Heat kernels on 2d Liouville quantum gravity: a numerical study

We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore, when diffusion is started from a high point of the underlying Gaussian free field, our numerics indicates superdiffusive space-time scaling with respect to the Euclidean metric in the small space-to-time regime. The implications of this result require further investigation, but seem to coincide with the notion that the Euclidean metric is not the right geodesic for characterizing the geometry of LQG.Comment: Preliminary repor

Constructing a class of topological solitons in magnetohydrodynamics

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t \in \mathbb{Z}^+$ and $n_p=1$ these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity and estimate the soliton lifetime in such a medium as a function of the toroidal winding number.Comment: 5 pages, 3 figure

Scarlatinal arthritis: a clinical and statistical study

It is one of the compensations of work in a fever¡ hospital, that, although dealing with a comparatively limited number of diseases, in addition to various conditions which may be beset by an infectious disease, the scope of our observations in the field of medicine is considerably widened by the incidence of the complications which are a more or less constant feature of the exanthems and the other infectious fevers. Scarlet fever provides a rich selection of such complications and of these none is more interesting than Scarlatinal rheumatism or arthritis. This complication has an interest for its own sake in view of the marked attention paid at the present day to the generals question of rheumatism, and the prevention of heart disease associated therewith. From another point of view even the most modern and complete text -books show a certain amount of divergency of opinion in regard to certain clinical points that could be fairly easily cleared up by a little careful observation, and certain gaps in know - ledge, especially from the statistical standpoint, that could be filled in after a little consideration of the abundant records available in the Edinburgh City Hospital. The writer also originally set out with the intention of completing the work by making some bacteriological researches into the condition, but this was prevented by various circumstances, the main difficulty being that it was almost impossible to carry out this part of the work when not actually resident in the hospital. Most modern fever experts have adopted the term "arthritis" in place of the old "rheumatism's and although this may have something to commend it from a scientific point of view, in so far as the modern term denotes a certain condition in certain tissues, the old term had its conveniences, for it could be held to include associated inflammations in tendon sheaths and muscular tissues as well as in joints - so obviously manifestations of the same process that the new habit of separating them into arthritis, tondo-synovitis, and myositis, seems clumsy by comparison. Reference to this point is rendered necessary by the fact that in all statistical considerations the use of the term arthritis is held to include these other manifestations as well

Some factors in the rooting of Ilex

The Hollies constitute one of the more important groups of plants in Ornamental Horticulture. The Genus Ilex is of value to the commercial nurseryman, the home owner as landscape material, and to those who wish to conserve our native trees. Since Hollies are becoming more important in the nursery industry, satisfactory methods for increasing the best selections should be developed. Male as well as female plants should be made available for planting since most of the genus is dioecious. Better methods of propagation for the more difficult to root species must be developed to make this possible. This work was designed to test some of the external factors which affect the rooting of Hollies. The factors tested were mediums and watering methods under controlled humidity and bottom heat. The mediums selected were those which had proved useful to nurserymen as well as those which some experimental papers recommended Hollies. The watering systems were selected for ease of installing, adaptability to propagating benches already in operation, relative low installation cost, and ease of operation. All Ilex species of which cutting wood was available in quantity were tested in these experiments. These species were aquifolium, cassine, cornute, cornute clon Burford, cremate clon Spreading, crenate clon Convexleaf, crenate clon Roundleaf, decidua, opace, and vomitoria

Rich Tags: Cross-Repository Browsing

We present RichTags, a system for cross-site browsing and exploration of digital repositories. Categorical and faceted search across repositories is poorly supported, especially compared to the support of keyword search through internet search engines. We combine a variety of information retrieval techniques to determine categories of papers, to enable cross-repository browsing by category. The browsing and exploration of this metadata is achieved through a multi-faceted dynamic exploration interface. Social interaction features have also been added to enable cross-repository tagging, commenting and sharing of papers into groups. These social features are available via an API to enable future work to add plugins to pull comments back to the repositories