Problemas matemáticos sin resolver que cualquier niño puede entender

Un lastre que incide en el rechazo a las matemáticas es su imagen de ser una ciencia inerte, sin nada por descubrir y limitada a unos pocos expertos. Esta charla pretende mostrar que la investigación en matemáticas está muy viva y que cualquiera puede acercarse a ella. Para ello se tratarán algunos problemas muy sencillos de entender (comprensibles para un niño) que los investigadores matemáticos siguen intentando resolver. Se propondrá a los asistentes que jueguen con estos problemas, se explicará cómo resolver algunos casos y se contará la trayectoria histórica de cada problema.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the atomic decomposition length of graphs and tensegrities

In this study, a complexity measure for graphs and tensegrities is proposed, based on the concept of atomic decomposition.We state several results on the relationship between atomic decompositions and spaces of self-stresses for generically rigid graphs, and study the computational complexity of finding atomic decompositions of minimal length.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. The present work was developed during a stay of Jose David Fernández Rodríguez at the Universidad de Alcalá, partially supported by the Departamento de Matemáticas de la Universidad de Alcalá. Jose David Fernández Rodríguez is partially supported by the Ministerio de Educación del Gobierno de España through a FPU grant (AP2007-03704). David Orden Martín is partially supported by grants MTM2008- 04699-C03-02/MTM and MTM2011-22792

On the number of pseudo-triangulations of certain point sets

We compute the exact number of pseudo-triangulations for two prominent point sets, namely the so-called double circle and the double chain. We also derive a new asymptotic lower bound for the maximal number of pseudotriangulations which lies significantly above the related bound for triangulations.Acciones Integradas 2003-2004Acción Integrada España-AustriaDirección General de Investigación Científic

The free-linking task: a graph-inspired method for generating non-disjoint similarity data with food products

"Free sorting", in which subjects are asked to sort a set of items into groups of "most similar" items, is increasingly popular as a technique for profiling sets of foods. However, free sorting implies an unrealistic model of sample similarity: that similarity is purely binary (is/is not similar) and that similarity is fully transitive (similarities {A, B} and {B, C} imply {A, C}). This paper proposes a new method of rapid similarity testing -- the "free-linking" task -- that solves both problems: in free linking, subjects draw a similarity graph in which they connect pairs of samples with a line if they are similar, according to the subject s individual criteria. This simple task provides a more realistic model of similarity which allows degrees of similarity through the graph distance metric and does not require transitive similarity. In two pilot studies with spice blends (10 samples, 58 subjects) and chocolate bars (10 samples, 63 subjects), free linking and free sorting are evaluated and compared using DISTATIS, RVb, and the graph parameters degree, transitivity, and connectivity; subjects also indicated their preferences and ease-of-use for the tasks. In both studies, the first two dimensions of the DISTATIS consensus were highly comparable across tasks; however, free linking provided more discrimination in dimensions three and four. RVb stability was equivalent for the two methods. Graph statistics indicated that free linking had greater discrimination power: on average subjects made similarity groupings with lower degree, lower transitivity, and higher connectivity for free linking in both studies. However, subjects did overall find free sorting easier and liked it more, indicating a higher cognitive difficulty of free linking. The free-linking task, therefore, provides more robust, realistic similarity maps at the cost of higher panelist effort, and should prove a valuable alternative for rapid sensory assessment of product sets.Agencia Estatal de Investigació

More about lower bounds for the number of k-facets

In this paper we present two results dealing with the number of (• k)-facets of a set of points: •² In R2, we use the notion of ²-net to give structural properties of sets that achieve the optimal lower bound 3¡k+22 ¢ of (• k)-edges for a ¯xed 0 • k • bn=3c ¡ 1;² •In Rd, we show that for k < bn=(d + 1)c the number of (• k)-facets of a set of n points in general position is at least (d + 1)¡k+dd ¢, and that this bound is tight in that range

