A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.Comment: Minor changes and clarifications; corrected some typo

Evidence for a parsec scale X-ray jet from the accreting neutron star Circinus X-1

We analyzed the zero-order image of a 50 ks Chandra gratings observation of Circinus X-1, taken in 2005 during the source's low-flux state. Circinus X-1 is an accreting neutron star that exhibits ultra-relativistic arcsecond-scale radio jets and diffuse arcminute-scale radio jets and lobes. The image shows a clear excess along the general direction of the north-western counter-jet, coincident with the radio emission, suggesting that it originates either in the jet itself or in the shock the jet is driving into its environment. This makes Circinus X-1 the first neutron star for which an extended X-ray jet has been detected. The kinetic jet power we infer is significantly larger than the minimum power required for the jet to inflate the large scale radio nebula.Comment: Added journal reference, corrected on reference and typo in labels for Fig. 1; 5 pages, 3 figures, ApJ Letter, in pres

Discovery of a large and bright bow shock nebula associated with low mass X-ray binary SAX J1712.6-3739

In a multiwavelength program dedicated to identifying optical counterparts of faint persistent X-ray sources in the Galactic Bulge, we find an accurate X-ray position of SAX J1712.6-3739 through Chandra observations, and discover its faint optical counterpart using our data from EFOSC2 on the ESO 3.6m telescope. We find this source to be a highly extincted neutron star LMXB with blue optical colours. We serendipitously discover a relatively bright and large bow shock shaped nebula in our deep narrowband H alpha imaging, most likely associated with the X-ray binary. A nebula like this has never been observed before in association with a LMXB, and as such provides a unique laboratory to study the energetics of accretion and jets. We put forward different models to explain the possible ways the LMXB may form this nebulosity, and outline how they can be confirmed observationally.Comment: Accepted for publication in MNRAS-Letters; 5 pages, 4 figures, 2 tables. Quality of figure 2 downgraded because of arXiv file size limit

Temperature dependent sound velocity in hydrodynamic equations for relativistic heavy-ion collisions

We analyze the effects of different forms of the sound-velocity function cs(T) on the hydrodynamic evolution of matter formed in the central region of relativistic heavy-ion collisions. At high temperatures (above the critical temperature Tc) the sound velocity is calculated from the recent lattice simulations of QCD, while in the low temperature region it is obtained from the hadron gas model. In the intermediate region we use different interpolations characterized by the values of the sound velocity at the local maximum (at T = 0.4 Tc) and local minimum (at T = Tc). In all considered cases the temperature dependent sound velocity functions yield the entropy density, which is consistent with the lattice QCD simulations at high temperature. Our calculations show that the presence of a distinct minimum of the sound velocity leads to a very long (about 20 fm/c) evolution time of the system, which is not compatible with the recent estimates based on the HBT interferometry. Hence, we conclude that the hydrodynamic description is favored in the case where the cross-over phase transition renders the smooth sound velocity function with a possible shallow minimum at Tc.Comment: 6 pages, 3 figures, talk given at SQM'07 Levoca, Slovaki

Investigation of octupole vibrational states in 150Nd via inelastic proton scattering (p,p'g)

Octupole vibrational states were studied in the nucleus $^{150}\mathrm{Nd}$ via inelastic proton scattering with \unit[10.9]{MeV} protons which are an excellent probe to excite natural parity states. For the first time in $^{150}\mathrm{Nd}$, both the scattered protons and the $\gamma$ rays were detected in coincidence giving the possibility to measure branching ratios in detail. Using the coincidence technique, the $B(E1)$ ratios of the decaying transitions for 10 octupole vibrational states and other negative-parity states to the yrast band were determined and compared to the Alaga rule. The positive and negative-parity states revealed by this experiment are compared with Interacting Boson Approximation (IBA) calculations performed in the (spdf) boson space. The calculations are found to be in good agreement with the experimental data, both for positive and negative-parity states

The Origins of X-ray Line Emissions in Circinus~X-1 at Very Low X-ray Flux

Accretion conditions and morphologies of X-ray transients containing neutron stars are still poorly understood. Circinus X-1 is an enigmatic case where we observe X-ray flux changes covering four orders of magnitude. We observed Circinus X-1 several times at its very lowest X-ray flux using the high energy transmission grating spectrometer on board the Chandra X-ray Observatory. At a flux of 1.8$\times10^{-11}$ \ergcm we observed a single 1.6 keV blackbody spectrum. The observed continuum luminosity of 10$^{35}$ \ergsec is about two orders of magnitude too low to explain the observed photoionized luminosity suggesting a much more complex structure of the X-ray source which is partially or entirely obscured as had been previously suggested. This affects most emissions from the accretion disk including previously observed accretion disk coronal line emissions. Instead, the strongest observed photoionized lines are blueshifted by about $\sim 400$ \kms\ and we suggest that they originate in the ionized wind of a B5Ia supergaint companion supporting a previous identification. The neutron star in Cir X-1 is very young and should have a high magnetic field. At the observed luminosity the emission radius of the blackbody is small enough to be associated with the accretion hot spot as the X-ray emitting region. The small emission radius then points to a field strength below $10^{12}$ G which would be consistent with the observation of occasional type I X-ray bursts at high magnetic fields. We discuss Cir X-1 in the context of being a high-mass X-ray binary with some emphasis on a possible Be-star X-ray binary nature.Comment: 11 pages, 9 figures, 3 table

Analytic Solution of the Pion-Laser Model

Brooding over bosons, wave packets and Bose - Einstein correlations, we find that a generalization of the pion-laser model for the case of overlapping wave-packets is analytically solvable with complete n-particle symmetrization. The effective radius parameter of the two-particle correlation function is reduced for low values and enlargened for high values of the mean momentum in the rare gas limiting case, as compared to the case when multi-particle symmetrization effects are neglected. These results explicitly depend on the multiplicity, providing a theoretical basis for event-by-event analysis of high energy heavy ion reactions.Comment: LaTeX, ReVTeX 3.1, 7 pages, uses 1 eps figure and epsfig.sty (shortened version

Metric fluctuations and decoherence

Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization of the inertial mass tensor results from a local space average over the fluctuations of the metric over a fixed background metric. Here, we demonstrate that the metric fluctuations of this model lead to a further physical effect, namely to an effective decoherence of the quantum particle. We derive a quantum master equation for the particle's density matrix, discuss in detail its dissipation and decoherence properties, and estimate the corresponding decoherence time scales. By contrast to other models discussed in the literature, in the present approach the metric fluctuations give rise to a decay of the coherences in the energy representation, i. e., to a localization in energy space.Comment: 7 page