Brownian couplings, convexity, and shy-ness

Benjamini, Burdzy, and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component processes of the coupling staying at least a given positive distance away from each other for all time. Among other results, they showed that no shy couplings could exist for reflected Brownian motions in C-2 bounded convex planar domains whose boundaries contain no line segments. Here we use potential-theoretic methods to extend this Benjamini et al. (2007) result (a) to all bounded convex domains (whether planar and smooth or not) whose boundaries contain no line segments, (b) to all bounded convex planar domains regardless of further conditions on the boundary

Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fréchet means) of independent nonidentically distributed random variables taking values in Riemannian manifolds. In order to prove these theorems we describe and prove a simple kind of Lindeberg–Feller central approximation theorem for vector-valued random variables, which may be of independent interest and is therefore the subject of a self-contained section. This vector-valued result allows us to clarify the number of conditions required for the central limit theorem for empirical Fréchet means, while extending its scope

Coupling iterated Kolmogorov diffusions

The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals

Development of hexagrammids (Pisces: Scorpaeniformes) in the northeastern Pacific Ocean

Larvae of Oxylebius pictus, Zaniolepis sp., Ophiodon elongatus, Hexagrommos stelleri, H. decagrammus, H. lagocephalus, H. octogrammus, and Pleurogrammus monopterygius are described and illustrated from field collections which were supplemented by laboratory reared specimens of some species. Larvae hatch at a rather large size (3-9 mm), are heavily pigmented, and undergo direct development to an epipelagic prejuvenile stage. Larvae or the five genera are separable on the basis of body shape, pigmentation, and meristic characters. Larvae or the four species of Hexagrammos, which are quite similar in appearance, are separable on the basis of a combination of several pigmentation characters. Developmental evidence indicates that Oxylebius and Zaniolepis are similar to each other and are more similar to presumed primitive coUids than the other included genera. Ophiodon is dissimilar to the other four genera. Pleurogrammus and Hexagrommos have similar appearing larvae. Among the species of Hexagrammos a progression or increasing larval pigmentation can be seen from H. stelleri to H. decagrammus, H. lagocephalus, and H. octogrammus. (PDF file contains 50 pages.

N-fold way simulated tempering for pairwise interaction point processes

Pairwise interaction point processes with strong interaction are usually difficult to sample. We discuss how Besag lattice processes can be used in a simulated tempering MCMC scheme to help with the simulation of such processes. We show how the N-fold way algorithm can be used to sample the lattice processes efficiently and introduce the N-fold way algorithm into our simulated tempering scheme. To calibrate the simulated tempering scheme we use the Wang-Landau algorithm

Effects of turbulence in the atmosphere of Venus on Pioneer Venus radio, phase 2

Two problems related to the effects of turbulence in the atmosphere of Venus on the Pioneer entry probe radio link were studied. In the first problem, the cross correlation between the log amplitude and phase fluctuations of the Pioneer Venus communications link is examined. Data show that for fluctuation frequencies above approximately 1 Hz there is little or no correlation. For frequencies below this region the correlation is weak and the square root of the coherence has a peak value close to 0.65. The second problem consists of interferring turbulence characteristics of the Venus atmosphere from the Mariner 5 phase fluctuations. Data show that with the data processing techniques developed and currently available, the phase error due to oscillator drift, assumed trajectory delay, and spline curve fit exceed the turbulence induced fluctuations. Results show that it is not possible to interfere with the turbulence characteristics from Mariner 5 phase fluctuations

Coping with unobservable and mis-classified states in capture-recapture studies

Multistate mark-recapture methods provide an excellent conceptual framework for considering estimation in studies of marked animals. Traditional methods include the assumptions that (1) each state an animal occupies is observable, and (2) state is assigned correctly at each point in time. Failure of either of these assumptions can lead to biased estimates of demographic parameters. I review design and analysis options for minimizing or eliminating these biases. Unobservable states can be adjusted for by including them in the state space of the statistical model, with zero capture probability, and incorporating the robust design, or observing animals in the unobservable state through telemetry, tag recoveries, or incidental observations. Mis¿classification can be adjusted for by auxiliary data or incorporating the robust design, in order to estimate the probability of detecting the state an animal occupies. For both unobservable and mis-classified states, the key feature of the robust design is the assumption that the state of the animal is static for at least two sampling occasion

Further studies of the coupled chemically reacting boundary layer and charring ablator. Part 1 - Summary Final report

Computer program development for charring ablative materials, chemically reacting laminar boundary layers, and turbulent boundary layer initiatio