Multiple Time Scale Dynamics Research Articles

Conductance-Based Refractory Density Approach for a Population of Bursting Neurons.

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modelling interacting populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study, we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting population model makes use of slow-fast analysis, which leads to a novel methodology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explorations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).

Dopaminergic Modulation of Synaptic Plasticity, Its Role in Neuropsychiatric Disorders, and Its Computational Modeling.

Neuromodulators modify intrinsic characteristics of the nervous system in order to reconfigure the functional properties of neural circuits. This reconfiguration is crucial for the flexibility of the nervous system to respond on an input-modulated basis. Such a functional rearrangement is realized by modification of intrinsic properties of the neural circuits including synaptic interactions. Dopamine is an important neuromodulator involved in motivation and stimulus-reward learning process, and adjusts synaptic dynamics in multiple time scales through different pathways. The modification of synaptic plasticity by dopamine underlies the change in synaptic transmission and integration mechanisms, which affects intrinsic properties of the neural system including membrane excitability, probability of neurotransmitters release, receptors’ response to neurotransmitters, protein trafficking, and gene transcription. Dopamine also plays a central role in behavioral control, whereas its malfunction can cause cognitive disorders. Impaired dopamine signaling is implicated in several neuropsychiatric disorders such as Parkinson’s disease, drug addiction, schizophrenia, attention-deficit/hyperactivity disorder, obsessive-compulsive disorder and Tourette’s syndrome. Therefore, dopamine plays a crucial role in the nervous system, where its proper modulation of neural circuits may enhance plasticity-related procedures, but disturbances in dopamine signaling might be involved in numerous neuropsychiatric disorders. In recent years, several computational models are proposed to formulate the involvement of dopamine in synaptic plasticity or neuropsychiatric disorders and address their connection based on the experimental findings.

Amplified Sensitivity of Nitrogen-Vacancy Spins in Nanodiamonds Using All-Optical Charge Readout.

Nanodiamonds containing nitrogen-vacancy (NV) centers offer a versatile platform for sensing applications spanning from nanomagnetism to in vivo monitoring of cellular processes. In many cases, however, weak optical signals and poor contrast demand long acquisition times that prevent the measurement of environmental dynamics. Here, we demonstrate the ability to perform fast, high-contrast optical measurements of charge distributions in ensembles of NV centers in nanodiamonds and use the technique to improve the spin-readout signal-to-noise ratio through spin-to-charge conversion. A study of 38 nanodiamonds with sizes ranging between 20 and 70 nm, each hosting a small ensemble of NV centers, uncovers complex, multiple time scale dynamics due to radiative and nonradiative ionization and recombination processes. Nonetheless, the NV-containing nanodiamonds universally exhibit charge-dependent photoluminescence contrasts and the potential for enhanced spin readout using spin-to-charge conversion. We use the technique to speed up a T1 relaxometry measurement by a factor of 5.

Understanding the free energy barrier and multiple timescale dynamics of charge separation in organic photovoltaic cells.

By employing several lattice model systems, we investigate the free energy barrier and real-time dynamics of charge separation in organic photovoltaic (OPV) cells. It is found that the combined effects of the external electric field, entropy, and charge delocalization reduce the free energy barrier significantly. The dynamic disorder reduces charge carrier delocalization and results in the increased charge separation barrier, while the effect of static disorder is more complicated. Simulation of the real-time dynamics indicates that the free charge generation process involves multiple time scales, including an ultrafast component within hundreds of femtoseconds, an intermediate component related to the relaxation of the hot charge transfer (CT) state, and a slow component on the time scale of tens of picoseconds from the thermally equilibrated CT state. Effects of hot exciton dissociation as well as its dependence on the energy offset between the Frenkel exciton and the CT state are also analyzed. The current results indicate that only a small energy offset between the band gap and the lowest energy CT state is needed to achieve efficient free charge generation in OPV devices, which agrees with recent experimental findings.

Reference tracking controller design for anesthesia

Abstract This paper addresses the problem of tracking a constant BIS reference during anesthesia taking into account control input saturation, multiple time scale dynamics and inter-patient variability. LMIs conditions are proposed to compute a state feedback involving an integral action to ensure a perfect output tracking. These conditions guarantee that the trajectories of the closed-loop system remain in an invariant ellipsoidal set. The theoretical conditions are numerically illustrated on a set of adult patients as a proof of principle.

