We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete phase-space, i.e. on a finite discrete square grid. These discrete Wigner functions possess a number of properties similar to the Wigner function for a continuous quant...

We propose an analog current-mode subthreshold CMOS circuit implementing a piecewise linear neuromorphic oscillator. Our circuit was derived from a piecewise linear oscillator model proposed by Matsuoka, well known as a building block for constructing a robot locomotion controller. We modified Matsuoka’s oscillator to be suitable for analog current-mode integrated circuit implementation, and de...

A biochemical oscillator can be reconstituted in vitro with three purified proteins, that displays the salient properties of circadian (daily) rhythms, including self-sustained 24-h periodicity that is temperature compensated. We analyze the biochemical basis of this oscillator by quantifying the time-dependent interactions of the three proteins (KaiA, KaiB, and KaiC) by electron microscopy and...

A coupled-oscillators-model-based method for measuring speech rhythm is presented. This model explains crosslinguistic differences in rhythm as deriving from varying degrees of coupling strength between a syllable oscillator and a phrase stress oscillator. The method was applied to three texts read aloud in French, in Brazilian and European Portuguese by seven speakers. The results reproduce th...

Background: Synchronization in music has been a popular experimental basis for studying social interactions, as musicians are required to synchronize to each other’s beats and integrate abstract social information in order to coordinate their actions as part of a non-verbal communication process. A finger-tapping paradigm has been used in studies of sensorimotor synchronization as well as coord...

Genetic oscillators are a major theme of interest in the emerging field of synthetic biology. Until recently, most work has been carried out using intra-cellular oscillators, but this approach restricts the broader applicability of such systems. Motivated by a desire to develop large-scale, spatially distributed cell-based computational systems, we present an initial design for a population-lev...

We study theoretically the baryon spectra in terms of a deformed oscillator quark (DOQ) model. This model is motivated by confinement of quarks and chiral symmetry breaking, which are the most important non-perturbative phenomena of QCD. The minimization of the DOQ hamiltonian with respect to the deformation for each principal quantum number results in deformations for the intrinsic states of e...

Categorical perception is a well studied phenomenon in, for example, colour perception, phonetics and music. In this article we implement a dynamical systems model of categorical rhythm perception based on the resonance theory of rhythm perception developed by Large (2010). This model is used to simulate the categorical choices of participants in two experiments of Desain and Honing (2003). The...

The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible onl...

This paper presents the derivations of the voltage transfer functions of the amplifier A, the feedback network β, and the loop gain T of the common-drain (CD) Colpitts oscillator, using the small-signal model of the CD Colpitts oscillator. The derivation of the characteristic equation of the CD Colpitts oscillator is presented. Using the characteristic equation, the equation for the oscillation...