Time-scale Approach Research Articles

Averaging principle on infinite intervals for stochastic ordinary differential equations

<p style='text-indent:20px;'>In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert space with Poisson stable (in particular, periodic, quasi-periodic, almost periodic, almost automorphic etc) coefficients. Under some appropriate conditions we prove that there exists a unique recurrent solution to the original equation, which possesses the same recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this recurrent solution converges to the stationary solution of averaged equation uniformly on the whole real axis when the time scale approaches zero.</p>

Dynamics of a stochastic excitable system with slowly adapting feedback.

We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic bursting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance or effectively control the features of the stochastic bursting. The setup can be considered a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.

Nonlinear Dynamics and Parametric Excitation of Piezo-Micro Biological Sensor

In this work, nonlinear dynamics and parametric excitation of piezoelectric micro beam subjected a combination of DC and AC voltages is investigated for micro biological sensor applications. The governing differential equation of the motion is derived by the Hamiltonian principle and then by using the Galerkin approach, this partial differential equation (PDE) is simplified into an ordinary differential equation (ODE) in terms of forced damped Mathieu equation with cubic nonlinearity. A perturbation technique, i.e. multiple time scales approach is used for investigation of superharmonic resonances of orders 1/2 and 1/3 and obtaining of the modulation equations in the amplitude and phase. Numerical results of different parameters effects on the piezoelectric micro beam behavior are presented graphically.

Trading Cost and Throughput in Geo-Distributed Analytics With A Two Time Scale Approach

In the era of global-scale services, analytical queries are performed on datasets that span multiple data centers (DCs). Such geo-distributed queries generate a large amount of inter-DC data transfers at run time. Due to the expensive inter-DC bandwidth, various methods have been proposed to reduce the traffic cost in geo-distributed data analytics. However, current methods do not attempt to address the throughput issue in geo-distributed analytics. In this article, we target at characterizing and optimizing a cost-throughput tradeoff problem in geo-distributed data analytics. Our objectives are two-fold: (1) we minimize the inter-DC traffic cost when serving geo-distributed analytics with uncertain query demand, and (2) we maximize the system throughput, in terms of the number of query requests that can be successfully served with guaranteed queuing delay. Specifically, we formulate a stochastic optimization problem that seamlessly combines these two objectives. To solve this problem, we take advantage of Lyapunov optimization techniques to design and analyze a two-timescale online control framework. Without prior knowledge of future query requests, this framework makes online decisions on input data placement and admission control of query requests. Rigorous theoretical analyses show that our framework can achieve a near-optimal solution and maintain system stability and robustness as well. Extensive trace-driven simulation results further demonstrate that our framework is capable of reducing inter-DC traffic cost, improving system throughput, and guaranteeing a maximum delay for each query request.

Living la Vida T-LoCoH: site fidelity of Florida ranched and wild white-tailed deer (Odocoileus virginianus) during the epizootic hemorrhagic disease virus (EHDV) transmission period

BackgroundEpizootic hemorrhagic disease virus (EHDV) is a pathogen vectored by Culicoides midges that causes significant economic loss in the cervid farming industry and affects wild deer as well. Despite this, its ecology is poorly understood. Studying movement and space use by ruminant hosts during the transmission season may elucidate EHDV ecology by identifying behaviors that can increase exposure risk. Here we compared home ranges (HRs) and site fidelity metrics within HRs using the T-LoCoH R package and GPS data from collared deer.MethodsHere, we tested whether white-tailed deer (Odocoileus virginianus) roaming within a high-fenced, private deer farm (ranched) and native deer from nearby state-managed properties (wild) exhibited differences in home range (HR) size and usage during the 2016 and 2017 EHDV seasons. We captured male and female individuals in both years and derived seasonal HRs for both sexes and both groups for each year. HRs were calculated using a time-scale distance approach in T-LoCoH. We then derived revisitation and duration of visit metrics and compared between years, sexes, and ranched and wild deer.ResultsWe found that ranched deer of both sexes tended to have smaller activity spaces (95% HR) and revisited sites within their HR more often but stayed for shorter periods than wild deer. However, core area (25% HR) sizes did not significantly differ between these groups.ConclusionsThe contrast in our findings between wild and ranched deer suggest that home range usage, rather than size, in addition to differences in population density, likely drive differences in disease exposure during the transmission period.

Development of Emotion Regulation Dynamics Across Early Childhood: a Multiple Time-Scale Approach.

