Time Scale Parameter Research Articles

Recursively Convolutional CFS-PML in 3-D Laguerre-FDTD Scheme for Arbitrary Media

Weighted Laguerre finite-difference time-domain (Laguerre-FDTD) method is an efficient and unconditionally stable time-domain numerical method. The complex frequency-shifted perfectly matched layer (CFS-PML) is the main absorbing boundary condition in the Laguerre-FDTD method. The implementations of CFS-PML in the Laguerre-FDTD method, which have been reported, include the use of auxiliary variables and auxiliary differential equations. These implementations make CFS-PML sensitive to its parameters and timescale parameter s of weighted Laguerre polynomials and result in potential instability and poor absorption issues in numerical simulations. In this paper, we proposed an efficient and stable implementation of CFS-PML based on recursive convolution in the Laguerre-FDTD method. The accuracy of the proposed implementation is theoretically validated. Its numerical dispersion is theoretically derived for choosing the key parameters of CFS-PML in the Laguerre-FDTD scheme. The numerical dispersion demonstrates that the timescale factor s needs to match the simulated signal frequency and the CFS-PML parameter $\alpha $ is chosen as $0.5s\varepsilon _{0}$ to obtain the minimum dispersive error. Numerical examples validate the theoretical predictions and verify that the proposed implementation of CFS-PML is robust and retains the advantages of CFS-PML in classical FDTD method, such as effectively absorbing evanescent as well as guided waves. It requires nonsplits of electromagnetic field components, no auxiliary variables, and no modifications when applying it to inhomogeneous, lossy, and dispersive media. The CFS-PML formulas can directly be converted into computer codes of the Laguerre-FDTD method.

An improved preference method for the FAST TCP protocol parameter

Aiming at the weaknesses of FAST TCP in choosing protocol parameter for static mapping. A slow time-scale iterative search preference parameter method based on the difference between each path traffic service intensity and its transmission bandwidth is proposed. The stochastic model and its fluid model was derived, in which each path TCP connection followed Poisson process and the size of transport files obeyed the exponential distribution. A Lyapunov function including TCP connection’s mean waiting time was constructed to prove that, for those links which are in heavy traffic, if each path’s traffic service intensity was equal to its transmission bandwidth, the number of each path’s active TCP connection would stay stable, and the average waiting time will reach the minimum. Thereby the proposed method is theoretically feasible. Moreover, NS-2 simulations are presented to verify this effective method.

Coronal Electron Density Temperature and Solar Spectral Irradiance during Solar Cycles 23 and 24

Abstract Plasma parameters such as the electron density and temperature play a key role in the dynamics of the solar atmosphere. These characteristics are important in solar physics because they can help us to understand the physics of the solar corona, the ultimate goal being the reconstruction of the electron density and temperature distributions in the solar corona. The relations between emission and plasma parameters in different timescales are studied. We present a physics-based model to reconstruct the density, temperature, and emission in the EUV band. This model, called COronal DEnsity and Temperature (CODET), is composed of a flux transport model, an extrapolation model, an emission model, and an optimization algorithm. The CODET model parameters were constrained by comparing the model’s output to the TIMED/SEE record instead of direct observations because it covers a longer time interval than the direct solar observations currently available. The most important results of the current work are the recovery of SSI variability in specific wavelengths in the EUV band, as well as the variations in density and temperature during large timescales through the solar atmosphere with the CODET model. The evolution of the electron density and temperature profiles through the solar corona in different layers during solar cycles 23 and 24 will be presented. The emission maps were obtained and they are in accordance with the observations. Additionally, the density and temperature maps are related to the variations of the magnetic field in different layers through the solar atmosphere.