New results on lower bounds for the number of k-facets

In this paper we present three different results dealing with the number of (≤ k)- facets of a set of points: (i) We give structural properties of sets in the plane that achieve the optimal lower bound 3_k+2 2 _ of (≤ k)-edges for a fixed k ≤ [n/3 ]− 1; (ii) We show that the new lower bound 3((k+2) 2 ) + 3((k−(n/ 3)+2) 2 ) for the number of (≤ k)-edges of a planar point set is optimal in the range [n/3] ≤ k ≤ [5n/12] − 1; (iii) We show that for k < n/4 the number of (≤ k)-facets of a set of n points in R3 in general position is at least 4((k+3 )3 ), and that this bound is tight in that range

On the Benefits of Channel Bonding in Dense, Decentralized Wi-Fi 4 Networks

Channel bonding is a technique first defined in the IEEE 802.11n standard to increase the throughput in wireless networks by means of using wider channels. In IEEE 802.11n (nowadays also known as Wi-Fi 4), it is possible to use 40 MHz channels instead of the classical 20 MHz channels. Although using channel bonding can increase the throughput, the classic 802.11 setting only allows for two orthogonal channels in the 2.4 GHz frequency band, which is not enough for proper channel assignment in dense settings. For that reason, it is commonly accepted that channel bonding is not suitable for this frequency band. However, to the best of our knowledge, there is not any accurate study that deals with this issue thoroughly. In this work, we study in depth the effect of channel bonding in Wi-Fi 4 dense, decentralized networks operating in the 2.4 GHz frequency band. We confirm the negative effect of using channel bonding in the 2.4 GHz frequency band with 11 channels which are 20 MHz wide (as in North America), but we also show that when there are 13 or more channels at hand (as in many other parts of the world, including Europe and Japan), the use of channel bonding yields consistent throughput improvements. For that reason, we claim that the common assumption of not considering channel bonding in the 2.4 GHz band should be revised

Uso de técnicas de negociación automática para la asignación de canales en IEEE 802.11

XII Jornadas de Ingeniería Telemática (JITEL 2015), 14/10/2015-16/10/2015, Palma de Mallorca, EspañaLas redes inalámbricas actuales deben dar soporte a cada vez más servicios telemáticos que demandan mayores prestaciones. Puesto que el espectro radioeléctrico en el que estas redes se basan es limitado, aumentar su eficiencia es ya una exigencia. En este trabajo se aborda el problema de la asignación de canales a puntos de acceso IEEE 802.11n con el objetivo de que los clientes de la red vean mejorada su experiencia de utilización. Las técnicas que se emplean con tal objetivo se basan en la negociación automática, comparándose con otras alternativas. Los resultados muestran que las técnicas de negociación son muy adecuadas para resolver el problema en cuestión, siendo capaces de obtener prestaciones superiores al resto de métodos con los que se han comparado.Comunidad de MadridMinisterio de Economía y Competitivida

SensoGraph: Using proximity graphs for sensory analysis

Sensory evaluation of foods is as important as chemical, physical or microbiological examinations, being specially relevant in food industries. Classical methods can be long and costly, making them less suitable for certain industries like the wine industry. Some alternatives have arisen recently, including Napping®, where the tasters represent the sensory distances between products by positioning them on a tablecloth; the more similar they perceive the products, the closer they position them on the tablecloth. This method uses multiple factor analysis (MFA) to process the data collected. The present paper introduces the software SensoGraph, which makes use of proximity graphs to analyze those data. The application is described and experimental results are presented in order to compare the performances of SensoGraph and Napping®, using eight wines from the Toro region and two groups of twelve tasters with different expertise.Ministerio de Ciencia e InnovaciónEuropean Science FoundationJunta de Castilla y Leó

Flips in combinatorial pointed pseudo-triangulations with face degree at most four

In this paper we consider the flip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the flip graph of combinatorial 4-PPTs with triangular outer face is connected and has diameter O(n2).European Science FoundationAustrian Science FundMinisterio de Ciencia e InnovaciónJunta de Castilla y Leó