Kenneth A. Lindsay

On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations

A method for estimating the parameters of stochastic differential equations (SDEs) by simulated maximum likelihood is presented. This method is feasible whenever the underlying SDE is a Markov process. Estimates are compared to those generated by indirect inference, discrete and exact maximum likelihood. The technique is illustrated with reference to a one-factor model of the term structure of interest rates using 3-month US Treasury Bill data.

Mobius-Like Mappings and Their Use in Kernel Density Estimation

It is well known that the manipulation of sample data by means of a parametric function can improve the performance of kernel density estimation. This article proposes a two-parameter Mobius-like function to map sample data drawn from a semi-infinite space into [−1,1). A standard kernel method is then used to estimate the density. The proposed method is shown to yield effective estimates of density and is computationally more efficient than other well-known transformation methods. The efficacy of the technique is demonstrated in a practical setting by application to two datasets.

Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics

PREFACE CONTRIBUTORS FOREWORD INTRODUCTION TO MODELING IN THE NEUROSCIENCES George N. Reeke PATTERNS OF GENETIC INTERACTIONS: ANALYSIS OF MRNA LEVELS FROM CDNA MICROARRAYS Larry S. Liebovitch, Lina A. Shehadeh, andd Viktor K. Jirsa CALCIUM SIGNALING IN DENDRITIC SPINES William R. Holmes PHYSIOLOGICAL AND STATISTICAL APPROACHES TO MODELING OF SYNAPTIC RESPONSES Parag G. Patil, Mike West, Howard V. Wheal, and Dennis A. Turner NATURAL VARIABILITY IN THE GEOMETRY OF DENDRITIC BRANCHING PATTERNS Jaap van Pelt and Harry B.M. Uylings MULTICYLINDER MODELS FOR SYNAPTIC AND GAP-JUNCTIONAL INTEGRATION Jonathan D. Evans VOLTAGE TRANSIENTS IN BRANCHING MULTIPOLAR NEURONS WITH TAPERING DENDRITES AND SODIUM CHANNELS Lloyd L. Glenn and Jeffrey R. Knisley ANALYTICAL SOLUTIONS OF THE FRANKENHAEUSER-HUXLEY EQUATIONS MODIFIED FOR DENDRITIC BACKPROPAGATION OF A SINGLE SODIUM SPIKE Roman R. Poznanski INVERSE PROBLEMS FOR SOME CABLE MODELS OF DENDRITES Jonathan Bell EQUIVALENT CABLES-ANALYSIS AND CONSTRUCTION Kenneth A. Lindsay, Jay R. Rosenberg, and Gayle Tucker THE REPRESENTATION OF THREE-DIMENSIONAL DENDRITIC STRUCTURE BY A ONE-DIMENSIONAL MODEL-THE CONVENTIONAL CABLE EQUATION AS THE FIRST MEMBER OF A HIERARCHY OF EQUATIONS Kenneth A. Lindsay, Jay R. Rosenberg, and Gayle Tucker SIMULATION ANALYSES OF RETINAL CELL RESPONSES Yoshimi Kamiyama, Akito Ishihara, Toshihiro Aoyama, and Shiro Usui MODELING INTRACELLULAR CALCIUM: DIFFUSION, DYNAMICS, AND DOMAINS Gregory D. Smith EPHAPTIC INTERACTIONS BETWEEN NEURONS Robert Costalat and Bruno Delord CORTICAL PYRAMIDAL CELLS Roger D. Orpwood SEMI-QUANTITATIVE THEORY OF BISTABLE DENDRITES WITH POTENTIAL-DEPENDENT FACILITATION OF INWARD CURRENT Aron Gutman, Armantas Baginskas, Jorn Hounsgaard, Natasha Svirskiene, and Gytis Svirskis BIFURCATION ANALYSIS OF THE HODGKIN-HUXLEY EQUATIONS Shunsuke Sato, Hidekazu Fukai, Taishin Nomura, and Shinji Doi HIGHLY EFFICIENT PROPAGATION OF RANDOM IMPULSE TRAINS ACROSS UNMYELINATED AXONAL BRANCH POINTS: MODIFICATIONS BY PERIAXONAL K+ ACCUMULATION AND SODIUM CHANNEL KINETICS Mel D. Goldfinger DENDRITIC INTEGRATION IN A TWO-NEURON RECURRENT EXCITATORY NETWORK MODEL Roman R. Poznanski SPIKE-TRAIN ANALYSIS FOR NEURAL SYSTEMS David M. Halliday THE POETICS OF TREMOR G.P. Moore and Helen M. Bronte-Stewart PRINCIPLES AND METHODS IN THE ANALYSIS OF BRAIN NETWORKS Olaf Sporns THE DARWIN BRAIN-BASED AUTOMATA: SYNTHETIC NEURAL MODELS AND REAL-WORLD DEVICES Jeffrey L. Krichmar and George N. Reeke TOWARD NEURAL ROBOTICS: FROM SYNTHETIC MODELS TO NEUROMIMETIC IMPLEMENTATIONS Olaf Sporns BIBLIOGRAPHY INDEX

