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

Polar Perturbations of Self-gravitating Supermassive Global Monopoles

Spontaneous global symmetry breaking of O(3) scalar field gives rise to point-like topological defects, global monopoles. By taking into account self-gravity,the qualitative feature of the global monopole solutions depends on the vacuum expectation value v of the scalar field. When v < sqrt{1 / 8 pi}, there are global monopole solutions which have a deficit solid angle defined at infinity. When sqrt{1 / 8 pi} <= v < sqrt{3 / 8 pi}, there are global monopole solutions with the cosmological horizon, which we call the supermassive global monopole. When v >= sqrt{3 / 8 pi}, there is no nontrivial solution. It was shown that all of these solutions are stable against the spherical perturbations. In addition to the global monopole solutions, the de Sitter solutions exist for any value of v. They are stable against the spherical perturbations when v sqrt{3 / 8 pi}. We study polar perturbations of these solutions and find that all self-gravitating global monopoles are stable even against polar perturbations, independently of the existence of the cosmological horizon, while the de Sitter solutions are always unstable.Comment: 10 pages, 6 figures, corrected some type mistakes (already corrected in PRD version

Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension

We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.Comment: 25 pages, important references added, two remarks added, typos correcte

Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

An Immune Gene Expression Signature Associated With Development of Human Hepatocellular Carcinoma Identifies Mice That Respond to Chemopreventive Agents

Program (HEPCAR, reference no. 667273-2); US Department of Defense(CA150272P3); an Accelerator Award (CRUCK, AECC, AIRC) (HUNTER,reference no. C9380/A26813), NCI Cancer Center Support Grant, National Cancer Institute; Tisch Cancer Institute (P30-CA196521); Samuel Waxman Cancer Research Foundation; Spanish National Health Institute (SAF2016-76390); and the Generalitat de Catalunya/AGAUR (SGR-1358). Agrin Moeini is supported by Spanish National Health Institute. Sara Torrecilla and Judit Peix are funded by Centro de Investigación Biomedica en Red de Enfermedades Hepáticas y Digestivas (Ciberehd-ISCIII). Carla Montironi is a recipient of Josep Font grant. Carmen Andreu-Oller is supported by "la Caixa" INPhINIT Fellowship Grant (LCF/BQ/IN17/11620024). Roser Pinyol is supported by HEPCAR and AECC. Daniela Sia is supported by the Gilead Sciences Research Scholar Program in Liver Disease. Scott L. Friedman is supported by the National Institutes of Health Research project grant (R01,DK5662) and US Department of Defense (CA150272P3). Mathias Heikenwälder was supported by an ERC Consolidator grant (HepatoMetaboPath), the SFBTR 209, 1335 and SFBTR179.Background & Aims: Cirrhosis and chronic inflammation precede development of hepatocellular carcinoma (HCC) in approximately 80% of cases. We investigated immune-related gene expression patterns in liver tissues surrounding early-stage HCCs and chemopreventive agents that might alter these patterns to prevent liver tumorigenesis. Methods: We analyzed gene expression profiles of nontumor liver tissues from 392 patients with early-stage HCC (training set, N = 167 and validation set, N = 225) and liver tissue from patients with cirrhosis without HCC (N = 216, controls) to identify changes in expression of genes that regulate the immune response that could contribute to hepatocarcinogenesis. We defined 172 genes as markers for this deregulated immune response, which we called the immune-mediated cancer field (ICF). We analyzed the expression data of liver tissues from 216 patients with cirrhosis without HCC and investigated the association between this gene expression signature and development of HCC and outcomes of patients (median follow-up, 10 years). Human liver tissues were also analyzed by histology. C57BL/6J mice were given a single injection of diethylnitrosamine (DEN) followed by weekly doses of carbon tetrachloride to induce liver fibrosis and tumorigenesis. Mice were then orally given the multiple tyrosine inhibitor nintedanib or vehicle (controls); liver tissues were collected and histology, transcriptome, and protein analyses were performed. We also analyzed transcriptomes of liver tissues collected from mice on a choline-deficient high-fat diet, which developed chronic liver inflammation and tumors, orally given aspirin and clopidogrel or the anti-inflammatory agent sulindac vs mice on a chow (control) diet. Results: We found the ICF gene expression pattern in 50% of liver tissues from patients with cirrhosis without HCC and in 60% of nontumor liver tissues from patients with early-stage HCC. The liver tissues with the ICF gene expression pattern had 3 different features: increased numbers of effector T cells; increased expression of genes that suppress the immune response and activation of transforming growth factor β signaling; or expression of genes that promote inflammation and activation of interferon gamma signaling. Patients with cirrhosis and liver tissues with the immunosuppressive profile (10% of cases) had a higher risk of HCC (hazard ratio, 2.41; 95% confidence interval, 1.21-4.80). Mice with chemically induced fibrosis or diet-induced steatohepatitis given nintedanib or aspirin and clopidogrel down-regulated the ICF gene expression pattern in liver and developed fewer and smaller tumors than mice given vehicle. Conclusions: We identified an immune-related gene expression pattern in liver tissues of patients with early-stage HCC, called the ICF, that is associated with risk of HCC development in patients with cirrhosis. Administration of nintedanib or aspirin and clopidogrel to mice with chronic liver inflammation caused loss of this gene expression pattern and development of fewer and smaller liver tumors. Agents that alter immune regulatory gene expression patterns associated with carcinogenesis might be tested as chemopreventive agents in patients with cirrhosis

Charge Form Factor and Cluster Structure of 6^6Li Nucleus

The charge form factor of ${}^6$Li nucleus is considered on the basis of its cluster structure. The charge density of ${}^6$Li is presented as a superposition of two terms. One of them is a folded density and the second one is a sum of ${}^4$He and the deuteron densities. Using the available experimental data for ${}^4$He and deuteron charge form factors, a good agreement of the calculations within the suggested scheme is obtained with the experimental data for the charge form factor of ${}^6$Li, including those in the region of large transferred momenta.Comment: 12 pages 5 figure

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

A transcribed enhancer dictates mesendoderm specification in pluripotency.

Enhancers and long noncoding RNAs (lncRNAs) are key determinants of lineage specification during development. Here, we evaluate remodeling of the enhancer landscape and modulation of the lncRNA transcriptome during mesendoderm specification. We sort mesendodermal progenitors from differentiating embryonic stem cells (ESCs) according to Eomes expression, and find that enhancer usage is coordinated with mesendoderm-specific expression of key lineage-determining transcription factors. Many of these enhancers are associated with the expression of lncRNAs. Examination of ESC-specific enhancers interacting in three-dimensional space with mesendoderm-specifying transcription factor loci identifies MesEndoderm Transcriptional Enhancer Organizing Region (Meteor). Genetic and epigenetic manipulation of the Meteor enhancer reveal its indispensable role during mesendoderm specification and subsequent cardiogenic differentiation via transcription-independent and -dependent mechanisms. Interestingly, Meteor-deleted ESCs are epigenetically redirected towards neuroectodermal lineages. Loci, topologically associating a transcribed enhancer and its cognate protein coding gene, appear to represent therefore a class of genomic elements controlling developmental competence in pluripotency

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde