713 research outputs found
Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems
We report an approach based upon vertical cavity surface emitting lasers (VCSELs) to reproduce optically different behaviors exhibited by biological neurons but on a much faster timescale. The technique proposed is based on the polarization switching and nonlinear dynamics induced in a single VCSEL under polarized optical injection. The particular attributes of VCSELs and the simple experimental configuration used in this work offer prospects of fast, reconfigurable processing elements with excellent fan-out and scaling potentials for use in future computational paradigms and artificial neural networks. © 2012 American Institute of Physics
Optimizing periodicity and polymodality in noise-induced genetic oscillators
Many cellular functions are based on the rhythmic organization of biological
processes into self-repeating cascades of events. Some of these periodic
processes, such as the cell cycles of several species, exhibit conspicuous
irregularities in the form of period skippings, which lead to polymodal
distributions of cycle lengths. A recently proposed mechanism that accounts for
this quantized behavior is the stabilization of a Hopf-unstable state by
molecular noise. Here we investigate the effect of varying noise in a model
system, namely an excitable activator-repressor genetic circuit, that displays
this noise-induced stabilization effect. Our results show that an optimal noise
level enhances the regularity (coherence) of the cycles, in a form of coherence
resonance. Similar noise levels also optimize the multimodal nature of the
cycle lengths. Together, these results illustrate how molecular noise within a
minimal gene regulatory motif confers robust generation of polymodal patterns
of periodicity.Comment: 9 pages, 6 figure
The Dynamics of Hybrid Metabolic-Genetic Oscillators
The synthetic construction of intracellular circuits is frequently hindered
by a poor knowledge of appropriate kinetics and precise rate parameters. Here,
we use generalized modeling (GM) to study the dynamical behavior of topological
models of a family of hybrid metabolic-genetic circuits known as
"metabolators." Under mild assumptions on the kinetics, we use GM to
analytically prove that all explicit kinetic models which are topologically
analogous to one such circuit, the "core metabolator," cannot undergo Hopf
bifurcations. Then, we examine more detailed models of the metabolator.
Inspired by the experimental observation of a Hopf bifurcation in a
synthetically constructed circuit related to the core metabolator, we apply GM
to identify the critical components of the synthetically constructed
metabolator which must be reintroduced in order to recover the Hopf
bifurcation. Next, we study the dynamics of a re-wired version of the core
metabolator, dubbed the "reverse" metabolator, and show that it exhibits a
substantially richer set of dynamical behaviors, including both local and
global oscillations. Prompted by the observation of relaxation oscillations in
the reverse metabolator, we study the role that a separation of genetic and
metabolic time scales may play in its dynamics, and find that widely separated
time scales promote stability in the circuit. Our results illustrate a generic
pipeline for vetting the potential success of a potential circuit design,
simply by studying the dynamics of the corresponding generalized model
Conedy: a scientific tool to investigate Complex Network Dynamics
We present Conedy, a performant scientific tool to numerically investigate
dynamics on complex networks. Conedy allows to create networks and provides
automatic code generation and compilation to ensure performant treatment of
arbitrary node dynamics. Conedy can be interfaced via an internal script
interpreter or via a Python module
Numerical Solution of Differential Equations by the Parker-Sochacki Method
A tutorial is presented which demonstrates the theory and usage of the
Parker-Sochacki method of numerically solving systems of differential
equations. Solutions are demonstrated for the case of projectile motion in air,
and for the classical Newtonian N-body problem with mutual gravitational
attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a
university web site, but has now been cited and praised in one or more
refereed journals. I am therefore submitting it to the Cornell arXiv so that
it may be read in response to its citations. See "Spiking neural network
simulation: numerical integration with the Parker-Sochacki method:" J. Comput
Neurosci, Robert D. Stewart & Wyeth Bair and
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
We study the effects of network topology on the response of networks of
coupled discrete excitable systems to an external stochastic stimulus. We
extend recent results that characterize the response in terms of spectral
properties of the adjacency matrix by allowing distributions in the
transmission delays and in the number of refractory states, and by developing a
nonperturbative approximation to the steady state network response. We confirm
our theoretical results with numerical simulations. We find that the steady
state response amplitude is inversely proportional to the duration of
refractoriness, which reduces the maximum attainable dynamic range. We also
find that transmission delays alter the time required to reach steady state.
Importantly, neither delays nor refractoriness impact the general prediction
that criticality and maximum dynamic range occur when the largest eigenvalue of
the adjacency matrix is unity
Higher order approximation of isochrons
Phase reduction is a commonly used techinque for analyzing stable
oscillators, particularly in studies concerning synchronization and phase lock
of a network of oscillators. In a widely used numerical approach for obtaining
phase reduction of a single oscillator, one needs to obtain the gradient of the
phase function, which essentially provides a linear approximation of isochrons.
In this paper, we extend the method for obtaining partial derivatives of the
phase function to arbitrary order, providing higher order approximations of
isochrons. In particular, our method in order 2 can be applied to the study of
dynamics of a stable oscillator subjected to stochastic perturbations, a topic
that will be discussed in a future paper. We use the Stuart-Landau oscillator
to illustrate the method in order 2
Episodic synchronization in dynamically driven neurons
We examine the response of type II excitable neurons to trains of synaptic
pulses, as a function of the pulse frequency and amplitude. We show that the
resonant behavior characteristic of type II excitability, already described for
harmonic inputs, is also present for pulsed inputs. With this in mind, we study
the response of neurons to pulsed input trains whose frequency varies
continuously in time, and observe that the receiving neuron synchronizes
episodically to the input pulses, whenever the pulse frequency lies within the
neuron's locking range. We propose this behavior as a mechanism of rate-code
detection in neuronal populations. The results are obtained both in numerical
simulations of the Morris-Lecar model and in an electronic implementation of
the FitzHugh-Nagumo system, evidencing the robustness of the phenomenon.Comment: 7 pages, 8 figure
Identifying dynamical systems with bifurcations from noisy partial observation
Dynamical systems are used to model a variety of phenomena in which the
bifurcation structure is a fundamental characteristic. Here we propose a
statistical machine-learning approach to derive lowdimensional models that
automatically integrate information in noisy time-series data from partial
observations. The method is tested using artificial data generated from two
cell-cycle control system models that exhibit different bifurcations, and the
learned systems are shown to robustly inherit the bifurcation structure.Comment: 16 pages, 6 figure
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
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