Discrete-Time Statistical Inference for Multiscale Diffusions

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization regimes, based on an appropriate misspecified model motivated by a second-order stochastic Taylor expansion of the slow process with respect to a function of the time-scale separation parameter. In the case of a fixed number of observations, we establish consistency, asymptotic normality, and asymptotic statistical efficiency of a minimum contrast estimator (MCE), the limiting variance having been identified explicitly; we furthermore establish consistency and asymptotic normality of a simplified MCE, which is, however, not, in general, efficient. These results are then extended to the case of high-frequency observations under a condition restricting the rate at which the number of observations may grow vis-a-vis the separation of scales. Numerical simulations illustrate the ...

Mining Outlier Data in Mobile Internet-Based Large Real-Time Databases

Mining outlier data guarantees access security and data scheduling of parallel databases and maintains high-performance operation of real-time databases. Traditional mining methods generate abundant interference data with reduced accuracy, efficiency, and stability, causing severe deficiencies. This paper proposes a new mining outlier data method, which is used to analyze real-time data features, obtain magnitude spectra models of outlier data, establish a decisional-tree information chain transmission model for outlier data in mobile Internet, obtain the information flow of internal outlier data in the information chain of a large real-time database, and cluster data. Upon local characteristic time scale parameters of information flow, the phase position features of the outlier data before filtering are obtained; the decision-tree outlier-classification feature-filtering algorithm is adopted to acquire signals for analysis and instant amplitude and to achieve the phase-frequency characteristics of outlier data. Wavelet transform threshold denoising is combined with signal denoising to analyze data offset, to correct formed detection filter model, and to realize outlier data mining. The simulation suggests that the method detects the characteristic outlier data feature response distribution, reduces response time, iteration frequency, and mining error rate, improves mining adaptation and coverage, and shows good mining outcomes.

A Novel Sleep Respiratory Rate Detection Method for Obstructive Sleep Apnea Based on Characteristic Moment Waveform.

Obstructive sleep apnea (OSA) affecting human's health is a kind of major breathing-related sleep disorders and sometimes leads to nocturnal death. Respiratory rate (RR) of a sleep breathing sound signal is an important human vital sign for OSA monitoring during whole-night sleeping. A novel sleep respiratory rate detection with high computational speed based on characteristic moment waveform (CMW) method is proposed in this paper. A portable and wearable sound device is used to acquire the breathing sound signal. And the amplitude contrast decreasing has been done first. Then, the CMW is extracted with suitable time scale parameters, and the sleep RR value is calculated by the extreme points of CMW. Experiments of one OSA case and five healthy cases are tested to validate the efficiency of the proposed sleep RR detection method. According to manual counting, sleep RR can be detected accurately by the proposed method. In addition, the apnea sections can be detected by the sleep RR values with a given threshold, and the time duration of the segmentation of the breath can be calculated for detailed evaluation of the state of OSA. The proposed method is meaningful for continued research on the sleep breathing sound signal.

Singularly Perturbed Algorithms for Velocity Consensus and Shape Control of Single Integrator Multi-Agent Systems

Abstract This paper studies a distributed multi-agent control problem in which the agents have single-integrator dynamics. A distributed control law is proposed to drive the agents to attain a desired formation shape and acquire an identical velocity. Using singular perturbation theory and stability results for nonlinear cascade systems, it is shown that agents can achieve the desired formation shape and velocity at different time scales. Moreover, it is shown that there exists an upper bound for a time-scale parameter (perturbation parameter) in the control law such that for time-scale parameters less than this bound, the initial conditions of the shape control error system will remain in a stability basin of the equilibrium. Simulation results are provided to validate the proposed algorithm.

A simple parameter can switch between different weak-noise–induced phenomena in a simple neuron model

In recent years, several, apparently quite different, weak-noise–induced resonance phenomena have been discovered. Here, we show that at least two of them, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR), can be related by a simple parameter switch in one of the simplest models, the FitzHugh-Nagumo (FHN) neuron model. We consider a FHN model with a unique fixed point perturbed by synaptic noise. Depending on the stability of this fixed point and whether it is located to either the left or right of the fold point of the critical manifold, two distinct weak-noise–induced phenomena, either SISR or ISR, may emerge. SISR is more robust to parametric perturbations than ISR, and the coherent spike train generated by SISR is more robust than that generated deterministically. ISR also depends on the location of initial conditions and on the time-scale separation parameter of the model equation. Our results could also explain why real biological neurons having similar physiological features and synaptic inputs may encode very different information.

