Unique continuation for solutions to the induced Cauchy-Riemann equations

AbstractLet M be a real infinitely differentiable closed hypersurface in X, a complex manifold of dimension n ⩾ 2, and let \̄t6M denote the induced Cauchy-Riemann operator on M. The problem considered in this paper is unique continuation for distribution solutions to the equation \̄t6Mu = 0 (these solutions are called CR distributions). In a local version of the problem it is shown that a CR distribution u in an open set U ⊂M which vanishes on one side of a C1 hypersurface S ⊂U which is noncharacteristic at a point p ϵ S necessarily vanishes in a neighborhood of p. If the CR distribution u is a continuous function on U, then it is only necessary to assume that u vanishes on S in order to prove that u vanishes in a neighborhood of p in M. It is also proved that if u is a CR distribution on M, then the boundary of the support of u is foliated by complex hypersurfaces. Thus a global unique continuation theorem is obtained by assuming that such a set is not contained in M

A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

Training in oesophageal surgery – The gold standard: A prospective study

AbstractIntroductionCompetency in complex oesophagogastric surgery, within the current climate of changes to medical training and reduced hours, requires repeated, focused, hands-on training. We describe the training methods for oesophagectomy in our institution.MethodsAll oesophageal resections under the care of one consultant surgeon are regarded as training cases. When trainees start they are shown the first resection; subsequently, the trainees then perform every case with the consultant scrubbed. Consultant input consists of retraction and tips in difficult situations. All data were collected on a prospective database.ResultsTwo hundered and seventy patients (215 males, median age=64 years) underwent primary oesophagectomy under the consultant, between January 2000 and May 2007. Fifteen resections (6%) were performed solely by the consultant. ASA grading was: I=15, II=154, III=95, IV=5, and unrecorded=1. In-hospital mortality and clinically apparent leak rate was 1.9% (5 deaths) and 6.2% (n=17), respectively. Reoperation was required in 15 patients (5.5%). The median length of hospital stay was 14 days (range=8–95 days). Median lymph node yield was 13 (range=0–64).ConclusionsTrainees under supervision can competently perform an oesophagectomy without compromising patient care. An early hands-on approach leads to a rapid ascent of the learning curve and is essential in today's climate of limited training opportunity

Successful multiple segment coronary angioplasty: Effect of completeness of revascularization in single-vessel multilesions and multivessels

A long-term follow-up study was performed to evaluate the long-term value of performing multiple dilatations according to their procedural (single-vessel multilesion or mutltivessel dilatations) and anatomic types (single-vessel disease with multiple dilatations or multivessel disease dilatations with complete and incomplete revascularization). From 1980 until 1988, 248 patients met the following criteria: (1) at least two lesions dilated (range: 2 to 4) and (2) all attempted lesions successfully dilated. The mean length of follow-up was 33 months. The end points analyzed were death, myocardial infarction, redilatation, and bypass surgery. No differences were found for these events between the single-vessel multilesion group (144 patients) and the multivessel group (104 patients). The 4.5-year probability of event-free survival was 68% and 70%, respectively, for the multilesion group and the multivessel group. In the event-free patients, 57% versus 59% were asymptomatic and 45% versus 46% were not taking antianginal drugs. In the anatomic subgroups, there were less event-free patients in the cohort of incompletely revascularized multivessel disease patients (55% of 55 patients) when compared with the cohort of those who were completely revascularized (84% of 79 patients) or when compared with the single-vessel disease multiple dilatation patients (74% of 107 patients). The 4.5-year event-free survival probability for each group was 44%, 78%, and 74%, respectively. This difference was caused by more infarctions (9% versus 2% versus 4%, respectively) and bypass operations in the multivessel disease, incomplete revascularization group (20% versus 5% versus 10%, respectively). In event-free patients, improvement of angina was similar and was documented in over 85% of patients in each group. Furthermore, the number of asymptomatic patients at follow-up was similar in all groups except that within the incomplete revascularization group, less patients were free of antianginal drugs (21% versus 51% versus 48%). Finally, 48% of the entire cohort performed an exercise test 4.6 months (mean) after dilatation and no difference was found in any of the variables in any group. About 10% of the patients experienced angina and approximately 30% had a positive exercise test for ischemia by ST segment criteria. The functional performance in every group was over 90% of the predicted work load. These results suggest that completeness of revascularization in multivessel disease patients is an important prognostic variable. However, the symptomatic improvement after dilatation is very rewarding in all subsets of patients and argues in favor of the continued use of multiple dilatations as a treatment strategy

Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a single point: each finite energy solution converges as time goes to plus or minus infinity to the set of all ``nonlinear eigenfunctions'' of the form \psi(x)e\sp{-i\omega t}. The global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation. We justify this mechanism by the following novel strategy based on inflation of spectrum by the nonlinearity. We show that any omega-limit trajectory has the time-spectrum in the spectral gap [-m,m] and satisfies the original equation. This equation implies the key spectral inclusion for spectrum of the nonlinear term. Then the application of the Titchmarsh Convolution Theorem reduces the spectrum of each omega-limit trajectory to a single harmonic in [-m,m]. The research is inspired by Bohr's postulate on quantum transitions and Schroedinger's identification of the quantum stationary states to the nonlinear eigenfunctions of the coupled U(1)-invariant Maxwell-Schroedinger and Maxwell-Dirac equations.Comment: 29 pages, 1 figur

Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves

We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions and the possible profiles of the traveling waves solutions of semi-linear Schr\"odinger equations.Comment: 23 page

Further education improves cognitive reserve and triggers improvement in selective cognitive functions in older adults: The Tasmanian Healthy Brain Project

Introduction The strong link between early-life education and subsequent reduced risk of dementia suggests that education in later life could enhance cognitive function and may reduce age-related cognitive decline and protect against dementia. Methods Episodic memory, working memory, executive function, and language processing performances were assessed annually over 4 years in 359 healthy older adults who attended university for a minimum of 12 months (intervention) and were compared against 100 healthy adult controls. Results Multiple group latent growth curve modeling revealed a significant improvement in language processing capacity over time in the intervention group. No changes were detected for episodic memory, working memory, or executive function. Discussion These results suggest that complex mental stimulation resulting from late-life further education results in improved crystallized knowledge but no changes to fluid cognitive functions. © 2017 The Author

Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.Comment: To appear in Phys Rev

A new approach to social behavior simulation: the mask model

This paper proposes a new perspective, based on the concept of social masks, for the simulation of a realistic NPC (Non-Player Character) behavior. The Mask Model goal is to support AI techniques for autonomous agents by encouraging or discouraging behaviors according to the social environment and by providing knowledge about possible reactions to the agent actions. In this approach, the NPC tendencies are controlled by the interactions of three overlapping mask layers: self- perception layer, social layer and interpersonal layer. The masks mould the tendencies, the feelings and the ethics of a NPC. By changing the links between characters and masks, a wide variety of different behaviors and story-lines may arise. The paper present an algorithm for the selection of the actions and an example implementation