An $$O^{*}(1.4366^n)$$-time exact algorithm for maximum $$P_2$$P2-packing in cubic graphs

Given a graph \(G=(V, E)\), a \(P_2\)-packing \(\mathcal {P}\) is a collection of vertex disjoint copies of \(P_2\)s in \(G\) where a \(P_2\) is a simple path with three vertices and two edges. The Maximum \(P_2\)-Packing problem is to find a \(P_2\)-packing \(\mathcal {P}\) in the input graph \(G\) of maximum cardinality. This problem is NP-hard for cubic graphs. In this paper, we give a branch-and-reduce algorithm for the Maximum \(P_2\)-Packing problem in cubic graphs. We analyze the running time of the algorithm using measure-and-conquer and show that it runs in time \(O^{*}(1.4366^n)\) which is faster than previous known exact algorithms where \(n\) is the number of vertices in the input graph.     

A Standardized Normal-Laplace Mixture Distribution Fitted to Symmetric Implied Volatility Smiles

This article proposes to use a standardized version of the normal-Laplace mixture distribution for the modeling of tail-fatness in an asset return distribution and for the fitting of volatility smiles implied by option prices. Despite the fact that only two free parameters are used, the proposed distribution allows arbitrarily high kurtosis and uses one shape parameter to adjust the density function within three standard deviations for any specified kurtosis. For an asset price model based on this distribution, the closed-form formulas for European option prices are derived, and subsequently the volatility smiles can be easily obtained. A regression analysis is conducted to show that the kurtosis, which is commonly used as an index of tail-fatness, is unable to explain the smiles satisfactorily under the proposed model, because the additional shape parameter also significantly accounts for the deviations revealed in smiles. The effectiveness of the proposed parsimonious model is demonstrated in the practical examples where the model is fitted to the volatility smiles implied by the NASDAQ market traded foreign exchange options.     

Cox regression for current status data with mismeasured covariates

Covariate measurement error problems have been extensively studied in the context of right‐censored data but less so for current status data. Motivated by the zebrafish basal cell carcinoma (BCC) study, where the occurrence time of BCC was only known to lie before or after a sacrifice time and where the covariate (Sonic hedgehog expression) was measured with error, the authors describe a semiparametric maximum likelihood method for analyzing current status data with mismeasured covariates under the proportional hazards model. They show that the estimator of the regression coefficient is asymptotically normal and efficient and that the profile likelihood ratio test is asymptotically Chi‐squared. They also provide an easily implemented algorithm for computing the estimators. They evaluate their method through simulation studies, and illustrate it with a real data example. The Canadian Journal of Statistics 39: 73–88; 2011 © 2011 Statistical Society of Canada     

Simultaneous prediction intervals for all patrwise differences among several future sample means

Hahn (1977) suggested a procedure for constructing prediction intervals for the difference between the means of two future samples from normal populations having equal variance, based on past samples selected from both populations. In this paper, we extend Hahn's work by constructing simultaneous prediction intervals for all pairwise differences among the means of k ≥ 2 future samples from normal populations with equal variances, using past samples taken from each of the k populations. For K = 2, this generalization reduces to Hahn's special case. These prediction intervals may be used when one has sampled the performance of several products and wishes to simultaneously as- sess the differences in future sample mean performance of these products with a predetermined overall coverage probability. The use of the new procedure is demonstrated with a numerical example.     

Optimal Bayesian strategies for the infinite-armed Bernoulli bandit

We consider the bandit problem with an infinite number of Bernoulli arms, of which the unknown parameters are assumed to be i.i.d. random variables with a common distribution F. Our goal is to construct optimal strategies of choosing “arms” so that the expected long-run failure rate is minimized. We first review a class of strategies and establish their asymptotic properties when F is known. Based on the results, we propose a new strategy and prove that it is asymptotically optimal when F is unknown. Finally, we show that the proposed strategy performs well for a number of simulation scenarios.     

Gratitude and Adolescent Athletes’ Well-Being: The Multiple Mediating Roles of Perceived Social Support from Coaches and Teammates

Since the positive psychology was emerged from 2000s, these positive constructs contribute to athlete’s well-being received much attention in sport. However, gratitude is a topic rarely discussed in the sport psychology. Thus, the current study aims at investigated the relationship between gratitude and athlete well-being. Furthermore, the mechanisms underlie the relationship was also explored. We proposed that the perceived social support from coach and teammate would be mediators. Participants were 291 adolescent athletes. Structural equation modeling was used to examine the hypothesis. Results indicated that gratitude is a positive related to athlete’s well-being. Besides, multiple-mediators analysis indicated that both perceived coach and teammate social support partially mediated the relationship between gratitude and athlete’s well-being. This study contributes to the gratitude and well-being literature by unpacking the essential psychological process behind the relationship. Implication and application were discussed in term of gratitude theory and social support.     

Do Rural Students Really Perform Worse than Urban Students Do? Empirical Evidence from a University Entrance Program in Taiwan

Despite a major expansion in the number of students in higher education, students from rural areas continue to be underrepresented at selective universities. To reduce the urban‐rural imbalance of entry to selective universities, institutions in many countries of the world have implemented admission policies favoring rural students. Previous evidence has shown that rural students have lower academic performance than their urban peers, which leads to concern that rural students will reduce the academic excellence of selective universities. Using the introduction of a university admission policy favoring rural students in Taiwan and a unique administrative data set of students' academic records, we compare the academic performance of students from rural areas with that of their urban counterparts during their college years. The results show that rural students have consistently outperformed urban students in semester grade point averages and class rank percentile across time; however, the differences in academic performance are mainly attributed to the rural students' initial outperformance in the first semester of the freshman year.     

Constructions of given-depth and optimal multirate rearrangeably nonblocking distributors

Rearrangeable multirate multicast switching networks are customarily called rearrangeable multirate distributors. It has been known for a long time that rearrangeable multirate distributors with cross-point complexity O(nlog?² n) can be constructed, where n is the number of inputs (and outputs) of the switching network. The problem of constructing optimal distributors remains open thus far. This paper gives a general construction of rearrangeable multirate distributors with given depths. One byproduct is a rearrangeable multirate distributor with crosspoint complexity O(nlog?n). We also show that this cross-point complexity is optimal, settling the aforementioned open problem. One of the key ingredients of our new construction is the notion of multirate concentrators. The second ingredient is a multirate version of the Pippenger network. We show how to construct given-depth multirate concentrators and given-depth multirate Pippenger networks with small sizes. When the depth is chosen to optimize the size, we obtain the optimal O(nlog?n) cross-point complexity.     

A comparison of two large sample confidence intervals for a proportion: A Monte Carlo simulation

SUMMARY Two pairs of confidence intervals for a proportion, similar to that of Larson, are compared. It can be shown through computer simulation experiments that, for certain values of p, the confidence interval obtained by the approximation is superior.