Global asymptotic stability analysis of two-time-scale competitive neural networks with time-varying delays

In this paper, the global asymptotic stability of two-time-scale competitive neural networks(CNNs) with multiple time-varying delays is investigated. By constructing a new ε-dependent Lyapunov functional, sufficient conditions for the global asymptotic stability of the concerned systems are established, and an optimization problem is formulated to get the best estimate of the ε-bound. Compared with the existing results, the proposed results are more general and less conservative in the sense of determining an upper bound for the time-scale parameter ε. Finally, three examples are given to illustrate the advantages of the obtained results.

A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields

We extend a current result in the literature by introducing a parametric family of matrix-valued cross-covariance functions, which would help describe multivariate space–time dependence structures for any number of variables. All the direct and cross-covariance functions belong to the Matérn class. The smoothness, space–time separability and scale parameters are allowed to be different for each variable.

Is a hyperchaotic attractor superposition of two multifractals?

In the context of chaotic dynamical systems with exponential divergence of nearby trajectories in phase space, hyperchaos is defined as a state where there is divergence or stretching in at least two directions during the evolution of the system. Hence the detection and characterization of a hyperchaotic attractor is usually done using the spectrum of Lyapunov Exponents (LEs) that measure this rate of divergence along each direction. Though hyperchaos arise in different dynamical situations and find several practical applications, a proper understanding of the geometric structure of a hyperchaotic attractor still remains an unsolved problem. In this paper, we present strong numerical evidence to suggest that the geometric structure of a hyperchaotic attractor can be characterized using a multifractal spectrum with two superimposed components. In other words, apart from developing an extra positive LE, there is also a structural change as a chaotic attractor makes a transition to the hyperchaotic phase and the attractor changes from a simple multifractal to a dual multifractal, equivalent to two inter-mingled multifractals. We argue that a cross-over behavior in the scaling region for computing the correlation dimension is a manifestation of such a structure. In order to support this claim, we present an illustrative example of a synthetically generated set of points in the unit interval (a Cantor set with a variable iteration scheme) displaying dual multifractal spectrum. Our results are also used to develop a general scheme to generate both hyperchaotic as well as high dimensional chaotic attractors by coupling two low dimensional chaotic attractors and tuning a time scale parameter.

Crash testing difference-smoothing algorithm on a large sample of simulated light curves from TDC1

In this work, we propose refinements to the difference-smoothing algorithm for measurement of time delay from the light curves of the images of a gravitationally lensed quasar. The refinements mainly consist of a more pragmatic approach to choose the smoothing time-scale free parameter, generation of more realistic synthetic light curves for estimation of time delay uncertainty and using a plot of normalized $\chi^2$ computed over a wide range of trial time delay values to assess the reliability of a measured time delay and also for identifying instances of catastrophic failure. We rigorously tested the difference-smoothing algorithm on a large sample of more than thousand pairs of simulated light curves having known true time delays between them from the two most difficult `rungs' -- rung3 and rung4 -- of the first edition of Strong Lens Time Delay Challenge (TDC1) and found an inherent tendency of the algorithm to measure the magnitude of time delay to be higher than the true value of time delay. However, we find that this systematic bias is eliminated by applying a correction to each measured time delay according to the magnitude and sign of the systematic error inferred by applying the time delay estimator on synthetic light curves simulating the measured time delay. Following these refinements, the TDC performance metrics for the difference-smoothing algorithm are found to be competitive with those of the best performing submissions of TDC1 for both the tested `rungs'. The MATLAB codes used in this work and the detailed results are made publicly available at https://github.com/rathnakumars/difference-smoothing

