1,354,456 research outputs found
Ricci curvature and monotonicity for harmonic functions
No full textOriginal manuscript September 20, 2012In this paper we generalize the monotonicity formulas of “Colding (Acta Math 209:229–263, 2012)” for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., “Almgren (Preprint)”, “Colding and Minicozzi II (PNAS, 2012)”, “Garofalo and Lin (Indiana Univ Math 35:245–267, 1986)” for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green’s function on open manifolds with nonnegative Ricci curvature are asymptotically umbilic.National Science Foundation (U.S.) (Grant DMS 11040934)National Science Foundation (U.S.) (Grant DMS 1206827)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501
Extending an example by Colding and Minicozzi
No full textExtending an example by Colding and Minicozzi (Trans Am Math Soc 356(1):283–289, 2003), we construct a sequence of properly embedded minimal disks \Sigma _i in an infinite Euclidean cylinder around the x_3-axis with curvature blow-up at a single point. The sequence converges to a non-smooth and non-proper minimal lamination in the cylinder. Moreover, we show that the disks \Sigma _i are not properly embedded in a sequence of open subsets of \mathbb {R}^3 that exhausts \mathbb {R}^3.peerReviewe
Monitoring Insulin-Aggregated Structures in the Presence of Epigallocatechin-3-gallate and Melatonin by Molecular Dynamics Simulations
No full textIn the present work we illustrate the results of classical molecular dynamics simulations of model systems composed of six insulin molecules in water in the presence and in the absence of either epigallocatechin-3-gallate or melatonin molecules. For each model system, we performed three independent simulations (replicas) to study the aggregate formation dynamics and insulin interaction with epigallocatechin-3-gallate and melatonin. We find that melatonin is less stably close to insulin with respect to epigallocatechin-3-gallate, which interacts more stably with insulin molecules and mainly with insulin's chain B hydrophobic residues. We observe that the shape of the insulin-aggregated structures in the three model systems is different and depends on whether epigallocatechin-3-gallate is present or not. Simulations show that in the absence of epigallocatechin-3-gallate, insulin molecules tend to form linear aggregates, while in the presence of epigallocatechin-3-gallate, aggregates display a globular shape, less prone to form fibril structures
Carcinoma colorettale: nuove metodiche diagnostiche.Ricerche sperimentali con spettroscopia di risonanza magnetica
No full textABSTRACT
Questa tesi di dottorato è stata elaborata nella prospettiva di studiare l’applicazione della spettroscopia di risonanza magnetica protonica (1H MRS) nella possibile diagnosi istologica non invasiva dei polipi e del carcinoma colorettale.
In particolare, la sua utilizzazione nella stadiazione del cancro del retto dopo trattamento neoadiuvante (chemioradioterapia concomitanti), che risulta fortemente deficitaria con le metodiche tradizionali (EUS, MRI, TC e PET- TC), potrebbe consentire diagnosi più accurate soprattutto di risposte cliniche complete o di residuo minimo di malattia.
A tale scopo sono stati dapprima ricordati nella letteratura i risultati dell’uso delle metodiche di imaging tradizionali che non consentono scelte terapeutiche adeguate alla presenza della neoplasia, scelte che variano dalla astensione chirurgica ad interventi allargati e mutilanti.
E’ stata rivista la utilizzazione su tumori umani (in vivo, ex-vivo e in studi sperimentali) della MRS, in modo specifico e più dettagliato, sul carcinoma colorettale.
Infine nell’ultima parte della tesi sono stati riportati scopi, metodi, apparati tecnologici e risultati della ricerca attuata, costituita dall’uso della 1H MRS su pezzi operatori umani.
Parole chiave: spettroscopia di risonanza magnetica, carcinoma colorettaleThis PhD thesis has been prepared with a view to the study of the application of proton magnetic resonance spectroscopy (1H MRS) in the possible non-invasive histological diagnosis of colorectal polyps and cancer.
In particular, its use in staging of rectal cancer after neoadjuvant treatment (concurrent chemoradiotherapy), which is heavily deficient with traditional methods (EUS, MRI, CT and PET-CT), could allow more accurate diagnosis, overall of clinical complete responses or minimal residual disease.
choices ranging from abstention widened and mutilating surgical interventions.For this purpose, the results of the use of traditional imaging methods have been first of all remembered in the literature, results which do not allow appropriate therapeutic choices for cancer, ranging from surgical abstention to extended operations.
The use of the MRS on human tumors (in vivo, ex vivo and in experimental studies) was reviewed, in a more specific and detailed matter, on colorectal carcinoma.
Finally in the last part of the thesis aims, methods, technological equipments and results of implemented research, made of use of 1H MRS on human surgical specimens, have been reported
New method for internal anal sphincter measurements: Feasibility study
No full textThe aim of this paper is to provide a method for measuring the internal anal sphincter on the basis of the quantitative analysis of three-dimensional endosonographic images. A software calculates a large set of measurements which are able to describe the three-dimensional shape of the muscle. The software provides four types of measurements: thickness, length, area and volume. The different magnitudes are estimated using the same reference system. The measurements obtained are modeled by functions that describe their spatial tren
Theoretical Study of Vibrational Properties of Peptides: Force Fields in Comparison and Ab Initio Investigation
No full textInfrared (IR) spectroscopy is a valuable tool to obtain information about protein secondary structure. The far-infrared (FIR) spectrum is characterized by a complex combination of different molecular contributions which, for small molecules, may be interpreted with the help of quantum-mechanical (QM) calculations. Unfortunately, the high computational cost of QM calculations makes them inapplicable to larger molecules, such as proteins and peptides. In this work, we present a theoretical study on the secondary structure, molecular properties, and vibrational spectra of different peptides, using both a classical and a QM approach. Our results show that the amide I main peak value, and related quantities, such as dipole strength (DS) and transition dipole moment (TDM), depends on protein secondary structure; in particular, from QM calculations arises that α-rich molecular systems present lower intensities than β-rich ones. Furthermore, it is possible to decouple and identify the intensity of the different contributions of the inter- and intra-molecular motions which characterize the FIR spectrum, starting from the results obtained with QM calculations
Li-Yau Conformal Volume and Colding-Minicozzi Entropy of Self-Shrinkers
No full textWe show the (normalized) Li-Yau conformal volume of a self-shrinker of mean curvature flow in Euclidean space bounds its Colding-Minicozzi entropy from below. This bound is independent of codimension and sharp on planes. As an application we verify a conjecture of Colding-Minicozzi about the entropy of closed self-shrinkers of arbitrary codimension for self-shrinkers that are topologically two-dimensional real projective planes. As part of the proof we introduce two auxiliary functionals which we call stable conformal volume and virtual entropy which should be of independent interest.28 page
Generic mean curvature flow I; generic singularities
No full textAuthor Manuscript August 26, 2009It has long been conjectured that starting at a generic smooth closed embedded surface in R[superscript 3], the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which the flow looks like concentric spheres or cylinders. That is, the only singularities of a generic flow are spherical or cylindrical. We will address this conjecture here and in a sequel. The higher dimensional case will be addressed elsewhere. The key to showing this conjecture is to show that shrinking spheres, cylinders, and planes are the only stable self-shrinkers under the mean curvature flow. We prove this here in all dimensions. An easy consequence of this is that every singularity other than spheres and cylinders can be perturbed away.National Science Foundation (U.S.) (Grant DMS-0606629)National Science Foundation (U.S.) (Grant DMS-0405695)National Science Foundation (U.S.). Focused Research Group (Grant DMS-0854774)National Science Foundation (U.S.). Focused Research Group (Grant DMS-0853501
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