Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Bonds between fibronectin and fibronectin-binding proteins on Staphylococcus aureus and Lactococcus lactis.

Bacterial cell-wall-associated fibronectin binding proteins A and B (FnBPA and FnBPB) form bonds with host fibronectin. This binding reaction is often the initial step in prosthetic device infections. Atomic force microscopy was used to evaluate binding interactions between a fibronectin-coated probe and laboratory-derived Staphylococcus aureus that are (i) defective in both FnBPA and FnBPB (fnbA fnbB double mutant, DU5883), (ii) capable of expressing only FnBPA (fnbA fnbB double mutant complemented with pFNBA4), or (iii) capable of expressing only FnBPB (fnbA fnbB double mutant complemented with pFNBB4). These experiments were repeated using Lactococcus lactis constructs expressing fnbA and fnbB genes from S. aureus. A distinct force signature was observed for those bacteria that expressed FnBPA or FnBPB. Analysis of this force signature with the biomechanical wormlike chain model suggests that parallel bonds form between fibronectin and FnBPs on a bacterium. The strength and covalence of bonds were evaluated via nonlinear regression of force profiles. Binding events were more frequent (p < 0.01) for S. aureus expressing FnBPA or FnBPB than for the S. aureus double mutant. The binding force, frequency, and profile were similar between the FnBPA and FnBPB expressing strains of S. aureus. The absence of both FnBPs from the surface of S. aureus removed its ability to form a detectable bond with fibronectin. By contrast, ectopic expression of FnBPA or FnBPB on the surface of L. lactis conferred fibronectin binding characteristics similar to those of S. aureus. These measurements demonstrate that fibronectin-binding adhesins FnBPA and FnBPB are necessary and sufficient for the binding of S. aureus to prosthetic devices that are coated with host fibronectin.

Dimensions, issues, and bills: Appropriations voting on the house floor

One of the fundamental findings in the congressional literature is that one or sometimes two dimensions can successfully describe roll-call voting. In this paper we investigate if we can reach the same conclusions about low dimensionality when we divide the roll-call agenda into subsets of relatively homogeneous subject matter. We are primarily interested in the degree to which the same ordering of representatives is yielded across these different groups of votes. To conduct our analysis we focus on all roll calls on the 13 annual appropriations bills across eight congresses. When we concentrate on these smaller issue areas, we find that voting is multidimensional and members do not vote in a consistent ideological fashion across all issue areas. Copyright © Southern Political Science Association 2010.