Smooth Approximation of Lipschitz functions on Riemannian manifolds

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $\epsilon:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leq\epsilon(p)$ for every $p\in M$ and $\textrm{Lip}(g)\leq\textrm{Lip}(f)+r$. Consequently, every separable Riemannian manifold is uniformly bumpable. We also present some applications of this result, such as a general version for separable Riemannian manifolds of Deville-Godefroy-Zizler's smooth variational principle.Comment: 10 page

The Morse-Sard theorem revisited

Let $n, m, k$ be positive integers with $k=n-m+1$. We establish an abstract Morse-Sard-type theorem which allows us to deduce, on the one hand, a previous result of De Pascale's for Sobolev $W^{k,p}_{\textrm{loc}}(\mathbb{R}^n, \mathbb{R}^m)$ functions with $p>n$ and, on the other hand, also the following new result: if $f\in C^{k-1}(\mathbb{R}^n, \mathbb{R}^m)$ satisfies $$\limsup_{h\to 0}\frac{|D^{k-1}f(x+h)-D^{k-1}f(x)|}{|h|}<\infty$$ for every $x\in\mathbb{R}^n$ (that is, $D^{k-1}f$ is a Stepanov function), then the set of critical values of $f$ is Lebesgue-null in $\mathbb{R}^m$. In the case that $m=1$ we also show that this limiting condition holding for every $x\in\mathbb{R}^n\setminus\mathcal{N}$, where $\mathcal{N}$ is a set of zero $(n-2+\alpha)$-dimensional Hausdorff measure for some $0<\alpha<1$, is sufficient to guarantee the same conclusion.Comment: We corrected some misprints and made some changes in the introductio

Oasification: la solución forestal a muchos problemas de desertificación

Desertification is a widespread process worldwide, particularly acute on deforested sloping lands under arid, semiarid or dry sub-humid conditions. To counteract this environmental threat, we have opted for an approach promoting the opposite process, which has been termed oasification. It entails the building of small earth structures to collect and infiltrate as much precipitation and runoff as possible by modifying a slope’s physiography in a convenient and non-aggressive manner. As a result, better soil moisture conditions will prevail and the chances of the establishment and growth of woody vegetation will be markedly improved, thus redressing the dangerous process of desertification. Since ancient times, many water harvesting strategies (microcatchments, ridging, terracing, etc.) have been successfully employed to check, collect and infiltrate surface runoff in those regions of the world where precipitation is scarce. All these structures can be currently designed according to enlightened hydrologic criteria based on sound knowledge of water economy, water requirements, soil erosion, building costs and landscape impacts. These criteria should help land managers and technicians in deciding the appropriate planting densities and micropond sizes that will yield the best seedling survival rates with minimal disturbance to the original physiography of the slope.La desertificaci&oacute;n es un proceso muy frecuente en laderas deforestadas bajo clima &aacute;rido, semi&aacute;rido o seco subh&uacute;medo. Frente a este problema se apuesta por el proceso contrario, es decir, la oasificaci&oacute;n. Se trata de dotar a la ladera de unas peque&ntilde;as estructuras de tierra que recojan e infiltren la escorrent&iacute;a, modificando levemente su fisiograf&iacute;a. De esta forma se consigue mejorar las condiciones de humedad del suelo y se posibilita el desarrollo de una vegetaci&oacute;n forestal, invirti&eacute;ndose el temido proceso de desertificaci&oacute;n. Las estructuras que consiguen frenar, captar e infiltrar la escorrent&iacute;a (por ejemplo: microcuencas, aterrazados o acaballonados), y que act&uacute;an como trampas de suelo y nutrientes a su vez, deben dise&ntilde;arse con unos criterios adecuados y basados en la econom&iacute;a del agua, para evitar impactos ambientales excesivos y el incremento innecesario de los costes de ejecuci&oacute;n. Estos criterios sirven para orientar al t&eacute;cnico encargado de la restauraci&oacute;n sobre el tama&ntilde;o de los alcorques a realizar, con vistas a aumentar la supervivencia del repoblado reduciendo la alteraci&oacute;n del microrrelieve a lo m&iacute;nimo indispensable

