Rationality properties of manifolds containing quasi-lines

Let X be a complex, rationally connected, projective manifold. We show that X admits a modification X' that contains a quasi-line, ie a smooth rational curve whose normal bundle is a direct sum of copies of O_{P^1}(1). For manifolds containing quasi-lines, a sufficient condition of rationality is exploited: There is a unique quasi-line from a given family passing through two general points. We define a numerical birational invariant, e(X), and prove that X is rational if and only if e(X)=1. If X is rational, there is a modification X' which is strongly-rational We prove that strongly-rational varieties are stable under smooth, small deformations. Finally, we relate the previous results and formal geometry. This relies on \tilde{e}(X,Y), a numerical invariant of a given quasi-line Y that depends only on the formal completion of X along Y. As applications we show various instances in which X is determined by this formal completion. We also formulate a basic question about the birational invariance of \tilde{e}(X,Y).Comment: 25 page

Equivariant Schr\"odinger Maps in two spatial dimensions

We consider equivariant solutions for the Schr\"odinger map problem from $\mathbb{R}^{2+1}$ to $\mathbb{S}^2$ with energy less than $4\pi$ and show that they are global in time and scatter

Global Schr\"{o}dinger maps

We consider the Schr\"{o}dinger map initial-value problem in dimension two or greater. We prove that the Schr\"{o}dinger map initial-value problem admits a unique global smooth solution, provided that the initial data is smooth and small in the critical Sobolev space. We prove also that the solution operator extends continuously to the critical Sobolev space.Comment: 60 page

Focussed ion beam based fabrication of micro-electro-mechanical resonators

A simple and fast process to fabricate micro-electro-mechanical (MEM) resonators with deep sub-micron transduction gaps in thin SOI is presented. The proposed process is realized on both 350nm and 1.5μm thin silicon-on-insulator (SOI) substrates, evaluating the possibilities for MEMS devices on thin SOI for future co-integration with CMOS circuitry on a single chip. Through the combination of conventional UV-lithography and focused ion beam (FIB) milling the process needs only two lithography steps, achieving ∼100nm gaps, thus ensuring an effective transduction. Different FIB parameters and etching parameters and their effect on the process are reporte

Animated movie genre detection using symbolic fusion of text and image descriptors

International audienceThis paper addresses the automatic movie genre classification in the specific case of animated movies. Two types of information are used. The first one are movie synopsis. For each genre, a symbolic representation of a thematic intensity is extracted from synopsis. Addressed visually, movie content is described with symbolic representations of different mid-level color and activity features. A fusion between the text and image descriptions is performed using a set of symbolic rules conveying human expertise. The approach is tested on a set of 107 animated movies in order to estimate their "drama" character. It is observed that the text-image fusion achieves a precision up to 78% and a recall of 44%

Methane Production in Oxic Lake Waters Potentially Increases Aquatic Methane Flux to Air

Active methane production in oxygenated lake waters challenges the long-standing paradigm that microbial methane production occurs only under anoxic conditions and forces us to rethink the ecology and environmental dynamics of this powerful greenhouse gas. Methane production in the upper oxic water layers places the methane source closer to the air–water interface, where convective mixing and microbubble detrainment can lead to a methane efflux higher than that previously assumed. Microorganisms may produce methane in oxic environments by being equipped with enzymes to counteract the effects of molecular oxygen during methanogenesis or using alternative pathways that do not involve oxygen-sensitive enzymes. As this process appears to be influenced by thermal stratification, water transparency, and primary production, changes in lake ecology due to climate change will alter methane formation in oxic water layers, with far-reaching consequences for methane flux and climate feedback

Learning Analytics Mobile Application for the Bucharest University of Economic Studies’ Students

Learning analytics refers to improving the educational process by providing feedback and in-volving all the stakeholders. It is a very useful method with positive effects on both students and teachers. In ASE, the idea of learning analytics is not very well shaped, so development is needed on this side. This article proposes a learning analytics app for better exploitation of SIMUR database content in order to improve the educational processes in the university

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

When myocardial infarction is choosing young victims

We present the case of a 31-year-old patient, without cardiovascular risk factors, without significant pathological or family history of cardiovascular disease, who was diagnosed with severe coronary artery disease, left main bifurcation localization, which required surgical coronary revascularization. The angiographic and intraoperative aspect excluded the most common causes of non-atherosclerotic causes of coronary lesions. Vasculitis was another possible etiology but was also excluded based on the normal clinical examination, negative inflammation markers, lack of diffuse vascular impairment, TPHA and negative VDRL. Prolonged mental stress can lead to accelerated progression of atherosclerosis by inducing endothelial dysfunction, our patient describing a “burnout syndrome” in the last few months. The particularity of the presented case is the severe coronary artery disease in a young patient without discovering the main etiology of the advanced atherosclerotic process