Children should become more effective at regulating emotion as they age. Longitudinal evidence of such change, however, is scarce. This study uses a multiple-time scale approach to test the hypothesis that the self-regulation of emotion-the engagement of executive processes to influence the dynamics of prepotent emotional responses-becomes more effective as children move through early childhood. Second-by-second time-series data obtained from behavioral observation of 120 children (46% female) during an 8-min frustration-eliciting wait task completed at four ages (24 months, 36 months, 48 months, 5 years) were modeled using bivariate coupled differential equation models designed to capture age-related changes in the intrinsic dynamics and bidirectional coupling of prepotent and executive processes. Results revealed indirect influences of executive processes on the intrinsic dynamics of children's desire and frustration increased with age but also revealed complex and non-linear age-related changes in how specific aspects of the dynamic interplay between prepotent responses and executive processes influence the effectiveness of regulation at different ages. The findings illustrate the utility of using a dynamics system approach to articulate and study how specific aspects of emotion regulation change with age.

Active Vibration Control of a Fluid-Conveying Functionally Graded Cylindrical Shell using Piezoelectric Material

Active vibration control of a smart FG (functionally graded) cylindrical shell conveying fluid in thermal environment is studied theoretically by using a laminated piezoelectric actuator. Velocity feedback control law is implemented to activate the piezoelectric actuator. Considering the electric-thermo-fluid-structure interaction effect, a nonlinear dynamic model of the smart fluid-conveying FG cylindrical shell is developed based on Hamilton’s principle and von-Karman type geometrical nonlinear relationship. The inviscid, incompressible, isentropic and irrotational fluid is coupled into governing equations using the linearized potential theory. The Galerkin’s method is used to obtain the nonlinear governing equations of motion of the coupled system. The multiple time scales approach is applied to solve the resulting governing equations for analysing the nonlinear dynamic characteristics of the coupled system. The influence of fluid flow velocity, feedback control gains of piezoelectric voltage, external excitation and material properties of FGM on the frequency-response curves of system are investigated. The results indicate that the piezoelectric voltage is an effective controlling parameter for vibration control of the system, and the flow velocity can effect significantly the vibration amplitude and nonlinearity of the coupled system.

Big data analytics using multi-fractal wavelet leaders in high-frequency Bitcoin markets

Abstract We employ a time-scale multi-fractal decomposition approach to investigate the properties of Bitcoin prices and volume at different sampling rates using high-frequency data. We provide evidence of multi-fractality at all rates. The big data-driven analysis combined with statistical testing shows evidence of dominant multi-fractal traits within the intervals of 5 mn–90 mn, and 120 mn up to 720 mn. Wavelet leaders comprise a promising algorithmic technique that provides a richer description of the singularity spectrum. In particular, we reveal the distinct heterogeneity of the three log-cumulants for prices and volume between the two distinctive high-frequency sampling intervals. Our findings may assist in devising profitable high-frequency trading strategies in crypto-currency markets.

Mean square consensus of double-integrator multi-agent systems under intermittent control: A stochastic time scale approach

We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a μ−varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.

Impact of molecular mixing and scalar dissipation rate closures on turbulent bluff-body flames with increasing local extinction

Bluff-body turbulent CH4: H2 (1:1) flames at 50% (HM1), 75% (HM2) and 91% (HM3) of the blow-off velocity (235 m s−1) were studied experimentally by Masri and co-workers and found to exhibit gradually increasing periodic and shear layer instabilities. The latter are coupled with increasing levels of local extinction with subsequent re-ignition further downstream. This study provides a systematic evaluation of the sensitivity of predictions to molecular mixing and scalar dissipation rate closures. The latter include extended forms of the Euclidean Minimum Spanning Tree (EMST) and modified Curl’s (MC) models, applicable to premixed turbulent flames via a closure that accounts for local Damköhler number effects (EEMST and EMC), and a conceptually related blended scalar time-scale approach (BEMST and BMC). Computations are performed using a hybrid finite volume (FV) – transported Joint Probability Density Function (JPDF) algorithm featuring stochastic Lagrangian particles, a comprehensive 48-scalar systematically reduced C/H/N/O mechanism, and a second moment method based on the Generalised Langevin Model that provides a partial resolution of the unsteady fluid motion. The sensitivity to solution parameters affecting the temporal resolution is quantified using Fourier transforms of the time histories of velocity and scalar traces. Radial profiles, conditional means and scatter plots are compared to the experimental data along with burning indices based on the conditional mean temperature. Vortex related instabilities ∼ 1 kHz in the outer shear layer appear for all closures with EMC showing periodic local extinction and re-ignition in the neck region for HM3 and flame turbules (i.e., discrete pockets of hot gas) separating periodically at frequencies ∼ 85 Hz. Results are similar to well–resolved JPDF/LES simulations for HM1. It is shown that the EMC and (E)EMST models essentially enclose the experimental data for HM2 and HM3. For HM3, emissions of NO are controlled by local extinction events that become increasingly sensitive to the molecular mixing closure as blow-off is approached.