Coupled Multiple Timescale Dynamics in Populations of Endocrine Neurons: Pulsatile and Surge Patterns of GnRH Secretion

The gonadotropin-releasing hormone (GnRH) is secreted by hypothalamic neurons into the pituitary portal blood in a pulsatile manner. The alternation between a frequency-modulated pulsatile regime and the ovulatory surge is the hallmark of the GnRH secretion pattern in ovarian cycles of female mammals. In this work, we aim at modeling additional features of the GnRH secretion pattern: the possible occurrence of a two-bump surge (``camel surge'') and an episode of partial desynchronization before the surge. We propose a six-dimensional extension of a former four-dimensional model with three timescales and introduce two mutually coupled, slightly heterogenous GnRH subpopulations (secretors) regulated by the same slow oscillator (regulator). We consider two types of coupling functions between the secretors, including dynamic state-dependent coupling, and we use numerical and analytic tools to characterize the coupling parameter values leading to the generation of a two-bump surge in both coupling cases. We reveal the impact of the slowly varying control exerted by the regulator onto the pulsatile dynamics of the secretors, which leads to dynamic bifurcations and gives rise to desynchronization. To assess the occurrence time of desynchronization during the pulsatile phase, we introduce asymptotic tools based on quasi-static and geometric approaches, as well as analytic tools based on the H-function derived from the phase equation and numerical tracking of period-doubling bifurcations. We discuss the role of coupling parameters in the two-bump surge generation and the speed of desynchronization.

Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking

The firing activities of multiple timescale dynamics for single neurons can be treated with fractional-order derivative. It has been shown in previous studies (theoretical and experimental) that the passive properties of membranes may be considered by fractional-order dynamics as it can produce various types of memory-dependent dynamics. Spiking and bursting play major role in information processing for cortical neurons. However, it is not completely clear to what extent the dynamics of fractional-order excitable systems may redesign the properties of excitable cells. It is demonstrated that the fractional dynamics of Izhikevich neuron model is capable to exhibit various oscillations for cortical neurons such as regular spiking and various bursting patterns, mixed mode oscillations, chattering, fast spiking. It characterizes various firing modes (hence the firing frequency) better than the classical-order model. It shows the dynamical differences between the integer-order and fractional-order system. The firing frequency is increased with the decrease of fractional exponents. Further, the responses of a network of excitatory and inhibitory Izhikevich neurons with a controlled parameter set show different dynamical behavior at various fractional orders and it controls the long-term interactions.

Quantitative Assessment on Multiple Timescale Features and Dynamics of Sea Surface Suspended Sediment Concentration Using Remote Sensing Data

AbstractWind‐waves, tidal currents, and some other dynamic factors dominate the suspended sediment concentration (SSC) variations in shallow seas and it is difficult to quantitatively evaluate the effects of individual dynamic factors on SSC modulation. This work used the long‐term Moderate Resolution Imaging Spectroradiometer (MODIS) and the high temporal‐resolution Geostationary Ocean Color Imager (GOCI) remote sensing data to quantify the sea surface SSC variations on multiple timescales (intratidal, spring‐neap, seasonal, and long‐term timescales) in the Bohai Sea, and further quantitatively evaluated the effects of corresponding dynamic factors on the SSC modulation. The results indicated that the monsoon associated wind‐waves and stratification played the most important role in modulating SSC, with seasonal SSC variation of 8.1 mg/L in the Bohai Sea. The intratidal current variations played the secondary important role, causing SSC variation of 5.8 mg/L. The spring‐neap tidal current variations led to SSC variation of 3.1 mg/L in the Bohai Sea. In the long run (2003–2014), the SSC of the Bohai Sea decreased slightly with SSC variation of 2.8 mg/L (decline rate: 0.23 mg/L/year), which may be caused by the weakening wind, decreasing sediment load from the Yellow River or the massive reclamation in recent decades. Probably due to the topography, sea bed sediment grain size and river plume, SSC variations in the southern Bohai Sea were more pronounced than those in the northern Bohai Sea.

Delay induced high order locking effects in semiconductor lasers.