Estimating the parameters of stochastic differential equations

Two maximum likelihood methods for estimating the parameters of stochastic differential equations (SDEs) from time-series data are proposed. The first is that of simulated maximum likelihood in which a nonparametric kernel is used to construct the transitional density of an SDE from a series of simulated trials. The second approach uses a spectral technique to solve the Kolmogorov equation satisfied by the transitional probability density. The exact likelihood function for a geometric random walk is used as a benchmark against which the performance of each method is measured. Both methods perform well with the spectral method returning results which are practically identical to those derived from the exact likelihood. The technique is illustrated by modelling interest rates in the UK gilts market using a fundamental one-factor term-structure equation for the instantaneous rate of interest.

Spiking neural networks for reconfigurable POEtic tissue

Vertebrate and most invertebrate organisms interact with their environment through processes of adaptation and learning. Such processes are generally controlled by complex networks of nerve cells, or neurons, and their interactions. Neurons are characterized by all-or-none discharges - the spikes - and the time series corresponding to the sequences of the discharges - the spike trains - carry most of the information used for intercellular communication. This paper describes biologically inspired spiking neural network models suitable for digital hardware implementation. We consider bio-realism, hardware friendliness, and performance as factors which influence the ability of these models to integrate into a flexible computational substrate inspired by evolutionary, developmental and learning aspects of living organisms. Both software and hardware simulations have been used to assess and compare the different models to determine the most suitable spiking neural network model.

Biomechanical efficiency is impaired in patients with chronic heart failure

Patients with chronic heart failure (CHF) have a lower peak oxygen consumption (pVO2) than normal subjects, and for a given quantity of work, have a lower total oxygen consumption (VO2) than controls. This apparent increase in biomechanical efficiency (BE) might be due to a higher proportion of anaerobic metabolism which, although leading to lower VO2 during steady state exercise, must be compensated for during recovery.

The Devil is in the Detail: Hints for Practical Optimisation

Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples.

Estimating the parameters of stochastic differential equations by Monte Carlo methods

We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo experiment. The fit between the two distributions is assessed by means of the chi-square goodness-of-fit statistic leading to a confidence function computed from an incomplete gamma function. A numerical optimisation algorithm then optimises the choice of parameters to maximise this function. Preliminary evidence is presented which suggests that it is possible to estimate the coefficients of the generating SDE very accurately.

Metabolic gas kinetics depend upon the level of exercise performed.

The kinetics of oxygen and carbon dioxide at the onset of and recovery from exercise are slowed in patients with chronic heart failure (CHF). The aim of the present study was to establish whether the kinetics of O2 are influenced by the work rate.

Analytical and numerical construction of equivalent cables.

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.