Reliability of a new analysis to compute time to stabilization following a single leg drop jump landing in children.

Although a number of different methods have been proposed to assess the time to stabilization (TTS), none is reliable in every axis and no tests of this type have been carried out on children. The purpose of this study was thus to develop a new computational method to obtain TTS using a time-scale (frequency) approach [i.e. continuous wavelet transformation (WAV)] in children. Thirty normally-developed children (mean age 10.16 years, SD = 1.52) participated in the study. Every participant performed 30 single-leg drop jump landings with the dominant lower limb (barefoot) on a force plate from three different heights (15cm, 20cm and 25cm). Five signals were used to compute the TTS: i) Raw, ii) Root mean squared, iii) Sequential average processing, iv) the fitting curve of the signal using an unbounded third order polynomial fit, and v) WAV. The reliability of the TTS was determined by computing both the Intraclass Correlation Coefficient (ICC) and the Standard Error of the Measurement (SEM).In the antero-posterior and vertical axes, the values obtained with the WAV signal from all heights were similar to those obtained by raw, root mean squared and sequential average processing. The values obtained for the medio-lateral axis were relatively small. This WAV provided substantial-to-good ICC values and low SEM for almost all the axes and heights. The results of the current study thus suggest the WAV method could be used to compute overall TTS when studying children’s dynamic postural stability.

The “Heliópolis Case” and the political urban dispute in Brazil

Abstract This article uses a case study to analyze the actions of ruling classes and social movement organizations in urban politics. The study observes these groups’ disputes and interactions with the state, and how different strategies, actions, and political projects of the subaltern classes have influenced the orientation of urban development. In a broad time-scale approach, the article discusses relations of hegemony, the process of institutionalization of movements, disputes in society and within the state, and the heterogeneity of the political projects that guide the subaltern classes.

Predicting wintertime windy days in Beijing with the preceding autumn sea surface temperature and large-scale circulation patterns

In this study, we investigate the role of sea surface temperature and large-scale circulation patterns in the preceding autumn for the prediction of wintertime windy days in Beijing during the period of 1979–2016, based on a time-scale decomposition approach. A windy day is defined according to the threshold of 2 m·s−1, which can effectively remove or reduce air pollution of Beijing. Wintertime windy days in Beijing, preceding autumn sea surface temperature and large-scale climate indices are separated into the interannual and interdecadal components. For the interannual component, the preceding autumn sea surface temperature in central western Pacific Ocean, Polar/Eurasia pattern, and Scandinavia pattern are identified as predictors of wintertime windy days in Beijing. For the interdecadal component, the identified predictors include the preceding autumn sea surface temperature in northeastern part of North Atlantic Ocean, Arctic Oscillation, and North Atlantic Oscillation. We develop statistical models for the interannual and interdecadal components based on these preceding autumn predictors, and take them together to predict wintertime windy days in Beijing. The leave-one-out cross-validation for 1979–2016 time series shows that 76% of the total variance of observed wintertime windy days in Beijing can be predicted. Hindcast experiments for the period of 1999–2016 also yield the high prediction skills. The physical mechanisms responsible for links between these predictors and wintertime windy days in Beijing are also discussed. The statistical models proposed herein are expected to be applied to and aid to improve seasonal forecasting of wintertime windy days in Beijing.

Wheeze type classification using non-dyadic wavelet transform based optimal energy ratio technique

Background and objectiveWheezes in pulmonary sounds are anomalies which are often associated with obstructive type of lung diseases. The previous works on wheeze-type classification focused mainly on using fixed time-frequency/scale resolution based on Fourier and wavelet transforms. The main contribution of the proposed method, in which the time-scale resolution can be tuned according to the signal of interest, is to discriminate monophonic and polyphonic wheezes with higher accuracy than previously suggested time and time-frequency/scale based methods. MethodsAn optimal Rational Dilation Wavelet Transform (RADWT) based peak energy ratio (PER) parameter selection method is proposed to discriminate wheeze types. Previously suggested Quartile Frequency Ratios, Mean Crossing Irregularity, Multiple Signal Classification, Mel-frequency Cepstrum and Dyadic Discrete Wavelet Transform approaches are also applied and the superiority of the proposed method is demonstrated in leave-one-out (LOO) and leave-one-subject-out (LOSO) cross validation schemes with support vector machine (SVM), k nearest neighbor (k-NN) and extreme learning machine (ELM) classifiers. ResultsThe results show that the proposed RADWT based method outperforms the state-of-the-art time, frequency, time-frequency and time-scale domain approaches for all classifiers in both LOO and LOSO cross validation settings. The highest accuracy values are obtained as 86% and 82.9% in LOO and LOSO respectively when the proposed PER features are fed into SVM. ConclusionsIt is concluded that time and frequency domain characteristics of wheezes are not steady and hence, tunable time-scale representations are more successful in discriminating polyphonic and monophonic wheezes when compared with conventional fixed resolution representations.

