1,257 research outputs found
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 ) 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
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
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
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 âcommonâ 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 âcalibrationâ. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: ( 1 ) constrained spherical harmonic deconvolution ( CSHD )âa technique that exploits spherical harmonic basis sets and ( 2 ) damped RichardsonâLucy ( dRL ) deconvolutionâa technique based on the standard RichardsonâLucy deconvolution. Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed ( âTargetâ ) 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 "bestâ 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 "bestâ represents the region. Since the classifier is trained by a user, the "best shapeâ 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.
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