Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u= 0, where L is a linear second order hypoelliptic operator and V belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem

On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators

This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form $$\partial_t u (x,t) = \sum_{j=1}^m X_j^2 u(x,t) + X_0 u(x,t) \qquad (x,t) \in \mathbb{R}^N \times\, ]- \infty ,T[,$$ proved by a functional analytic approach based on Choquet theory. As a consequence, we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem.Comment: The results of the present version recover most of the ones in the previous version, but, on top of it, this new version contains some further new and interesting result

Bounds on short cylinders and uniqueness results for degenerate Kolmogorov equation

We consider the Cauchy problem for hypoelliptic Kolmogorov equations in both divergence and non divergence form. We prove that, if |u(x,t)| < M exp(a(t^{-\beta}+|x|^2)) for some positive constants a, M, \beta in ]0,1[ and u(x,0) = 0, then u(x,t) = 0 for positive t. The proof of the main result is based on some previous uniqueness result and on the application of some estimates in short cylinders, first introduced by Safonov in the study of uniformly parabolic operators

A linear systems analysis of the yaw dynamics of a dynamically scaled insect model

Recent studies suggest that fruit flies use subtle changes to their wing motion to actively generate forces during aerial maneuvers. In addition, it has been estimated that the passive rotational damping caused by the flapping wings of an insect is around two orders of magnitude greater than that for the body alone. At present, however, the relationships between the active regulation of wing kinematics, passive damping produced by the flapping wings and the overall trajectory of the animal are still poorly understood. In this study, we use a dynamically scaled robotic model equipped with a torque feedback mechanism to study the dynamics of yaw turns in the fruit fly Drosophila melanogaster. Four plausible mechanisms for the active generation of yaw torque are examined. The mechanisms deform the wing kinematics of hovering in order to introduce asymmetry that results in the active production of yaw torque by the flapping wings. The results demonstrate that the stroke-averaged yaw torque is well approximated by a model that is linear with respect to both the yaw velocity and the magnitude of the kinematic deformations. Dynamic measurements, in which the yaw torque produced by the flapping wings was used in real-time to determine the rotation of the robot, suggest that a first-order linear model with stroke-average coefficients accurately captures the yaw dynamics of the system. Finally, an analysis of the stroke-average dynamics suggests that both damping and inertia will be important factors during rapid body saccades of a fruit fly

Adverse reactions of amiodarone

Adverse drug reaction is defined by the World Health Organization as any response to a drug that is noxious and unintended and occurs at a dose normally used in man. Older people are at elevated risk of adverse drug reactions-because of changes in pharmacodynamics, concurrent use of multiple medications and the related drug interactions. However, adverse drug reactions are significantly underestimated in the elderly population that is also exposed to inappropriate drugs. Amiodarone is an antiarrhythmic drug used commonly for the treatment of atrial fibrillation and is increasingly prescribed in older people. While amiodarone is an efficient drug for rhythm control, it's a carrier of different adverse reactions, and pro and cons must be carefully evaluated before its use especially in older people

Harnack inequality and no-arbitrage bounds for self-financing portfolios

We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant. We discuss some possible implication of the Harnack inequality in finance: specifically we infer no-arbitrage bounds for the value of self-financing portfolios in terms of the initial wealth.Harnack inequality; no-arbitrage principle; self-financing portfolio; Kolmogorov equation; linear stochastic equation

Harnack Inequality for Hypoelliptic Second Order Partial Differential Operators

We consider non-negative solutions (Formula presented.) of second order hypoelliptic equations(Formula presented.) where \u3a9 is a bounded open subset of (Formula presented.) and x denotes the point of \u3a9. For any fixed x0 08 \u3a9, we prove a Harnack inequality of this type(Formula presented.) where K is any compact subset of the interior of the (Formula presented.)-propagation set ofx0 and the constant CK does not depend on u

SIP-based mobility management in next generation networks

The ITU-T definition of next generation networks includes the ability to make use of multiple broadband transport technologies and to support generalized mobility. Next generation networks must integrate several IP-based access technologies in a seamless way. In this article, we first describe the requirements of a mobility management scheme for multimedia real-time communication services; then, we report a survey of the mobility management schemes proposed in the recent literature to perform vertical handovers between heterogeneous networks. Based on this analysis, we propose an application-layer solution for mobility management that is based on the SIP protocol and satisfies the most important requirements for a proper implementation of vertical handovers. We also implemented our proposed solution, testing it in the field, and proving its overall feasibility and its interoperability with different terminals and SIP servers

Adapting a Survey-Class AUV for High Resolution Seafloor Imaging

Over the past four years, development work at the MIT AUV Lab focused on a vehicle that is now almost a decade old. “Xanthos,” one of the last surviving examples of the venerable Odyssey II series of AUVs (developed at MIT in the early 1990s), is a small, deep-rated, low- drag vehicle originally intended for oceanographic survey work. In this project, the AUV Lab pushed the limits of the Odyssey II platform to bring this aging vehicle up to the state of the art in underwater imaging. Originally designed to carry a CTD and ADCP, Xanthos was refit with DVL and AHRS for navigation, and sidescan sonar, high-resolution digital still camera, and high-powered strobe for seafloor imaging. No part of the original vehicle was left untouched; several subsystems were redesigned and rebuilt from scratch to accommodate the new sensors. The ultimate goal: to turn a simple CTD profiler into a tool for deep-water marine archaeology. Xanthos’ rebirth culminated in a visit to Greece, aboard the Hellenic Center for Marine Research’s R/V “Aegaeo.” This attempt at AUV-based archaeology demonstrated the strengths and weaknesses of the re-design, as Xanthos contended with strong currents, navigation failures, sensor limitations, and mechanical damage. Lessons learned from the development of Xanthos as an imaging platform form the foundation of the MIT AUV Lab’s latest project. The “Odyssey IV,” capable of hovering and holonomic maneuvers at depths of up to 3000m, will carry a stereo camera and sonar as its primary sensor payloads

Untargeted lipidomic features associated with colorectal cancer in a prospective cohort.

BackgroundEpidemiologists are beginning to employ metabolomics and lipidomics with archived blood from incident cases and controls to discover causes of cancer. Although several such studies have focused on colorectal cancer (CRC), they all followed targeted or semi-targeted designs that limited their ability to find discriminating molecules and pathways related to the causes of CRC.MethodsUsing an untargeted design, we measured lipophilic metabolites in prediagnostic serum from 66 CRC patients and 66 matched controls from the European Prospective Investigation into Cancer and Nutrition (Turin, Italy). Samples were analyzed by liquid chromatography-high-resolution mass spectrometry (LC-MS), resulting in 8690 features for statistical analysis.ResultsRather than the usual multiple-hypothesis-testing approach, we based variable selection on an ensemble of regression methods, which found nine features to be associated with case-control status. We then regressed each selected feature on time-to-diagnosis to determine whether the feature was likely to be either a potentially causal biomarker or a reactive product of disease progression (reverse causality).ConclusionsOf the nine selected LC-MS features, four appear to be involved in CRC etiology and merit further investigation in prospective studies of CRC. Four other features appear to be related to progression of the disease (reverse causality), and may represent biomarkers of value for early detection of CRC