Insight into human pubertal growth by applying the QEPS growth model

BackgroundComputerized mathematical models describing absolute and relative individual growth during puberty in both cm and standard deviation (SD)-scores are lacking. The present study aimed to fill this gap, by applying the QEPS-model that delineates mathematically the specific pubertal functions of the total growth curve.MethodsStudy population used was the individual growth curves of the longitudinally followed cohort GrowUp1974 Gothenburg (n = 2280). The QEPS-model describes total height as (T)otal-function: a combination of four shape-invariant growth functions, modified by time-scale and height-scale parameters: a (Q)uadratic-function for the continuous growth from fetal life to adulthood; a negative (E)xponential-function adds the rapid, declining fetal/infancy growth; a (P)ubertal-function the specific pubertal growth spurt; a (S)top-function the declining growth until adult height. A constructed variable, MathSelect, was developed for assessing data-quality. CIs and SD-scores for growth estimates were calculated for each individual.QEPS-model estimates used for pubertal growth; from the T-function: onset of puberty as minimal height velocity (AgeTONSET); mid-puberty as peak height velocity (AgeTPHV); end of puberty as height velocity decreased to 1 cm/year (AgeTEND); duration of different intervals and gain (AgeTONSET–END and Tpubgain); from the P-function: onset of puberty, estimated as growth at 1% or 5% (AgeP1,AgeP5); mid-puberty as 50% (AgeP50) and PHV (AgePPHV); end of pubertal growth at 95 or 99% (AgeP95, AgeP99); duration of different intervals and pubertal gain (Ppubgain; Pmax); from the QES-function: gain (QESpubgain).ResultsApplication of these mathematical estimates for onset, middle and end of puberty of P-function, QES-function, and T-function during puberty showed: the later the onset of puberty, the greater the adult height; pubertal gain due to the P-function growth was independent of age at onset of puberty; boys had higher total gain during puberty due to P-function growth than to QES-function growth; for girls it was reversed.ConclusionsQEPS is the first growth model to provide individualized estimates of both the specific pubertal growth function and the total growth during puberty, with accompanying SD-scores and Cis for each individual. These QEPS-derived estimates enable more in-depth analysis of different aspects of pubertal growth than previously possible.

Inferring the Heliospheric Magnetic Field Back through Maunder Minimum

Abstract Recent solar conditions include a prolonged solar minimum (2005–2009) and a solar maximum that has not fully recovered in terms of the Heliospheric Magnetic Field (HMF) strength when compared to the previous maximum values. These anomalies may indicate that we are entering an era of lower solar activity than observed at other times during the space age. We study past solar grand minima, especially the Maunder period (1645–1715) to gain further insight into grand minima. We find the timescale parameters associated with three processes attributed to the magnetic flux balance in the heliosphere using chi-square analysis. We use HMF time series reconstructed based on geomagnetic data and near-Earth spacecraft measurements (OMNI) data to find the fundamental timescales that influence heliospheric field evolution through conversion or opening of magnetic flux from coronal mass ejections (CMEs) into the ambient heliospheric field, removal or loss of the ambient heliospheric field through magnetic reconnection, and interchange reconnection between CME magnetic flux and ambient heliospheric magnetic flux. We also investigate the existence of a floor in the heliospheric magnetic flux, in the absence of CMEs, and show that a floor nT is sufficient to successfully describe the HMF evolution. The minimum value for the HMF at 1 au in the model-predicted historic record is 3.13 ± 0.35 nT. Our model results favorably reproduce paleocosmic data and near-Earth spacecraft measurements data and show how the HMF may evolve through periods of extremely low activity.

