Charles E. M. Pearce

Inequalities for differentiable mappings with application to special means and quadrature formulæ

Abstract Improvements are obtained to some recent error estimates of Dragomir and Agarwal, based on convexity, for the trapezoidal formula. Corresponding estimates are established for the midpoint formula. A parallel development is made based on concavity.

QUASI-CONVEX FUNCTIONS AND HADAMARD'S INEQUALITY

Some extensions of quasi-convexity appearing in the literature are explored and relations found between them. Hadamards inequality is connected tenaciously with convexity and versions of it are shown to hold in our setting. Our theorems extend and unify a number of known results. In particular, we derive a generalised Kenyon-Klee theorem.

Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance

Mark D. McDonnell, ∗ Nigel G. Stocks, † Charles E.M. Pearce, ‡ and Derek Abbott § 1 School of Electrical and Electronic Engineering & Centre for Biomedical Engineering, The University of Adelaide, SA 5005, Australia School of Engineering, The University of Warwick, Coventry CV4 7AL, United Kingdom 3 School of Mathematical Sciences, The University of Adelaide, SA 5005, Australia (Dated: February 2, 2008)

Closed queueing networks with batch services

In this paper we study queueing networks which allow multiple changes at a given time. The model has a natural application to discrete-time queueing networks but describes also queueing networks in continuous time.It is shown that product-form results which are known to hold when there are single changes at a given instant remain valid when multiple changes are allowed.

A CHARACTERIZATION OF SUPRATHRESHOLD STOCHASTIC RESONANCE IN AN ARRAY OF COMPARATORS BY CORRELATION COEFFICIENT

Suprathreshold Stochastic Resonance (SSR), as described recently by Stocks, is a new form of Stochastic Resonance (SR) which occurs in arrays of nonlinear elements subject to aperiodic input signals and noise. These array elements can be threshold devices or FitzHugh-Nagumo neuron models for example. The distinguishing feature of SSR is that the output measure of interest is not maximized simply for nonzero values of input noise, but is maximized for nonzero values of the input noise to signal intensity ratio, and the effect occurs for signals of arbitrary magnitude and not just subthreshold signals. The original papers described SSR in terms of information theory. Previous work on SR has used correlation based measures to quantify SR for aperiodic input signals. Here, we argue the validity of correlation based measures and derive exact expressions for the cross-correlation coefficient in the same system as the original work, and show that the SSR effect also occurs in this alternative measure. If the output signal is thought of as a digital estimate of the input signal, then the output noise can be considered simply as quantization noise. We therefore derive an expression for the output signal to quantization noise ratio, and show that SSR also occurs in this measure.

An M/M /1 retrial queue with control policy and general retrial times.

We consider anM/M/1 retrial queueing system in which the retrial time has a general distribution and only the customer at the head of the queue is allowed to retry for service. We find a necessary and sufficient condition for ergodicity and, when this is satisfied, the generating function of the distribution of the number of customers in the queue and the Laplace transform of the waiting time distribution under steady-state conditions. The results agree with known results for special cases.

QUANTIZATION IN THE PRESENCE OF LARGE AMPLITUDE THRESHOLD NOISE

Signal quantization in the presence of independent, identically distributed, large amplitude threshold noise is examined. It has previously been shown that when all quantization thresholds are set to the same value, this situation exhibits a form of stochastic resonance known as suprathreshold stochastic resonance. This means the optimal quantizer performance occurs for a small input signal-to-noise ratio. Here we examine the performance of this stochastic quantization in terms of both mutual information and mean square error distortion. It is also shown that for low input signal-to-noise ratios that the case of all thresholds being identical provides the optimal mean square error distortion performance for the given noise conditions.

The exact solution of the general stochastic rumour

A characterization is given of the complete time-dependent evolution of a general stochastic rumour which includes the two Daley-Kendall models and the Maki-Thompson model as special cases.

Some new bounds for singular values and eigenvalues of matrix products

For two Hermitian matrices A and B, at least one of which is positive semidefinite, we give upper and lower bounds for each eigenvalue of AB in terms of the eigenvalues of A and B. For two complex matrices A,B with known singular values, upper and lower bounds are deduced for each singular value of AB.

Invariant measures for quasi-birth-and-death processes

Abstract: We show that an irreducible level-independent quasi-birth-and-death process always has a matrix-geometric invariant measure. Furthermore we give a construction for this invariant measure. The invariant measure is, of course, not summable over the state space if the process is null-recurrent or transient When the process is level-dependent, there exists a matrix-product-form invariant measure. We discuss how this measure may be constructed