Competition and adaptation in an Internet evolution model

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and the total number of connections in the Internet, both empirically measurable quantities. This fact place our model apart from others in which this exponent depends on parameters that need to be adjusted in a model dependent way. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity and traffic of the network.Comment: Minor content changes and inset of fig.

Stability and relapse after orthodontic treatment of deep bite cases—a long-term follow-up study

The purpose of this long-term follow-up study was twofold—firstly, to assess prevalence of relapse after treatment of deep bite malocclusion and secondly, to identify risk factors that predispose patients with deep bite malocclusion to relapse. Sixty-one former patients with overbite more than 50% incisor overlap before treatment were successfully recalled. Clinical data, morphometrical measurements on plaster casts before treatment, after treatment and at long-term follow-up, as well as cephalometric measurements before and after treatment were collected. The median follow-up period was 11.9 years. Patients were treated by various treatment modalities, and the majority of patients received at least a lower fixed retainer and an upper removable bite plate during retention. Relapse was defined as increase in incisor overlap from below 50% after treatment to equal or more than 50% incisor overlap at long-term follow-up. Ten per cent of the patients showed relapse to equal or larger than 50% incisor overlap, and their amount of overbite increase was low. Among all cases with deep bite at follow-up, gingival contact and palatal impingement were more prevalent in partially corrected noncompliant cases than in relapse cases. In this sample, prevalence and amount of relapse were too low to identify risk factors of relaps

mcov : Moving Cross-covariance Matrix

The function mcov computes estimates of the lag l moving cross-covariance matrix of non-stationary (and stationary) time series. Notice that the following library is needed to be installed before using the mcov function: library(roll

QMDPCA : Quadratic Moving Dynamic Principal Component Analysis for Non-Stationary Multivariate Time Series

This function reduce the dimension of non-stationary (and stationary) multivariate time series by performing eigenanalysis on the quadratic moving cross-covriance matrix of the extended data matrix up to some specified lag. Notice that the following libraries are needed to be installed before using the MDPCA function: library(roll); library(expm)

GTSPCA : Generalized Principal Component Analysis for Non-Stationary Vector Time Series

This function is used to segment a stationary/nonstationary multivariate series into n uncorrelated subseries. Notice that the following libraries are needed to be installed before using the GTSPCA function: library(roll);library(expm

MDPCA : Moving Dynamic Principal Component Analysis for Non-Stationary Multivariate Time Series

This function reduce the dimension of non-stationary (and stationary) multivariate time series by performing eigenanalysis on the moving cross-covriance matrix of the extended data matrix up to some specified lag. Notice that thefollowing libraries are needed to be installed before using the MDPCA function: library(roll); library(expm)

MpermutMax : The Maximum Moving Cross-Correlation Method

This method is a permutation method. It is used to test for significant correlations between the variables of both stationary and non-stationary multivariate time series. This method extended the Maximum Cross-Correlation methodof Change et al. (2018) to account for non-stationary high-dimensional time series. Notice that the following library is needed to be installed before using the mpermutMax function: library(roll

RCCM : Retained Component Criterion for the Moving Dynamic Principal Component Analysis

The RCC_MDPCA criterion is a new tool to determine the optimal number of components (i.e. MDPCs) to retain for the Moving Dynamic Principal Component Analysis (MDPCA). This criterion balances between the following two desires, reducing the dimension of the data and increasing the accuracy of the final results of MDPCA; See Alshammri and Pan (2019). Notice that the following libraries are needed to be installed before using the mcov function: library(roll); library(MDPCA