2,753 research outputs found
Estimating the master stability function from the time series of one oscillator via machine learning
The master stability function (MSF) yields the stability of the globally
synchronized state of a network of identical oscillators in terms of the
eigenvalues of the adjacency matrix. In order to compute the MSF, one must have
an accurate model of an uncoupled oscillator, but often such a model does not
exist. We present a machine learning technique for estimating the MSF given
only the time series of a single, uncoupled oscillator. We demonstrate the
generality of our technique by considering a variety of coupling configurations
of networks consisting of Lorenz oscillators or H{\'e}non maps
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
Experimental observation of chimera and cluster states in a minimal globally coupled network
A "chimera state" is a dynamical pattern that occurs in a network of coupled
identical oscillators when the symmetry of the oscillator population is broken
into synchronous and asynchronous parts. We report the experimental observation
of chimera and cluster states in a network of four globally coupled chaotic
opto-electronic oscillators. This is the minimal network that can support
chimera states, and our study provides new insight into the fundamental
mechanisms underlying their formation. We use a unified approach to determine
the stability of all the observed partially synchronous patterns, highlighting
the close relationship between chimera and cluster states as belonging to the
broader phenomenon of partial synchronization. Our approach is general in terms
of network size and connectivity. We also find that chimera states often appear
in regions of multistability between global, cluster, and desynchronized
states
Vertex-Unfoldings of Simplicial Polyhedra
We present two algorithms for unfolding the surface of any polyhedron, all of
whose faces are triangles, to a nonoverlapping, connected planar layout. The
surface is cut only along polyhedron edges. The layout is connected, but it may
have a disconnected interior: the triangles are connected at vertices, but not
necessarily joined along edges.Comment: 10 pages; 7 figures; 8 reference
Continuous Blooming of Convex Polyhedra
We construct the first two continuous bloomings of all convex polyhedra.
First, the source unfolding can be continuously bloomed. Second, any unfolding
of a convex polyhedron can be refined (further cut, by a linear number of cuts)
to have a continuous blooming.Comment: 13 pages, 6 figure
Recommendations and illustrations for the evaluation of photonic random number generators
The never-ending quest to improve the security of digital information
combined with recent improvements in hardware technology has caused the field
of random number generation to undergo a fundamental shift from relying solely
on pseudo-random algorithms to employing optical entropy sources. Despite these
significant advances on the hardware side, commonly used statistical measures
and evaluation practices remain ill-suited to understand or quantify the
optical entropy that underlies physical random number generation. We review the
state of the art in the evaluation of optical random number generation and
recommend a new paradigm: quantifying entropy generation and understanding the
physical limits of the optical sources of randomness. In order to do this, we
advocate for the separation of the physical entropy source from deterministic
post-processing in the evaluation of random number generators and for the
explicit consideration of the impact of the measurement and digitization
process on the rate of entropy production. We present the Cohen-Procaccia
estimate of the entropy rate as one way to do this. In order
to provide an illustration of our recommendations, we apply the Cohen-Procaccia
estimate as well as the entropy estimates from the new NIST draft standards for
physical random number generators to evaluate and compare three common optical
entropy sources: single photon time-of-arrival detection, chaotic lasers, and
amplified spontaneous emission
Time-shift selection for reservoir computing using a rank-revealing QR algorithm
Reservoir computing, a recurrent neural network paradigm in which only the
output layer is trained, has demonstrated remarkable performance on tasks such
as prediction and control of nonlinear systems. Recently, it was demonstrated
that adding time-shifts to the signals generated by a reservoir can provide
large improvements in performance accuracy. In this work, we present a
technique to choose the time-shifts by maximizing the rank of the reservoir
matrix using a rank-revealing QR algorithm. This technique, which is not task
dependent, does not require a model of the system, and therefore is directly
applicable to analog hardware reservoir computers. We demonstrate our
time-shift selection technique on two types of reservoir computer: one based on
an opto-electronic oscillator and the traditional recurrent network with a
activation function. We find that our technique provides improved
accuracy over random time-shift selection in essentially all cases
Synchronizing Chaos using Reservoir Computing
We attempt to achieve isochronal synchronization between a drive system
unidirectionally coupled to a response system, under the assumption that
limited knowledge on the states of the drive is available at the response.
Machine learning techniques have been previously implemented to estimate the
states of a dynamical system from limited measurements. We consider situations
in which knowledge of the non-measurable states of the drive system is needed
in order for the response system to synchronize with the drive. We use a
reservoir computer to estimate the non-measurable states of the drive system
from its measured states and then employ these measured states to synchronize
the response system with the drive
Characterizing Switching and Congruency Effects In the Implicit Association Test as Reactive and Proactive Cognitive Control
Recent research has identified an important role for task switching, a cognitive control process often associated with executive functioning, in the Implicit Association Test (IAT). However, switching does not fully account for IAT effects, particularly when performance is scored using more recent d-score formulations. The current study sought to characterize multiple control processes involved in IAT performance through the use of event-related brain potentials (ERPs). Participants performed a race-evaluative IAT while ERPs were recorded. Behaviorally, participants experienced superadditive reaction time costs of incongruency and task switching, consistent with previous studies. The ERP showed a marked medial frontal negativity (MFN) 250–450 ms post-stimulus at midline fronto-central locations that were more negative for incongruent than congruent trials but more positive for switch than for no-switch trials, suggesting separable control processes are engaged by these two factors. Greater behavioral IAT bias was associated with both greater switch-related and congruency-related ERP activity. Findings are discussed in terms of the Dual Mechanisms of Control model of reactive and proactive cognitive control
- …