Bottom Quark Cross Sections at Collider and Fixed-Target Energies at the SSC and LHC

Calculations of inclusive cross sections for the production of bottom quarks in proton-proton collisions are presented as a function of energy, transverse momentum, and Feynman $x_F$ for values of $\sqrt{s}$ from $100~$GeV to $40~$TeV. In addition, we provide simple parametrizations of our theoretical results that should facilitate estimates of rates, acceptances, and efficiencies of proposed new detectors.Comment: 6 pages plus 11 topdraw figures appended as ps-files(uuencoded), Latex, ANL-HEP-CP-93-63 & CERN-TH.6987/9

Community Detection by L0L_0-penalized Graph Laplacian

Community detection in network analysis aims at partitioning nodes in a network into $K$ disjoint communities. Most currently available algorithms assume that $K$ is known, but choosing a correct $K$ is generally very difficult for real networks. In addition, many real networks contain outlier nodes not belonging to any community, but currently very few algorithm can handle networks with outliers. In this paper, we propose a novel model free tightness criterion and an efficient algorithm to maximize this criterion for community detection. This tightness criterion is closely related with the graph Laplacian with $L_0$ penalty. Unlike most community detection methods, our method does not require a known $K$ and can properly detect communities in networks with outliers. Both theoretical and numerical properties of the method are analyzed. The theoretical result guarantees that, under the degree corrected stochastic block model, even for networks with outliers, the maximizer of the tightness criterion can extract communities with small misclassification rates even when the number of communities grows to infinity as the network size grows. Simulation study shows that the proposed method can recover true communities more accurately than other methods. Applications to a college football data and a yeast protein-protein interaction data also reveal that the proposed method performs significantly better.Comment: 40 pages, 15 Postscript figure

Detecting Cohomology for Lie Superalgebras

In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras. These results are used later to affirmatively answer questions, which were originally posed in \cite{BKN1} and \cite{BaKN}, about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras