Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra

Particle Collisions on Stringy Black Hole Background

The collision of two particles in the background of a Sen black hole is studied. With the equations of motion of the particles, the center-of-mass energy is investigated when the collision takes place at the horizon of a Sen black hole. For an extremal Sen black hole, we find that the center-of-mass energy will be arbitrarily high with two conditions: (1) spin $a\neq 0$ and (2) one of the colliding particles has the critical angular momentum $l_{\text{c}}=2$. For a nonextremal Sen black hole, we show that, in order to obtain an unlimited center-of-mass energy, one of the colliding particles should have the critical angular momentum $l'_{\text{c}}=2 r_{+}/a$ ($r_{+}$ is the radius of the outer horizon for a nonextremal black hole). However, a particle with the angular momentum $l=l'_{\text{c}}$ could not approach the black hole from outside of the horizon through free fall, which implies that the collision with arbitrarily high center-of-mass energy could not take place. Thus, there is an upper bound of the center-of-mass energy for the nonextremal black hole. We also obtain the maximal center-of-mass energy for a near-extremal black hole and the result implies that the Planck-scale energy is hard to be approached. Furthermore, we also consider the back-reaction effects. The result shows that, neglecting the gravitational radiation, it has a weak effect on the center-of-mass energy. However, we argue that the maximum allowed center-of-mass energy will be greatly reduced to below the Planck-scale when the gravitational radiation is included.Comment: 17 pages, 4 figures, published versio

Dietary polyacetylenic oxylipins falcarinol and falcarindiol prevent inflammation and colorectal neoplastic transformation:A mechanistic and dose-response study in a rat model

Falcarinol (FaOH) and falcarindiol (FaDOH) are cytotoxic and anti-inflammatory polyacetylenic oxylipins, which are commonly found in the carrot family (Apiaceae). FaOH and FaDOH have previously demonstrated a chemopreventive effect on precursor lesions of colorectal cancer (CRC) in azoxymethane (AOM)-induced rats. The purpose of the present study was to elucidate possible mechanisms of action for the preventive effect of FaOH and FaDOH on colorectal precancerous lesions and to determine how this effect was dependent on dose. Gene expression studies performed by RT-qPCR of selected cancer biomarkers in tissue from biopsies of neoplastic tissue revealed that FaOH and FaDOH downregulated NF-κβ and its downstream inflammatory markers TNFα, IL-6, and COX-2. The dose-dependent anti-neoplastic effect of FaOH and FaDOH in AOM-induced rats was investigated in groups of 20 rats receiving a standard rat diet (SRD) supplemented with 0.16, 0.48, 1.4, 7 or 35 µg FaOH and FaDOH g−1 feed in the ratio 1:1 and 20 rats were controls receiving only SRD. Analysis of aberrant crypt foci (ACF) showed that the average number of small ACF (<7 crypts) and large ACF (>7 crypts) decreased with increasing dose of FaOH and FaDOH and that this inhibitory effect on early neoplastic formation of ACF was dose-dependent, which was also the case for the total number of macroscopic neoplasms. The CRC protective effects of apiaceous vegetables are mainly due to the inhibitory effect of FaOH and FaDOH on NF-κB and its downstream inflammatory markers, especially COX-2

Investigating the biological properties of carbohydrate derived fulvic acid (CHD-FA) as a potential novel therapy for the management of oral biofilm infections.

Background: A number of oral diseases, including periodontitis, derive from microbial biofilms and are associated with increased antimicrobial resistance. Despite the widespread use of mouthwashes being used as adjunctive measures to control these biofilms, their prolonged use is not recommended due to various side effects. Therefore, alternative broad-spectrum antimicrobials that minimise these effects are highly sought after. Carbohydrate derived fulvic acid (CHD-FA) is an organic acid which has previously demonstrated to be microbiocidal against Candida albicans biofilms, therefore, the aims of this study were to evaluate the antibacterial activity of CHD-FA against orally derived biofilms and to investigate adjunctive biological effects.<p></p> Methods: Minimum inhibitory concentrations were evaluated for CHD-FA and chlorhexidine (CHX) against a range of oral bacteria using standardised microdilution testing for planktonic and sessile. Scanning electron microscopy was also employed to visualise changes in oral biofilms after antimicrobial treatment. Cytotoxicity of these compounds was assessed against oral epithelial cells, and the effect of CHD-FA on host inflammatory markers was assessed by measuring mRNA and protein expression.<p></p> Results: CHD-FA was highly active against all of the oral bacteria tested, including Porphyromonas gingivalis, with a sessile minimum inhibitory concentration of 0.5%. This concentration was shown to kill multi-species biofilms by approximately 90%, levels comparable to that of chlorhexidine (CHX). In a mammalian cell culture model, pretreatment of epithelial cells with buffered CHD-FA was shown to significantly down-regulate key inflammatory mediators, including interleukin-8 (IL-8), after stimulation with a multi-species biofilm.<p></p> Conclusions: Overall, CHD-FA was shown to possess broad-spectrum antibacterial activity, with a supplementary function of being able to down-regulate inflammation. These properties offer an attractive spectrum of function from a naturally derived compound, which could be used as an alternative topical treatment strategy for oral biofilm diseases. Further studies in vitro and in vivo are required to determine the precise mechanism by which CHD-FA modulates the host immune response.<p></p&gt

Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a non-degenerate CKY tensor.Comment: 24 pages, LaTeX; v2: references added, published versio

Hidden Symmetries and Black Holes

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.Comment: 13 pages, 3 figures. To appear in the proceedings of the NEB-13 conferenc