Mathematical Models and Methods for Monitoring and Predicting the State of Globally Distributed Computing Systems

Monitoring events and predicting the behavior of a dynamic information system are becoming increasingly important due to the globalization of cloud services and a sharp increase in the volume of processed data. Well-known monitoring systems are used for the timely detection and prompt correction of the anomaly, which require new, more effective and proactive forecasting tools. At the CMG-2013 conference, a method for predicting memory leaks in Java applications was presented, which allows IT teams to automatically release resources by safely restarting services when a certain critical threshold value is reached. Article’s solution implements a simple linear mathematical model for describing the historical trend function. However, in practice, the degradation of memory and other computational resources may not occur gradually, but very quickly, depending on the workload, and therefore, solving the forecasting problem using linear methods is not effective enough.

The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

The main goal of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO2 emissions in Morocco and concretely using a new process, in which the trend function is proportional to the modified Lundqvist-Korf growth curve. First, the main characteristics of the process are studied, then we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. When we are estimating the parameters of the process, a non-linear equation is obtained and the simulated annealing method is proposed to solve it after bounding the parametric space by a stagewise procedure. Also, to validate this methodology, we include the results obtained from several examples of simulation. Finally, the process and the methodology established are applied to real data corresponding to the evolution of CO2 emissions in Morocco.

Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

A Stochastic Lomax Diffusion Process: Statistical Inference and Application

In this paper, we discuss a new stochastic diffusion process in which the trend function is proportional to the Lomax density function. This distribution arises naturally in the studies of the frequency of extremely rare events. We first consider the probabilistic characteristics of the proposed model, including its analytic expression as the unique solution to a stochastic differential equation, the transition probability density function together with the conditional and unconditional trend functions. Then, we present a method to address the problem of parameter estimation using maximum likelihood with discrete sampling. This estimation requires the solution of a non-linear equation, which is achieved via the simulated annealing method. Finally, we apply the proposed model to a real-world example concerning adolescent fertility rate in Morocco.

Evaluation of bone mineral density through radiographic optical densitometry in 42 canine femures

This study evaluates the bone mineral density of 42 canine femurs using radiographic optical densitometry and validates radiographic optical densitometry as a parameter to standardize bone tissue samples used in biomechanical tests, contributing to the diagnosis of osteoporosis in dogs. The ImageJ 1.46r® program was used for the radiographic optical densitometry. After selecting the aluminum steps and the area of interest in the femur, the data obtained were stored in a table and converted into mm/Al using the MS Excel® trend function. Statistical analysis demonstrated the absence of atypical values (outiliers) in the samples analyzed. The samples evaluated were homogeneous and the densitometric data obtained may contribute to reducing the scarcity of densitometric references in the veterinary literature. Ex vivo biomechanical studies may benefit from the method used in this study to standardize their sample when evaluating bone mineral density, validating their respective projects

SSA-based hybrid forecasting models and applications

This study attempted to combine SSA (Singular Spectrum Analysis) with other methods to improve the performance of forecasting model for time series with a complex pattern. This work discussed two modifications of TLSAR (Two-Level Seasonal Autoregressive) modeling by considering the SSA decomposition results, namely TLSNN (Two-Level Seasonal Neural Network) and TLCSNN (Two-Level Complex Seasonal Neural Network). TLSAR consisted of a linear trend, harmonic, and autoregressive component. In contrast, the two proposed hybrid approaches consisted of flexible trend function, harmonic, and neural networks. Trend and harmonic function were considered as the deterministic part identified based on SSA decomposition. Meanwhile, NN was intended to handle the nonlinearity relationship in the stochastic part. These two SSA-based hybrid models were contemplated to be more flexible than TLSAR and more applicable to the series with an intricate pattern. The experimental studies to the monthly accidental deaths in USA and daily electricity load Jawa-Bali showed that the proposed SSA-based hybrid model reduced RMSE for the testing data from that obtained by TLSAR model up to 95%.

The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

In this article, we provided a numerical simulation for asymptotic normality of a kernel type estimator for the intensity obtained as a product of a periodic function with the power trend function of a nonhomogeneous Poisson Process. The aim of this simulation is to observe how convergence the variance and bias of the estimator. The simulation shows that the larger the value of power function in intensity function, it is required the length of the observation interval to obtain the convergent of the estimator.

Nonparametric estimation of trend function for stochastic differential equations driven by a bifractional Brownian motion

The main objective of this paper is to investigate the problem of estimating the trend function St = S(xt) for process satisfying stochastic differential equations of the type {\rm{d}}{{\rm{X}}_{\rm{t}}} = {\rm{S}}\left( {{{\rm{X}}_{\rm{t}}}} \right){\rm{dt + }}\varepsilon {\rm{dB}}_{\rm{t}}^{{\rm{H,K}}},\,{{\rm{X}}_{\rm{0}}} = {{\rm{x}}_{\rm{0}}},\,0 \le {\rm{t}} \le {\rm{T,}}where {{\rm{B}}_{\rm{t}}^{{\rm{H,K}}},{\rm{t}} \ge {\rm{0}}} is a bifractional Brownian motion with known parameters H ∈ (0, 1), K ∈ (0, 1] and HK ∈ (1/2, 1). We estimate the unknown function S(xt) by a kernel estimator ̂St and obtain the asymptotic properties as ε → 0. Finally, a numerical example is provided.