Relative frequencies in multitype branching processes

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell biology. Specifically, the reported limiting results are of advantage in cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement. Relevant statistical applications are discussed in the context of asymptotic maximum likelihood inference for multitype branching processes.Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Direct Urca Process in a Neutron Star Mantle

We show that the direct Urca process of neutrino emission is allowed in two possible phases of nonspherical nuclei (inverse cylinders and inverse spheres) in the mantle of a neutron star near the crust-core interface. The process is open because neutrons and protons move in a periodic potential created by inhomogeneous nuclear structures. In this way the nucleons acquire large quasimomenta needed to satisfy momentum-conservation in the neutrino reaction. The appropriate neutrino emissivity in a nonsuperfluid matter is about 2--3 orders of magnitude higher than the emissivity of the modified Urca process in the stellar core. The process may noticeably accelerate the cooling of low-mass neutron stars.Comment: 7 pages, 3 figures, submitted to A&

Thermal Evolution of a Pulsating Neutron Star

We have derived a set of equations to describe the thermal evolution of a neutron star which undergoes small-amplitude radial pulsations. We have taken into account, in the frame of the General Theory of Relativity, the pulsation damping due to the bulk and shear viscosity and the accompanying heating of the star. The neutrino emission of a pulsating non-superfluid star and its heating due to the bulk viscosity are calculated assuming that both processes are determined by the non-equilibrium modified Urca process. Analytical and numerical solutions to the set of equations of the stellar evolution are obtained for linear and strongly non-linear deviations from beta-equilibrium. It is shown that a pulsating star may be heated to very high temperatures, while the pulsations damp very slowly with time (a power law damping for 100-1000 years), as long as the damping is determined by the bulk viscosity. The contribution of the shear viscosity to the damping becomes important in a rather cool star with a low pulsation energy.Comment: 10 pages, 3 figures, an important reference to the paper by Finzi & Wolf (1968) is added; analytical consideration of the problem (Section 5) is essentially extende

Branching Populations of Cells Bearing a Continuous Label

2000 Mathematics Subject Classification: 60J80.This paper is concerned with an age-dependent branching process with particles (cells) bearing a label, the latter being treated as a continuous parameter. The proposed stochastic model is motivated by applications in cell biology. It is assumed that the mitotic division results in a random distribution of the label among daughter cells in accordance with some bivariate probability distribution. In the event of cell death the label borne by that cell disappears. The main focus is on the label distribution as a function of the time elapsed from the moment of label administration. Explicit expressions for this distribution are derived in some particular cases which are of practical interest in the analysis of cell cycle. The Markov branching process with the same evolution of a continuously distributed label is considered as well.This research is supported in part by NIH/NINDS grant NS39511 (Yakovlev), ECO-NET-06 action 12634TJ funded by French Foreign Office (Yanev) and grant VU-MI-105/2005 by NSF

Cooling of Akmal-Pandharipande-Ravenhall neutron star models

We study the cooling of superfluid neutron stars whose cores consist of nucleon matter with the Akmal-Pandharipande-Ravenhall equation of state. This equation of state opens the powerful direct Urca process of neutrino emission in the interior of most massive neutron stars. Extending our previous studies (Gusakov et al. 2004a, Kaminker et al. 2005), we employ phenomenological density-dependent critical temperatures T_{cp}(\rho) of strong singlet-state proton pairing (with the maximum T_{cp}^{max} \sim 7e9 K in the outer stellar core) and T_{cnt}(\rho) of moderate triplet-state neutron pairing (with the maximum T_{cnt}^{max} \sim 6e8 K in the inner core). Choosing properly the position of T_{cnt}^{max} we can obtain a representative class of massive neutron stars whose cooling is intermediate between the cooling enhanced by the neutrino emission due to Cooper pairing of neutrons in the absence of the direct Urca process and the very fast cooling provided by the direct Urca process non-suppressed by superfluidity.Comment: 9 pages, 6 figures; accepted for publication in MNRA

The direct evaluation of attosecond chirp from a streaking measurement

We derive an analytical expression, from classical electron trajectories in a laser field, that relates the breadth of a streaked photoelectron spectrum to the group-delay dispersion of an isolated attosecond pulse. Based on this analytical expression, we introduce a simple, efficient and robust procedure to instantly extract the attosecond pulse's chirp from the streaking measurement.Comment: 4 figure

Theory of cooling neutron stars versus observations

We review current state of neutron star cooling theory and discuss the prospects to constrain the equation of state, neutrino emission and superfluid properties of neutron star cores by comparing the cooling theory with observations of thermal radiation from isolated neutron stars.Comment: 9 pages, 4 figures, 3 tables, to appear in the proceedings of "40 Years of Pulsars" held in Montreal, Canada, August 12-17, 2007, eds. C. Bassa, Z. Wang, A. Cumming, V. Kaspi, AIP, in press (v.2 - minor bibliography corrections