Let D be a strongly connected digraph. The average distance σ̄(v) of vertex v is the arithmetic mean distances from to all other vertices D. remoteness ρ(D) and proximity π(D) are maximum minimum D, respectively. We obtain sharp upper lower bounds on as function order n describe extreme digraphs for bounds. also such strong tournaments. show that tournament T, we have π(T)=ρ(T) if only T regular...

In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

Let $D$ be a $k$-regular bipartite tournament on $n$ vertices. We show that, for every $p$ with $2 \le p n/2-2$, has cycle $C$ of length $2p$ such that $D \setminus C$ is hamiltonian unless isomorphic to the special digraph $F_{4k}$. This statement was conjectured by Manoussakis, Song and Zhang [K. Zhang, Y. Z. Song. Complementary cycles containing fixed arc in diregular tournaments. Discrete M...

OBJECTIVE To profile training habits and injuries in football players participating in a national Masters tournament. METHODS A cross-sectional retrospective study design was used to survey male football players attending the 2008 New Zealand Masters Games. Information regarding player demographics, football injuries, football related training, and risk factors for injury were collected. RE...

We propose a new way of quantifying a team’s strength of schedule for NCAA basketball. This strength of a schedule is defined as the number of games a team on the borderline of the annual national tournament would expect to win if they played that schedule. This gives a direct way of quantifying how well different teams have done relative to the schedules they have played. Our motivation for co...

A directed graph where there is exactly one edge between every pair of vertices is called a tournament. Finding the “best” set of vertices of a tournament is a well studied problem in social choice theory. A tournament solution takes a tournament as input and outputs a subset of vertices of the input tournament. However, in many applications, for example, choosing the best set of drugs from a g...

A common goal of epidemiologic research is to study the association between a certain exposure and a certain outcome, while controlling for important covariates. This is often done by fitting a restricted mean model for the outcome, as in generalized linear models (GLMs) and in generalized estimating equations (GEEs). If the covariates are high-dimensional, then it may be difficult to well spec...