Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

F18-FDG PET/CT imaging early predicts pathologic complete response to induction chemoimmunotherapy of locally advanced head and neck cancer: preliminary single-center analysis of the checkrad-cd8 trial

Aim In the CheckRad-CD8 trial patients with locally advanced head and neck squamous cell cancer are treated with a single cycle of induction chemo-immunotherapy (ICIT). Patients with pathological complete response (pCR) in the re-biopsy enter radioimmunotherapy. Our goal was to study the value of F-18-FDG PET/CT in the prediction of pCR after induction therapy. Methods Patients treated within the CheckRad-CD8 trial that additionally received FDG- PET/CT imaging at the following two time points were included: 3–14 days before (pre-ICIT) and 21–28 days after (post-ICIT) receiving ICIT. Tracer uptake in primary tumors (PT) and suspicious cervical lymph nodes (LN +) was measured using different quantitative parameters on EANM Research Ltd (EARL) accredited PET reconstructions. In addition, mean FDG uptake levels in lymphatic and hematopoietic organs were examined. Percent decrease (Δ) in FDG uptake was calculated for all parameters. Biopsy of the PT post-ICIT acquired after FDG-PET/CT served as reference. The cohort was divided in patients with pCR and residual tumor (ReTu). Results Thirty-one patients were included. In ROC analysis, ΔSUVmax PT performed best (AUC = 0.89) in predicting pCR (n = 17), with a decline of at least 60% (sensitivity, 0.77; specificity, 0.93). Residual SUVmax PT post-ICIT performed best in predicting ReTu (n = 14), at a cutpoint of 6.0 (AUC = 0.91; sensitivity, 0.86; specificity, 0.88). Combining two quantitative parameters (ΔSUVmax ≥ 50% and SUVmax PT post-ICIT ≤ 6.0) conferred a sensitivity of 0.81 and a specificity of 0.93 for determining pCR. Background activity in lymphatic organs or uptake in suspected cervical lymph node metastases lacked significant predictive value. Conclusion FDG-PET/CT can identify patients with pCR after ICIT via residual FDG uptake levels in primary tumors and the related changes compared to baseline. FDG-uptake in LN + had no predictive value. Trial registry ClinicalTrials.gov identifier: NCT03426657

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

Exendin-4 Improves Glycemic Control, Ameliorates Brain and Pancreatic Pathologies, and Extends Survival in a Mouse Model of Huntington's Disease

OBJECTIVE—The aim of this study was to find an effective treatment for the genetic form of diabetes that is present in some Huntington's disease patients and in Huntington's disease mouse models. Huntington's disease is a neurodegenerative disorder caused by a polyglutamine expansion within the huntingtin protein. Huntington's disease patients exhibit neuronal dysfunction/degeneration, chorea, and progressive weight loss. Additionally, they suffer from abnormalities in energy metabolism affecting both the brain and periphery. Similarly to Huntington's disease patients, mice expressing the mutated human huntingtin protein also exhibit neurodegenerative changes, motor dysfunction, perturbed energy metabolism, and elevated blood glucose levels

Early Energy Deficit in Huntington Disease: Identification of a Plasma Biomarker Traceable during Disease Progression

Huntington disease (HD) is a fatal neurodegenerative disorder, with no effective treatment. The pathogenic mechanisms underlying HD have not been elucidated, but weight loss, associated with chorea and cognitive decline, is a characteristic feature of the disease that is accessible to investigation. We, therefore, performed a multiparametric study exploring body weight and the mechanisms of its loss in 32 presymptomatic carriers and HD patients in the early stages of the disease, compared to 21 controls. We combined this study with a multivariate statistical analysis of plasma components quantified by proton nuclear magnetic resonance (1H NMR) spectroscopy. We report evidence of an early hypermetabolic state in HD. Weight loss was observed in the HD group even in presymptomatic carriers, although their caloric intake was higher than that of controls. Inflammatory processes and primary hormonal dysfunction were excluded. 1H NMR spectroscopy on plasma did, however, distinguish HD patients at different stages of the disease and presymptomatic carriers from controls. This distinction was attributable to low levels of the branched chain amino acids (BCAA), valine, leucine and isoleucine. BCAA levels were correlated with weight loss and, importantly, with disease progression and abnormal triplet repeat expansion size in the HD1 gene. Levels of IGF1, which is regulated by BCAA, were also significantly lower in the HD group. Therefore, early weight loss in HD is associated with a systemic metabolic defect, and BCAA levels may be used as a biomarker, indicative of disease onset and early progression. The decreased plasma levels of BCAA may correspond to a critical need for Krebs cycle energy substrates in the brain that increased metabolism in the periphery is trying to provide

On shape dependence of holographic entanglement entropy in AdS4/CFT3

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence

Heterocerus rectus Waterh

Volume: 1891Start Page: 312End Page: 31