Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres

Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres

A graph-theory method for pattern identification in geographical epidemiology - a preliminary application to deprivation and mortality

Background: Graph theoretical methods are extensively used in the field of computational chemistry to search datasets of compounds to see if they contain particular molecular substructures or patterns. We describe a preliminary application of a graph theoretical method, developed in computational chemistry, to geographical epidemiology in relation to testing a prior hypothesis. We tested the methodology on the hypothesis that if a socioeconomically deprived neighbourhood is situated in a wider deprived area, then that neighbourhood would experience greater adverse effects on mortality compared with a similarly deprived neighbourhood which is situated in a wider area with generally less deprivation. Methods: We used the Trent Region Health Authority area for this study, which contained 10,665 census enumeration districts (CED). Graphs are mathematical representations of objects and their relationships and within the context of this study, nodes represented CEDs and edges were determined by whether or not CEDs were neighbours (shared a common boundary). The overall area in this study was represented by one large graph comprising all CEDs in the region, along with their adjacency information. We used mortality data from 1988-1998, CED level population estimates and the Townsend Material Deprivation Index as an indicator of neighbourhood level deprivation. We defined deprived CEDs as those in the top 20% most deprived in the Region. We then set out to classify these deprived CEDs into seven groups defined by increasing deprivation levels in the neighbouring CEDs. 506 (24.2%) of the deprived CEDs had five adjacent CEDs and we limited pattern development and searching to these CEDs. We developed seven query patterns and used the RASCAL (Rapid Similarity Calculator) program to carry out the search for each of the query patterns. This program used a maximum common subgraph isomorphism method which was modified to handle geographical data. Results: Of the 506 deprived CEDs, 10 were not identified as belonging to any of the seven groups because they were adjacent to a CED with a missing deprivation category quintile, and none fell within query Group 1 (a deprived CED for which all five adjacent CEDs were affluent). Only four CEDs fell within Group 2, which was defined as having four affluent adjacent CEDs and one non-affluent adjacent CED. The numbers of CEDs in Groups 3-7 were 17, 214, 95, 81 and 85 respectively. Age and sex adjusted mortality rate ratios showed a non-significant trend towards increasing mortality risk across Groups (Chi-square = 3.26, df = 1, p = 0.07). Conclusion: Graph theoretical methods developed in computational chemistry may be a useful addition to the current GIS based methods available for geographical epidemiology but further developmental work is required. An important requirement will be the development of methods for specifying multiple complex search patterns. Further work is also required to examine the utility of using distance, as opposed to adjacency, to describe edges in graphs, and to examine methods for pattern specification when the nodes have multiple attributes attached to them

Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation

I show that the hamiltonian theory of Composite Fermions (CF) is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure

Families of Graphs With Chromatic Zeros Lying on Circles

We define an infinite set of families of graphs, which we call $p$-wheels and denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$) graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at $q=0,1,...p+1$ for $n-p$ even and $q=0,1,...p+2$ for $n-p$ odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle $|q-(p+1)|=1$ in the complex $q$ plane. In the $n \to \infty$ limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function $W(\{(Wh)^{(p)}\},q)$ is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late

Data assimilation for the Martian atmosphere using MGS Thermal Emission Spectrometer observations

From the introduction: Given the quantity of data expected from current and forthcoming spacecraft missions to Mars, it is now possible to use data assimilation as a means of atmospheric analysis for the first time for a planet other than the Earth. Several groups have described plans to develop assimilation schemes for Mars [Banfield et al., 1995; Houben, 1999; Lewis and Read, 1995; Lewis et al., 1996, 1997; Zhang et al., 2001]. Data assimilation is a technique for the analysis of atmospheric observations which combines currently valid information with prior knowledge from previous observations and dynamical and physical constraints, via the use of a numerical model. Despite the number of new missions, observations of the atmosphere of Mars in the near future are still likely to be sparse when compared to those of the Earth, perhaps comprising one orbiter and a few surface stations at best at any one time. Data assimilation is useful as a means to extract the maximum information from such observations, both by a form of interpolation in space and time using model constraints and by the combination of information from different observations, e.g. temperature profiles and surface pressure measurements which may be irregularly distributed. The procedure can produce a dynamically consistent set of meteorological fields and can be used directly to test and to refine an atmospheric model against observations

Tunneling spectroscopy studies of aluminum oxide tunnel barrier layers

We report scanning tunneling microscopy and ballistic electron emission microscopy studies of the electronic states of the uncovered and chemisorbed-oxygen covered surface of AlOx tunnel barrier layers. These states change when chemisorbed oxygen ions are moved into the oxide by either flood gun electron bombardment or by thermal annealing. The former, if sufficiently energetic, results in locally well defined conduction band onsets at ~1 V, while the latter results in a progressively higher local conduction band onset, exceeding 2.3 V for 500 and 600 C thermal anneals

Bulk and edge correlations in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral Fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of {\em electrons} (with an appropriate boundary condition). We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.Comment: package now includes the file epsfig.sty, needed to incorporate properly the 8 magnificent figure

Assimilation of TES data from the Mars Global Surveyor scientifc mapping phase

The Thermal Emission Spectrometer (TES)aboard Mars Global Surveyor has produced data which cover almost two Martian years so far (during its scientific mapping phase). Thermal profiles for the atmosphere below 40 km and total dust opacities can be retrieved from TES nadir spectra and assimilated into a Mars general circulation model (MGCM), by using the assimilation techniques described in detail by Lewis et al. (2002). This paper describes some preliminary results from assimilations of temperature data from the period Ls=141°- 270° corresponding to late northern summer until winter solstice on Mars. Work in progress is devoted to assimilate both temperature and total dust opacity data for the full period for which they are already available

Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times L_y$ and arbitrarily great length $L_z$, for sizes $L_x \times L_y = 2 \times 3$ and $2 \times 4$ and boundary conditions (a) $(FBC_x,FBC_y,FBC_z)$ and (b) $(PBC_x,FBC_y,FBC_z)$, where $FBC$ ($PBC$) denote free (periodic) boundary conditions. In the limit of infinite-length, $L_z \to \infty$, we calculate the resultant ground state degeneracy per site $W$ (= exponent of the ground-state entropy). Generalizing $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the analytic structure of $W$ and the related singular locus ${\cal B}$ which is the continuous accumulation set of zeros of the chromatic polynomial. For the $L_z \to \infty$ limit of a given family of lattice sections, $W$ is analytic for real $q$ down to a value $q_c$. We determine the values of $q_c$ for the lattice sections considered and address the question of the value of $q_c$ for a $d$-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph $K_{m,m}$.Comment: 28 pages, latex, six postscript figures, two Mathematica file