scholarly journals Using phase dynamics to study partial synchrony: three examples

2021 ◽  
Author(s):  
Erik Teichmann
Keyword(s):  
Weak Coupling ◽  
Phase Response Curve ◽  
Mean Field ◽  
Weak Coupling Limit ◽  
Kuramoto Model ◽  
Phase Approximation ◽  
Phase Dynamics ◽  
First Order ◽  
Oscillatory Systems ◽  
Partial Synchrony

AbstractPartial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

scholarly journals An obstacle to sub-AdS holography for SYK-like models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang ◽  
Yingfei Gu ◽  
Alexei Kitaev
Keyword(s):  
Lyapunov Exponent ◽  
Weak Coupling ◽  
Kinetic Coefficient ◽  
Weak Coupling Limit ◽  
Branching Time ◽  
Quasiparticle Lifetime

Abstract We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

A Nonstationary Hidden Markov Model with Approximately Infinitely-Long Time-Dependencies

2016 ◽  
Vol 25 (05) ◽  
pp. 1640001 ◽  
Author(s):  
Sotirios Chatzis ◽  
Dimitrios Kosmopoulos ◽  
George Papadourakis
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Mean Field ◽  
Sequential Data ◽  
First Order ◽  
Order Markov Chain ◽  
Inference Algorithms ◽  
Unrealistic Assumption ◽  
Long Time ◽  
Time Dependencies

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first-order Markov chain. In other words, only one-step back dependencies are modeled which is a rather unrealistic assumption in most applications. In this paper, we propose a method for postulating HMMs with approximately infinitely-long time-dependencies. Our approach considers the whole history of model states in the postulated dependencies, by making use of a recently proposed nonparametric Bayesian method for modeling label sequences with infinitely-long time dependencies, namely the sequence memoizer. We manage to derive training and inference algorithms for our model with computational costs identical to simple first-order HMMs, despite its entailed infinitely-long time-dependencies, by employing a mean-field-like approximation. The efficacy of our proposed model is experimentally demonstrated.

ENERGY BAND OVERLAPPING IN HIGH-Tc SUPERCONDUCTORS

1996 ◽  
Vol 10 (30) ◽  
pp. 1483-1490 ◽  
Author(s):  
M. MORENO ◽  
R. M. MÉNDEZ-MORENO ◽  
M. A. ORTIZ ◽  
S. OROZCO
Keyword(s):  
Weak Coupling ◽  
Cuprate Superconductors ◽  
Weak Coupling Limit ◽  
Band Model ◽  
Coupling Constant ◽  
High Tc Superconductors ◽  
Energy Bands ◽  
Effective Coupling ◽  
High Tc ◽  
Two Band Model

Multi-band superconductors are analyzed and the relevance of overlapping energy bands to the high-T c of these materials is studied. Within the BCS framework, a two band model with generalized Fermi surface topologies is developed. Values of the overlapped occupancy parameters for typical cuprate superconductors are obtained as a function of the ratio R and the effective coupling constant, λ, in the weak-coupling limit. The overlap scale is of the order or lower than the cutoff (Debye) energy. The typical behavior of the isotope effect is obtained. As these superconductors have transition temperatures above the phonon barrier, the results of this approach are important to the generic understanding of the high-T c superconducting mechanism.

scholarly journals Investigation of Preferred Orientations in Planar Polycrystals

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
M. R. Tonks ◽  
A. J. Beaudoin ◽  
F. Schilder ◽  
D. A. Tortorelli
Keyword(s):  
Texture Evolution ◽  
Mean Field ◽  
Homogenization Method ◽  
Process Models ◽  
Kuramoto Model ◽  
Taylor Model ◽  
Crystal Plasticity Finite Element ◽  
Polycrystal Plasticity ◽  
Taylor Hypothesis ◽  
The Kuramoto Model

More accurate manufacturing process models come from better understanding of texture evolution and preferred orientations. We investigate the texture evolution in the simplified physical framework of a planar polycrystal with two slip systems used by Prantil et al. (1993, “An Analysis of Texture and Plastic Spin for Planar Polycrystal,” J. Mech. Phys. Solids, 41(8), pp. 1357–1382). In the planar polycrystal, the crystal orientations behave in a manner similar to that of a system of coupled oscillators represented by the Kuramoto model. The crystal plasticity finite element method and the stochastic Taylor model (STM), a stochastic method for mean-field polycrystal plasticity, predict the development of a steady-state texture not shown when employing the Taylor hypothesis. From this analysis, the STM appears to be a useful homogenization method when using representative standard deviations.

Phosphofructokinase controls the acetaldehyde-induced phase shift in isolated yeast glycolytic oscillators

2019 ◽  
Vol 476 (2) ◽  
pp. 353-363
Author(s):  
David D. van Niekerk ◽  
Anna-Karin Gustavsson ◽  
Martin Mojica-Benavides ◽  
Caroline B. Adiels ◽  
Mattias Goksör ◽  
...  
Keyword(s):  
Phase Shift ◽  
Phase Response Curve ◽  
Mechanistic Model ◽  
Phase Response ◽  
Yeast Cells ◽  
Emergent Properties ◽  
Functional Coupling ◽  
External Signal ◽  
Oscillatory Systems ◽  
External Perturbations

Abstract The response of oscillatory systems to external perturbations is crucial for emergent properties such as synchronisation and phase locking and can be quantified in a phase response curve (PRC). In individual, oscillating yeast cells, we characterised experimentally the phase response of glycolytic oscillations for external acetaldehyde pulses and followed the transduction of the perturbation through the system. Subsequently, we analysed the control of the relevant system components in a detailed mechanistic model. The observed responses are interpreted in terms of the functional coupling and regulation in the reaction network. We find that our model quantitatively predicts the phase-dependent phase shift observed in the experimental data. The phase shift is in agreement with an adaptation leading to synchronisation with an external signal. Our model analysis establishes that phosphofructokinase plays a key role in the phase shift dynamics as shown in the PRC and adaptation time to external perturbations. Specific mechanism-based interventions, made possible through such analyses of detailed models, can improve upon standard trial and error methods, e.g. melatonin supplementation to overcome jet-lag, which are error-prone, specifically, since the effects are phase dependent and dose dependent. The models by Gustavsson and Goldbeter discussed in the text can be obtained from the JWS Online simulation database: (https://jjj.bio.vu.nl/models/gustavsson5 and https://jjj.bio.vu.nl/models/goldbeter1)

scholarly journals Estimation of Delay Times in Coupling Between Autonomic Regulatory Loops of Human Heart Rate and Blood Flow Using Phase Dynamics Analysis

2017 ◽  
Vol 9 (1) ◽  
pp. 16-22 ◽  
Author(s):  
Vladimir S Khorev ◽  
Anatoly S Karavaev ◽  
Elena E Lapsheva ◽  
Tatyana A Galushko ◽  
Mikhail D Prokhorov ◽  
...  
Keyword(s):  
Heart Rate ◽  
Delay Time ◽  
Healthy Subjects ◽  
Low Frequency ◽  
Phase Dynamics ◽  
Oscillatory Systems ◽  
Low Frequency Oscillations ◽  
Delay Times ◽  
The Difference ◽  
Regulatory Loop

Objective: We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations. Material and Methods: In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops. Results: Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds. Conclusion: Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

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