85 research outputs found
Effective phase description of noise-perturbed and noise-induced oscillations
An effective description of a general class of stochastic phase oscillators
is presented. For this, the effective phase velocity is defined either by
invariant probability density or via first passage times. While the first
approach exhibits correct frequency and distribution density, the second one
yields proper phase resetting curves. Their discrepancy is most pronounced for
noise-induced oscillations and is related to non-monotonicity of the phase
fluctuations
Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern Generators
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare´ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control
Automated scoring of pre-REM sleep in mice with deep learning
Reliable automation of the labor-intensive manual task of scoring animal
sleep can facilitate the analysis of long-term sleep studies. In recent years,
deep-learning-based systems, which learn optimal features from the data,
increased scoring accuracies for the classical sleep stages of Wake, REM, and
Non-REM. Meanwhile, it has been recognized that the statistics of transitional
stages such as pre-REM, found between Non-REM and REM, may hold additional
insight into the physiology of sleep and are now under vivid investigation. We
propose a classification system based on a simple neural network architecture
that scores the classical stages as well as pre-REM sleep in mice. When
restricted to the classical stages, the optimized network showed
state-of-the-art classification performance with an out-of-sample F1 score of
0.95 in male C57BL/6J mice. When unrestricted, the network showed lower F1
scores on pre-REM (0.5) compared to the classical stages. The result is
comparable to previous attempts to score transitional stages in other species
such as transition sleep in rats or N1 sleep in humans. Nevertheless, we
observed that the sequence of predictions including pre-REM typically
transitioned from Non-REM to REM reflecting sleep dynamics observed by human
scorers. Our findings provide further evidence for the difficulty of scoring
transitional sleep stages, likely because such stages of sleep are
under-represented in typical data sets or show large inter-scorer variability.
We further provide our source code and an online platform to run predictions
with our trained network.Comment: 14 pages, 5 figure
Optimal Phase Description of Chaotic Oscillators
We introduce an optimal phase description of chaotic oscillations by
generalizing the concept of isochrones. On chaotic attractors possessing a
general phase description, we define the optimal isophases as Poincar\'e
surfaces showing return times as constant as possible. The dynamics of the
resultant optimal phase is maximally decoupled of the amplitude dynamics, and
provides a proper description of phase resetting of chaotic oscillations. The
method is illustrated with the R\"ossler and Lorenz systems.Comment: 10 Pages, 14 Figure
- …