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Charles E. M. Pearce

Other affiliations: University of South Australia
Bio: Charles E. M. Pearce is an academic researcher from University of Adelaide. The author has contributed to research in topics: Rearrangement inequality & Convex function. The author has an hindex of 28, co-authored 218 publications receiving 5939 citations. Previous affiliations of Charles E. M. Pearce include University of South Australia.


Papers
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Book
01 Jan 2008
TL;DR: In this article, a theoretical approach based on linear response theory (LRT) is described, and two new forms of stochastic resonance, predicted on the basis of LRT and subsequently observed in analogue electronic experiments, are described.
Abstract: Stochastic resonance (SR) - a counter-intuitive phenomenon in which the signal due to a weak periodic force in a nonlinear system can be {\it enhanced} by the addition of external noise - is reviewed A theoretical approach based on linear response theory (LRT) is described It is pointed out that, although the LRT theory of SR is by definition restricted to the small signal limit, it possesses substantial advantages in terms of simplicity, generality and predictive power The application of LRT to overdamped motion in a bistable potential, the most commonly studied form of SR, is outlined Two new forms of SR, predicted on the basis of LRT and subsequently observed in analogue electronic experiments, are described

2,403 citations

Posted Content
TL;DR: The Hermite-Hadamard double inequality for convex functions has been studied extensively in the literature, see as discussed by the authors for a survey of the Hermite Hadamard inequalities.
Abstract: The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this monograph we present the basic facts related to Hermite- Hadamard inequalities for convex functions and a large number of results for special means which can naturally be deduced. Hermite-Hadamard type inequalities for other concepts of convexities are also given. The properties of a number of functions and functionals or sequences of functions which can be associated in order to refine the result are pointed out. Recent references that are available online are mentioned as well.

685 citations

Journal ArticleDOI
TL;DR: Improvements are obtained to some recent error estimates of Dragomir and Agarwal, based on convexity, for the trapezoidal formula, for which a parallel development is made based on concavity.

264 citations

Book
23 Oct 2009
TL;DR: Stochastic resonance in the auditory system, SSR, neural coding, and performance tradeoffs, and the future of stochastic resonance and suprathreshold stochastics resonance Appendices References Index.
Abstract: Preface 1. Introduction and motivation 2. Stochastic resonance: its definitions, history and debates 3. Stochastic quantization 4. Suprathreshold stochastic resonance: encoding 5. Suprathreshold stochastic resonance: large N encoding 6. Suprathreshold stochastic resonance: decoding 7. Suprathreshold stochastic resonance: large N decoding 8. Optimal stochastic quantization 9. SSR, neural coding, and performance tradeoffs 10. Stochastic resonance in the auditory system 11. The future of stochastic resonance and suprathreshold stochastic resonance Appendices References Index.

242 citations


Cited by
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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Journal ArticleDOI
TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

6,437 citations

Journal ArticleDOI
TL;DR: Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Abstract: Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

2,834 citations

Journal ArticleDOI
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

2,548 citations