Complejidad de estructuras geométricas y combinatorias

En la presente memoria, se abordan cuatro problemas, existiendo en todos ellos una gran interacción entre la combinatoria y la geometría. El primer problema que se estudia es la introducción de varias extensiones del concepto de tipo de orden para nubes de puntos. Concretamente, se introducen los tipos de orden circulares y triángulares, en las versiones orientada y no orientada. Se han demostrado resultados combinatorios análogos a resultados bien conocidos sobre tipos de orden ordinarios, introducidos por Goodman y Pollack como es el llamado Teorema de ordenación geométrica. Se ha estudiado también la información geométrica que proporciona cada uno de estos conceptos. El segundo problema estudia el empaquetamiento plano de grafos; esto es, el trazado de grafos, disjuntos en aristas, en el plano. Hemos obtenido varios resultados sobre el empaquetamiento plano de árboles y ciclos. Concretamente, para árboles que no sean estrellas, se ha demostrado que siempre admiten empaquetamiento plano: dos copias de un árbol cualquiera, un árbol cualquiera y un camino, un árbol cualquiera y un ciclo. También se han obtenido resultados sobre empaquetamiento plano de dos o tres ciclos. La principal herramienta que se ha utilizado es la representación de un árbol en un polígono convexo con propiedades muy concretas. En tercer lugar se estudia el grafo T (P) de árboles geométricos de una nube de puntos P, siendo este grafo el que tiene por vértices los árboles generadores sin cortes de P y dos de tales árboles T1, T2 son aduacentes si y sólo s, T2C=t1e+f para ciertas aristas e y f. Se han obtenido propiedades combinatorias de estos grafos, especialmente en el caso particular en que el conjunto de puntos esta en posición convexa. En este caso se ha determinado el centro, radio y grupo de automofismos de estos grafos, y demostrado que son hamiltonianos y de conectividad máxima. Finalmente, también se ha estudiado el grafo Mm de los emparejamientos perfectos sin cortes de una nube de 2m puntos en posición convexa. Entre los resultados obtenidos cabe destacar que se ha demostrado que Mm es bipartito, hamiltoniano sólo si m es par y que el diámetro de Mm es igual a m-1, siendo todos los emparejamientos de excentricidad máxima.Postprint (published version

On perfect and quasiperfect dominations in graphs

A subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect dominating set in G is denoted by ¿ 1 k ( G ). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers n = ¿ 11 ( G ) = ¿ 12 ( G ) = ... = ¿ 1 ¿ ( G ) = ¿ ( G ) in order to indicate how far is G from being perfectly dominated. In this paper we study properties, existence and realization of graphs for which the chain is short, that is, ¿ 12 ( G ) = ¿ ( G ). Among them, one can find cographs, claw-free graphs and graphs with extremal values of ¿ ( G ).Postprint (published version

Complejidad de estructuras geométricas y combinatorias

En la presente memoria, se abordan cuatro problemas, existiendo en todos ellos una gran interacción entre la combinatoria y la geometría. El primer problema que se estudia es la introducción de varias extensiones del concepto de tipo de orden para nubes de puntos. Concretamente, se introducen los tipos de orden circulares y triángulares, en las versiones orientada y no orientada. Se han demostrado resultados combinatorios análogos a resultados bien conocidos sobre tipos de orden ordinarios, introducidos por Goodman y Pollack como es el llamado Teorema de ordenación geométrica. Se ha estudiado también la información geométrica que proporciona cada uno de estos conceptos. El segundo problema estudia el empaquetamiento plano de grafos; esto es, el trazado de grafos, disjuntos en aristas, en el plano. Hemos obtenido varios resultados sobre el empaquetamiento plano de árboles y ciclos. Concretamente, para árboles que no sean estrellas, se ha demostrado que siempre admiten empaquetamiento plano: dos copias de un árbol cualquiera, un árbol cualquiera y un camino, un árbol cualquiera y un ciclo. También se han obtenido resultados sobre empaquetamiento plano de dos o tres ciclos. La principal herramienta que se ha utilizado es la representación de un árbol en un polígono convexo con propiedades muy concretas. En tercer lugar se estudia el grafo T (P) de árboles geométricos de una nube de puntos P, siendo este grafo el que tiene por vértices los árboles generadores sin cortes de P y dos de tales árboles T1, T2 son aduacentes si y sólo s, T2C=t1e+f para ciertas aristas e y f. Se han obtenido propiedades combinatorias de estos grafos, especialmente en el caso particular en que el conjunto de puntos esta en posición convexa. En este caso se ha determinado el centro, radio y grupo de automofismos de estos grafos, y demostrado que son hamiltonianos y de conectividad máxima. Finalmente, también se ha estudiado el grafo Mm de los emparejamientos perfectos sin cortes de una nube de 2m puntos en posición convexa. Entre los resultados obtenidos cabe destacar que se ha demostrado que Mm es bipartito, hamiltoniano sólo si m es par y que el diámetro de Mm es igual a m-1, siendo todos los emparejamientos de excentricidad máxima

