Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_D$ and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle's death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.Comment: Published in at http://dx.doi.org/10.1214/12-AOP778 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Recombining Plasma & Gamma-ray Emission in the Mixed-morphology Supernova Remnant 3C 400.2

3C 400.2 belongs to the mixed morphology supernova remnant class, showing center-filled X-ray and shell-like radio morphology. We present a study of 3C 400.2 with archival Suzaku and Fermi-LAT observations. We find recombining plasma (RP) in the Suzaku spectra of north-east and south-east regions. The spectra of these regions are well described by two-component thermal plasma models: The hard component is in RP, while the soft component is in collisional ionization equilibrium (CIE) conditions. The RP has enhanced abundances indicating that the X-ray emission has an ejecta origin, while the CIE has solar abundances associated with the interstellar material. The X-ray spectra of north-west and south-west regions are best fitted by a two-component thermal plasma model: an ionizing and a CIE plasma. We have detected GeV gamma-ray emission from 3C 400.2 at the level of $\sim$5$\sigma$ assuming a point-like source model with a power-law (PL) type spectrum. We have also detected a new GeV source at the level of $\sim$13$\sigma$ assuming a Gaussian extension model with a PL type spectrum in the neighborhood of the SNR. We report the analysis results of 3C 400.2 and the new extended gamma-ray source and discuss the nature of gamma-ray emission of 3C 400.2 in the context of existing NANTEN CO data, DRAO HI data, and the Suzaku X-ray analysis results.Comment: Accepted to be published in the Astrophysical Journa

Making the right call: Redesigning call centres from the bottom up

First author at the time at Department of Management, London School of Economics

Application of Self Tuning Fuzzy Logic Control to Full Railway Vehicle Model

AbstractThis paper presents the dynamic modeling and intelligent control of the full railway vehicle against the railway irregularities. In order to safe and comfortable transportation of passengers, vibration analysis and control studies are investigated by using Matlab–Simulink software. The 54 degrees of freedom railway vehicle model is used for analysis. The controllers are placed between the car body and bogies. For reducing the car body vibrations caused by a lateral and two vertical sinusoidal track irregularities, fuzzy logic and self-tuning fuzzy logic control schemes are applied to railway vehicle. The fuzzy logic based algorithms herein are used for realizing the active control of car body vibrations. The simulations of vibration analysis are obtained in time and frequency domains and compared with uncontrolled case. A good vibration reduction performance is achieved by using applied control algorithms