Synchronization of Coupled Boolean Phase Oscillators

We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bi-directional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.Comment: 8 pages, 8 figure

Multirhythmicity in an optoelectronic oscillator with large delay

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square-waves is substantiated analytically by determining stable fixed points of a map.Comment: 14 pages, 7 figure

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators

We study networks of non-locally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast timescale of our oscillators (on the order of $100\;\mathrm{ns}$) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.Comment: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.03090

Excitability in autonomous Boolean networks

We demonstrate theoretically and experimentally that excitable systems can be built with autonomous Boolean networks. Their experimental implementation is realized with asynchronous logic gates on a reconfigurabe chip. When these excitable systems are assembled into time-delay networks, their dynamics display nanosecond time-scale spike synchronization patterns that are controllable in period and phase.Comment: 6 pages, 5 figures, accepted in Europhysics Letters (epljournal.edpsciences.org

Reservoir computing with a single time-delay autonomous Boolean node

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which we show is sufficient for reservoir computing. We then characterize the dependence of computational performance on system parameters to find the best operating point of the reservoir. When the best parameters are chosen, the reservoir is able to classify short input patterns with performance that decreases over time. In particular, we show that four distinct input patterns can be classified for 70 ns, even though the inputs are only provided to the reservoir for 7.5 ns.Comment: 5 pages, 5 figure

A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data

Diffusion weighted ( DW ) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation ( with various well-documented limitations ), towards more complex high angular resolution diffusion imaging ( HARDI ) analysis techniques. Spherical deconvolution ( SD ) approaches assume that the fibre orientation density function ( fODF ) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: ( 1 ) constrained spherical harmonic deconvolution ( CSHD )—a technique that exploits spherical harmonic basis sets and ( 2 ) damped Richardson–Lucy ( dRL ) deconvolution—a technique based on the standard Richardson–Lucy deconvolution. Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed ( ‘Target’ ) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks ( consistent with well known ringing artefacts ) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration ( with a calibration response function for a highly anisotropic fibre being optimal ). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography

Abstract art by shape classification

his paper shows that classifying shapes is a tool useful in nonphotorealistic rendering (NPR) from photographs. Our classifier inputs regions from an image segmentation hierarchy and outputs the "best” fitting simple shape such as a circle, square, or triangle. Other approaches to NPR have recognized the benefits of segmentation, but none have classified the shape of segments. By doing so, we can create artwork of a more abstract nature, emulating the style of modern artists such as Matisse and other artists who favored shape simplification in their artwork. The classifier chooses the shape that "best” represents the region. Since the classifier is trained by a user, the "best shape” has a subjective quality that can over-ride measurements such as minimum error and more importantly captures user preferences. Once trained, the system is fully automatic, although simple user interaction is also possible to allow for differences in individual tastes. A gallery of results shows how this classifier contributes to NPR from images by producing abstract artwork. INDEX TERM