Mathematical Properties of a Class of Four-dimensional Neutral Signature Metrics

While the Lorenzian and Riemanian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the four-dimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses: the Walker and Kundt metrics. In this paper we have chosen an example from each of the two subcases of the Ricci-flat VSI Walker metrics respectively. To investigate the difference between the metrics we determine the existence of a null, geodesic, expansion-free, shear-free and vorticity-free vector, and classify these spaces using their infinitesimal holonomy algebras. The geometric implications of the holonomy algebras are further studied by identifying the recurrent or covariantly constant null vectors, whose existence is required by the holonomy structure in each example. We conclude the paper with a simple example of the equivalence algorithm for these pseudo-Riemannian manifolds, which is the only approach to classification that provides all necessary information to determine equivalence.Comment: 18 page

An Unusual Case of Tertiary Syphilis Behaving Like Tongue Squamous Cell Carcinoma.

Syphilis may present with a myriad of oral manifestations in the primary, secondary, and tertiary stages, and may be confused with malignancy. Despite a rise in the incidence of syphilis, tertiary syphilis is exceedingly rare. Tertiary syphilis gummas usually affect the hard palate, while tongue involvement is very rare. A 55-year-old male with extensive smoking and alcohol use was referred for malignancy evaluation with an ulcerative mass creating a tongue cleft, and a positron emission tomography scan suggestive for malignancy. Biopsy results demonstrated no carcinoma but histology demonstrated granulomatous inflammation. Further laboratory results demonstrated elevated rapid plasma reagin titers with Treponema pallidum immunoglobulin G antibodies present. The patient was diagnosed with tertiary syphilis, received appropriate antibiotic therapy, and had healing of the tongue with a persistent cleft. Syphilis may mimic many disease processes. As such, it is important to include this disease in the differential of an unusual tongue lesion. An oral lesion may be the first sign of infection

An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142

Low EUV Luminosities Impinging on Protoplanetary Disks

The amount of high-energy stellar radiation reaching the surface of protoplanetary disks is essential to determine their chemistry and physical evolution. Here, we use millimetric and centimetric radio data to constrain the EUV luminosity impinging on 14 disks around young (~2-10Myr) sun-like stars. For each object we identify the long-wavelength emission in excess to the dust thermal emission, attribute that to free-free disk emission, and thereby compute an upper limit to the EUV reaching the disk. We find upper limits lower than 10$^{42}$ photons/s for all sources without jets and lower than $5 \times 10^{40}$ photons/s for the three older sources in our sample. These latter values are low for EUV-driven photoevaporation alone to clear out protoplanetary material in the timescale inferred by observations. In addition, our EUV upper limits are too low to reproduce the [NeII] 12.81 micron luminosities from three disks with slow [NeII]-detected winds. This indicates that the [NeII] line in these sources primarily traces a mostly neutral wind where Ne is ionized by 1 keV X-ray photons, implying higher photoevaporative mass loss rates than those predicted by EUV-driven models alone. In summary, our results suggest that high-energy stellar photons other than EUV may dominate the dispersal of protoplanetary disks around sun-like stars.Comment: Accepted for publication to The Astrophysical Journa

Modal expansions and non-perturbative quantum field theory in Minkowski space

We introduce a spectral approach to non-perturbative field theory within the periodic field formalism. As an example we calculate the real and imaginary parts of the propagator in 1+1 dimensional phi^4 theory, identifying both one-particle and multi-particle contributions. We discuss the computational limits of existing diagonalization algorithms and suggest new quasi-sparse eigenvector methods to handle very large Fock spaces and higher dimensional field theories.Comment: new material added, 12 pages, 6 figure

Tunable Cavity Optomechanics with Ultracold Atoms

We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective sub-wavelength positioning of the atomic ensemble allows for tuning the linear and quadratic optomechanical coupling parameters, varying the sensitivity to the displacement and strain of a compressible gaseous cantilever. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.Comment: 4 pages, 5 figure