A non-parametric Bayesian approach to decompounding from high frequency data

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density \(f_0\) of its jump sizes, as well as of its intensity \(\lambda _0.\) We take a Bayesian approach to the problem and specify the prior on \(f_0\) as the Dirichlet location mixture of normal densities. An independent prior for \(\lambda _0\) is assumed to be compactly supported and to possess a positive density with respect to the Lebesgue measure. We show that under suitable assumptions the posterior contracts around the pair \((\lambda _0,\,f_0)\) at essentially (up to a logarithmic factor) the \(\sqrt{n\Delta }\)-rate, where n is the number of observations and \(\Delta \) is the mesh size at which the process is sampled. The emphasis is on high frequency data, \(\Delta \rightarrow 0,\) but the obtained results are also valid for fixed \(\Delta .\) In either case we assume that \(n\Delta \rightarrow \infty .\) Our main result implies existence of Bayesian point estimates converging (in the frequentist sense, in probability) to \((\lambda _0,\,f_0)\) at the same rate. We also discuss a practical implementation of our approach. The computational problem is dealt with by inclusion of auxiliary variables and we develop a Markov chain Monte Carlo algorithm that samples from the joint distribution of the unknown parameters in the mixture density and the introduced auxiliary variables. Numerical examples illustrate the feasibility of this approach.     

Graphs G for which both G and G¯ are Contraction Critically k-Connected

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement Gˉ are contraction critically k-connected, then |V(G)|<k ^5/3+4k ^3/2. Received: October, 2001 Final version received: September 18, 2002 AMS Classification: 05C40     

Life span of solutions with large initial data for a semilinear parabolic system

We investigate the initial-boundary value problem

     

Power operations in elliptic cohomology and representations of loop groups

Part I of this paper describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. Part II discusses a relationship between equivariant elliptic cohomology and representations of loop groups. Part III investigates the representation of theoretic considerations which give rise to the power operations discussed in Part I.

     

Coexistence of solvated electrons and solvent valence anions in negatively charged acetonitrile clusters, (CH3CN)-n(n=10-100)

Anion photoelectron spectroscopy of acetonitrile cluster anions, (CH3CN)(-)(n) (n=10-100), successfully demonstrates the competitive coexistence of two different anionic species: a solvated electron and a solvent-bound valence anion. The distinctly different nature of these anions is revealed by hole-burning-type photoelectron spectroscopy and relative photodetachment cross section measurements. This unusual coexistence is attributed to the closely lying nature of their anionic states at just the number of solvent molecules sufficient to almost complete the first solvation layer.     

Ultrasonic intensity microscopy for imaging of living cells

Ultrasound intensity microscopy was developed for in vivo imaging. This paper describes the preliminary results obtained using 300 MHz ultrasound intensity microscopy for in vitro characterization of cell cultures. The novelty of the approach lies in the fact that it allows remote, non-contact and disturbance-free imaging of cultured synovial cells and the changes in the cells’ properties due to external stimulants such as transforming growth factor beta-1 (TGF-β1). The intensity imaging method has potential for extracting mechanical cell properties and monitoring the effects of drugs.Ultrasound propagates through a thin specimen such as cultured cells and is reflected at the interface between the specimen and substrate. A two-dimensional distribution of the ultrasonic intensity, which is closely related to the mechanical properties, is visualized to analyze cell organs, such as the nucleus at the central part and the cytoskeleton at the peripheral zone. After stimulation with TGF-β1, the ultrasonic intensity at the actin zone was significantly increased compared with the control.     

Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Multiple bosonic mode coupling in the electron self-energy of (La2-xSrx)CuO4

High resolution angle-resolved photoemission spectroscopy data along the (0,0)-(pi,pi) nodal direction with significantly improved statistics reveal fine structure in the electron self-energy of the underdoped (La2-xSrx)CuO4 samples in the normal state. Fine structure at energies of (40-46) meV and (58-63) meV, and possible fine structure at energies of (23-29) meV and (75-85) meV, have been identified. These observations indicate that, in (La2-xSrx)CuO4, more than one bosonic modes are involved in the coupling with electrons.     

Propagating beam analysis of fiber wavelength filters with a depressed-index section

A wavelength filter consisting of single-mode and few-mode fibers is investigated numerically. A simple finite-difference beam-propagation method, in which a transparent boundary condition can be imposed, is developed for circularly symmetric waveguides. After confirming the validity of the numerical method by the mode-mismatch loss, we calculate the propagating field in the fiber wavelength filter, in which interference between LP₀₁, and LP₀₂ modes occurs. To improve the filtering operation, a depressed-index fiber is employed for the few-mode fiber. The effects of the radius and refractive index of the depressed section on the transmission power are revealed and discussed. Power is suppressed to less than 0.1% at 1.3 μm, while maintaining power transmission of more than 85% at 1.55 μm. It is also found that the filtering operation shifts to higher wavelengths as the input power is increased when we choose a self-focusing nonlinear material in the depressed section.