Inflow, Outflow, Yields, and Stellar Population Mixing in Chemical Evolution Models

Abstract Chemical evolution models are powerful tools for interpreting stellar abundance surveys and understanding galaxy evolution. However, their predictions depend heavily on the treatment of inflow, outflow, star formation efficiency (SFE), the stellar initial mass function, the SN Ia delay time distribution, stellar yields, and stellar population mixing. Using flexCE, a flexible one-zone chemical evolution code, we investigate the effects of and trade-offs between parameters. Two critical parameters are SFE and the outflow mass-loading parameter, which shift the knee in [O/Fe]–[Fe/H] and the equilibrium abundances that the simulations asymptotically approach, respectively. One-zone models with simple star formation histories follow narrow tracks in [O/Fe]–[Fe/H] unlike the observed bimodality (separate high-α and low-α sequences) in this plane. A mix of one-zone models with inflow timescale and outflow mass-loading parameter variations, motivated by the inside-out galaxy formation scenario with radial mixing, reproduces the two sequences better than a one-zone model with two infall epochs. We present [X/Fe]–[Fe/H] tracks for 20 elements assuming three different supernova yield models and find some significant discrepancies with solar neighborhood observations, especially for elements with strongly metallicity-dependent yields. We apply principal component abundance analysis to the simulations and existing data to reveal the main correlations among abundances and quantify their contributions to variation in abundance space. For the stellar population mixing scenario, the abundances of α-elements and elements with metallicity-dependent yields dominate the first and second principal components, respectively, and collectively explain 99% of the variance in the model. flexCE is a python package available at https://github.com/bretthandrews/flexCE.

The Impact of Vertical Measurement Depth on the Information Content of Soil Moisture for Latent Heat Flux Estimation

Abstract This study aims to identify the impact of vertical support on the information content of soil moisture (SM) for latent heat flux estimation. This objective is achieved via calculation of the mutual information (MI) content between multiple soil moisture variables (with different vertical supports) and current/future evaporative fraction (EF) using ground-based soil moisture and latent/sensible heat flux observations acquired from the AmeriFlux network within the contiguous United States. Through the intercomparison of MI results from different SM–EF pairs, the general value (for latent heat flux estimation) of superficial soil moisture observations , vertically integrated soil moisture observations , and vertically extrapolated soil moisture time series [soil wetness index (SWI) from a simple low-pass transformation of ] are examined. Results suggest that, contrary to expectations, 2-day averages of and have comparable mutual information with regards to EF. That is, there is no clear evidence that the information content for flux estimation is enhanced via deepening the vertical support of superficial soil moisture observations. In addition, the utility of SWI in monitoring and forecasting EF is partially dependent on the adopted parameterization of time-scale parameter T in the exponential filter. Similar results are obtained when analyses are conducted at the monthly time scale, only with larger error bars. The contrast between the results of this paper and past work focusing on utilizing soil moisture to predict vegetation condition demonstrates that the particular application should be considered when characterizing the information content of soil moisture time series measurements.

Automated Selection of Pure Base Flows from Regular Daily Streamflow Data: Objective Algorithm

AbstractThe identification of base flow from an available record of streamflow measurements for recession rate analysis is often a difficult and time-consuming process affected by unavoidable errors and subjective aspects. Here, several stringent criteria are proposed for automated selection of base flows for this method and are applied to select pure base flows in 26 catchments from the United States, Australia, and China. The characteristic drainage timescale parameter (K) of the linear response function was chosen as the effectiveness measure of the automated method; the K values estimated using this method are 44.5±13.2 days compared with 45.7±10.5 days estimated manually for the catchments with long records. The effects of different imposed criteria on the base flow selection are also quantified using this parameter. The proposed algorithm provides a faster and more objective methodology for automated selection of base flows for recession rate analysis and will thus greatly facilitate its application.

