We have measured directly the forces across water between hydrophilic surfaces covered with a random mosaic of positive and negative charged domains. We find a strong, long-ranged attraction between them at a surface separation comparable with the charge domain size (many tens of nanometers). This attraction persists at higher salt concentration, but its range then becomes comparable to the Deb...

When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditiona...

Frazzled (Fra) is the DCC-like Netrin receptor in Drosophila that mediates attraction; Roundabout (Robo) is a Slit receptor that mediates repulsion. Both ligands are expressed at the midline; both receptors have related structures and are often expressed by the same neurons. To determine if attraction versus repulsion is a modular function encoded in the cytoplasmic domain of these receptors, w...

Limit distributions of the maximum independent copies a transformation Gaussian random variable are studied. Sufficient and necessary conditions found for transformations belonging to Fréchet Weibull domains attraction. Simple sufficient also given.

We prove conditional local limit theorems for Gibbs-Markov processes whose marginals are in the domain of attraction of a stable law with order in (0;2). c 1996.

We show how piecewise quadratic Lyapunov functions can be used to estimate regions of attraction for linear systems with saturation. The central issues of how to restrict the analysis region and how to optimize the size of the domain of attraction are addressed, and the approach is demonstrated on several examples. We observe that the piecewise quadratic Lyapunov functions yield significant imp...

Using the local potential approximation of the exact renormalization group (RG) equation , we show the various domains of values of the parameters of the O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the usual critical surface S c (attraction domain of the Wilson-Fisher fixed point), we explicitly show the existence of a first-order phase transition domain S f separated...