Triangle areas in line arrangements

A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been generalized in many directions. In this paper we propose the following variants. Consider planar arrangements of $n$ lines. Determine the maximum number of triangles of unit area, maximum area or minimum area, determined by these lines. Determine the minimum size of a subset of these $n$ lines so that all triples determine distinct area triangles. We prove that the order of magnitude for the maximum occurrence of unit areas lies between $\Omega(n^2)$ and $O(n^{9/4})$. This result is strongly connected to both additive combinatorial results and Szemer\'edi--Trotter type incidence theorems. Next we show a tight bound for the maximum number of minimum area triangles. Finally we present lower and upper bounds for the maximum area and distinct area problems by combining algebraic, geometric and combinatorial techniques.Comment: Title is shortened. Some typos and small errors were correcte

Neogene paleoceanography of the eastern equatorial Pacific based on the radiolarian record of IODP drill sites off Costa Rica

The Integrated Ocean Drilling Program (IODP) Expedition 344 drilled cores following a transect across the convergent margin off Costa Rica. Two of the five sites (U1381 and U1414) are the subject of the present study. Major radiolarian faunal breaks and characteristic species groups were defined with the aid of cluster analysis, nodal analysis, and discriminant analysis of principal components. A middle-late Miocene to Pleistocene age (radiolarian zones RN5 to RN16) was determined for the sites, which agrees with the nannofossil zonations and 40Ar/39Ar and tephra layers. Considering the northward movement of the Cocos plate (∼7.3 cm/yr), and a paleolatitude calculator, it is assumed that during the Miocene the two sites were located ∼1000 km to the southwest of their current position, slightly south of the equator. The radiolarian faunas retrieved were thus seemingly formed under the influence of different oceanic currents and sources of nutrients. Changes in the radiolarian assemblages at Site U1414 point at dissimilar environmental settings associated with the colder South Equatorial Current and the warmer Equatorial Countercurrent, as well as to coastal upwelling. These differences are best reflected by changes in the abundance of the morphotype Spongurus spp., with noticeably higher values during the Miocene, than in the Pliocene and the Pleistocene. Because Spongurus spp. is generally associated with cooler waters, these abundance variations (as well as those of several other species) suggest that during the Miocene the area had a stronger influence of colder waters than during younger periods. During the Pliocene and the lowermost Pleistocene, biogenic remains are scarce, presumably due to the terrigenous input, which could have diluted and affected the preservation of pelagic fossils, as well as to the displacement of the site to warmer waters. A typically tropical fauna characterized the Pleistocene, yet with widespread presence of colder water species, most probably indicative of the influence of coastal upwelling processes.Fil: Sandoval, María I.. Universidad de Costa Rica; Costa Rica. Universite de Lausanne; SuizaFil: Boltovskoy, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; ArgentinaFil: Baxter, Alan T.. University of New England; Australia. McGill University; CanadáFil: Baumgartner, Peter O.. Universite de Lausanne; Suiz

Optimal Policy Derivation for Transmission Duty-Cycle Constrained LPWAN

Low-power wide-area network (LPWAN) technologies enable Internet of Things (IoT) devices to efficiently and robustly communicate over long distances, thus making them especially suited for industrial environments. However, the stringent regulations on the usage of certain industrial, scientific, and medical bands in many countries in which LPWAN operate limit the amount of time IoT motes can occupy the shared bands. This is particularly challenging in industrial scenarios, where not being able to report some detected events might result in the failure of critical assets. To alleviate this, and by mathematically modeling LPWAN-based IoT motes, we have derived optimal transmission policies that maximize the number of reported events (prioritized by their importance) while still complying with current regulations. The proposed solution has been customized for two widely known LPWAN technologies: 1) LoRa and 2) Sigfox. Analytical results reveal that our solution is feasible and performs remarkably close to the theoretical limit for a wide range of network activity patterns

Squeezing the Efimov effect

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.Comment: 11 pages, 4 figures, comments are most welcom

Relacion de la lateralizacion y disfagia en pacientes con accidente vascular encefalico (ave), mayores de 50 anos, tratados en el Hospital Regional de Talca, en su primera semana de evolucion

97 p.La alteración del mecanismo deglutorio denominado disfagia, es una patología que va en aumento en los pacientes hospitalizados, esta puede provocar diversos trastornos como neumonía, deshidratación, desnutrición y obstrucciones de la vía aérea, pudiendo llegar a provocar la muerte en algunos pacientes. En la región del Maule no existe en la actualidad un modelo de trabajo, pesquisa o tratamiento de esta alteración, por lo cual la realización de este estudio se plantea como un aporte a la identificación de la problemática. El presente estudio se basa en la exploración de la disfagia en pacientes producto de un Accidente Vascular Encefálico (AVE), relacionando la Lateralización del AVE, con las características del proceso de deglución que se puedan ver alterados en el sujeto. Además, de proporcionar adecuaciones no invasivas al paciente respecto a la disfagia que presenta

A quantitative study of disfluencies in formal, informal and media spontaneous speech in Spanish

Proceedings of IberSpeech 2012 (Madrid, Spain)A descriptive study of the prevalence of different types of disfluencies (fragmented words, restarts and vocalic supports) in spontaneous Spanish is presented based on a hand-annotated corpus. A quantitative account of differences among three types of registers (formal, informal and media) and several subtypes of text for each register is provided to analyze the importance of each disfluency class for a given register