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

The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory

Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z(t)$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z(t)$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system ``conditioned'' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.Comment: 9 page

Non-thermal dark matter via Affleck-Dine baryogenesis and its detection possibility

The formation and late time decays of Q-balls are generic consequences of the Affleck-Dine (AD) baryogenesis. A substantial amount of the lightest supersymmetry (SUSY) particles (LSPs) are produced non-thermally as the decay products of these Q-balls. This requires a significantly large annihilation cross section of the LSP so as not to overclose the universe, which predicts a higgsino- or wino-like LSP instead of the standard bino LSP. We have reexamined the AD baryogenesis with special attention to the late-time decays of the Q-balls, and then specified the parameter regions where the LSPs produced by the Q-ball decays result in a cosmologically interesting mass density of dark matter by adopting several SUSY breaking models. This reveals new cosmologically interesting parameter regions, which have not attracted much attention so far. We have also investigated the prospects of direct and indirect detection of these dark matter candidates, and found that there is an intriguing possibility to detect them in various next generation dark matter searches.Comment: 51 pages, 18 figures, version accepted for publication in Physical Review

Topological R4R^4 Inflation

We consider the possibility that higher-curvature corrections could drive inflation after the compactification to four dimensions. Assuming that the low-energy limit of the fundamental theory is eleven-dimensional supergravity to the lowest order, including curvature corrections and taking the descent from eleven dimensions to four via an intermediate five-dimensional theory, as favored by recent considerations of unification at some scale around $\sim 10^{16}$ GeV, we may obtain a simple model of inflation in four dimensions. The effective degrees of freedom are two scalar fields and the metric. The scalars arise as the large five-dimensional modulus and the self-interacting conformal mode of the metric. The effective potential has a local maximum in addition to the more usual minimum. However, the potential is quite flat at the top, and admits topological inflation. We show that the model can resolve cosmological problems and provide a mechanism for structure formation with very little fine tuning.Comment: 25 pages, latex, 2 eps figures, minor changes, accepted for publication in Phys. Rev.

Pan-African Agricultural and Veterinary Conference, Pretoria, 1st to 17th August, 1929 : papers veterinary section

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Molecular cloning and characterization of the alkaline ceramidase from Pseudomonas aeruginosa PA01

Ceramidase (CDase) hydrolyzes the amide bond in ceramides to yield free fatty acid and sphingosine. From a 3-L Pseudomonas aeruginosa PA01 culture, 70 μg of extracellular alkaline, Ca2+-dependent CDase, was purified to homogeneity, the N-terminal sequence was determined, and the CDase gene was cloned. The CDase gene encodes a 670 amino acid protein with a 26 amino acid signal peptide. CDase was expressed in five prokaryotic and eukaryotic expression systems. Small amounts of recombinant active extracellular CDase were expressed by Pseudomonas putida KT2440. In Pichia pastoris GS115 low amounts of recombinant extracellular glycosylated CDase were expressed. High levels of intracellular CDase were expressed by Escherichia coli DH5α and E. coli BL21 cells under control of the lac-promoter and T7-promoter, respectively. From a 3-L E. coli DH5α culture, 280 μg of pure CDase was obtained after a three-step purification protocol. Under control of the T7-promotor CDase, without its signal peptide, was produced in inclusion bodies in E. coli BL21 cells. After refolding, 1.8mg of pure active CDase was obtained from a 2.4-L culture after ammonium sulfate precipitation and gel filtration. Both the recombinant and wild-type CDases have a pH optimum of 8.5. The recombinant enzyme was partially characterized. This is the first report of a high yield CDase production system allowing detailed characterization of the enzyme at the molecular level. © 2003 Elsevier Science (USA). All rights reserved