scholarly journals Normality of Ethernet Traffic at Large Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Large Time ◽  
Statistical Tests ◽  
Traffic Data ◽  
Different Time Scales

We contribute the quantitative descriptions of the large time scales for the Ethernet traffic to be Gaussian. We focus on the normality property of the accumulated traffic data under different time scales. The investigation is carried out graphically by the quantile-quantile (QQ) plots and numerically by statistical tests. The present results indicate that the larger the time scale, the more normal the Ethernet traffic.

scholarly journals Stationarity Testing of Accumulated Ethernet Traffic

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Time Scales ◽  
Unit Root ◽  
Time Scale ◽  
Unit Root Tests ◽  
Quantitative Results ◽  
Different Time Scales

We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.

EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES

1995 ◽  
Vol 03 (02) ◽  
pp. 591-602 ◽  
Author(s):  
PIERRE AUGER ◽  
JEAN-CHRISTOPHE POGGIALE
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Time Scale ◽  
Population Level ◽  
Nonlinear Process ◽  
Linear Process ◽  
Fast Time ◽  
Slow Part ◽  
Spatial Patches ◽  
Different Time Scales

The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbation theory is used in order to aggregate the initial system of ordinary differential equations for the patch sub-populations into a macro-system of two differential equations governing the total populations. Firstly, we study the case of a linear process of migration for which the aggregated system is formally identical to the slow part of the full system. Then, we study an example of a nonlinear process of migration. We show that under these conditions emerging properties appear at the population level.

scholarly journals Multi-Time Scale Economic Optimization Dispatch of the Park Integrated Energy System

2021 ◽  
Vol 9 ◽  
Author(s):  
Peng Li ◽  
Fan Zhang ◽  
Xiyuan Ma ◽  
Senjing Yao ◽  
Zhuolin Zhong ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Time Scales ◽  
Time Scale ◽  
Energy Systems ◽  
Energy System ◽  
Optimal Operation ◽  
Utilization Efficiency ◽  
Integrated Energy System ◽  
Operation Cost ◽  
Different Time Scales

The park integrated energy system (PIES) plays an important role in realizing sustainable energy development and carbon neutral. Furthermore, its optimization dispatch can improve the energy utilization efficiency and reduce energy systems operation cost. However, the randomness and volatility of renewable energy and the instability of load all bring challenges to its optimal operation. An optimal dispatch framework of PIES is proposed, which constructs the operation models under three different time scales, including day-ahead, intra-day and real-time. Demand response is also divided into three levels considering its response characteristics and cost composition under different time scales. The example analysis shows that the multi-time scale optimization dispatch model can not only meet the supply and demand balance of PIES, diminish the fluctuation of renewable energy and flatten load curves, but also reduce the operation cost and improve the reliability of energy systems.

scholarly journals Modelling of UV radiation variations at different time scales

2008 ◽  
Vol 26 (3) ◽  
pp. 441-446 ◽  
Author(s):  
J. L. Borkowski
Keyword(s):  
Uv Radiation ◽  
Time Scales ◽  
Time Scale ◽  
Global Radiation ◽  
Regression Method ◽  
Ozone Content ◽  
Explanatory Variables ◽  
Solar Uv ◽  
Solar Global Radiation ◽  
Different Time Scales

Abstract. Solar UV radiation variability in the period 1976–2006 is discussed with respect to the relative changes in the solar global radiation, ozone content, and cloudiness. All the variables were decomposed into separate components, representing variations of different time scales, using wavelet multi-resolution decomposition. The response of the UV radiation to the changes in the solar global radiation, ozone content, and cloudiness depends on the time scale, therefore, it seems reasonable to model separately the relation between UV and explanatory variables at different time scales. The wavelet components of the UV series are modelled and summed to obtain the fit of observed series. The results show that the coarser time scale components can be modelled with greater accuracy than fine scale components and the fitted values calculated by this method are in better agreement with observed values than values calculated by the regression method, in which variables were not decomposed. The residual standard error in the case of modelling with the use of wavelets is reduced by 14% in comparison to the regression method without decomposition.

Detection of Rainfall and Runoff Trends of the Adda River in Lecco (1845-2014) at Different Time Scales

10.29007/gbqh ◽  
2018 ◽  
Author(s):  
Roberto Ranzi ◽  
Massimo Tomirotti ◽  
Michele Brunetti ◽  
Alice Crespi ◽  
Maurizio Maugeri
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Statistical Tests ◽  
Annual Runoff ◽  
Water Levels ◽  
Cycle Period ◽  
Catchment Scale ◽  
Significance Level ◽  
Runoff Series ◽  
Different Time Scales

A recovery of ancient records of the Como Lake water levels at the Fortilizio in Lecco hydrometric station enabled the reconstruction of a time series of daily water level and runoff from the Como Lake spanning the 1845-2014 period. In parallel, the monthly areal precipitation at the Adda river catchment scale was estimated for the same 170 years- long period. This time series, which is one of the longest available for Italian riverbasins will support analyses of the reasons of changes in the runoff regime in response to climatic and anthropogenic changes. A comparison of the two series applying the Mann- Kendall, Spearman and Theil-Sen trend tests, shows a decline, in the long term, of runoff and a more significant one of precipitation. Because some changes in the operation at the outlet of the Como Lake occurred after 1946 and also in the storage capacity of the upstream reservoirs the time series was splitted in two periods, before and after 1946. The results of the statistical tests for both precipitation and runoff in three time periods are consistent, but only for the time series of annual runoff the decline is statistically significant with 5% significance level. To analyse if changes occurred at different time scales the wavelet transform was applied to the daily runoff series. Finally the Fourier power spectrum of the the daily runoff data shows a signal of higher energy corresponding to a period between 11 and 13 years, close to the sunspots cycle period, and its significance is under investigation.