Fine grained pointing recognition for natural drone guidance

Human action recognition systems are typically focused on identifying different actions, rather than fine grained variations of the same action. This work explores strategies to identify different pointing directions in order to build a natural interaction system to guide autonomous systems such as drones. Commanding a drone with hand-held panels or tablets is common practice but intuitive user-drone interfaces might have significant benefits. The system proposed in this work just requires the user to provide occasional high-level navigation commands by pointing the drone towards the desired motion direction. Due to the lack of data on these settings, we present a new benchmarking video dataset to validate our framework and facilitate future research on the area. Our results show good accuracy for pointing direction recognition, while running at interactive rates and exhibiting robustness to variability in user appearance, viewpoint, camera distance and scenery

Do University-Industry co-publication volumes correspond with university funding from business firms?

Trabajo presentado a la 19th Science and Technology Indicators Conference: "Context counts: Pathways to Master Big and Little Data" celebrada en leiden (Paises Bajos) del 3 al 9 de 2014.Analysts of university-industry interaction sometimes measure it through numbers of university-industry co-publications (UICs), because of their relative availability and international comparability. However, we do not know whether UICs correspond to a more direct measure of interaction: university funding from firms. We propose a conceptual model on four types of relationships between UICs and university funding from firms, emphasising the interactive nature of their relation. We test the model with UIC and income data from the Polytechnic University of Valencia at individual level: around 6-7% of researchers participating in projects with firms were authors of UICs published in 2008-2011; and around 27% of those UIC authors were participating in projects with firms during that period. Overall, we do not find evidence of any significant positive correlation between UIC output and university funding from the business sector in general. The one exception is a minority of authors who participate in business-funded projects, where we found a positive association of current UICs and business funding.Peer Reviewe

Combined homogeneous and heterogeneous hydrogenation to yield catalyst-free solutions of parahydrogen-hyperpolarized [1-13C]succinate

We show that catalyst-free aqueous solutions of hyperpolarized [1-13C]succinate can be produced using parahydrogen-induced polarization (PHIP) and a combination of homogeneous and heterogeneous catalytic hydrogenation reactions. We generate hyperpolarized [1-13C]fumarate via PHIP using para-enriched hydrogen gas with a homogeneous ruthenium catalyst, and subsequently remove the toxic catalyst and reaction side products via a purification procedure. Following this, we perform a second hydrogenation reaction using normal hydrogen gas to convert the fumarate into succinate using a solid Pd/Al2O3 catalyst. This inexpensive polarization protocol has a turnover time of a few minutes, and represents a major advance for in vivo applications of [1-13C]succinate as a hyperpolarized contrast agent

Delocalisation patterns in University-Industry interaction: Evidence from the 6th R&D Framework Programme

Increasing university-industry interaction (UII) and university contribution to the local economy are compatibleconventional wisdom would say. However, similar to other university activities, interaction with industry may be limited due to a lack of absorptive capacity in local firms. The data of those participating in the European Union's (EU's) Sixth R&D Framework Programme (FP6) were used to obtain values for the number and, notably, the budgets of UII projects at the regional level for the EU27. Two types of interactions were considered: inside and outside the region. Our analysis indicates that universities from regions whose firms have low absorptive capacity participate more often in FP6 projects with firms outside the region. Our results highlight the value of policies that facilitate firm R&D to enhance collaboration with regional universities.Azagra Caro, JM.; Pontikakis, D.; Varga, A. (2013). Delocalisation patterns in University-Industry interaction: Evidence from the 6th R&D Framework Programme. European Planning Studies. 21(10):1676-1701. doi:10.1080/09654313.2012.722949S16761701211

