A Reciprocity Theorem for Monomer-Dimer Coverings

The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a reciprocity principle governing the number $N(m,n)$ of dimer coverings of an $m$ by $n$ rectangular grid (also known as perfect matchings), where $m$ is fixed and $n$ is allowed to vary. As reinterpreted by Propp, Stanley's result concerns the unique way of extending $N(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $N(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. In particular, Stanley shows that $N(m,n)$ is always an integer satisfying the relation $N(m,-2-n) = \epsilon_{m,n}N(m,n)$ where $\epsilon_{m,n} = 1$ unless $m\equiv$ 2(mod 4) and $n$ is odd, in which case $\epsilon_{m,n} = -1$. Furthermore, Propp's method is applicable to higher-dimensional cases. This paper discusses similar investigations of the numbers $M(m,n)$, of monomer-dimer coverings, or equivalently (not necessarily perfect) matchings of an $m$ by $n$ rectangular grid. We show that for each fixed $m$ there is a unique way of extending $M(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $M(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. We show that $M(m,n)$, a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp. Lastly, we give a new statement of reciprocity in terms of multivariate generating functions from which Stanley's result follows.Comment: 13 pages, 12 figures, to appear in the proceedings of the Discrete Models for Complex Systems (DMCS) 2003 conference. (v2 - some minor changes

Australian Fathers\u27 Study: What influences paternal engagement with antenatal care?

This mixed-methods study explores factors associated with and levels of engagement of fathers in antenatal care. One hundred expectant fathers were recruited from antenatal clinics and community settings in Western Australia. They completed validated questionnaires. Eighty-three percent of expectant fathers reported a lack of engagement with antenatal care. Factors significantly associated with lack of engagement in multivariate analysis were working more than 40 hours a week and lack of adequate consultation by antenatal care staff. In qualitative analysis, 6 themes emerged in association with a lack of engagement. They were role in decision making, time pressures, the observer effect, lack of knowledge, barriers to attendance, and feeling unprepared or anxious. Care providers should involve fathers in consultations to improve paternal engagement

Land use change detection with LANDSAT-2 data for monitoring and predicting regional water quality degradation

The author has identified the following significant results. Comparison between LANDSAT 1 and 2 imagery of Arkansas provided evidence of significant land use changes during the 1972-75 time period. Analysis of Arkansas historical water quality information has shown conclusively that whereas point source pollution generally can be detected by use of water quality data collected by state and federal agencies, sampling methodologies for nonpoint source contamination attributable to surface runoff are totally inadequate. The expensive undertaking of monitoring all nonpoint sources for numerous watersheds can be lessened by implementing LANDSAT change detection analyses

Drilling of shallow marine sulfide-sulfate mineralisation in south-eastern Tyrrhenian Sea, Italy; Seafloor sulfides, Tyrrhenian Sea, highsulfidation; hydrothermal systems, Palinuro

Semi-massive to massive sulfides with abundant late native sulfur were drilled in a shallowwater hydrothermal system in an island arc volcanic setting at the Palinuro volcanic complex in the Tyrrhenian Sea, Italy. Overall, 12.7 m of sulfide mineralisation were drilled in a sediment-filled depression at a water depth of 630 - 650 m using the lander-type Rockdrill I drill rig of the British Geological Survey. Polymetallic (Zn, Pb, Sb, As, Ag) sulfides overlie massive pyrite. The massive sulfide mineralisation contains a number of atypical minerals, including enargite-famatinite, tennantite-tetrahedrite, stibnite, bismuthinite, and Pb-,Sb-, and Ag-sulfosalts, that do not commonly occur in mid-ocean ridge massive sulfides. Analogous to subaerial epithermal deposits, the occurrence of these minerals and the presence of abundant native sulfur suggest an intermediate to high sulfidation and/or high oxididation state of the hydrothermal fluids in contrast to the near-neutral and reducing fluids from which base metal-rich massive sulfides along mid-ocean ridges typically form. Oxidised conditions during sulfide deposition are likely related to the presence of magmatic volatiles in the mineralising fluids that were derived from a degassing magma chamber below the Palinuro volcanic complex

