Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05We consider subcritical Bellman-Harris branching processes with two types of immigration - one appears whenever the process hits zero state and an other one is in accordance of an independent renewal process. The law of large numbers (LLN) for the total progeny of these processes and Anscombe's type central limit theorem (CLT) for the total number of particles in the cycles completely finished by the moment t are obtained.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables, respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981).Comment: revised version, to appear in: Stoch. Process. App

Optical Pulse-Phased Photopolarimetry of PSR B0656+14

We have observed the optical pulse profile of PSR B0656+14 in 10 phase bins at a high signal-to-noise ratio, and have measured the linear polarization profile over 30% of the pulsar period with some significance. The pulse profile is double-peaked, with a bridge of emission between the two peaks, similar to gamma-ray profiles observed in other pulsars. There is no detectable unpulsed flux, to a 1-sigma limit of 16% of the pulse-averaged flux. The emission in the bridge is highly (~ 100%) polarized, with a position angle sweep in excellent agreement with the prediction of the Rotating Vector Model as determined from radio polarization observations. We are able to account for the gross features of the optical light curve (i.e., the phase separation of the peaks) using both polar cap and outer gap models. Using the polar cap model, we are also able to estimate the height of the optical emission regions.Comment: 27 pages, 11 figures, accepted by ApJ (scheduled v597 n2, November 10, 2003

Tailoring electron beams with high-frequency self-assembled magnetic charged particle micro optics

Tunable electromagnets and corresponding devices, such as magnetic lenses or stigmators, are the backbone of high-energy charged particle optical instruments, such as electron microscopes, because they provide higher optical power, stability, and lower aberrations compared to their electric counterparts. However, electromagnets are typically macroscopic (super-)conducting coils, which cannot generate swiftly changing magnetic fields, require active cooling, and are structurally bulky, making them unsuitable for fast beam manipulation, multibeam instruments, and miniaturized applications. Here, we present an on-chip microsized magnetic charged particle optics realized via a self-assembling micro-origami process. These micro-electromagnets can generate alternating magnetic fields of about ±100 mT up to a hundred MHz, supplying sufficiently large optical power for a large number of charged particle optics applications. That particular includes fast spatiotemporal electron beam modulation such as electron beam deflection, focusing, and wave front shaping as required for stroboscopic imaging

HST/WFPC2 observations of the LMC pulsar PSR B0540-69

The study of the younger, and brighter, pulsars is important to understand the optical emission properties of isolated neutron stars. PSRB0540-69, the second brightest (V~22) optical pulsar, is obviously a very interesting target for these investigations. The aim of this work is threefold: constraining the pulsar proper motion and its velocity on the plane of the sky through optical astrometry, obtaining a more precise characterisation of the pulsar optical spectral energy distribution (SED) through a consistent set of multi-band, high-resolution, imaging photometry observations, measuring the pulsar optical phase-averaged linear polarisation, for which only a preliminary and uncertain measurement was obtained so far from ground-based observations. We performed high-resolution observations of PSRB0540-69 with the WFPC2 aboard the HST, in both direct imaging and polarimetry modes. From multi-epoch astrometry we set a 3sigma upper limit of 1 mas/yr on the pulsar proper motion, implying a transverse velocity <250 km/s at the 50 kpc LMC distance. Moreover, we determined the pulsar absolute position with an unprecedented accuracy of 70 mas. From multi-band photometry we characterised the pulsar power-law spectrum and we derived the most accurate measurement of the spectral index (0.70+/-0.07) which indicates a spectral turnover between the optical and X-ray bands. Finally, from polarimetry we obtained a new measurement of the pulsar phase-averaged polarisation degree (16+/-4%),consistent with magnetosphere models depending on the actual intrinsic polarisation degree and depolarisation factor, and we found that the polarisation vector (22+/-12deg position angle) is possibly aligned with the semi-major axis of the pulsar-wind nebula and with the apparent proper motion direction of its bright emission knot.Comment: 14 pages, 12 figures, accepted for publication in Astronomy & Astrophysic

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Hausdorff dimension of operator semistable L\'evy processes

Let $X=\{X(t)\}_{t\geq0}$ be an operator semistable L\'evy process in \rd with exponent $E$, where $E$ is an invertible linear operator on \rd and $X$ is semi-selfsimilar with respect to $E$. By refining arguments given in Meerschaert and Xiao \cite{MX} for the special case of an operator stable (selfsimilar) L\'evy process, for an arbitrary Borel set B\subseteq\rr_+ we determine the Hausdorff dimension of the partial range $X(B)$ in terms of the real parts of the eigenvalues of $E$ and the Hausdorff dimension of $B$.Comment: 23 page

VSI: the VLTI spectro-imager

The VLTI Spectro Imager (VSI) was proposed as a second-generation instrument of the Very Large Telescope Interferometer providing the ESO community with spectrally-resolved, near-infrared images at angular resolutions down to 1.1 milliarcsecond and spectral resolutions up to R=12000. Targets as faint as K=13 will be imaged without requiring a brighter nearby reference object. The unique combination of high-dynamic-range imaging at high angular resolution and high spectral resolution enables a scientific program which serves a broad user community and at the same time provides the opportunity for breakthroughs in many areas of astrophysic including: probing the initial conditions for planet formation in the AU-scale environments of young stars; imaging convective cells and other phenomena on the surfaces of stars; mapping the chemical and physical environments of evolved stars, stellar remnants, and stellar winds; and disentangling the central regions of active galactic nuclei and supermassive black holes. VSI will provide these new capabilities using technologies which have been extensively tested in the past and VSI requires little in terms of new infrastructure on the VLTI. At the same time, VSI will be able to make maximum use of new infrastructure as it becomes available; for example, by combining 4, 6 and eventually 8 telescopes, enabling rapid imaging through the measurement of up to 28 visibilities in every wavelength channel within a few minutes. The current studies are focused on a 4-telescope version with an upgrade to a 6-telescope one. The instrument contains its own fringe tracker and tip-tilt control in order to reduce the constraints on the VLTI infrastructure and maximize the scientific return.Comment: 12 pages, to be published in Proc. SPIE conference 7013 "Optical and Infrared Interferometry", Schoeller, Danchi, and Delplancke, F. (eds.). See also http://vsi.obs.ujf-grenoble.f

Milli-arcsecond astrophysics with VSI, the VLTI spectro-imager in the ELT era

Nowadays, compact sources like surfaces of nearby stars, circumstellar environments of stars from early stages to the most evolved ones and surroundings of active galactic nuclei can be investigated at milli-arcsecond scales only with the VLT in its interferometric mode. We propose a spectro-imager, named VSI (VLTI spectro-imager), which is capable to probe these sources both over spatial and spectral scales in the near-infrared domain. This instrument will provide information complementary to what is obtained at the same time with ALMA at different wavelengths and the extreme large telescopes.Comment: 8 pages. To be published in the proceedings of the ESO workshop "Science with the VLT in the ELT Era", held in Garching (Germany) on 8-12 October 2007, A. Moorwood edito