Multiple time scales appear in many nonlinear dynamical systems. Semiconductor lasers, in particular, provide a fertile testing ground for multiple time scale dynamics. For solitary semiconductor lasers, the two fundamental time scales are the cavity repetition rate and the relaxation oscillation frequency which is a characteristic of the field-matter interaction in the cavity. Typically, these two time scales are of very different orders, and mutual resonances do not occur. Optical feedback endows the system with a third time scale: the external cavity repetition rate. This is typically much longer than the device cavity repetition rate and suggests the possibility of resonances with the relaxation oscillations. We show that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking. Two different laser types--a quantum dot based device and a quantum well based device-are analysed experimentally yielding qualitatively identical dynamics. A rate equation model is also employed showing an excellent agreement with the experimental results.

Time-optimal control for the induction phase of anesthesia

This paper deals with the control of the induction phase of anesthesia. The objective during this first phase is to bring the patient from its awake state to a final state corresponding to some given depth of anesthesia, measured by the BIS (Bispectral index), within a minimum time. This optimal time control strategy is addressed by means of the maximum principle of Pontryagin. Furthermore, since the anesthesia model presents multiple time scale dynamics that can be split in two groups : fast and slow and since the BIS is a direct function of the fast ones, we only consider the optimal control of fast states. The final state of the slow dynamics is let free. The synthesis approach of the optimal control is detailed then tested in the case of a nominal patient.

Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics

Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing.

A Multi-Timescale and Bilevel Coordination Approach for Matching Uncertain Wind Supply With EV Charging Demand

The matching between random wind supply and electric vehicle (EV) charging demand can reduce the requirement of traditional power sources and the emission of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . This problem is of great practical interest but involves system dynamics in multiple timescales. We consider this an important problem in this paper. In order to capture the randomness in the wind supply and EV charging demand, we formulate the problem as a bilevel Markov decision process. At the upper level, the charging demand of EVs in different locations is aggregated into multiple aggregators. The system operator dispatches power among the aggregators in a coarse timescale to maximize the wind power utilization. At the lower level, the aggregator schedules the charging process of individual EVs at a finer timescale to minimize the charging cost. In order to solve this large-scale problem, a bilevel simulation-based policy improvement (SBPI) method is developed. It is mathematically proved that the SBPI can improve from base policies in both levels. The performance of this multi-timescale and bilevel coordination approach is demonstrated through case studies in the city of Beijing.

Hamiltonian analogs of combustion engines: A systematic exception to adiabatic decoupling.

Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of adiabatic decoupling: the high-frequency modes "dress" the low-frequency modes, and renormalize their Hamiltonian, but they do not steadily inject energy into the low-frequency sector. Here, however, we identify a broad class of dynamical systems in which adiabatic decoupling fails to hold, and steady energy transfer across a large gap in natural frequency ("steady downconversion") instead becomes possible, through nonlinear resonances of a certain form. Instead of adiabatic decoupling, the special features of multiple time scale dynamics lead in these cases to efficiency constraints that somewhat resemble thermodynamics.

Data-Driven Dynamic Modeling of Coupled Thermal and Electric Outputs of Microturbines

Microturbines (MTs) are among the most successfully commercialized distributed energy resources, especially when they are used for combined heat and power generation. However, the interrelated thermal and electrical system dynamic behaviors have not been fully investigated. This is technically challenging due to the complex thermo-fluid-mechanical energy conversion processes, which introduce multiple time-scale dynamics and strong nonlinearity into the analysis. To tackle this problem, this paper proposes a simplified model which can predict the coupled thermal and electric output dynamics of MTs. Considering the time-scale difference of various dynamic processes occurring within MTs, the electromechanical subsystem is treated as a fast quasi-linear process, while the thermo-mechanical subsystem is treated as a slow process with high nonlinearity. A three-stage subspace identification method is utilized to capture the dominant dynamics and predict the electric power output. For the thermo-mechanical process, a radial basis function model trained by the particle swarm optimization method is employed to handle the strong nonlinear characteristics. Experimental tests on a Capstone C30 MT show that the proposed modeling method can well capture the system dynamics, and produce a good prediction of the coupled thermal and electric outputs in various operating modes.

Controller design for analgesia with quantized pupil size variation output and saturating infusion rate

Abstract: This paper proposes a strategy for the design of a dynamic output-feedback controller for analgesia taking into account the saturation of the input and the quantization of the output. Besides that, the design of this controller takes into account the multiple time scale dynamics in the analgesia model, accelerates the fast dynamics and establishes global stability. The control design is cast into a two-step strategy. The controller is first designed for the fast system and the stability analysis is then performed on the full model to evaluate domains of safe behavior.