Distilling Wikipedia mathematical knowledge into neural network models

Machine learning applications to symbolic mathematics are becoming increasingly popular, yet there lacks a centralized source of real-world symbolic expressions to be used as training data. In contrast, the field of natural language processing leverages resources like Wikipedia that provide enormous amounts of real-world textual data. Adopting the philosophy of "mathematics as language," we bridge this gap by introducing a pipeline for distilling mathematical expressions embedded in Wikipedia into symbolic encodings to be used in downstream machine learning tasks. We demonstrate that a $\textit{mathematical}$ $\textit{language}$ $\textit{model}$ trained on this "corpus" of expressions can be used as a prior to improve the performance of neural-guided search for the task of symbolic regression.Comment: 6 pages, 4 figure

UrQMD calculations of two-pion HBT correlations in p+p and Pb+Pb collisions at LHC energies

Two-pion Hanbury-Brown-Twiss (HBT) correlations for p+p and central Pb+Pb collisions at the Large-Hadron-Collider (LHC) energies are investigated with the ultra-relativistic quantum molecular dynamics model combined with a correlation afterburner. The transverse momentum dependence of the Pratt-Bertsch HBT radii $R_{long}$, $R_{out}$, and $R_{side}$ is extracted from a three-dimensional Gaussian fit to the correlator in the longitudinal co-moving system. In the p+p case, the dependence of correlations on the charged particle multiplicity and formation time is explored and the data allows to constrain the formation time in the string fragmentation to $\tau_f \leq 0.8$ fm/c. In the Pb+Pb case, it is found that $R_{out}$ is overpredicted by nearly 50%. The LHC results are also compared to data from the STAR experiment at RHIC. For both energies we find that the calculated $R_{out}/R_{side}$ ratio is always larger than data, indicating that the emission in the model is less explosive than observed in the data.Comment: 9 pages, 4 figures, 1 table. Talk given by Qingfeng Li at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

A new neurosurgical tool incorporating differential geometry and cellular automata techniques

Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to minimize the amount of resection necessary during surgical therapeutic interventions for epilepsy and is typically done approximately from visual inspection of optical coherence imaging stills. In this paper, we create an algorithm with the potential to pinpoint the source of a seizure from an optical coherence imaging still. To accomplish this, a grid is overlaid on optical coherence imaging stills. This then serves as a grid for a two-dimensional cellular automation. Each cell is associated with a Riemannian curvature tensor representing the curvature of the brain's surface in all directions for a cell. Cells which overlay portions of the image which show neurons that are firing are considered "depolarized"

Influence of a magnetic field on the antiferromagnetic order in UPt_3

A neutron diffraction experiment was performed to investigate the effect of a magnetic field on the antiferromagnetic order in the heavy fermion superconductor UPt_3. Our results show that a field in the basal plane of up to 3.2 Tesla, higher than H_c2(0), has no effect: it can neither select a domain nor rotate the moment. This has a direct impact on current theories for the superconducting phase diagram based on a coupling to the magnetic order.Comment: 7 pages, RevTeX, 3 postscript figures, submitted to Phys. Rev.

Maternal inflammation at 0.7 gestation in ewes leads to intrauterine growth restriction and impaired glucose metabolism in offspring at 30 d of age

Fetal programming associated with intrauterine growth restriction (IUGR) leads to lifelong deficits in growth and metabolic function (Hales and Barker, 2013). IUGR arises when fetuses respond to poor in utero conditions by developing adaptations that repartition nutrients to critical tissues and away from skeletal muscle (Yates et al., 2012, 2018). This fetal programming is beneficial in utero but leads to persistent reductions in muscle mass and glucose homeostasis in offspring (DeFronzo et al., 1981). Recent studies by our laboratory in sheep and rats demonstrate that maternal inflammation during gestation induces fetal inflammatory adaptations that impair growth and disrupt muscle glucose metabolism (Cadaret et al., 2017, 2018). IUGR fetal skeletal muscle exhibits indicators of enhanced inflammatory sensitivity, which could disrupt glucose uptake and oxidation (Yates et al., 2016; Cadaret et al., 2018). Enhanced inflammatory responsiveness would help explain growth and metabolic deficits observed in IUGR offspring. We hypothesize that fetal programming induced by maternal inflammation persists in offspring and contributes to impaired growth and glucose metabolism at 30 d. Therefore, the objective of this study was to determine whether sustained maternal inflammation induced by bacterial endotoxin at 0.7 gestation leads to fetal programming that contributes to deficits in growth and glucose metabolism in offspring