Global Exponential Stability and Synchronization for Discrete-Time Inertial Neural Networks With Time Delays: A Timescale Approach.

This paper considers generalized discrete-time inertial neural network (GDINN). By timescale theory, the original network is rewritten as a timescale-type inertial NN. Two different scenarios are considered. In a first scenario, several criteria guaranteeing the global exponential stability for the addressed GDINN are obtained based on the generalized matrix measure concept. In this case, Lyapunov function or functional is not necessary. In a second scenario, some inequality analytical and scaling techniques are used to achieve the global exponential stability for the considered GDINN. The obtained criteria are also applied to the global exponential synchronization of drive-response GDINNs. Several illustrative examples, including applications to the pseudorandom number generator and encrypted image transmission, are given to show the effectiveness of the theoretical results.

A multiple timescales approach to bridging spiking- and population-level dynamics.

A rigorous bridge between spiking-level and macroscopic quantities is an on-going and well-developed story for asynchronously firing neurons, but focus has shifted to include neural populations exhibiting varying synchronous dynamics. Recent literature has used the Ott-Antonsen ansatz (2008) to great effect, allowing a rigorous derivation of an order parameter for large oscillator populations. The ansatz has been successfully applied using several models including networks of Kuramoto oscillators, theta models, and integrate-and-fire neurons, along with many types of network topologies. In the present study, we take a converse approach: given the mean field dynamics of slow synapses, we predict the synchronization properties of finite neural populations. The slow synapse assumption is amenable to averaging theory and the method of multiple timescales. Our proposed theory applies to two heterogeneous populations of N excitatory n-dimensional and N inhibitory m-dimensional oscillators with homogeneous synaptic weights. We then demonstrate our theory using two examples. In the first example, we take a network of excitatory and inhibitory theta neurons and consider the case with and without heterogeneous inputs. In the second example, we use Traub models with calcium for the excitatory neurons and Wang-Buzsáki models for the inhibitory neurons. We accurately predict phase drift and phase locking in each example even when the slow synapses exhibit non-trivial mean-field dynamics.

Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behavior increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic.This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behavior of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behavior below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

Oil–gold time varying nexus: A time–frequency analysis

This paper analyzes the time varying nexus for oil–goldpairwise by employing the dynamic conditional correlation generalized multivariate autoregressive conditional heteroscedasticity DCC-MGARCH model of Engle (2002) as well as the time-scale approach based on multi-resolution analysis. For this goal, we focus on three subsamples, before, during and after the 2008–2009 global financial crisis. Key findings are as follows. (i) Wavelet analysis is a splendid complement to analyze the nexus between oil and gold markets. (ii) Low nexus for oil–gold pairwise after the recent global financial crisis. (iii) Gold and oil moved in reverse direction in the mid-run and long-run horizons during the crisis. (iv) Thanks to wavelets for helping financial managers and investors to manage their investment risks and making decision strategies.

The Physics of Protoplanetary Dust Agglomerates. X. High-velocity Collisions between Small and Large Dust Agglomerates as a Growth Barrier

Abstract In a protoplanetary disk, dust aggregates in the μm to mm size range possess mean collision velocities of 10–60 m s−1 with respect to dm- to m-sized bodies. We performed laboratory collision experiments to explore this parameter regime and found a size- and velocity-dependent threshold between erosion and growth. By using a local Monte Carlo coagulation calculation and along with a simple semi-analytical timescale approach, we show that erosion considerably limits particle growth in protoplanetary disks and leads to a steady-state dust-size distribution from μm- to dm-sized particles.

Toward Hierarchical Mobile Edge Computing: An Auction-Based Profit Maximization Approach

The multi-tiered concept of Internet of Things (IoT) devices, cloudlets and clouds is facilitating a user-centric IoT. However, in such three tier network, it is still desirable to investigate efficient strategies to offer the computing, storage and communications resources to the users. To this end, this paper proposes a new hierarchical model by introducing the concept of field, shallow, and deep cloudlets where the cloudlet tier itself is designed in three hierarchical levels based on the principle of LTE-Advanced backhaul network. Accordingly, we explore a two time scale approach in which the computing resources are offered in an auction-based profit maximization manner and then the communications resources are allocated to satisfy the users' QoS.