We evaluate the 4-point function of the auxiliary field in the critical O(N) sigma model at O(1/N) and show that it describes the exchange of tensor currents of arbitrary even rank l > 0. These are dual to tensor gauge fields of the same rank in the AdS theory, which supports the recent hypothesis of Klebanov and Polyakov. Their couplings to two auxiliary fields are also derived.

Rivcst [5] defines the notion of a decision list as a representation for Boolean functions. He shows that k-decision lists, a generalization of k-CNF and k-DNF formulas, are learnable for constant k in the PAC (or distribution-free) learning model [&,3]. Ehrenfcucht and Haussler [l] define the notion of the rank of a decision tree, and prove that decision trees of constant rank are also learnab...

TO020 – Figure 1 Abstract TO020 – Figure 2 plot identified 30/55 centres within 2sd from the UK mean for % patients achieving PO4<1.8mmol/L but also outlying centres, 7 units outside the 99.9% CIs and 18 centres between the 95%-99.9% CIs. The Monte Carlo analysis (Figure 2) showed marked uncertainty surrounding unit ranking e.g. Bristol, actual rank 20th (CI 10th-32nd) due to a large % of units...

In macrophages and osteoclast precursors, the cytokines TNF and RANK-L induce similar downstream pathways and share some of the same adaptor molecules. However, despite these similarities, no defined signaling schematic has emerged to show how each cytokine favors particular pathways. In this report, we investigate whether TNF and RANK-L differentially regulate ADP-ribosyl cyclases-enzymes that...

X ′Xθ = X ′Y. Here, X ′X is called the “information matrix” of θ and var(θ̂) = σ(X ′X)−1 (provided Rank(X) = t). Let l′θ be an estimable linear parametric function. Then var(l′θ̂) = σ2l′(X ′X)−l. We choose a design d, with design matrix Xd, whose information matrix X ′ dXd is “large” (equivalently, (X ′ dXd) − is “small”) in some sense. Now, suppose we are interested in a component θ1 of θ. We write

We present low-rank methods for event detection. We assume that normal observation come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise. Correspondingly, we aim at recovering a representation of the subspace, and perform event detection by running point-to-subspace distance query in `∞, for each incoming observation. In particular, we use a variant of matrix ...