Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.