Sparse Biclustering of Transposable Data

We consider the task of simultaneously clustering the rows and columns of a large transposable data matrix. We assume that the matrix elements are normally distributed with a bicluster-specific mean term and a common variance, and perform biclustering by maximizing the corresponding log-likelihood. We apply an ?₁ penalty to the means of the biclusters to obtain sparse and interpretable biclusters. Our proposal amounts to a sparse, symmetrized version of k-means clustering. We show that k-means clustering of the rows and of the columns of a data matrix can be seen as special cases of our proposal, and that a relaxation of our proposal yields the singular value decomposition. In addition, we propose a framework for biclustering based on the matrix-variate normal distribution. The performances of our proposals are demonstrated in a simulation study and on a gene expression dataset. This article has supplementary material online.     

Two dimensional gauge theories revisited

Two dimensional quantum Yang-Mills theory is reexamined using a non-abelian version of the Duistermaat-Heckman integration formula to carry out the functional integral. This makes it possible to explain properties of the theory that are inaccessible to standard methods and to obtain general expressions for intersection pairings on moduli spaces of flat connections on a two dimensional surface. The latter expressions agree, for gauge group SU (2), with formulas obtained recently by several methods.     

Dual catalysis in enantioselective oxidopyrylium-based [5 + 2] cycloadditions

A new method for effecting catalytic enantioselective intramolecular [5 + 2] cycloadditions based on oxidopyrylium intermediates is reported. The dual catalyst system consists of a chiral primary aminothiourea and a second achiral thiourea. Experimental evidence points to a new type of cooperative catalysis with each species being necessary to generate a reactive pyrylium ion pair that undergoes subsequent cycloaddition with high enantioselectivity.     

The polymer mat: Arrested rebound of a compressed polymer layer

The European Physical Journal E - Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this...     

The antisymmetric tensor field in superstring theory

We discuss various aspects of the role of the antisymmetric tensor field in superstring theory, including the quantization law obeyed by its field strength and its role in topological defects and in vacuum configurations.     

New manifolds for superstring compactification

We construct new manifolds with SU(3) holonomy that are candidate vacua for superstring theory and give a detailed explanation of the techniques involved. Some of these manifolds have a non-abelian fundamental group and thus can lead to a rank five low energy gauge group. Models with an odd number of generations are obtained.CP violation is discussed in this context and shown to occur generically. Topological features of the Yukawa couplings are also discussed.     

Non-abelian isometries and dimensional reduction

Dimensional reduction is carried out for space-times, with or without torsion, which possess non-abelian isometries. The spectra and the equations of motion of the dimensionally reduced theory are obtained directly from the higher dimensional theory. The spectra of the reduced theories are naturally given in terms of scalar fields and antisymmetric tensor field strengths. A method of studying the dependence on the extra dimensions is suggested.     

The ferric chloride α-DI-imine systemVI: Electronic structure of the dimethyl formamide addcut of mono-1,10-phenanthroline ferric chloride and the by-product,tris-1,10-phenanthroline ferrous μ-oxo-bis[trichloro ferrate(III)]; field induced slow paramagnetic relaxation in monomeric ferric complexes

Magnetic susceptibility (1.45–300 K), zero and high field Mössbauer spectroscopy, IR and solution conductivity measurements were used to characterize the title DMR adduct, Fe(phen)Cl₃·DMF. The absence of magnetic hyperfine splitting in zero external field is correlated with D positive corresponding to an isolated, rapidly relaxing ground (M_s = ± $\text{1}\text{2}$ Kramers doublet. X-ray data show that the ferric ion centres are apparently sufficiently close (～ 7 Å) to allow for rapid spin-spin relaxation via dipolar interactions. The application of longitudinal magnetic fields (0–5 Tesla for 1.7–4.2 K) slows relaxation and results in fully resolved Zeeman split Mössbauer spectra for which the effective internal field, H_n = 354 kG at 1.7 K for H₀ = 5T. The complex [Fe(phen)₃] [O(FeCl₃)₂] contains an unusual binuclear anion based on tetrahedral FeOCl₃ units as recently found in [pyridinium]₂[O(FeCl₃)₂] and is obtained as a trace by-product in our preparation of Fe(phen)Cl₃·DMF. Further magnetic characterization of the latter pyridinium compound is presented.     

Supersymmetry algebras that include topological charges

We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.     

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.Supported in part by The National Science Foundation under Grant No. INT 782-5663.Supported in part by Consejo Nacional de Investigaciones Cientificas y Technologicas (CONICIT), Venezuela.