Close-packed dimers on nonorientable surfaces

The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem.Comment: 13 pages, 1 figure, typo corrected to the version published in Phys. Lett. A 293, 235 (2002

Classification using distance nearest neighbours

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2008). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm.Comment: 12 pages, 2 figures. To appear in Statistics and Computin

Criminal narrative experience: relating emotions to offence narrative roles during crime commission

A neglected area of research within criminality has been that of the experience of the offence for the offender. The present study investigates the emotions and narrative roles that are experienced by an offender while committing a broad range of crimes and proposes a model of Criminal Narrative Experience (CNE). Hypotheses were derived from the Circumplex of Emotions (Russell, 1997), Frye (1957), Narrative Theory (McAdams, 1988) and its link with Investigative Psychology (Canter, 1994). The analysis was based on 120 cases. Convicted for a variety of crimes, incarcerated criminals were interviewed and the data were subjected to Smallest Space Analysis (SSA). Four themes of Criminal Narrative Experience (CNE) were identified: Elated Hero, Calm Professional, Distressed Revenger and Depressed Victim in line with the recent theoretical framework posited for Narrative Offence Roles (Youngs & Canter, 2012). The theoretical implications for understanding crime on the basis of the Criminal Narrative Experience (CNE) as well as practical implications are discussed

Refined Razumov-Stroganov conjectures for open boundaries

Recently it has been conjectured that the ground-state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully-packed loop configurations (FPL) on a grid with special boundaries).We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground-state of a Markovian Hamiltonian with two boundary operators and arbitrary coefficients and some doubly refined (dependence on two parameters) FPL configurations. Our conjectures might be useful in the study of ground-states of the O(1) and XXZ models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure

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

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

Transport of metal sulfides in supercritical carbon dioxide

This report presents the results of studies of supercritical fluid extraction of selected organics and of transition metal sulfides using carbon dioxide with and without modifiers. For the metal sulfides, the modifiers water, aqueous EDTA, methanol, and methanolic 2,4-pentanedione (acetyl acetone) were added in amounts ranging from 1 to 10 wt% depending on the specific modifier used. Extraction efficiency was studied as a function of fluid composition and extraction temperature and pressure. The objective of the work was to investigate the scientific feasibility of using this type of extraction process for metallurgical or environmental applications. Theoretical modeling studies were performed in an attempt to develop predictive capabilities for both solubility calculations and extraction simulation. The experimental studies have established the scientific feasibility of extraction and transport of selected cations by these fluids. Depending on the metal and conditions, transport of up to 12% of the starting material has been observed; however, the observed extraction efficiencies for inorganics do not approach those typical for organics under similar conditions

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

Corrosion in supercritical fluids

Integrated studies were carried out in the areas of corrosion, thermodynamic modeling, and electrochemistry under pressure and temperature conditions appropriate for potential applications of supercritical fluid (SCF) extractive metallurgy. Carbon dioxide and water were the primary fluids studied. Modifiers were used in some tests; these consisted of 1 wt% water and 10 wt% methanol for carbon dioxide and of sulfuric acid, sodium sulfate, ammonium sulfate, and ammonium nitrate at concentrations ranging from 0.00517 to 0.010 M for the aqueous fluids. The materials studied were Types 304 and 316 (UNS S30400 and S31600) stainless steel, iron, and AISI-SAE 1080 (UNS G10800) carbon steel. The thermodynamic modeling consisted of development of a personal computer-based program for generating Pourbaix diagrams at supercritical conditions in aqueous systems. As part of the model, a general method for extrapolating entropies and related thermodynamic properties from ambient to SCF conditions was developed. The experimental work was used as a tool to evaluate the predictions of the model for these systems. The model predicted a general loss of passivation in iron-based alloys at SCF conditions that was consistent with experimentally measured corrosion rates and open circuit potentials. For carbon-dioxide-based SCFs, measured corrosion rates were low, indicating that carbon steel would be suitable for use with unmodified carbon dioxide, while Type 304 stainless steel would be suitable for use with water or methanol as modifiers