Effects of Topography and Surface Soil Cover on Erosion for Mining Reclamation: The Experimental Spoil Heap at El Machorro Mine (Central Spain)

Mining reclamation tries to reduce environmental impacts, including accelerated runoff, erosion and sediment load in the nearby fluvial networks and their ecosystems. This study compares the effects of topography and surface soil cover on erosion on man-made slopes coming from surface mining reclamation in Central Spain. Two topographic profiles, linear and concave, with two surface soil covers, subsoil and topsoil, were monitored for two hydrologic years. Sediment load, rill development and plant colonization from the four profiles were measured under field conditions. The results show that, in the case of this experiment, a thick and non-compacted topsoil cover on a linear slope yielded less sediment than carbonate colluvium or topsoil cover on a concave slope. This study also shows that vegetation establishment, which plays an important role in erosion control, depends on topography. Plant cover was more widespread and more homogeneous on linear profiles with topsoil cover. On concave slopes, plant establishment was severely limited on the steepest upper part and favoured in the bottom. This study suggests that management of topography and surface soil cover should be approached systematically, taking three outcomes into consideration: (i) topsoil can lead to a successful mining reclamation regardless of topography, (ii) created concave slopes can lead to a successful mining reclamation and (iii) topography determines the vegetation colonization pattern.The experiment was funded by a research contract between the Spanish mining company 602 CAOBAR S.A. and the Department of Geodynamics of the Complutense University of Madrid 603 (research contract numbers 234/2007, 290/2008 261/2009). The data analyses and manuscript 604 production were developed within two Research Projects, CGL2009-14508-C02-01 and 605 CGL2010-21754-C02, of the Spanish Ministry of Science and Technology and by the 606 Ecological Restoration network REMEDINAL-2 (S2009/AMB-1783).Peer reviewe

Detecting regime transitions in gas-solid fluidized beds from low frequency accelerometry signals

Low frequency accelerometry signals have been applied for detecting regime transitions in a gas solid fluidized bed. Three solids have been fluidized to promote bubbling, churn and slugging regime. The Kolmogorov entropy and the power spectral density have been used to determine the regime transitions as well as to analyze the dynamical features characterizing the different regimes. Pressure and external acceleration measurements have been taken simultaneously. The accelerometry signal was sampled at 10 kHz; then, the envelope was extracted and resampled at 400 Hz. Pressure signal was sampled at 10 kHz and resampled at 400 Hz. Two problems were found during the work: the colored noise present in the envelope and the lack of low frequency information for one of the tested solids. FIR, wavelet and EMD filter strategies have been applied to remove the noise present in the envelope. It is concluded that the envelope of the accelerometry signal might be used to detect regime transition in the same way as the pressure fluctuation signals. Both Kolmogorov and spectral analysis exhibit common features to those obtained from pressure signal analysis, supporting the hypothesis of using low frequency accelerometry instead of conventional pressure measurements for monitoring fluidized bedsThe authors would like to especially thank Prof. María C. Palancar for her contribution to this work and the useful guiding during those years. Moreover, the financial support from the Spanish Ministry of Research, project CTQ2006 15525 C02 01 is kindly acknowledgedPublicad

