Controlling neuronal spikes

We propose two control strategies for achieving desired firing patterns in a physiologically realistic model neuron. The techniques are powerful, efficient, and robust, and we have applied them successfully to obtain a range of targeted spiking behaviors. The methods complement each other: one involves the manipulation of only a parameter, the applied soma current, and the other involves the manipulation of only a state variable, the membrane potential. Both techniques have the advantage that they are not measurement-intensive nor do they involve much run-time computation, as knowledge of only the interspike interval is necessary to implement control

Dynamics based computation

We demonstrate the ability of lattices of coupled chaotic maps to perform simple computations. This dynamical system is shown to emulate logic gates, encode numbers, and perform specific arithmetic operations on those numbers such as addition and multiplication. We also demonstrate the ability of this dynamical system to perform the more specialized operation of determining the least common multiplier of a sequence of integers

Computing with distributed chaos

We describe and discuss in detail some recent results by Sinha and Ditto [Phys. Rev. Lett. 81, 2156 (1998)] demonstrating the capacity of a lattice of threshold coupled chaotic maps to perform computations. Such systems are shown to emulate logic gates, encode numbers, and perform specific arithmetic operations, such as addition and multiplication, as well as yield more specialized operations such as the calculation of the least common multiplier of a sequence of numbers. Furthermore, we extend the scheme to multidimensional continuous time dynamics, in particular to a system relevant to chaotic lasers

Coupling Reduces Noise

We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions

Flexible parallel implementation of logic gates using chaotic elements

We demonstrate the basic principles for the direct and flexible implementation of all basic logical operations utilizing low dimensional chaos. Then we generalize the concept to high dimensional chaotic systems, and show the parallelism inherent in such systems. As a case study we implement the proposed parallel computing architecture to obtain parallelized bit-by-bit addition with a two-dimensional chaotic neuronal and a three-dimensional chaotic laser model

Parallel computing with extended dynamical systems

We discuss the scope of parallelism based on extended dynamical systems, in particular, arrays of chaotic elements. As a case study we demonstrate the rapid solution of the Deutsch-Jozsa problem, utilizing the collective properties of such systems

Realization of the fundamental NOR gate using a chaotic circuit

We report the experimental verification of a simple threshold controller, which clips the chaos to periods of widely ranging orders, in a chaotic circuit. Then we use this to implement the fundamental NOR gate thus obtaining a proof of principle experiment demonstrating the universal computing capability of chaotic systems

Strange nonchaotic stars

The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Kepler's "golden" stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.Comment: 5 pages, 4 figures, published in Physical Review Letter

Pulsation period variations in the RRc Lyrae star KIC 5520878

Learned et. al. proposed that a sufficiently advanced extra-terrestrial civilization may tickle Cepheid and RR Lyrae variable stars with a neutrino beam at the right time, thus causing them to trigger early and jogging the otherwise very regular phase of their expansion and contraction. This would turn these stars into beacons to transmit information throughout the galaxy and beyond. The idea is to search for signs of phase modulation (in the regime of short pulse duration) and patterns, which could be indicative of intentional, omnidirectional signaling. We have performed such a search among variable stars using photometric data from the Kepler space telescope. In the RRc Lyrae star KIC 5520878, we have found two such regimes of long and short pulse durations. The sequence of period lengths, expressed as time series data, is strongly auto correlated, with correlation coefficients of prime numbers being significantly higher ($p=99.8$\%). Our analysis of this candidate star shows that the prime number oddity originates from two simultaneous pulsation periods and is likely of natural origin. Simple physical models elucidate the frequency content and asymmetries of the KIC 5520878 light curve. Despite this SETI null result, we encourage testing other archival and future time-series photometry for signs of modulated stars. This can be done as a by-product to the standard analysis, and even partly automated.Comment: Accepted for publication in ApJ. 49 pages, 16 figure