Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Spinodal decomposition, nuclear fog and two characteristic volumes in thermal multifragmentation

Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid-fog phase transition inside the spinodal region. The experimental data for p(8.1GeV) + Au collisions are analyzed within the framework of the statistical multifragmentation model (SMM) for the events with emission of at least two IMFs. It is found that the partition of hot nuclei is specified after expansion to a volume equal to Vt = (2.6+-0.3) Vo, with Vo as the volume at normal density. However, the freeze-out volume is found to be twice as large: Vf = (5+-1) Vo.Comment: 8 pages, 6 figures, to be published in Nucl.Phys.

Comparative Study of Multifragmentation of Gold Nuclei Induced by Relativistic Protons, 4^4He, and 12^{12}C

Multiple emission of intermediate-mass fragments has been studied for the collisions of p, $^4$He and $^{12}$C on Au with the $4\pi$ setup FASA. The mean IMF multiplicities (for the events with at least one IMF) are saturating at the value of $2.2\pm0.2$ for the incident energies above 6 GeV. The observed IMF multiplicities cannot be described in a two-stage scenario, a fast cascade followed by a statistical multifragmentation. Agreement with the measured IMF multiplicities is obtained by introducing an intermediate phase and modifying empirically the excitation energies and masses of the remnants. The angular distributions and energy spectra from the p-induced collisions are in agreement with the scenario of ``thermal'' multifragmentation of a hot and diluted target spectator. In the case of $^{12}$C+Au(22.4 GeV) and $^4$He(14.6 GeV)+Au collisions, deviations from a pure thermal break-up are seen in the energy spectra of the emitted fragments, which are harder than those both from model calculations and from the measured ones for p-induced collisions. This difference is attributed to a collective flow.Comment: 33 pages 15 figures, accepted in Nucl. Phys.

Adjustment to colostomy: stoma acceptance, stoma care self-efficacy and interpersonal relationships

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing. DOI: 10.1111/j.1365-2648.2007.04446.xThis paper is a report of a study to examine adjustment and its relationship with stoma acceptance and social interaction, and the link between stoma care self-efficacy and adjustment in the presence of acceptance and social interactions.Peer reviewe

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Black Holes and Instabilities of Negative Tension Branes

We consider the collision in 2+1 dimensions of a black hole and a negative tension brane on an orbifold. Because there is no gravitational radiation in 2+1 dimensions, the horizon area shrinks when part of the brane falls through. This provides a potential violation of the generalized second law of thermodynamics. However, tracing the details of the dynamical evolution one finds that it does not proceed from equilibrium configuration to equilibrium configuration. Instead, a catastrophic space-time singularity develops similar to the `big crunch' of $\Omega >1$ FRW space-times. In the context of classical general relativity, our result demonstrates a new instability of constructions with negative tension branes.Comment: 18 pages, 3 figures, uses RevTeX. Minor typos fixed. References and one footnote adde

Atom-optics hologram in the time domain

The temporal evolution of an atomic wave packet interacting with object and reference electromagnetic waves is investigated beyond the weak perturbation of the initial state. It is shown that the diffraction of an ultracold atomic beam by the inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram, whose thickness is proportional to the interaction time. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis a method for reconstruction of the object image with matter waves is offered.Comment: RevTeX, 13 pages, 8 figures; minor grammatical change