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

Superconducting Coherence and the Helicity Modulus in Vortex Line Models

We show how commonly used models for vortex lines in three dimensional superconductors can be modified to include k=0 excitations. We construct a formula for the k=0 helicity modulus in terms of fluctuations in the projected area of vortex loops. This gives a convenient criterion for the presence of superconducting coherence. We also present Monte Carlo simulations of a continuum vortex line model for the melting of the Abrikosov vortex lattice in pure YBCO.Comment: 4 pages RevTeX, 2 eps figures included using eps

Two-Loop g -> gg Splitting Amplitudes in QCD

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality argument of hep-th/0404092, and additional explanation of cut-reconstruction uniquenes

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.Comment: 32 pages, latex, 7 EPS figures. v2: references, comments added, typos corrected, incorrect `skeleton' conjecture in sect. 3 replaced by a more careful treatment. v3: typos corrected, final version published in JHE

Genetic variation at MECOM, TERT, JAK2 and HBS1L-MYB predisposes to myeloproliferative neoplasms

Clonal proliferation in myeloproliferative neoplasms (MPN) is driven by somatic mutations in JAK2, CALR or MPL, but the contribution of inherited factors is poorly characterized. Using a three-stage genome-wide association study of 3,437 MPN cases and 10,083 controls, we identify two SNPs with genome-wide significance in JAK2V617F-negative MPN: rs12339666 (JAK2; meta-analysis P=1.27 × 10−10) and rs2201862 (MECOM; meta-analysis P=1.96 × 10−9). Two additional SNPs, rs2736100 (TERT) and rs9376092 (HBS1L/MYB), achieve genome-wide significance when including JAK2V617F-positive cases. rs9376092 has a stronger effect in JAK2V617F-negative cases with CALR and/or MPL mutations (Breslow–Day P=4.5 × 10−7), whereas in JAK2V617F-positive cases rs9376092 associates with essential thrombocythemia (ET) rather than polycythemia vera (allelic χ2 P=7.3 × 10−7). Reduced MYB expression, previously linked to development of an ET-like disease in model systems, associates with rs9376092 in normal myeloid cells. These findings demonstrate that multiple germline variants predispose to MPN and link constitutional differences in MYB expression to disease phenotype

The clinical effectiveness and cost effectiveness of clozapine for inpatients with severe borderline personality disorder (CALMED study): A randomised placebo-controlled trial

Background: Data from case series suggest that clozapine may benefit inpatients with borderline personality disorder (BPD), but randomised trials have not been conducted. Methods: Multicentre, double-blind, placebo-controlled trial. We aimed to recruit 222 inpatients with severe BPD aged 18 or over, who had failed to respond to other antipsychotic medications. We randomly allocated participants on a 1:1 ratio to receive up to 400mg of clozapine per day or an inert placebo using a remote web-based randomisation service. The primary outcome was total score on the Zanarini Rating scale for Borderline Personality Disorder (ZAN-BPD) at six months. Secondary outcomes included self-harm, aggression, resource use and costs, side effects and adverse events. We used a modified intention to treat analysis (mITT) restricted to those who took one or more dose of trial medication, using a general linear model fitted at six months adjusted for baseline score, allocation group and site. Results: The study closed early due to poor recruitment and the impact of the COVID-19 pandemic. Of 29 study participants, 24 (83%) were followed up at six months, of whom 21 (72%) were included in the mITT analysis. At six months, 11 (73%) participants assigned to clozapine and 6 (43%) of those assigned to placebo were still taking trial medication. Adjusted difference in mean total ZAN-BPD score at six months was -3.86 (95% Confidence Intervals = -10.04 to 2.32, p=0.22). There were 14 serious adverse events; six in the clozapine arm and eight in the placebo arm of the trial. There was little difference in the cost of care between groups. Interpretation: We recruited insufficient participants to test the primary hypothesis. The study findings highlight problems in conducting placebo-controlled trials of clozapine and in using clozapine for people with BPD, outside specialist inpatient mental health units. Trial registration ISRCTN18352058. https://doi.org/10.1186/ISRCTN1835205