scholarly journals Small and large scale behavior of moments of Poisson cluster processes

2017 ◽  
Vol 21 ◽  
pp. 369-393
Author(s):  
Nelson Antunes ◽  
Vladas Pipiras ◽  
Patrice Abry ◽  
Darryl Veitch
Keyword(s):  
Large Scale ◽  
Point Processes ◽  
Real Life ◽  
Real Data ◽  
Internet Traffic ◽  
Model Parameters ◽  
Scale Free ◽  
Life Phenomena ◽  
Poisson Cluster ◽  
Cluster Processes

Poisson cluster processes are special point processes that find use in modeling Internet traffic, neural spike trains, computer failure times and other real-life phenomena. The focus of this work is on the various moments and cumulants of Poisson cluster processes, and specifically on their behavior at small and large scales. Under suitable assumptions motivated by the multiscale behavior of Internet traffic, it is shown that all these various quantities satisfy scale free (scaling) relations at both small and large scales. Only some of these relations turn out to carry information about salient model parameters of interest, and consequently can be used in the inference of the scaling behavior of Poisson cluster processes. At large scales, the derived results complement those available in the literature on the distributional convergence of normalized Poisson cluster processes, and also bring forward a more practical interpretation of the so-called slow and fast growth regimes. Finally, the results are applied to a real data trace from Internet traffic.

A cluster process representation of a self-exciting process

1974 ◽  
Vol 11 (3) ◽  
pp. 493-503 ◽  
Author(s):  
Alan G. Hawkes ◽  
David Oakes
Keyword(s):  
Point Processes ◽  
Generating Functional ◽  
Cluster Process ◽  
Process Representation ◽  
Age Dependent ◽  
Birth Processes ◽  
Poisson Cluster ◽  
Cluster Processes

It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.

scholarly journals A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1338
Author(s):  
Naif Alotaibi ◽  
Igor V. Malyk
Keyword(s):  
Residual Life ◽  
Real Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Conditional Moment ◽  
Failure Rate Function ◽  
New Model

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.

A new nonlinear polyconvex orthotropic material model for the robust simulation of technical fabrics in civil engineering applications at large strains – Validation with large-scale experiment/Ein neues polykonvexes orthotropes Materialmodell zur robusten Simulation von Textilmembranen im Bauingenieur- wesen unter Berücksichtigung großer Deformationen – Validierung anhand eines Großbauteilversuchs

Bauingenieur ◽  
2019 ◽  
Vol 94 (12) ◽  
pp. 488-497
Author(s):  
Mehran Motevalli ◽  
Jörg Uhlemann ◽  
Natalie Stranghöner ◽  
Daniel Balzani
Keyword(s):  
Nonlinear Model ◽  
Orthotropic Material ◽  
Large Scale ◽  
Real Life ◽  
Material Model ◽  
Woven Fabric ◽  
Model Parameters ◽  
Elastic Model ◽  
Engineering Applications ◽  
Strain Paths

Abstract A polyconvex orthotropic material model is proposed for the simulation of tensile membrane structures. The notion of anisotropic metric tensors is employed in the formulation of the polyconvex orthotropic term which allows for the description of the interaction of the warp and fill yarns. The model is adjusted to the stress-strain paths of uni- and biaxial tensile tests of a woven fabric and the results are compared with the linear elastic model. The lateral contraction in the uniaxial loading case is taken into account to also capture the strong crosswise interactions. An increased number of load cycles is considered in the experiments to reach a saturated elastic state of the material. A new method is proposed enabling in principle the identification of unique (linear) stiffness parameters by previously identifying the (nonlinear) model parameters. Eventually, the proposed nonlinear model contains only 4 material parameters to be identified for the individual membrane material. Moreover, a new large-scale experimental setting is presented which allows for the validation of the proposed model response in real-life engineering applications. The numerical robustness of the model is tested in an advanced simulation of a large roof structure under application of realistic boundary conditions.

scholarly journals Online Social Networks (OSN) Evolution Model Based on Homophily and Preferential Attachment

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 654 ◽  
Author(s):  
Jebran Khan ◽  
Sungchang Lee
Keyword(s):  
Social Networks ◽  
Structural Properties ◽  
Online Social Networks ◽  
Large Scale ◽  
Preferential Attachment ◽  
Real Life ◽  
Synthetic Data ◽  
Evolution Model ◽  
Scale Invariant ◽  
Scale Free

In this paper, we propose a new scale-free social networks (SNs) evolution model that is based on homophily combined with preferential attachments. Our model enables the SN researchers to generate SN synthetic data for the evaluation of multi-facet SN models that are dependent on users’ attributes and similarities. Homophily is one of the key factors for interactive relationship formation in SN. The synthetic graph generated by our model is scale-invariant and has symmetric relationships. The model is dynamic and sustainable to changes in input parameters, such as number of nodes and nodes’ attributes, by conserving its structural properties. Simulation and evaluation of models for large-scale SN applications need large datasets. One way to get SN data is to generate synthetic data by using SN evolution models. Various SN evolution models are proposed to approximate the real-life SN graphs in previous research. These models are based on SN structural properties such as preferential attachment. The data generated by these models is suitable to evaluate SN models that are structure dependent but not suitable to evaluate models which depend on the SN users’ attributes and similarities. In our proposed model, users’ attributes and similarities are utilized to synthesize SN graphs. We evaluated the resultant synthetic graph by analyzing its structural properties. In addition, we validated our model by comparing its measures with the publicly available real-life SN datasets and previous SN evolution models. Simulation results show our resultant graph to be a close representation of real-life SN graphs with users’ attributes.

