This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment. By eliminating an unmeasurable recovery variable from the FHN model, a parametric second order ordinary differential equation for the only measurable membrane potential variable can be obtained. In the presenc...

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European-style and American-style Asian options and for discretely and continuously monitored versions. In the present paper we focus on the European-style Asian options. The...

Allan Twynam BP Sunbury, England For help in preparation of this article, thanks to Curtis Boney, Ernie Brown, Steve Davies and George Hawkins, Sugar Land, Texas, USA; Jorge Gonzalez and Arthur Milne, Caracas, Venezuela; Satyaki Ray, Calgary, Alberta, Canada; and David Schoderbek, Burlington Resources Canada, Calgary. ClearFRAC, ClearPAC, CoalFRAC, FMI (Fullbore Formation MicroImager), FracCADE...

The rare biosphere, the low abundant microbial populations, is suggested to be a conserved way of microbial life. Here we conducted a molecular survey of rare methanogenic archaea in the environment targeting the mcrA gene in order to test if general concepts associated with the structure of the rare bacterial biosphere also apply to single functional groups. Similar to what is known about rare...

We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as ...

JERRY SWAN1, GABRIELA OCHOA1, GRAHAM KENDALL1, MARTIN EDJVET2 1Automated Scheduling, Optimisation and Planning (ASAP) Research Group, School of Computer Science and Information Technology, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK. Tel.: (+44) (0)115 846 6504, Fax: +44 (0)115 846 7877. 2School of Mathematical Sciences, University of Nottingham, University P...

When did you last hear mention of Dred Scott,1 the case, its many opinions, or the Justices who sat for it, without a near simultaneous use of the words “best” or “worst”? The majority and dissenting opinions of Dred Scott, as well as the Justices who wrote them, appear on a range of best and worst lists. Ranking Supreme Court Justices and Supreme Court opinions is no trivial pursuit, and for l...

Around the time that On the Origin of Species was published, Lord Kelvin authoritatively stated that the Earth was between 20 and 400 million years old, a range still quoted today by many who deny evolution. As it was difficult to conceive of life’s diversity arising via natural selection and speciation in so short a span, the apparent young Earth formed a serious barrier to the plausibility of...