Exact Enumeration and Sampling of Matrices with Specified Margins

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling

Exact sampling and counting for fixed-margin matrices

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1131 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1104.032

An unexpected oxidation : NaK5Cl2(S2O6)2 revisited

Acknowledgements We thank the EPSRC National Crystallography Service (University of Southampton) for the X-ray data collection.Peer reviewedPublisher PD

Orbital ordering in La0.5_{0.5}Sr1.5_{1.5}MnO4_4 studied by model Hartree-Fock calculation

We have investigated orbital ordering in the half-doped manganite La$_{0.5}$Sr$_{1.5}$MnO$_4$, which displays spin, charge and orbital ordering, by means of unrestricted Hartree-Fock calculations on the multiband $p$-$d$ model. From recent experiment, it has become clear that La$_{0.5}$Sr$_{1.5}$MnO$_4$ exhibits a cross-type $(z^2-x^2/y^2-z^2)$ orbital ordering rather than the widely believed rod-type $(3x^2-r^2/3y^2-r^2)$ orbital ordering. The calculation reveals that cross-type $(z^2-x^2/y^2-z^2)$ orbital ordering results from an effect of in-plane distortion as well as from the relatively long out-of-plane Mn-O distance. For the "Mn$^{4+}$" site, it is shown that the elongation along the c-axis of the MnO$_6$ octahedra leads to an anisotropic charge distribution rather than the isotropic one.Comment: 4 pages, 5 figure

Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).Comment: This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.270

Absence of Hybridization Gap in Heavy Electron Systems and Analysis of YbAl3 in terms of Nearly Free Electron Conduction Band

In the analysis of the heavy electron systems, theoretical models with c-f hybridization gap are often used. We point out that such a gap does not exist and the simple picture with the hybridization gap is misleading in the metallic systems, and present a correct picture by explicitly constructing an effective band model of YbAl_3. Hamiltonian consists of a nearly free electron model for conduction bands which hybridize with localized f-electrons, and includes only a few parameters. Density of states, Sommerfeld coefficient, f-electron number and optical conductivity are calculated and compared with the band calculations and the experiments.Comment: 9 pages, 9 figures, submitted to J. Phys. Soc. Jp