Point processes are a class of models where the notion of variable dimension is inherent. The main part of this discussion is concerned with the application of marked point processes as prior models in nonparametric Bayesian function estimation, reformulating and revising earlier joint work with Elja Arjas and listing some other related work (Section 2). Accordingly, the discussion is centered ...

The Kronecker product of two Schur functions s λ and s µ , denoted s λ * s µ , is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of n, λ and µ, respectively. The coefficient, g λ,µ,ν , of s ν in s λ * s µ is equal to the multiplicity of the irreducible representation indexed by ν in the tensor product...

This article aims to give an overview of Carnap’s 1928 book Logical Structure of the World or Aufbau and the most influential interpretations of its significance. After giving an outline of the book in Section 2, I turn to the first sustained interpretations of the book offered by Goodman and Quine in Section 3. Section 4 explains how this empirical reductionist interpretation was largely displ...

We prove that the Lam-Shimozono “down operator” on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of “near rectangles” in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of ...

The main goal of this paper is to give a precise description of rescaling behaviors of rational type global strong solutions to the PolubarinovaGalin equation. The Polubarinova-Galin equation is the reformulation of the zero surface tension Hele-Shaw problem with a single source at the origin by considering the moving domain as the Riemann mapping of the unit disk centered at the origin. The co...

which is considerably longer than previous measurements at the same mesh Reynolds number (Re = 48260). The stratified experiment resulted in a decay rate virtually identical to that of the neutral case through W,t/M = 275. However the decay rate sharply decreased after this time when the field of turbulence was replaced by internal gravity waves. A critical Richardson number marks the transitio...

Direct Numerical Simulations of a linearly stratified bounded fluid in decaying turbulence are performed. The abscence of vertical periodicity allows the stratification of the system to evolve in time. We observe that mixing efficiency increases as a function of the Richardson number Ri, and saturates to a maximum value of 0.25. This evolution adjusts quantitatively to the statistical predictio...

The natural mortality (M) and purse-seine catchability and selectivity were estimated for Trachurus novaezelandiae, Richardson, 1843 (yellowtail scad)-a small inshore pelagic species harvested off south-eastern Australia. Hazard functions were applied to two decades of data describing catches (mostly stable at a mean +- SE of 315 +- 14 t p.a.) and effort (declining from a maximum of 2289 to 642...

It has become increasingly clear that air-sea coupling is important to the earth's weather and climate [e.g., Grotzner et al. 1998, Xu et al. 1998]. The oceanic surface mixed layer is the link by which the air and sea are coupled. Further, the form and strength of the mixing motion are important to important concerns such as the fluxes of gases and nutrients and the growth and health of marine ...

We prove limit theorems for small-scale pair dispersion in synthetic velocity fields with power-law spatial spectra and wavenumber dependent correlation times. These limit theorems are related to a family of generalized Richardson’s laws with a limiting case corresponding to Richardson’s t3and 4/3-laws. We also characterize a regime of positive dissipation of passive scalars. © 2003 Elsevier Sc...