Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.

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Thermodynamics and Kinetics of a Brownian Motor

From the Publisher:
"Covering the latest issues and achievements, this well documented, precisely presented text is timely and suitable for graduate and upper undergraduate students in knowledge engineering, intelligent systems, AI, neural networks, fuzzy systems, and related areas. The author's goal is to explain the principles of neural networks and fuzzy systems and to demonstrate how they can be applied to building knowledge-based systems for problem solving. Especially useful are the comparisons between different techniques (AI rule-based methods, fuzzy methods, connectionist methods, hybrid systems) used to solve the same or similar problems."
-- Anca Ralescu, Associate Professor of Computer Science, University of Cincinnati Neural networks and fuzzy systems are different approaches to introducing human-like reasoning into expert systems. This text is the first to combine the study of these two subjects, their basics and their use, along with symbolic AI methods to build comprehensive artificial intelligence systems. 
In a clear and accessible style, Kasabov describes rule- based and connectionist techniques and then their combinations, with fuzzy logic included, showing the application of the different techniques to a set of simple prototype problems, which makes comparisons possible. A particularly strong feature of the text is that it is filled with applications in engineering, business, and finance. AI problems that cover most of the application-oriented research in the field (pattern recognition, speech and image processing, classification, planning, optimization, prediction, control, decision making, and game simulations) are discussed and illustrated with concrete examples.
Intended both as a text for advanced undergraduate and postgraduate students as well as a reference for researchers in the field of knowledge engineering, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering has chapters structured for various levels of teaching and includes original work by the author along with the classic material. 
Data sets for the examples in the book as well as an integrated software environment that can be used to solve the problems and do the exercises at the end of each chapter are available free through anonymous ftp.

Foundations of neural networks, fuzzy systems, and knowledge engineering

Stochastic resonance and sensory information processing: a tutorial and review of application

STOCHASTIC resonance1‡-4 (SR) is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular, non-zero level of noise5 ‡-7. SR has been proposed as a means for improving signal detection in a wide variety of systems, including superconducting quantum interference devices8, and may be used in some natural systems such as sensory neurons9‡-15. But for SR to be effective in a singleunit system (such as a sensory neuron or a single ion channel), the optimal intensity of the noise must be adjusted as the nature of the signal to be detected changes15. This has been thought to impose a limitation on the practical and natural uses of SR. Here we show that the ability of a summing network of excitable units to detect a range of weak (sub-threshold) signals (either periodic or aperiodic) can be optimized by a fixed level of noise, irrespective of the nature of the input signal. We also show that this noise does not significantly degrade the ability of the network to detect suprathreshold signals. Thus, large nonlinear networks do not suffer from the limitations of SR in single units, and might be able to use a single noise level, such as that provided by the intrinsic noise of the individual components, to enhance the system's sensitivity to weak inputs. This suggests a functional role for neuronal noise14,16‡-18 in sensory systems.

Stochastic resonance without tuning

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations— e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being ''suboptimal''. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significant- ly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the ''neural code''. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neurosci- entists and biologists, both computational and experi- mental, to embrace a very broad definition of stochastic resonance in terms of signal-processing ''noise benefits'', and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

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What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Stochastic resonance in a single neuron model: theory and analog simulation.

A simple superconducting loop with a Josephson junction subject to a time‐sinusoidal magnetic flux embedded in a noise background is considered. Cooperative effects, arising from the interplay between the noise and modulation are described; they manifest themselves in the response, measured as an output signal‐to‐noise ratio. In particular, it is shown that the response displays the stochastic resonance effect, wherein the output signal‐to‐noise ratio passes through a maximum at a critical value of the noise strength. A simple theory, based on the characterization of the superconducting quantum interference device as a bistable switching element, is seen to yield good qualitative agreement with the experimental results.

Stochastic resonance in a superconducting loop with a josephson junction

We consider the effect of weak additive noise on the homoclinic threshold of a driven dissipative nonlinear system. A new ``generalized'' Melnikov function is derived for the system and is seen to be the Melnikov function for the corresponding noise-free system plus a correction term that depends on the second-order noise characteristics. The correction term is explicitly calculated for three model systems [Duffing oscillator, Josephson junction, and rf superconducting quantum interference device (SQUID)]. The effect of a distribution of dc driving terms on the chaotic attractor of a dissipative system is also examined via numerical simulation of the rf SQUID.

Homoclinic chaos in systems perturbed by weak Langevin noise.

Noise effects in a nonlinear dynamic system: The rf superconducting quantum interference device

We consider a simple model of the flux in a rf superconducting quantum-interference device (SQUID) ring subjected to an external periodic magnetic field. The dynamic equation describing the flux response of the SQUID is solved analytically in the absence of damping and external driving terms. We then introduce these terms as small perturbations, and construct, for this system, the Melnikov function, the zeros of which indicate the onset of homoclinic behavior. For the parameter values under consideration, excellent agreement is obtained between our theoretical predictions and numerical calculations of the stable and unstable (i.e., time-reversed) solution manifolds. A chaotic attractor is shown to appear somewhat above the homoclinic threshold.

E. W. Jacobs

Papers

Stochastic resonance in a single neuron model: theory and analog simulation.

Stochastic resonance in a superconducting loop with a josephson junction

Homoclinic chaos in systems perturbed by weak Langevin noise.

Noise effects in a nonlinear dynamic system: The rf superconducting quantum interference device

Homoclinic Chaos in the RF Superconducting Quantum-Interference Device