Data-driven stochastic model for cross-interacting processes with different time scales

2021 ◽  
Author(s):  
Andrey Gavrilov ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Alexander Feigin
Keyword(s):  
Time Series ◽  
Stochastic Model ◽  
Time Scales ◽  
Time Scale ◽  
Sampling Interval ◽  
Bayesian Optimization ◽  
Data Driven ◽  
Middle Pleistocene ◽  
Model Based ◽  
Different Time Scales

<p>The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.</p><p>To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].</p><p>The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).</p><p>1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.032</p><p>2. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.1</p><p>3. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-7</p><p>4. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3</p>

Problems with different time scales

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 101-139 ◽  
Author(s):  
Heinz-Otto Kreiss
Keyword(s):  
Time Scales ◽  
Complex Number ◽  
Initial Value Problem ◽  
Time Scale ◽  
Homogeneous Equation ◽  
Simple Problem ◽  
Initial Value ◽  
Small Constant ◽  
Image Position ◽  
Different Time Scales

In this section we discuss a very simple problem. Consider the scalar initial value problemHere ε > 0 is a small constant and a = a1 + ia2, a1, a2 real, is a complex number with |a| = 1. We can write down the solution of (1.1) explicity. It iswhereis the forced solution andis a solution of the homogeneous equationyS varies on the time scale ‘1’ while yF varies on the much faster scale 1/ε. We say that yS, yF vary on the slow and fast scale, respectively. We use also the phrase: yS and yF are the slow and the fast part of the solution, respectively.

Transport equations on different time scales for intermediately and strongly collisional regimes

1996 ◽  
Vol 56 (1) ◽  
pp. 45-65
Author(s):  
J. W. Edenstrasser ◽  
M. M. M. Kassab
Keyword(s):  
Time Scales ◽  
Transit Time ◽  
Time Scale ◽  
Transport Equations ◽  
Mhd Equations ◽  
Plasma Transport ◽  
Collision Time ◽  
Ideal Mhd ◽  
Collisional Regime ◽  
Different Time Scales

The plasma transport equations for a weakly collisional plasma have previously been derived for four different time scales. This paper is devoted to the derivation of the plasma transport equations for the two other complementary regimes: the intermediately collisional regime (ICR) (i.e. for the case where the transit time w1 is of the same order as the collision time is of the same order as the collision time ), and the strongly collisional regime (SCR) (i.e. for the case of ) for different time scales. It is shown that the lowest-order gyromotion is unperturbed by collisions. On the Alfvén time scale, one merely obtains for both the intermediately collisional case and the strongly collisional case the single-fluid ideal MHD equations, if certain additional requirements are satisfied. On the MHD-collision time scale, one arrives at the full set of transport equations, where in both cases, contrary to the weakly collisional case, no turbulent terms are found. On the resistive diffusion timescale, one ends up with the known transport equations, with the addition of turbulent contributions.

scholarly journals Multi-scale event synchronization analysis for unravelling climate processes: A wavelet-based approach

2017 ◽  
Author(s):  
Ankit Agarwal ◽  
Norbert Marwan ◽  
Maheswaran Rathinasamy ◽  
Bruno Merz ◽  
Jürgen Kurths
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Time Scale ◽  
Temporal Dynamics ◽  
Multiple Scales ◽  
Nonlinear Interactions ◽  
Reference Time ◽  
Multi Scale ◽  
Spatio Temporal ◽  
Different Time Scales

Abstract. The temporal dynamics of climate processes are spread across different time scales and, as such, the study of these processes only at one selected time scale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. For capturing the nonlinear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analyse the time series at one reference time scale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, wavelet based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various time scales. The proposed method allows the study of spatio-temporal patterns across different time scales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different time scales.

scholarly journals Comparison Analysis of Different Time-Scale Heart Rate Variability Signals for Mental Workload Assessment in Human-Robot Interaction

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Shiliang Shao ◽  
Ting Wang ◽  
Yawei Li ◽  
Chunhe Song ◽  
Yihan Jiang ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Time Scales ◽  
Time Scale ◽  
Mental Workload ◽  
Human Robot Interaction ◽  
Machine Learning Algorithms ◽  
Robot Interaction ◽  
Ecg Signals ◽  
Different Time Scales

Excessive mental workload affects human health and may lead to accidents. This study is motivated by the need to assess mental workload in the process of human-robot interaction, in particular, when the robot performs a dangerous task. In this study, the use of heart rate variability (HRV) signals with different time scales in mental workload assessment was analyzed. A humanoid dual-arm robot that can perform dangerous work was used as a human-robot interaction object. Electrocardiogram (ECG) signals of six subjects were collected in two states: during the task and in a relaxed state. Multiple time-scale (1, 3, and 5 min) HRV signals were extracted from ECG signals. Then, we extracted the same linear and nonlinear features from the HRV signals at different time scales. The performance of machine learning algorithms using the different time-scale HRV signals obtained during the human-robot interaction was evaluated. The results show that for the per-subject case with a 3 min HRV signal length, the K -nearest neighbor classifier achieved the best mental workload classification performance. For the cross-subject case with a 5 min time-scale signal length, the gentle boost classifier achieved the best mental workload classification accuracy. This study provides a novel research idea for using HRV signals to measure mental workload during human-robot interaction.

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