An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fund...

PURPOSE To determine the normal distribution of corneal diameter in a 40- to 64-year-old population and its association with other biometric components. METHODS In a cross-sectional population-based study, subjects were selected through multistage cluster sampling from the 40- to 64-year-old citizens of Shahroud in northern Iran. After obtaining informed consents, optometry tests including re...

We present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the nearest neighbors, the clustering coefficient, the "betweenness," the distance between two nodes, and the diameter of a network. All these measures are well established for unweighted networks but have...

We have predicted theoretically and detected in laboratory experiments a tangling clustering of inertial particles in a stably stratified turbulence with imposed mean vertical temperature gradient. In the stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, i.e., the inertial particles are accumulate...

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Phys. Rev. Lett. 89, 258702 (2002)]. Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering...

We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in [0, A], with sample complexities independent of domain size permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other param...

In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...

In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...