vertebrates is caused by a surge of luteinising hormone (LH) from the pituitary. The LH surge is initiated by rising oestradiol concentration, although the precise mechanism of oestradiol action in humans and primates is not yet understood. Recent advances in labelling and three-dimensional imaging have revealed a rich pituitary structure of(More)
A mathematical model for cholera is formulated that incorporates direct and indirect transmission, patch structure, and both water and human movement. The basic reproduction number R0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoff's Matrix Tree Theorem from graph theory is used to investigate(More)
Deaths from cholera in London, UK, were recorded weekly from 1824 to 1901. Three features of the time series stand out: (i) cholera deaths were strongly seasonal, with peak mortality almost always in the summer, (ii) the only non-summer outbreaks occurred in the spring of 1832, the autumn of 1848 and the winter of 1853, and (iii) extraordinarily severe(More)
Working memory corresponds to our ability to store and manipulate information for a short time in order to carry out complex cognitive tasks. The brain region most closely associated with working memory is the prefrontal cortex; neurons within the PFC show sustained elevated activity that persists after the removal of a stimulus. It is believed that this(More)
We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).