816 research outputs found
Reconstructing networks of pulse-coupled oscillators from spike trains
We present an approach for reconstructing networks of pulse-coupled
neuron-like oscillators from passive observation of pulse trains of all nodes.
It is assumed that units are described by their phase response curves and that
their phases are instantaneously reset by incoming pulses. Using an iterative
procedure, we recover the properties of all nodes, namely their phase response
curves and natural frequencies, as well as strengths of all directed
connections.Comment: 7 pages, 7 figure
On the equivalence of phase-oscillator and integrate-and-fire models
A quantitative comparison of various classes of oscillators
(integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the
weak-coupling limit for a fully connected network of identical units. An almost
perfect agreement is found, with only tiny differences among the models. We
also show that the regime of self-consistent partial synchronization [SCPS] is
rather general and can be observed for arbitrarily small coupling strength in
any model class. As a by-product of our study, we are able to show that an
integrate-and-fire model with a generic pulse shape can be always transformed
into a similar model with -pulses and a suitable phase response curve.Comment: 28 pages; 8 figures - accepted in PR
Inferring the phase response curve from observation of a continuously perturbed oscillator
Phase response curves are important for analysis and modeling of oscillatory
dynamics in various applications, particularly in neuroscience. Standard
experimental technique for determining them requires isolation of the system
and application of a specifically designed input. However, isolation is not
always feasible and we are compelled to observe the system in its natural
environment under free-running conditions. To that end we propose an approach
relying only on passive observations of the system and its input. We illustrate
it with simulation results of an oscillator driven by a stochastic force.Comment: 11 pages (+6 supplementary), 7 figures (+8 supplementary
Targeted Maximum Likelihood Estimation using Exponential Families
Targeted maximum likelihood estimation (TMLE) is a general method for
estimating parameters in semiparametric and nonparametric models. Each
iteration of TMLE involves fitting a parametric submodel that targets the
parameter of interest. We investigate the use of exponential families to define
the parametric submodel. This implementation of TMLE gives a general approach
for estimating any smooth parameter in the nonparametric model. A computational
advantage of this approach is that each iteration of TMLE involves estimation
of a parameter in an exponential family, which is a convex optimization problem
for which software implementing reliable and computationally efficient methods
exists. We illustrate the method in three estimation problems, involving the
mean of an outcome missing at random, the parameter of a median regression
model, and the causal effect of a continuous exposure, respectively. We conduct
a simulation study comparing different choices for the parametric submodel,
focusing on the first of these problems. To the best of our knowledge, this is
the first study investigating robustness of TMLE to different specifications of
the parametric submodel. We find that the choice of submodel can have an
important impact on the behavior of the estimator in finite samples
Reconstructing phase dynamics of oscillator networks
We generalize our recent approach to reconstruction of phase dynamics of
coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205
(2008)] to cover the case of small networks of coupled periodic units. Starting
from the multivariate time series, we first reconstruct genuine phases and then
obtain the coupling functions in terms of these phases. The partial norms of
these coupling functions quantify directed coupling between oscillators. We
illustrate the method by different network motifs for three coupled oscillators
and for random networks of five and nine units. We also discuss nonlinear
effects in coupling.Comment: 6 pages, 5 figures, 27 reference
interAdapt -- An Interactive Tool for Designing and Evaluating Randomized Trials with Adaptive Enrollment Criteria
The interAdapt R package is designed to be used by statisticians and clinical
investigators to plan randomized trials. It can be used to determine if certain
adaptive designs offer tangible benefits compared to standard designs, in the
context of investigators' specific trial goals and constraints. Specifically,
interAdapt compares the performance of trial designs with adaptive enrollment
criteria versus standard (non-adaptive) group sequential trial designs.
Performance is compared in terms of power, expected trial duration, and
expected sample size. Users can either work directly in the R console, or with
a user-friendly shiny application that requires no programming experience.
Several added features are available when using the shiny application. For
example, the application allows users to immediately download the results of
the performance comparison as a csv-table, or as a printable, html-based
report.Comment: 14 pages, 2 figures (software screenshots); v2 includes command line
function descriptio
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