Modelling individual longitudinal human growth from fetal to adult life − QEPS I

BackgroundOnly one mathematical model to date describes human growth and its different phases from fetal life until adult height. AimTo develop a model describing growth from fetal life to adult height taking maturation/biological tempo into consideration. MethodsSubjects: The model was developed based on longitudinal mean height values obtained from published growth references for a cohort of 3650 healthy Swedish children followed from birth circa 1974 until adult height combined with birth-length for circa 400 000 healthy infants born 1990-1995. ResultsThe QEPS-model for individual growth was constructed with a combination of four basic shape-invariant growth functions: a quadratic Q-function and a negative exponential E-function, both started during fetal life, 8 months before birth; the E-function levelled off after birth, whereas the Q-function continued until end of growth. A specific nonlinear pubertal P-function started at onset of puberty, and a stop S-function ended growth according to both the Q-function continuing during puberty and the specific P-function. For each function, an individual height-scale parameter was defined, and for the E- and P-functions, a time-scale parameter; giving six modifying parameters in total. In addition standardized proportional scores were used for biological interpretations.The QEPS-model was used to fit and generate mathematical functions suitable to describe the growth of the healthy population of Swedish children; thereafter, the model was modified using four height-scale parameters to model individual height in cm, and two time-scale parameters to adjust for the individual tempo of growth. Individual confidence intervals were calculated for all parameters. ConclusionsA new shape-invariant growth model, QEPS, was developed, that requires only four basic growth functions to describe the total pattern of growth in height from fetal life to adult height, with addition of height- and time-scale parameters describing individual growth. The model can describe a wide variety of growth curves. Moreover, it is the first model to provide confidence intervals which enable us to describe the precision/quality of individual parameters.

High chlorophyll a concentration in a low nutrient context: discussions in a subtropical lake dominated by Cyanobacteria

<p>Temporal variability in some water quality parameters can play an important role in determining the presence and abundance of primary producers, and consequently in the trophic state and other characteristics and uses of lake ecosystems. In this sense, the present study aimed at understanding temporal dynamics of some trophic relevant water quality parameters in different time scales and their correlation and influence in phytoplankton biomass (chlorophyll <em>a</em>) in a shallow subtropical coastal lake. Peri Lake is located in Florianópolis island in Southern Brazil and samples were taken monthly between March 2007 and February 2013. The lake showed low dissolved nutrients concentration, especially phosphorus (P) (median dissolved P: 2.0 µg.l<sup>-1</sup>) and high chlorophyll <em>a</em> (median: 20.8 µg.l<sup>-1</sup>) concentration. Total nitrogen (TN) concentration varied broadly, with a median of 672.8 µg L<sup>-1</sup>, and total P (TP) concentration was low (median: 13.5 µg L<sup>-1</sup>). A seasonal pattern of variation concerning dissolved and total P and chlorophyll a concentration was observed, associated mainly with temperature and wind speeds, but no clear pattern was observed for nitrogen (N) fractions. Significant differences were observed in different years for some parameters, with higher chlorophyll a and lower N concentration in the last three years sampled. The lake was considered potentially P limited during the majority of the study period and a positive correlation was found between chlorophyll <em>a</em> and total and dissolved P concentration. Phytoplankton biomass (as chlorophyll <em>a</em>) was apparently controlled by water temperature and P availability (TN:TP ratio and dissolved P). Water transparency (as Secchi depth) was strongly and negatively influenced by chlorophyll <em>a</em> concentration. <em>Cylindrospermopsis raciborskii</em> abilities to compete for P and light seem to be important factors determining its success and dominance in this low P coastal ecosystem. The fluctuating P supply, probably associated to sediment resuspension by wind in this shallow waterbody, is an advantageous factor for cyanobacteria and has an important role in chlorophyll <em>a</em> dynamics. Thus, high chlorophyll <em>a</em> concentration in this subtropical lake seems to be related to the P-limited condition, shallowness and low water column transparency, which are probably favouring the dominance of <em>C. raciborskii</em>, especially in higher summer temperatures, and leading to high chlorophyll <em>a</em> concentration even in a low dissolved nutrient environment.</p>

A Bayesian approach for temporally scaling climate for modeling ecological systems.

With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre‐1970] and contemporary [post‐2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet–dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.