Development of compositional and contextual communicable congruence in robots by using dynamic neural network models

The current study presents neurorobotics experiments on acquisition of skills for “communicable congruence” with human via learning. A dynamic neural network model which is characterized by its multiple timescale dynamics property was utilized as a neuromorphic model for controlling a humanoid robot. In the experimental task, the humanoid robot was trained to generate specific sequential movement patterns as responding to various sequences of imperative gesture patterns demonstrated by the human subjects by following predefined compositional semantic rules. The experimental results showed that (1) the adopted MTRNN can achieve generalization by learning in the lower feature perception level by using a limited set of tutoring patterns, (2) the MTRNN can learn to extract compositional semantic rules with generalization in its higher level characterized by slow timescale dynamics, (3) the MTRNN can develop another type of cognitive capability for controlling the internal contextual processes as situated to on-going task sequences without being provided with cues for explicitly indicating task segmentation points. The analysis on the dynamic property developed in the MTRNN via learning indicated that the aforementioned cognitive mechanisms were achieved by self-organization of adequate functional hierarchy by utilizing the constraint of the multiple timescale property and the topological connectivity imposed on the network configuration. These results of the current research could contribute to developments of socially intelligent robots endowed with cognitive communicative competency similar to that of human.

New approach for the control of anesthesia based on dynamics decoupling

This paper deals with a new strategy for the control of anesthesia taking into account the saturation of the actuator and the target interval tolerated for the depth of anesthesia during a surgery. In addition, to take into account multiple time scale dynamics in the anesthesia model, the system is re-expressed by decoupling the fast dynamics from the slow ones. These slow dynamics are then considered as disturbances for the fast system. Similarly the fast states correspond to disturbances for the slow subsystem. Taking into account the variability of the patient by using the polytopic uncertainty framework, robust control design is proposed through quasi-LMI (linear matrix inequalities) conditions. The characterization of domains of stability and invariance for both the slow and fast subsystems is provided. Then associated convex optimization issues are discussed. Finally, the theoretical conditions are evaluated on a panel of simulated patients.

Multiple Scale Dynamics in Proteins Probed at Multiple Time Scales through Fluctuations of NMR Chemical Shifts

Fluctuations of NMR resonance frequency shifts and their relation with protein exchanging conformations are usually analyzed in terms of simple two-site jump processes. However, this description is unable to account for the presence of multiple time scale dynamics. In this work, we present an alternative model for the interpretation of the stochastic processes underlying these fluctuations of resonance frequencies. Time correlation functions of (15)N amide chemical shifts computed from molecular dynamics simulations (MD) were analyzed in terms of a transiently fractional diffusion process. The analysis of MD trajectories spanning dramatically different time scales (∼ 200 ns and 1 ms [ Shaw, D. E.; Science 2010, 330, 341 - 346]) allowed us to show that our model could capture the multiple scale structure of chemical shift fluctuations. Moreover, the predicted exchange contribution Rex to the NMR transverse relaxation rate is in qualitative agreement with experimental results. These observations suggest that the proposed fractional diffusion model may provide significative improvement to the analysis of NMR dispersion experiments.

Neuronal Spike Timing Adaptation Described with a Fractional Leaky Integrate-and-Fire Model

The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.

Multiple time step integrators in ab initio molecular dynamics

Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions are described by empirical potentials is now well established, their application to ab initio molecular dynamics calculations has been limited by difficulties associated with splitting the ab initio potential into fast and slowly varying components. Here we present two schemes that enable efficient time-scale separation in ab initio calculations: one based on fragment decomposition and the other on range separation of the Coulomb operator in the electronic Hamiltonian. We demonstrate for both water clusters and a solvated hydroxide ion that multiple time-scale molecular dynamics allows for outer time steps of 2.5 fs, which are as large as those obtained when such schemes are applied to empirical potentials, while still allowing for bonds to be broken and reformed throughout the dynamics. This permits computational speedups of up to 4.4x, compared to standard Born-Oppenheimer ab initio molecular dynamics with a 0.5 fs time step, while maintaining the same energy conservation and accuracy.