scholarly journals Clustered Based Prediction for Batteries in the Data Centers

2020 ◽  
Author(s):  
Syed Naeem Haider ◽  
Qianchuan Zhao ◽  
Xueliang Li
Keyword(s):  
Large Scale ◽  
Data Centers ◽  
Arima Model ◽  
Real Life ◽  
Real Data ◽  
Battery Life ◽  
Battery Management System ◽  
Battery Management ◽  
Failure Data ◽  
One Year

This paper proposes an ARIMA approach to battery health forecasting with accuracy improvement by K shape-based clustered predictors. The health prediction of the battery pack is an important function of a battery management system in data centers. Accurate forecasting of battery life turns out to be very difficult without failure data to train a good forecasting model in real life. The conventional ARIMA model is compared with total and clustered predictors for battery health forecasting. Results show that the forecasting accuracy of the ARIMA model significantly improved by utilizing the results of the clustered predictors for 40 batteries in a real data center. One year of actual historical data of 40 batteries of large scale datacenter is presented to validate the effectiveness of the proposed methodology.

scholarly journals A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1462
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Family ◽  
Renyi’S Entropy

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

scholarly journals Cluster-Based Prediction for Batteries in Data Centers

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1085
Author(s):  
Syed Naeem Haider ◽  
Qianchuan Zhao ◽  
Xueliang Li
Keyword(s):  
Data Center ◽  
Large Scale ◽  
Data Centers ◽  
Moving Average ◽  
Arima Model ◽  
Real Life ◽  
Real Data ◽  
Data Sets ◽  
Multiple Time ◽  
Battery Management

Prediction of a battery’s health in data centers plays a significant role in Battery Management Systems (BMS). Data centers use thousands of batteries, and their lifespan ultimately decreases over time. Predicting battery’s degradation status is very critical, even before the first failure is encountered during its discharge cycle, which also turns out to be a very difficult task in real life. Therefore, a framework to improve Auto-Regressive Integrated Moving Average (ARIMA) accuracy for forecasting battery’s health with clustered predictors is proposed. Clustering approaches, such as Dynamic Time Warping (DTW) or k-shape-based, are beneficial to find patterns in data sets with multiple time series. The aspect of large number of batteries in a data center is used to cluster the voltage patterns, which are further utilized to improve the accuracy of the ARIMA model. Our proposed work shows that the forecasting accuracy of the ARIMA model is significantly improved by applying the results of the clustered predictor for batteries in a real data center. This paper presents the actual historical data of 40 batteries of the large-scale data center for one whole year to validate the effectiveness of the proposed methodology.

scholarly journals Advances in constraining intrinsic alignment models with hydrodynamic simulations

2021 ◽  
Vol 508 (1) ◽  
pp. 637-664 ◽  
Author(s):  
S Samuroff ◽  
R Mandelbaum ◽  
J Blazek
Keyword(s):  
Large Scale ◽  
Real Data ◽  
Model Parameters ◽  
Proof Of Concept ◽  
Hydrodynamic Simulations ◽  
Data Vector ◽  
Galaxy Type ◽  
Zero Values ◽  
Novel Method ◽  
Alignment Model

ABSTRACT We use galaxies from the illustristng, massiveblack-ii, and illustris-1 hydrodynamic simulations to investigate the behaviour of large scale galaxy intrinsic alignments. Our analysis spans four redshift slices over the approximate range of contemporary lensing surveys z = 0−1. We construct comparable weighted samples from the three simulations, which we then analyse using an alignment model that includes both linear and quadratic alignment contributions. Our data vector includes galaxy–galaxy, galaxy–shape, and shape–shape projected correlations, with the joint covariance matrix estimated analytically. In all of the simulations, we report non-zero IAs at the level of several σ. For a fixed lower mass threshold, we find a relatively strong redshift dependence in all three simulations, with the linear IA amplitude increasing by a factor of ∼2 between redshifts z = 0 and z = 1. We report no significant evidence for non-zero values of the tidal torquing amplitude, A2, in TNG, above statistical uncertainties, although MBII favours a moderately negative A2 ∼ −2. Examining the properties of the TATT model as a function of colour, luminosity and galaxy type (satellite or central), our findings are consistent with the most recent measurements on real data. We also outline a novel method for constraining the TATT model parameters directly from the pixelized tidal field, alongside a proof-of-concept exercise using TNG. This technique is shown to be promising, although comparison with previous results obtained via other methods is non-trivial.

A cluster process representation of a self-exciting process

1974 ◽  
Vol 11 (03) ◽  
pp. 493-503 ◽  
Author(s):  
Alan G. Hawkes ◽  
David Oakes
Keyword(s):  
Point Processes ◽  
Generating Functional ◽  
Cluster Process ◽  
Process Representation ◽  
Age Dependent ◽  
Birth Processes ◽  
Poisson Cluster ◽  
Cluster Processes

It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.

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