Improved approximations for buy-at-bul and shallow-light $$$$-Steiner trees and $$(,2)$$(,2)-subgraph

In this paper we give improved approximation algorithms for some network design problems. In the bounded-diameter or shallow-light \(k\)-Steiner tree problem (SL\(k\)ST), we are given an undirected graph \(G=(V,E)\) with terminals \(T\subseteq V\) containing a root \(r\in T\), a cost function \(c:E\rightarrow \mathbb {R}^+\), a length function \(\ell :E\rightarrow \mathbb {R}^+\), a bound \(L>0\) and an integer \(k\ge 1\). The goal is to find a minimum \(c\)-cost \(r\)-rooted Steiner tree containing at least \(k\) terminals whose diameter under \(\ell \) metric is at most \(L\). The input to the buy-at-bulk \(k\)-Steiner tree problem (BB\(k\)ST) is similar: graph \(G=(V,E)\), terminals \(T\subseteq V\) containing a root \(r\in T\), cost and length functions \(c,\ell :E\rightarrow \mathbb {R}^+\), and an integer \(k\ge 1\). The goal is to find a minimum total cost \(r\)-rooted Steiner tree \(H\) containing at least \(k\) terminals, where the cost of each edge \(e\) is \(c(e)+\ell (e)\cdot f(e)\) where \(f(e)\) denotes the number of terminals whose path to root in \(H\) contains edge \(e\). We present a bicriteria \((O(\log ^2 n),O(\log n))\)-approximation for SL\(k\)ST: the algorithm finds a \(k\)-Steiner tree with cost at most \(O(\log ^2 n\cdot \text{ opt }^*)\) where \(\text{ opt }^*\) is the cost of an LP relaxation of the problem and diameter at most \(O(L\cdot \log n)\). This improves on the algorithm of Hajiaghayi et al. (2009) (APPROX’06/Algorithmica’09) which had ratio \((O(\log ^4 n), O(\log ^2 n))\). Using this, we obtain an \(O(\log ^3 n)\)-approximation for BB\(k\)ST, which improves upon the \(O(\log ^4 n)\)-approximation of Hajiaghayi et al. (2009). We also consider the problem of finding a minimum cost \(2\)-edge-connected subgraph with at least \(k\) vertices, which is introduced as the \((k,2)\)-subgraph problem in Lau et al. (2009) (STOC’07/SICOMP09). This generalizes some well-studied classical problems such as the \(k\)-MST and the minimum cost \(2\)-edge-connected subgraph problems. We give an \(O(\log n)\)-approximation algorithm for this problem which improves upon the \(O(\log ^2 n)\)-approximation algorithm of Lau et al. (2009).     

Cooperation versus competition: is there really such an issue?

This author argues that youth sports can move beyond the dichotomy of cooperation versus competition by redefining competition. This can be accomplished by considering the development of cooperative skills and achievement motivation. The article addresses how cooperative skills can be taught within a competitive sport. First, it is important to understand how children and youth understand and process competition based on their developmental stage. Parents need to consider whether a child is mentally, emotionally, socially, and physically mature enough to participate in an organized sport. Readiness for a sport is just as important as readiness for school. Teaching cooperative skills within a competitive context involves a focus on personal development rather than performance. By asking themselves a series of developmental questions, such as, "Is the sport appropriate for the developmental age of the child?" parents and coaches can form realistic expectations of young athletes. Motivation is also a key determinant of a child's readiness for youth sports and competition. Children want to play a sport when they feel competent. It is up to parents and coaches to create a motivational climate that is focused on doing one's best and not on external rewards like winning. Children and youth receive specific and constructive feedback that focuses on improvement in this type of climate. The author also discusses three models of competition: the military model, the reward model, and the partnership model. The partnership model is the approach that balances competition in youth sports. The author concludes by introducing the "athletic square" model as an important and appropriate way to promote youth sports.     

Development and pollution in the Middle East and North Africa: Democracy matters

The Middle East and North Africa (MENA) countries are among the world’s top emitters of CO₂ and SO₂ in per capita terms. The objective of this paper is to analyze whether investing in the democratic development of these countries is an effective tool to make the economic development in this region more environmentally compatible. Using panel data on the income-emission-democracy nexus in 17 MENA countries from 1980 to 2005, we find evidence that improvements in the democratic development of the MENA countries help to mitigate environmental problems. Our results clearly show that the quality of democratic institutions has a greater influence on local environmental problems than on global environmental issues in the MENA region.     

Two-Piece location-scale distributions based on scale mixtures of normal family

In this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm.     

Phase II monitoring of binary profiles in the presence of within-profile autocorrelation based on Markov Model

This paper introduces a Markov model in Phase II profile monitoring with autocorrelated binary response variable. In the proposed approach, a logistic regression model is extended to describe the within-profile autocorrelation. The likelihood function is constructed and then a particle swarm optimization algorithm (PSO) is tuned and utilized to estimate the model parameters. Furthermore, two control charts are extended in which the covariance matrix is derived based on the Fisher information matrix. Simulation studies are conducted to evaluate the detecting capability of the proposed control charts. A numerical example is also given to illustrate the application of the proposed method.     

Estimating the distribution function of symmetric pairs

We discuss three classes of bivariate symmetry models and study the estimation of their distribution functions (DFs). Under radial symmetry, an estimator based on the mean of the empirical and survival DFs is considered. For exchangeable symmetry, an estimator based on the mean of the empirical DF and its exchangeable image is presented. At their intersection, we define radial exchangeability and study estimation of its DF. The symmetrized estimators coincide with the non parametric maximum likelihood estimators of the DF under each model. We obtain their mean and variance and state their asymptotic normality. The relative efficiency of the estimators for the bivariate normal distribution is obtained.     

On a Skew Bimodal Normal–Normal distribution fitted to the Old-Faithful geyser data

The Bimodal Normal distribution introduced by Alavi (2011) is a symmetric distribution where its variance is three times the variance of the corresponding normal distribution. Azzalini (1985) introduced the univariate Skew Normal distribution to model asymmetry data. In this paper the Skew Bimodal Normal–Normal distribution is introduced as a skew-symmetric distribution generated by the cumulative function of standard normal. Some properties of the distribution and some methods for generating data from this distribution are introduced. The maximum likelihood estimation of parameters is obtained. The distribution is fitted to the Old Faithful Geyser data.     

Economic and economic–statistical designs of VSI Bayesian control chart using Monte Carlo method and ABC algorithm

The usual practice in using a Bayesian control chart to monitor a process is done by taking samples from the process with fixed sampling intervals. Recent studies on traditional control charts have shown that variable sampling interval (VSI) scheme compared to classical scheme (fixed ratio sampling, FRS) helps practitioners to detect process shifts more quickly. In this paper, the effectiveness of VSI scheme on performance of Bayesian control chart has been studied, based on economic (ED) and economic–statistical designs (ESD). Monte Carlo method and artificial bee colony algorithm have been utilized to obtain optimal design parameters of Bayesian control chart (sample size, sampling intervals, warning limit and control limit) since the statistic of this approach does not have any specified distribution. Finally, VSI Bayesian control chart has been compared to FRS Bayesian and VSI X-bar approaches based on ED and ESD, separately. According to the results, it has been found that the performance of VSI Bayesian scheme is better than FRS Bayesian and VSI X-bar approaches.