We discuss the two time-interval sequences which play a crucial role in studies of escape times in bistable systems driven by periodic functions embedded in noise. We demonstrate that the probability density of escape times for one of the sequences exhibits all the substantive features of experimental interspike interval histograms recorded from real, periodically forced sensory neurons. Our analysis relies on linking this interval sequence to the firing-reset mechanism of real neurons, and illustrates the importance of the noise, without which the substantive features cannot exist, for the transmission of sensory information.PACS numbers: 87.22.Jb, 42.66.Ew It has been well known for decades that a major component of sensory information is transmitted to the brain using a code based on the time intervals between firings of neurons, that is, action potentials or spikes [1,2]. Moreover, statistical analyses of experimentally obtained spike trains have concluded that the time intervals contain a significant random component [3]. Exactly how the sensory information is encoded and how this process is affected by noise-whether the noise simply obscures it by introducing random interval errors, or whether it plays a deeper role-is, however, presently not clear. A useful and widely used ensemble average of neural firing data is the interspike interval histogram (ISIH) in which the time intervals between successive spikes are assembled into a histogram. In this paper, we are interested in the properties of these ISIH's when the stimulus to a particular sensory modality is a periodic function of time. We reproduce in Fig. 1 two such histograms, obtained 23 years apart: the first from older experiments on single auditory nerve fibers of monkeys [4], shown in Fig. 1(a), and the second from recent experiments on single neutrons in the primary visual cortex of a cat [5], shown in Fig. 1(b). The histograms from these elegant experiments depict striking sequences of decaying peaks. The similarity is remarkable, even though the cat data were obtained from a neuron located within the visual cortex, in contrast to the monkey data, which were obtained from a nerve fiber much closer to the transducer (the ear), suggesting that these detailed patterns may play an essential role in neural information transfer. Two features of these data are notable: First, the modes are located at integer multiples of the stimulus period, and second, the mode amplitudes decay rapidly, approximately exponentially, as shown by the inset in Fig. 1 (a).We take a reductionist's view of these data; that is, our object here will not be to create a better or more detailed neuron model, but rather to discover the simplest possible physical mechanism which can capture the dominant features of the aforementioned ISIH's. Similar approaches have recently been used to address other questions in biology, for example, that of oscillator synchronization [6]. We take our initial clues from Landahl, McCulloch, and Pitts [7], who first modeled neurons with stochastic...

We enhance the response of a "stochastic resonator" by coupling it into a chain of identical resonators. Specifically, we show via numerical simulation that local linear coupling of overdamped nonlinear oscillators significantly enhances the signal-to-noise ratio of the response of a single oscillator to a time-periodic signal and noise. We relate this array enhanced stochastic resonance to the global spatiotemporal dynamics of the array and show how noise, coupling, and bistable potential cooperate to organize spatial order, temporal periodicity, and peak signal-to-noise ratio.

Two sweeping generalizations can be made about most natural systems: They are intrinsically nonlinear and they operate in noisy environments. Examples abound, ranging from weather systems to oscillating chemical reactions to the movements of an eel. The most complex example is arguably the human central nervous system, flooded as it is with the “noise” of modern life.

The response of a noisy nonlinear system to deterministic input signals can be enhanced by cooperative phenomena. We show that when one presents two square waves as input to a two-state system, the response of the system can produce a logical output (NOR/OR) with a probability controlled by the noise intensity. As one increases the noise (for fixed threshold or nonlinearity), the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Changing the nonlinearity (or the thresholds) of the system changes the output into another logic operation (NAND/AND) whose probability displays analogous behavior. The interplay of nonlinearity and noise can yield logic behavior, and the emergent outcome of such systems is a logic gate. This "logical stochastic resonance" is demonstrated via an experimental realization of a two-state system with two (adjustable) thresholds.

We present a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR. The logic function can be programmed (e.g., from AND to OR) dynamically, by adjusting the resonator's operating parameters. The device can access one of two stable steady states, according to a specific logic function; this operation is mediated by the noise floor which can be directly adjusted, or dynamically "tuned" via an adjustment of the underlying nonlinearity of the resonator, i.e., it is not necessary to have direct control over the noise floor. The demonstration of this reprogrammable nanomechanical logic gate affords a path to the practical realization of a new generation of mechanical computers.A practical realization of a nanomechanical logic device, capable of performing fundamental logic operations, is yet to be demonstrated despite a longstanding effort toward scalable mechanical computation. [1][2][3][4] This effort can be traced back to 1822 (at least), when Charles Babbage presented a mechanical computing device that he called the "Difference Engine", to the Royal Astronomical Society. 1 Before this event, though, the search for mechanical computing devices had already been inherent in attempts to build machines capable of computation. This search has, today, taken on added urgency as we seek to exploit emerging techniques for the manipulation of matter at nanometer length scales. With Boole's ideas on logic operations with two states an added dimension to computing, logic elements or gates have come to dominate modern computation. However mechanical logic, especially at the very small length scales and in the presence of a noise floor, has proven difficult to realize despite some recent experimental efforts. [5][6][7] The control and manipulation of mechanical response at nanometer scales can be realized by exploiting a (seemingly) counterintuitive physical phenomenon, stochastic resonance (SR): 8 in a noisy nonlinear mechanical system, the controlled addition of noise can enhance the system response to an external stimulus. Signal amplification in such a setup has been experimentally realized in nonlinear nanomechanical resonators configured as two-state devices. [9][10][11] Recently, it has been demonstrated 12 that when two square waves are applied as input stimuli to a two-state system, the response can result in a specific logical output with a probability (for obtaining this output) controlled by the noise intensity. Furthermore, changing the threshold (either via adjusting the nonlinearity strength or applying a controlled asymmetrizing dc signal) can change or "morph" the system output into a different logic operation. 12 Our experimental logic device consists of a nanomechanical resonator, operating in the nonlinear regime, wherein two different vibrational states coexist; for an underdamped system underpinned by an a priori monostable (but nonparabolic) potential energy function, these vibrational steady states are induced by biasing the...