Smooth extensions of functions on separable Banach spaces

Let $X$ be a Banach space with a separable dual $X^{*}$. Let $Y\subset X$ be a closed subspace, and $f:Y\to\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$.Comment: 19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma

Total Gastrectomy for locally advanced Cancer: The total Laparoscopic Approach

Total gastrectomy is the treatment of choice for adenocarcinoma of the upper and middle third of the stomach resected with curative intent. The laparoscopic approach allows satisfactory exploration of the peritoneal cavity and optimizes staging in borderline T3 or T4 tumours in patients affected by locally advanced tumours or intraperitoneal carcinomatosis. Laparoscopy can eliminate unnecessary laparotomies in 10 % of patients affected by these conditions with formal contraindications for resection [1] . Complete resection of the stomach associated with D2 lymph node dissection is also performed using a currently well-established technique [2, 3] . The specificity of laparoscopic gastric resection for cancer is that the stomach and the greatomentum are withdrawn separately.Reconstruction of the digestive tract is more complex, and requires a variety of techniques (supra-umbilical mini-laparotomy, Orvil® technique, enlarging a port-site for passage of a circular stapler, mechanical side to side anastomosis, etc), but none ofthese has become the gold standard [4-7] . This explains the difficulties encountered in promoting the widespread use of minimally invasive resection in western countries. Scientific societies insist on the need for prospective studies to establish the place of laparoscopy for gastric cancer (prophylactic gastrectomy for CDH-1 related gastric cancer, &lt; T3 Tumours, palliative gastrectomy) [4] . Here, we present our technique for total resection of the stomach and D2 lymph node dissection, which allows the manualcreation of a feasible, safe, tension-free and effective esojejunal anastomosis. It can be performed by any surgeon familiar with laparoscopic surgery and the principles of oncologic resection. The cost is also relatively low because neither a circular staplernor other special equipment is required. Finally, the incision for extraction of the specimen can be placed in any area of the abdomen (usually through a supra-pubic incision in our practice).Keywords: Gastric cancer, laparoscopy, total gastrectomy, lymphadenectomy, Intracorporeal anastomosis.Total gastrectomy is the treatment of choice for adenocarcinoma of the upper and middle third of the stomach resected with curative intent. The laparoscopic approach allows satisfactory exploration of the peritoneal cavity and optimizes staging in borderline T3 or T4 tumours in patients affected by locally advanced tumours or intraperitoneal carcinomatosis. Laparoscopy can eliminate unnecessary laparotomies in 10 % of patients affected by these conditions with formal contraindications for resection [1] . Complete resection of the stomach associated with D2 lymph node dissection is also performed using a currently well-established technique [2, 3] . The specificity of laparoscopic gastric resection for cancer is that the stomach and the great omentum are withdrawn separately.Reconstruction of the digestive tract is more complex, and requires a variety of techniques (supra-umbilical mini-laparotomy, Orvil® technique, enlarging a port-site for passage of a circular stapler, mechanical side to side anastomosis, etc), but none of these has become the gold standard [4-7] . This explains the difficulties encountered in promoting the widespread use of minimally invasive resection in western countries. Scientific societies insist on the need for prospective studies to establish the place of laparoscopy for gastric cancer (prophylactic gastrectomy for CDH-1 related gastric cancer, &lt; T3 Tumours, palliative gastrectomy) [4] . Here, we present our technique for total resection of the stomach and D2 lymph node dissection, which allows the manual creation of a feasible, safe, tension-free and effective esojejunal anastomosis. It can be performed by any surgeon familiar with laparoscopic surgery and the principles of oncologic resection. The cost is also relatively low because neither a circular stapler nor other special equipment is required. Finally, the incision for extraction of the specimen can be placed in any area of the abdomen (usually through a supra-pubic incision in our practice).Keywords: Gastric cancer, laparoscopy, total gastrectomy, lymphadenectomy, Intracorporeal anastomosis