A recent letter reports an upper limit on the galactic compact binary inspiral rate set by gravitational wave observations using the LIGO 40M prototype interferometer. The limit was set by imagining a threshold set equal to the amplitude of the loudest event and then considering the probability that only one event was observed with amplitude greater than the threshold. That limit can be improve...

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak ∼ Ck, k → ∞, p > 0, where C is a positive constant. The measures considered are associated with reversible coagulationfragmentation processes and combinatorial structures, known as assemblies. We prove a functional central limit theorem...

BACKGROUND Although reduced function of the respiratory system limits peak oxygen uptake in diseases affecting the lungs or airways, the healthy respiratory system is thought to have a spare capacity for oxygen transport and uptake, and is not considered a limiting factor for peak oxygen uptake in healthy people. However, lung function declines with age and could theoretically limit peak oxygen...

Scatter plots, bar charts, linear regressions, analysis of variance, and other graphics and tests are frequently used to document associations between an independent variable and an outcome. However, these methods are also frequently limited when understanding how to use an independent variable in subsequent research or patient management. A novel graphical approach to visualizing data-the thre...

We consider a three-term nonlinear recurrence relation involving a nonlinear filtering function with a positive threshold λ. We work out a complete asymptotic analysis for all solutions of this equation when the threshold varies from 0 to ∞. It is found that all solutions either tends to 0, a limit 1-cycle, or a limit 2-cycle, depending on whether the parameter λ is smaller than, equal to, or g...

The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of weights belong to given Borel sets. We extend several known limit theorems for the number of prescribed subgraphs to show that the strong law of large numbers can...

In distinction to the Neumann case the squeezing limit of a Dirichlet network leads in the threshold region generically to a quantum graph with disconnected edges, exceptions may come from threshold resonances. Our main point in this paper is to show that modifying locally the geometry we can achieve in the limit a nontrivial coupling between the edges including, in particular, the class of δ-t...