23 research outputs found
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
A chimera state is a spatio-temporal pattern in a network of identical
coupled oscillators in which synchronous and asynchronous oscillation coexist.
This state of broken symmetry, which usually coexists with a stable spatially
symmetric state, has intrigued the nonlinear dynamics community since its
discovery in the early 2000s. Recent experiments have led to increasing
interest in the origin and dynamics of these states. Here we review the history
of research on chimera states and highlight major advances in understanding
their behaviour.Comment: 26 pages, 3 figure
Basins of Attraction for Chimera States
Chimera states---curious symmetry-broken states in systems of identical
coupled oscillators---typically occur only for certain initial conditions. Here
we analyze their basins of attraction in a simple system comprised of two
populations. Using perturbative analysis and numerical simulation we evaluate
asymptotic states and associated destination maps, and demonstrate that basins
form a complex twisting structure in phase space. Understanding the basins'
precise nature may help in the development of control methods to switch between
chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including
description (PDF
A model balancing cooperation and competition explains our right-handed world and the dominance of left-handed athletes
An overwhelming majority of humans are right-handed. Numerous explanations
for individual handedness have been proposed, but this population-level
handedness remains puzzling. Here we use a minimal mathematical model to
explain this population-level hand preference as an evolved balance between
cooperative and competitive pressures in human evolutionary history. We use
selection of elite athletes as a test-bed for our evolutionary model and
account for the surprising distribution of handedness in many professional
sports. Our model predicts strong lateralization in social species with limited
combative interaction, and elucidates the rarity of compelling evidence for
"pawedness" in the animal world.Comment: 5 pages of text and 3 figures in manuscript, 8 pages of text and two
figures in supplementary materia
Chimera states in networks of phase oscillators: the case of two small populations
Chimera states are dynamical patterns in networks of coupled oscillators in
which regions of synchronous and asynchronous oscillation coexist. Although
these states are typically observed in large ensembles of oscillators and
analyzed in the continuum limit, chimeras may also occur in systems with finite
(and small) numbers of oscillators. Focusing on networks of phase
oscillators that are organized in two groups, we find that chimera states,
corresponding to attracting periodic orbits, appear with as few as two
oscillators per group and demonstrate that for the bifurcations that
create them are analogous to those observed in the continuum limit. These
findings suggest that chimeras, which bear striking similarities to dynamical
patterns in nature, are observable and robust in small networks that are
relevant to a variety of real-world systems.Comment: 13 pages, 16 figure
Model reconstruction from temporal data for coupled oscillator networks
© 2019 Author(s). In a complex system, the interactions between individual agents often lead to emergent collective behavior such as spontaneous synchronization, swarming, and pattern formation. Beyond the intrinsic properties of the agents, the topology of the network of interactions can have a dramatic influence over the dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network and attempt to learn about the dynamics of the model. Here, we consider the inverse problem: given data from a system, can one learn about the model and the underlying network? We investigate arbitrary networks of coupled phase oscillators that can exhibit both synchronous and asynchronous dynamics. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, machine learning can reconstruct the interaction network and identify the intrinsic dynamics
Can Subjective Pain Be Inferred From Objective Physiological Data? Evidence From Patients With Sickle Cell Disease
Patients with sickle cell disease (SCD) experience lifelong struggles with both chronic and acute pain, often requiring medical interventMaion. Pain can be managed with medications, but dosages must balance the goal of pain mitigation against the risks of tolerance, addiction and other adverse effects. Setting appropriate dosages requires knowledge of a patient\u27s subjective pain, but collecting pain reports from patients can be difficult for clinicians and disruptive for patients, and is only possible when patients are awake and communicative. Here we investigate methods for estimating SCD patients\u27 pain levels indirectly using vital signs that are routinely collected and documented in medical records. Using machine learning, we develop both sequential and non-sequential probabilistic models that can be used to infer pain levels or changes in pain from sequences of these physiological measures. We demonstrate that these models outperform null models and that objective physiological data can be used to inform estimates for subjective pain. Author summary: Understanding subjective human pain remains a major challenge. If objective data could be used in place of reported pain levels, it could reduce patient burdens and enable the collection of much larger data sets that could deepen our understanding of causes of pain and allow for accurate forecasting and more effective pain management. Here we apply two machine learning approaches to data from patients with sickle cell disease, who often experience debilitating pain crises. Using vital sign data routinely collected in hospital settings including respiratory rate, heart rate, and blood pressure and amidst the real-world challenges of irregular timing, missing data, and inter-patient variation, we demonstrate that these models outperform baseline models in estimating subjective pain, distinguishing between typical and atypical pain levels, and detecting changes in pain. Once trained, these types of models could be used to improve pain estimates in real time in the absence of direct pain reports
Model reconstruction from temporal data for coupled oscillator networks
In a complex system, the interactions between individual agents often lead to
emergent collective behavior like spontaneous synchronization, swarming, and
pattern formation. The topology of the network of interactions can have a
dramatic influence over those dynamics. In many studies, researchers start with
a specific model for both the intrinsic dynamics of each agent and the
interaction network, and attempt to learn about the dynamics that can be
observed in the model. Here we consider the inverse problem: given the dynamics
of a system, can one learn about the underlying network? We investigate
arbitrary networks of coupled phase-oscillators whose dynamics are
characterized by synchronization. We demonstrate that, given sufficient
observational data on the transient evolution of each oscillator, one can use
machine learning methods to reconstruct the interaction network and
simultaneously identify the parameters of a model for the intrinsic dynamics of
the oscillators and their coupling.Comment: 27 pages, 7 figures, 16 table
Inferring school district learning modalities during the COVID-19 pandemic with a hidden Markov model
In this study, learning modalities offered by public schools across the
United States were investigated to track changes in the proportion of schools
offering fully in-person, hybrid and fully remote learning over time. Learning
modalities from 14,688 unique school districts from September 2020 to June 2021
were reported by Burbio, MCH Strategic Data, the American Enterprise
Institute's Return to Learn Tracker and individual state dashboards. A model
was needed to combine and deconflict these data to provide a more complete
description of modalities nationwide.
A hidden Markov model (HMM) was used to infer the most likely learning
modality for each district on a weekly basis. This method yielded higher
spatiotemporal coverage than any individual data source and higher agreement
with three of the four data sources than any other single source. The model
output revealed that the percentage of districts offering fully in-person
learning rose from 40.3% in September 2020 to 54.7% in June of 2021 with
increases across 45 states and in both urban and rural districts. This type of
probabilistic model can serve as a tool for fusion of incomplete and
contradictory data sources in support of public health surveillance and
research efforts.Comment: 25 pages, 4 figure