A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

BELFAST centenarians: A Case of Optimal Cardiovascular Risk?

Introduction: Centenarians are reservoirs of genetic and environmental information to successful ageing and local centenarian groups may help us to understand some of the factors that contribute to longevity. The current centenarian cohort in Belfast survived the 1970s epidemic of death from coronary heart disease in Northern Ireland, where cardiovascular mortality was almost highest in the world. These centenarians provided an opportunity to assess biological and genetic factors important in cardiovascular risk and ageing. Methods: Thirty-five (27 female, 8 male) centenarians, participants of the Belfast Elderly Longitudinal Free-living Ageing STudy (BELFAST), were community-living and of good cognition at enrolment. Results: Centenarians showed median Body Mass Index (BMI) at 25.7, systolic blood pressure 140mmHg and diastolic blood pressure 90mmHg, and fasting glucose of 5.54 mmol/l with no sex-related difference. Lipoproteins showed median cholesterol 5.3, High Density Lipoprotein (HDL) 1.10 and Low Density Lipoprotein (LDL) 3.47umol/l respectively. Centenarian smokers showed no different blood pressure or lipid measurements compared with non-smokers. Malondialdehyde, a measure of lipid peroxidation, was low at 1.19 umol/l, and measures of antioxidant status were varied. Male centenarians did not carry any of the vascular risk genotypes studied-ApoE4 for Apolipoprotein E (ApoE), DD for Angiotensinogen Converting Enzyme (ACE) and tt for 5,10-methylenetetrahydrofolate reductase (MTFHR), though this was not true for female centenarians.. Conclusions: This small local study shows that Belfast centenarians carry a reasonably favourable risk profile, except for age, with respect to cardiovascular disease. There is also some evidence that vascular risk factors and genotypes may be tolerated differently between the male and female centenarians. Maintaining a favourable cardiovascular risk profile seems likely to improve the chance of becoming a centenarian, especially for males.