On the Red-Green-Blue Model

We experimentally study the red-green-blue model, which is a sytem of loops obtained by superimposing three dimer coverings on offset hexagonal lattices. We find that when the boundary conditions are ``flat'', the red-green-blue loops are closely related to SLE_4 and double-dimer loops, which are the loops formed by superimposing two dimer coverings of the cartesian lattice. But we also find that the red-green-blue loops are more tightly nested than the double-dimer loops. We also investigate the 2D minimum spanning tree, and find that it is not conformally invariant.Comment: 4 pages, 7 figure

Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur

On the partition function of the six-vertex model with domain wall boundary conditions

The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ``reconstruction'' formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.Comment: typos correcte

Exact sampling from non-attractive distributions using summary states

Propp and Wilson's method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to non-attractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such a slowing down can occur in the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at http://wol.ra.phy.cam.ac.uk/mackay/exac

Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques

The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics of random matrix techniques, the connections to the polynuclear growth models and a method using the Green's function.Comment: 41 pages, 10 figures, minor corrections, references adde

Content analysis, cultural grammars, and computers

This paper describes current theoretical work in a cognitive anthropological approach to the analysis of oral literature. A theory of narrative grammar is presented along with the description of a computer program, SAGE, that is currently under development. SAGE facilitates the labelling of clauses and sentences by different types of semantic features. It maps and counts the occurrences of these in the stories analyzed. © 1991 Human Sciences Press, Inc

The Role of Historical Narrative in Biblical Thought:the Tendencies Underlying Old Testament Historiography

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68403/2/10.1177_030908928100602102.pd

Diversity of hard-bottom fauna relative to environmental gradients in Kongsfjorden, Svalbard

A baseline study of hard-bottom zoobenthos in relation to environmental gradients in Kongsfjorden, a glacial fjord in Svalbard, is presented, based on collections from 1996 to 1998. The total species richness in 62 samples from 0 to 30 m depth along five transects was 403 species. Because 32 taxa could not be identified to species level and because 11 species are probably new to science, the total number of identified species was 360. Of these, 47 species are new for Svalbard waters. Bryozoa was the most diverse group. Biogeographic composition revealed features of both Arctic and sub-Arctic properties of the fauna. Species richness, frequency of species occurrence, mean abundance and biomass generally decreased towards the tidal glaciers in inner Kongsfjorden. Among eight environmental factors, depth was most important for explaining variance in the composition of the zoobenthos. The diversity was consistently low at shallow depths, whereas the non-linear patterns of species composition of deeper samples indicated a transitional zone between surface and deeper water masses at 15–20 m depth. Groups of “colonial” and “non-colonial” species differed in diversity, biogeographic composition and distribution by location and depth as well as in relation to other environmental factors. “Non-colonial” species made a greater contribution than “colonial” species to total species richness, total occurrence and biomass in samples, and were more influenced by the depth gradient. Biogeographic composition was sensitive to variation of zoobenthic characteristics over the studied depth range. A list of recorded species and a description of sampling sites are presented