An isostable coordinate based amelioration strategy to mitigate the effects of Jet lag

Commercial air travel has become extremely commonplace in the last 20 to 30 years especially as the world has moved towards new heights of globalization. Though air travel has greatly reduced transit times allowing people to cover thousand of miles within hours, it comes with its fair share of issues. jet-lag can be regarded to be at the top of those list of problems; jet-lag typically results from rapid travel through multiple time zones which causes a significant misalignment between the person\u27s internal circadian clock and the external time. A person\u27s circadian clock is governed by a population of coupled neurons entrained to a 24-hour light and dark cycle and thus after rapid air travel, the neuron population needs a certain time to get accustomed to the new time zone. This misalignment can result in a variety of health problems including, but not limited to, lethargy, insomnia and adverse effects to the sleep cycle. Various techniques have been proposed and are currently in use for jet-lag treatment like melatonin ingestion or making drastic changes to one\u27s own routine prior to air travel. However, these treatment strategies are normally accompanied with long re-entrainment times or following a strict schedule to help with correcting the sleep cycle. The presented work explores an alternate strategy for jet-lag treatment using the notion of operational phase and isostable coordinates for model reduction and then, applying optimal control to derive inputs which can be applied directly to the model. To show the framework\u27s efficacy, results are presented by applying the strategy to a 2-d model; preliminary results show that the proposed approach greatly reduces the reentrainment time required to acclimatize to the new time zone

N-Body Oscillator Interactions of Higher-Order Coupling Functions

We introduce a method to identify phase equations that include $N$-body interactions for general coupled oscillators valid far beyond the weak coupling approximation. This strategy is an extension of the theory from [Park and Wilson, SIADS 20.3 (2021)] and yields coupling functions for $N\geq2$ oscillators for arbitrary types of coupling (e.g., diffusive, gap-junction, chemical synaptic). These coupling functions enable the study of oscillator networks in terms of phase-locked states, whose stability can be determined using straightforward linear stability arguments. We demonstrate the utility of our approach with two examples. First, we use $N=3$ diffusively coupled complex Ginzburg-Landau (CGL) model and show that the loss of stability in its splay state occurs through a Hopf bifurcation \yp{as a function of non-weak diffusive coupling. Our reduction also captures asymptotic limit-cycle dynamics in the phase differences}. Second, we use $N=3$ realistic conductance-based thalamic neuron models and show that our method correctly predicts a loss in stability of a splay state for non-weak synaptic coupling. In both examples, our theory accurately captures model behaviors that weak and recent non-weak coupling theories can not.Comment: 29 pages, 6 figure

A STUDY ON DYNAMIC SYSTEMS RESPONSE OF THE PERFORMANCE CHARACTERISTICS OF SOME MAJOR BIOPHYSICAL SYSTEMS

Dynamic responses of biophysical systems - performance characteristic

Structures of nonequilibrium fluctuations: dissipation and activity

We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation between the response of observables to a perturation and correlation functions in the unperturbed system. Our contribution here is an investigation of the form of the response function for systems out of equilibrium. Furthermore, we use the theory of large deviations to examine dynamical fluctuations in systems out of equilibrium. In dynamical fluctuation theory we consider two kinds of observables: occupations (describing the fraction of time the system spends in each configuration) and currents (describing the changes of configuration the system makes). We explain how to compute the rate functions of the large deviations, and what the physical quantities are that govern their form.Comment: PhD thesis (defended in may 2010

Tackling the Inverse Problem for Non-Autonomous Systems: Application to the Life Sciences.

The common assumption that a dynamical system found in nature can be considered as isolated and autonomous is frequently a poor approximation. In reality, there are always external influences, and these are often too strong to ignore. In the case of an interacting oscillatory systems, they may e.g. modify their natural frequencies or coupling amplitudes. The main objective of this thesis is to study, detect and understand in greater detail the effect of external dynamical influences on interacting self-sustained oscillators. Theoretical framework for the analysis of synchronization between non-autonomous oscillating systems is discussed. Multiple-scale analysis is applied on a phase oscillators model with slowly varying frequency. This analysis revealed the analytic form of the synchronization state with respect to slow and fast time-variations. Limit-cycle oscillators are used to study amplitude dynamics and to investigate synchronization transitions, which occur in the bifurcation points where the equilibrium solution for the phase difference and amplitudes changes their stability. Bifurcation diagrams as functions of coupling parameters are also constructed. In a case of non-autonomous interacting oscillators, the phase difference varies dynamically, the external influences can be the cause for synchronization transitions between different synchronization orders, and lag synchronization is hardly achievable. It is also demonstrated that the time-variations of the form of the coupling function alone can be the cause for synchronization transitions. A method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. The technique is based on Bayesian inference of the time-evolving parameters, achieved by shaping the prior densities to incorporate knowledge of previous samples. The dynamics can be inferred from phase variables, in which case a finite number of Fourier base functions are used, or from state variables exploiting the model state base functions. The latter is used for detection of generalized synchronization. The method is tested numerically and applied to reveal and quantify the time-varying nature of synchronization, directionality and coupling functions from cardiorespiratory and analogue signals. It is found that, in contrast to many systems with time-invariant coupling functions, the functional relations for the interactions of an open (biological) system can in itself be a time-varying process. The cardiorespiratory analysis demonstrated that not only the parameters, but also the functional relationships, can be time-varying, and the new technique can effectively follow their evolution. The proposed theory and methods are applied for the analysis of biological oscillatory systems affected by external dynamical influences. The main investigation is performed on physiological measurements under conditions where the breathing frequency is varied linearly in a deterministic way, which introduces non-autonomous time-variability into the oscillating system. Methods able to track time-varying characteristics are applied to signals from the cardiovascular, and the sympathetic neural systems. The time-varying breathing process significantly affected the functioning and regulation of several physiological mechanisms, demonstrating a clear imprint of the particular form of externally induced time-variation. Specifically, the low breathing frequencies provoked more information flow, interfering the coordination and increasing the coupling strength between the oscillatory processes. Statistical analyses are performed to identify significant relationships. The proposed inferential method is applied to cardiorespiratory signals of this kind. The technique successfully identified that the cardiorespiratory coordination depends on, and is regulated to a great extent by, the respiration dynamics. The time-varying respiration acted as a cause for synchronization transitions between different orders. Additional complexity is encountered by the coupling functions which are also identified as time-varying processes. A technique based on wavelet synchrosqueezed transform shows how the instantaneous phase can be extracted from complex mixed-mode signals with time-varying characteristics. The latter is demonstrated on several physiological signals of this kind. The dynamical characterization for the reproducibility of blood flow is shown to be more appropriate than the time-averaged analysis. This also implies that care must be taken when external perturbations are made consecutively. Finally, the study focuses on analysis of analogue simulation of two non-autonomous van der Pol oscillators. The oscillators are unidirectionally coupled, and the frequency of the first oscillator is externally and periodically perturbed. The analogue simulation presents another model which encounters real experimental noise. The intermittent synchronization and the corresponding transitions are detected both through phase, and generalized synchronization, based on a common inferential basis