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Person-Specific Methods for Characterizing the Course and Temporal Dynamics of Concussion Symptomatology: A Pilot Study.
Better characterization of acute concussion symptomatology is needed in order to advance clinical and scientific understanding of persistent concussion symptoms. This paper aims to illustrate a novel framework for conceptualizing, collecting, and analyzing concussion symptom data. To that end, we describe the temporal and structural dynamics of acute concussion symptoms at the individual-patient level. Ten recently concussion adolescents and young adults completed 20 days of ecological momentary assessment (EMA) of post-concussion symptoms. Follow-up assessments were completed at 3 months post-injury. Network modeling revealed marked heterogeneity across participants. In the overall sample, temporal patterns explained the most variance in light sensitivity (48%) and the least variance in vomiting (5%). About half of the participants had symptom networks that were sparse after controlling for temporal variation. The other individualized symptom networks were densely interconnected clusters of symptoms. Networks were highly idiosyncratic in nature, yet emotional symptoms (nervousness, emotional, sadness), cognitive symptoms (mental fogginess, slowness), and symptoms of hyperacusis (sensitivity to light, sensitivity to noise) tended to cluster together across participants. Person-specific analytic techniques revealed a number of idiosyncratic features of post-concussion symptomatology. We propose applying this framework to future research to better understand individual differences in concussion recovery
Scaling Green-Kubo relation and application to three aging systems
The Green-Kubo formula relates the spatial diffusion coefficient to the
stationary velocity autocorrelation function. We derive a generalization of the
Green-Kubo formula valid for systems with long-range or nonstationary
correlations for which the standard approach is no longer valid. For the
systems under consideration, the velocity autocorrelation function asymptotically exhibits a certain scaling behavior and
the diffusion is anomalous . We
show how both the anomalous diffusion coefficient and exponent
can be extracted from this scaling form. Our scaling Green-Kubo relation thus
extends an important relation between transport properties and correlation
functions to generic systems with scale invariant dynamics. This includes
stationary systems with slowly decaying power law correlations as well as aging
systems, whose properties depend on the the age of the system. Even for systems
that are stationary in the long time limit, we find that the long time
diffusive behavior can strongly depend on the initial preparation of the
system. In these cases, the diffusivity is not unique and we
determine its values for a stationary respectively nonstationary initial state.
We discuss three applications of the scaling Green-Kubo relation: Free
diffusion with nonlinear friction corresponding to cold atoms diffusing in
optical lattices, the fractional Langevin equation with external noise recently
suggested to model active transport in cells and the L\'evy walk with numerous
applications, in particular blinking quantum dots. These examples underline the
wide applicability of our approach, which is able to treat very different
mechanisms of anomalous diffusion.Comment: 16 pages, 6 figures, 1 tabl
Improvement of speech recognition by nonlinear noise reduction
The success of nonlinear noise reduction applied to a single channel
recording of human voice is measured in terms of the recognition rate of a
commercial speech recognition program in comparison to the optimal linear
filter. The overall performance of the nonlinear method is shown to be
superior. We hence demonstrate that an algorithm which has its roots in the
theory of nonlinear deterministic dynamics possesses a large potential in a
realistic application.Comment: see urbanowicz.org.p
Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model
Bayesian calibration of computer models tunes unknown input parameters by
comparing outputs with observations. For model outputs that are distributed
over space, this becomes computationally expensive because of the output size.
To overcome this challenge, we employ a basis representation of the model
outputs and observations: we match these decompositions to carry out the
calibration efficiently. In the second step, we incorporate the non-stationary
behaviour, in terms of spatial variations of both variance and correlations, in
the calibration. We insert two integrated nested Laplace
approximation-stochastic partial differential equation parameters into the
calibration. A synthetic example and a climate model illustration highlight the
benefits of our approach
Cointegration and common factors
Alternative common factors representations for cointegrated vectors are studied. It is shown that dynamic factor models produce as particular cases the alternative common trend representations for cointegrated variables available in the literature, including the one of Stock and Watson(1988). Furthermore, it is proved that common factor representations with I(1) components imply cointegration. A more efficient procedure for fmding the numbers of cointegrated vectors based on this dynamic factors model is suggested
The Effect of Nonstationarity on Models Inferred from Neural Data
Neurons subject to a common non-stationary input may exhibit a correlated
firing behavior. Correlations in the statistics of neural spike trains also
arise as the effect of interaction between neurons. Here we show that these two
situations can be distinguished, with machine learning techniques, provided the
data are rich enough. In order to do this, we study the problem of inferring a
kinetic Ising model, stationary or nonstationary, from the available data. We
apply the inference procedure to two data sets: one from salamander retinal
ganglion cells and the other from a realistic computational cortical network
model. We show that many aspects of the concerted activity of the salamander
retinal neurons can be traced simply to the external input. A model of
non-interacting neurons subject to a non-stationary external field outperforms
a model with stationary input with couplings between neurons, even accounting
for the differences in the number of model parameters. When couplings are added
to the non-stationary model, for the retinal data, little is gained: the
inferred couplings are generally not significant. Likewise, the distribution of
the sizes of sets of neurons that spike simultaneously and the frequency of
spike patterns as function of their rank (Zipf plots) are well-explained by an
independent-neuron model with time-dependent external input, and adding
connections to such a model does not offer significant improvement. For the
cortical model data, robust couplings, well correlated with the real
connections, can be inferred using the non-stationary model. Adding connections
to this model slightly improves the agreement with the data for the probability
of synchronous spikes but hardly affects the Zipf plot.Comment: version in press in J Stat Mec
Qubit quantum-dot sensors: noise cancellation by coherent backaction, initial slips, and elliptical precession
We theoretically investigate the backaction of a sensor quantum dot with
strong local Coulomb repulsion on the transient dynamics of a qubit that is
probed capacitively. We show that the measurement backaction induced by the
noise of electron cotunneling through the sensor is surprisingly mitigated by
the recently identified coherent backaction [PRB 89, 195405] arising from
quantum fluctuations. This renormalization effect is missing in semiclassical
stochastic fluctuator models and typically also in Born-Markov approaches,
which try to avoid the calculation of the nonstationary, nonequilibrium state
of the qubit plus sensor. Technically, we integrate out the current-carrying
electrodes to obtain kinetic equations for the joint, nonequilibrium
detector-qubit dynamics. We show that the sensor-current response, level
renormalization, cotunneling, and leading non-Markovian corrections always
appear together and cannot be turned off individually in an experiment or
ignored theoretically. We analyze the backaction on the reduced qubit state -
capturing the full non-Markovian effects imposed by the sensor quantum dot on
the qubit - by applying a Liouville-space decomposition into quasistationary
and rapidly decaying modes. Importantly, the sensor cannot be eliminated
completely even in the simplest high-temperature, weak-measurement limit: The
qubit state experiences an initial slip that persists over many qubit cycles
and depends on the initial preparation of qubit plus sensor quantum dot. A
quantum-dot sensor can thus not be modeled as a 'black box' without accounting
for its dynamical variables. We furthermore find that the Bloch vector relaxes
(T1) along an axis that is not orthogonal to the plane in which the Bloch
vector dephases (T2), blurring the notions of T1 and T2 times. Finally, the
precessional motion of the Bloch vector is distorted into an ellipse in the
tilted dephasing plane.Comment: This is the version published in Phys. Rev.
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