Dilation-free graphs in the l1 metric

The dilation-free graph of a planar point set S is a graph that spans S in such a way that the distance between two points in the graph is no longer than their planar distance. Metrically speaking, those graphs are equivalent to complete graphs; however they have far fewer edges when considering the Manhattan distance (we give here an upper bound on the number of saved edges). This article provides several theoretical, algorithmic, and complexity features of dilation-free graphs in the l1-metric, giving several construction algorithms and proving some of their properties. Moreover, special attention is paid to the planar case due to its applications in the design of printed circuit boards

There are simple and robust refinements (almost) as good as Delaunay

A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and with a cheaper cost in computation. It will be proved that in most of the cases the 7T-QD is equal to the 7T-D. In addition, numerical tests will show that the difference on the minimum angle obtained by the 7T-QD and by the 7T-D is negligible

Local refinement based on the 7-triangle longest-edge partition

The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. In this paper we specifically introduce a new local refinement for triangulations based on the longest-edge trisection, the 7-triangle longest-edge (7T-LE) local refinement algorithm. Each triangle to be refined is subdivided in seven sub-triangles by determining its longest edge. The conformity of the new mesh is assured by an automatic point insertion criterion using the oriented 1-skeleton graph of the triangulation and three partial division patterns

Pottery grave goods from funerary contexts at the argaric site of Peñalosa (Jaén). A methodological approach

The need for interdisciplinary studies is the basis of ambitious research (ARCHEM Project) that is carried out in the argaric settlement of Peñalosa (Baños de la Encina, Jaén), combining organic residues analysis and techno-typological studies of pottery found in funerary contexts. Manufacture and use of pottery could inform us about customs and traditions that remain hidden in time and in the archaeological record. Knowing the implications and decisions of potters as well as the functionality of those vessels deposited inside the graves can approach the idiosyncrasy of a society in the Bronze Age in the southeast of the Iberian Peninsula. The methodology used to identify patterns of functionality is highlighted by the combination of cutting-edge analysis techniques in both fields such as the application of different chromatographic techniques (GC-MS, UPLC-HRMS and GC-CIRMS) that allow to identify the organic compounds in the ceramics and the application of analytical techniques from Earth Sciences (Stereomicroscopic, X-Ray Diffraction and Petrography), which allow us to characterize ceramic pastes and knowing the catchment of raw materials. This study highlights the Peñalosa site as a melting pot of new research and it brings us closer with the use of a complex methodology combined to the societies 4000 years ago.Spanish Ministry of Economy and Competitiveness HAR2015-66009-PJunta de Andalucía HUM 274 FQM 338Spanish Ministry of Economy, Industry and CompetitivinessUniversity of Granad

Reporting Bichromatic Segment Intersections from Point Sets

In this paper, we introduce a natural variation of the problem of computing all bichromatic intersections between two sets of segments. Given two sets R and B of n points in the plane defining two sets of segments, say red and blue, we present an O(n2) time and space algorithm for solving the problem of reporting the set of segments of each color intersected by segments of the other color. We also prove that this problem is 3-Sum hard and provide some illustrative examples of several point configurations

Monochromatic geometric k-factors for bicolored point sets with auxiliary points

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S

Monochromatic geometric k-factors in red-blue sets with white and Steiner points

We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible to find a k-factor we make use of auxiliary points: white points, whose position is given as a datum and which color is free; and Steiner points whose position and color is free. We present bounds on the number of white and/or Steiner points necessary and/or sufficient to draw a monochromatic planar geometric k-factor

Matrix metalloproteases and TIMPs as prognostic biomarkers in breast cancer patients treated with radiotherapy: A pilot study

Breast cancer (BC) is the most common tumour in women and one of the most important causes of cancer death worldwide. Radiation therapy (RT) is widely used for BC treatment. Some proteins have been identified as prognostic factors for BC (Ki67, p53, E‐cadherin, HER2). In the last years, it has been shown that variations in the expression of MMPs and TIMPs may contribute to the development of BC. The aim of this pilot work was to study the effects of RT on different MMPs (‐1, ‐2, ‐3, ‐7, ‐8, ‐9, ‐10, ‐12 and ‐13) and TIMPs (‐1 to ‐4), as well as their relationship with other variables related to patient characteristics and tumour biology. A group of 20 BC patients treated with RT were recruited. MMP and TIMP serum levels were analysed by immunoassay before, during and after RT. Our pilot study showed a slight increase in the levels of most MMP and TIMP with RT. However, RT produced a significantly decrease in TIMP‐1 and TIMP‐3 levels. Significant correlations were found between MMP‐3 and TIMP‐4 levels, and some of the variables studied related to patient characteristics and tumour biology. Moreover, MMP‐9 and TIMP‐3 levels could be predictive of RT toxicity. For this reason, MMP‐3, MMP‐9, TIMP‐3 and TIMP‐4 could be used as potential prognostic and predictive biomarkers for BC patients treated with RT.FUNDACIÓN PROGRESO Y SALUD, Grant/Award Number: PI‐730; Instituto de Salud Carlos III, Grant/Award Number: PIE16‐00045; Oncología Básica y Clínica, Grant/Award Number: CTS‐20

Cover contact graphs

We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by a set of other geometric objects called cover (e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, respectively, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in three types of tasks, both in the general case and in the special case of seeds on a line: (a) deciding whether a given seed set has a connected CCG, (b) deciding whether a given graph has a realization as a CCG on a given seed set, and (c) bounding the sizes of certain classes of CCG’s. Concerning (a) we give efficient algorithms for the case that seeds are points and show that the problem becomes hard if seeds and covers are disks. Concerning (b) we show that this problem is hard even for point seeds and disk covers (given a fixed correspondence between graph vertices and seeds). Concerning (c) we obtain upper and lower bounds on the number of CCG’s for point seeds