On perfect and quasiperfect domination in graphs

Preprin

Advanced displays and natural user interfaces to support learning

[EN] Advanced displays and Natural User Interfaces (NUI) are a very suitable combination for developing systems to provide an enhanced and richer user experience. This combination can be appropriate in several fields and has not been extensively exploited. One of the fields that this combination is especially suitable for is education. Nowadays, children are growing up playing with computer games, using mobile devices, and other technological devices. New learning methods that use these new technologies can help in the learning process. In this paper, two new methods that use advanced displays and NUI for learning about a period of history are presented. One of the methods is an autostereoscopic system that lets children see themselves as a background in the game and renders the elements in 3D without the need for special glasses; the second method is a frontal projection system that projects the image on a table in 2D and works similarly to a touch table. The Microsoft Kinect© is used in both systems for the interaction. A comparative study to check different aspects was carried out. A total of 128 children from 7 to 11 years old participated in the study. From the results, we observed that the different characteristics of the systems did not influence the children s acquired knowledge, engagement, or satisfaction. There were statistically significant differences for depth perception and presence in which the autostereoscopic system was scored higher. However, of the two systems, the children considered the frontal projection to be easier to use. We would like to highlight that the scores for the two systems and for all the questions were very high. These results suggest that games of this kind (advanced displays and NUI) could be appropriate educational games and that autostereoscopy is a technology to exploit in their development.This work was funded by the Spanish Ministry of Science and Innovation through the APRENDRA project (TIN2009-14319-C02-01).Martín San José, JF.; Juan, M.; Mollá Vayá, RP.; Vivó Hernando, RA. (2017). Advanced displays and natural user interfaces to support learning. Interactive Learning Environments. https://doi.org/10.1080/10494820.2015.1090455

Dominating 2- broadcast in graphs: complexity, bounds and extremal graphs

Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the associated parameter, the dominating 2-broadcast number. We prove that computing the dominating 2-broadcast number is a NP-complete problem, but can be achieved in linear time for trees. We also give an upper bound for this parameter, that is tight for graphs as large as desiredPostprint (published version

On perfect and quasiperfect dominations in graphs

Postprint (published version

Intracellular inflammatory and antioxidant pathways in postmortem frontal cortex of subjects with major depression: effect of antidepressants

Background: Studies show that Toll-like receptors (TLRs), members of the innate immune system, might participate in the pathogenesis of the major depressive disorder (MDD). However, evidence of this participation in the brain of patients with MDD has been elusive. Methods: This work explores whether the protein expression by immunodetection assays (Western blot) of elements of TLR-4 pathways controlling inflammation and the oxidative/nitrosative stress are altered in postmortem dorsolateral prefrontal cortex of subjects with MDD. The potential modulation induced by the antidepressant treatment on these parameters was also assessed. Thirty MDD subjects (15 antidepressant-free and 15 under antidepressant treatment) were matched for gender and age to 30 controls in a paired design. Results: No significant changes in TLR-4 expression were detected. An increased expression of the TLR-4 endogenous ligand Hsp70 (+ 33%), but not of Hsp60, and the activated forms of mitogen-activated protein kinases (MAPKs) p38 (+ 47%) and JNK (+ 56%) was observed in MDD. Concomitantly, MDD subjects present a 45% decreased expression of DUSP2 (a regulator of MAPKs) and reduced (- 21%) expression of the antioxidant nuclear factor Nrf2. Antidepressant treatment did not modify the changes detected in the group with MDD and actually increased (+ 25%) the expression of p11, a protein linked with the transport of neurotransmitters and depression. Conclusion: Data indicate an altered TLR-4 immune response in the brain of subjects with MDD. Additional research focused on the mechanisms contributing to the antidepressant-induced TLR-4 pathway modulation is warranted and could help to develop new treatment strategies for MDD.This work was supported by the Instituto de Salud Carlos III and Spanish Ministry of Economy, Industry and Competitiveness (MINECO) through the Plan Estatal de I+D+i 2013-2016 (FIS-PI13/01102 and SAF2016-75500-R to JCL), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (SAF2017-83053-R to JRC), the Basque Government (IT-616-13), CIBERSAM and the EDR Funds. JRC and BGB are Ramon y Cajal fellows (MINECO)