Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

Unconventional metallic conduction in two-dimensional Hubbard-Wigner lattices

The interplay between long-range and local Coulomb repulsion in strongly interacting electron systems is explored through a two-dimensional Hubbard-Wigner model. An unconventional metallic state is found in which collective low-energy excitations characteristic of the Wigner crystal induce a flow of electrical current despite the absence of one-electron spectral weight at the Fermi surface. Photoemission experiments on certain quarter-filled layered molecular crystals should observe a gap in the excitation spectrum whereas optical spectroscopy should find a finite Drude weight indicating metallic behavior.Comment: 10 pages, accepted for publication in PR

Delayed treatment with nimesulide reduces measures of oxidative stress following global ischemic brain injury in gerbils

Metabolism of arachidonic acid by cyclooxygenase is one of the primary sources of reactive oxygen species in the ischemic brain. Neuronal overexpression of cyclooxygenase-2 has recently been shown to contribute to neurodegeneration following ischemic injury. In the present study, we examined the possibility that the neuroprotective effects of the cyclooxygenase-2 inhibitor nimesulide would depend upon reduction of oxidative stress following cerebral ischemia. Gerbils were subjected to 5 min of transient global cerebral ischemia followed by 48 h of reperfusion and markers of oxidative stress were measured in hippocampus of gerbils receiving vehicle or nimesulide treatment at three different clinically relevant doses (3, 6 or 12 mg/kg). Compared with vehicle, nimesulide significantly (P<0.05) reduced hippocampal glutathione depletion and lipid peroxidation, as assessed by the levels of malondialdehyde (MDA), 4-hydroxy-alkenals (4-HDA) and lipid hydroperoxides levels, even when the treatment was delayed until 6 h after ischemia. Biochemical evidences of nimesulide neuroprotection were supported by histofluorescence findings using the novel marker of neuronal degeneration Fluoro-Jade B. Few Fluoro-Jade B positive cells were seen in CA1 region of hippocampus in ischemic animals treated with nimesulide compared with vehicle. These results suggest that nimesulide may protect neurons by attenuating oxidative stress and reperfusion injury following the ischemic insult with a wide therapeutic window of protection

On the Moyal deformation of Nahm Equations in seven dimensions

We show how the reduced (anti-)self-dual Yang-Mills equations in seven dimensions described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism. In the process some new solutions for the cases of gauge groups SU(2) and SL(2,R) are explicitly obtained.Comment: 16+1 pages, LaTeX, no figure

Quasar Microlensing: when compact masses mimic smooth matter

The magnification induced by gravitational microlensing is sensitive to the size of a source relative to the Einstein radius, the natural microlensing scale length. This paper investigates the effect of source size in the case where the microlensing masses are distributed with a bimodal mass function, with solar mass stars representing the normal stellar masses, and smaller masses (down to $8.5\times 10^{-5}$M$_\odot$) representing a dark matter component. It is found that there exists a critical regime where the dark matter is initially seen as individual compact masses, but with an increasing source size the compact dark matter acts as a smooth mass component. This study reveals that interpretation of microlensing light curves, especially claims of small mass dark matter lenses embedded in an overall stellar population, must consider the important influence of the size of the source.Comment: 6 pages, to appear in ApJ. As ever, quality of figures reduce