Extremal metrics on blow ups

Given a compact Kahler manifold with an extremal metric (M,\omega), we give sufficient conditions on finite sets points p_1,...,p_n and weights a_1,...a_n for which the blow up of M at p_1,...,p_n has an extremal metric in the Kahler class \pi^*[\omega] - \epsilon (a_1 PD[E_1] + .. + a_n PD[E_n]) for all \epsilon sufficiently small. In particular our result implies that if (M,\omega) is a toric manifold and p_1,...,p_n is any subset of the fixed locus of the torus action, then such metrics exist for any choice of the weights. The relationship with previous constructions of the first two authors for Kahler constant scalar curvature metrics is discussed.Comment: 39 page

Balanced metrics on Cartan and Cartan-Hartogs domains

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.Comment: 11 page

A magnetic internal mechanism for precise orientation of the camera in wireless endoluminal applications

Background and study aims: The use of magnetic fields to control operative devices has been recently described in endoluminal and transluminal surgical applications. The exponential decrease of magnetic field strength with distance has major implications for precision of the remote control. We aimed to assess the feasibility and functionality of a novel wireless miniaturized mechanism, based on magnetic forces, for precise orientation of the camera. Materials and methods: A remotely controllable endoscopic capsule was developed as proof of concept. Two intracapsular moveable permanent magnets allow fine positioning, and an externally applied magnetic field permits gross movement and stabilization. Performance was assessed in ex vivo and in vivo bench tests, using porcine upper and lower gastrointestinal tracts. Results: Fine control of capsule navigation and rotation was achieved in all tests with an external magnet held steadily about 15 cm from the capsule. The camera could be rotated in steps of 1.8°. This was confirmed by ex vivo tests; the mechanism could adjust the capsule view at 40 different locations in a gastrointestinal tract phantom model. Full 360° viewing was possible in the gastric cavity, while the maximal steering in the colonwas 45° in total. In vivo, a similar performance was verified, where the mechanism was successfully operated every 5 cm for 40 cm in the colon, visually sweeping from side to side of the lumen; 360° views were obtained in the gastric fundus and body, while antrally the luminal walls prevented full rotation. Conclusions: We report the feasibility and effectiveness of the combined use of external static magnetic fields and internal actuation to move small permanent intracapsular magnets to achieve wirelessly controllable and precise camera steering. The concept is applicable to capsule endoscopy as to other instrumentation for laparoscopic, endoluminal, or transluminal procedures

Why laparoscopists may opt for three-dimensional view: a summary of the full HTA report on 3D versus 2D laparoscopy by S.I.C.E. (Società Italiana di Chirurgia Endoscopica e Nuove Tecnologie)

Background: Three-dimensional view in laparoscopic general, gynaecologic and urologic surgery is an efficient, safe and sustainable innovation. The present paper is an extract taken from a full health technology assessment report on three-dimensional vision technology compared with standard two-dimensional laparoscopic systems. Methods: A health technology assessment approach was implemented in order to investigate all the economic, social, ethical and organisational implications related to the adoption of the innovative three-dimensional view. With the support of a multi-disciplinary team, composed of eight experts working in Italian hospitals and Universities, qualitative and quantitative data were collected, by means of literature evidence, validated questionnaire and self-reported interviews, applying a final MCDA quantitative approach, and considering the dimensions resulting from the EUnetHTA Core Model. Results: From systematic search of literature, we retrieved the following studies: 9 on general surgery, 35 on gynaecology and urology, both concerning clinical setting. Considering simulated setting we included: 8 studies regarding pitfalls and drawbacks, 44 on teaching, 12 on surgeons’ confidence and comfort and 34 on surgeons’ performances. Three-dimensional laparoscopy was shown to have advantages for both the patients and the surgeons, and is confirmed to be a safe, efficacious and sustainable vision technology. Conclusions: The objective of the present paper, under the patronage of Italian Society of Endoscopic Surgery, was achieved in that there has now been produced a scientific report, based on a HTA approach, that may be placed in the hands of surgeons and used to support the decision-making process of the health providers

Localization in the Discrete Non-linear Schrodinger Equation and Geometric Properties of the Microcanonical Surface

It is well known that, if the initial conditions have sufficiently high energy density, the dynamics of the classical Discrete Non-Linear Schrodinger Equation (DNLSE) on a lattice shows a form of breaking of ergodicity, with a finite fraction of the total charge accumulating on a few sites and residing there for times that diverge quickly in the thermodynamic limit. In this paper we show that this kind of localization can be attributed to some geometric properties of the microcanonical potential energy surface, and that it can be associated to a phase transition in the lowest eigenvalue of the Laplacian on said surface. We also show that the approximation of considering the phase space motion on the potential energy surface only, with effective decoupling of the potential and kinetic partition functions, is justified in the large connectivity limit, or fully connected model. In this model we further observe a synchronization transition, with a synchronized phase at low temperatures