Quantitative Tverberg theorems over lattices and other discrete sets

This paper presents a new variation of Tverberg's theorem. Given a discrete set $S$ of $R^d$, we study the number of points of $S$ needed to guarantee the existence of an $m$-partition of the points such that the intersection of the $m$ convex hulls of the parts contains at least $k$ points of $S$. The proofs of the main results require new quantitative versions of Helly's and Carath\'eodory's theorems.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1503.0611

Quantitative combinatorial geometry for continuous parameters

We prove variations of Carath\'eodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among our results, we present continuous quantitative versions of Lov\'asz's colorful Helly theorem, B\'ar\'any's colorful Carath\'eodory's theorem, and the colorful Tverberg theorem.Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:1503.0611

Quantitative Tverberg, Helly, & Carath\'eodory theorems

This paper presents sixteen quantitative versions of the classic Tverberg, Helly, & Caratheodory theorems in combinatorial convexity. Our results include measurable or enumerable information in the hypothesis and the conclusion. Typical measurements include the volume, the diameter, or the number of points in a lattice.Comment: 33 page

The importance of Opuntia in Mexico and routes of invasion and impact of Cactoblastis cactorum (Lepidoptera: Pyralidae)

This is the publisher's version, also available electronically from http://journals.fcla.edu/flaent/article/view/74992.The appearance of the cactus moth Cactoblastis cactorum in Florida has roused concern over its possible effects on the Opuntia-rich areas of Mexico and the southwestern United States. In this paper we discuss the economic importance of Opuntia in Mexico and propose a method to predict the invasion of the alien species C. cactorum. In Mexico, the products derived from Opuntia are mainly human food and fodder for livestock. Both cultivated and wild populations of Opuntia are currently used for these two purposes. By using bioclimatic modeling, we predicted the potential distribution of C. cactorum and overlaid this on the actual distribution of Opuntia species. The resulting maps indicate that the possible routes of invasion to Mexico are 1) along the northern border through Texas (most likely) and 2) via southeastern Mexico (less likely). The impacts of an invasion of C. cactorum on Opuntia products could be significant as well as being a threat to endemic species. Bioclimatic modeling can help to predict the areas of highest probability of attack and facilitate planning to mitigate future impacts

Leadership, institution building and pay-back of health systems research in Mexico

<p>Abstract</p> <p>Background</p> <p>Health systems research is being increasingly called upon to support scaling up of disease control interventions and to support rapid health sector change. Yet research capacity building and pay-back take years or even decades to be demonstrated, while leadership and institution building are critical for their success. The case of Mexico can be illustrative for middle income countries and emerging economies striving to build health research systems.</p> <p>Methods</p> <p>Historical reflection suggests the relationship between health sector reforms and economic crisis, on the one hand, and research capacity building and payback, on the other. Mexico's post-revolutionary background and its three health sector reforms are analyzed to identify the emphases given to health systems research.</p> <p>Results</p> <p>The first wave of health reform in the 1940s emphasized clinical and epidemiological research. Health systems research was not encouraged in a context of rapid economic development and an authoritarian regime. In contrast, health systems research was given a privileged place with the second wave of health reforms in the 1980s, which addressed health system coordination, decentralization and the universal right to health in a context of a deep economic crisis. The third wave of health reforms between 2003 and 2006 was based on the health system models proposed through research in the 90s. The credibility gained by research institutions was critical to ensure government uptake. Research influence can be traced through the role it played in defining a problem, in designing innovative insurance mechanisms and in establishing evaluation frameworks. It is argued that the Ministry of Health's budget increase of 56% between 2003 and 2006 and the reductions in inequity are pay-back to research investments since the 1980s.</p

Psychometric analysis in knowledge-evaluation questionnaires, identification and implication

The experience achieved using the tool “Questionnaires”, available inside the Virtual Campus of architectural engineering school in northeast Spain, is presented. “Questionnaires” is an adequate and simple instrument to evaluate the knowledge level achieved by students. This work shows and identifies the control indices of adaptation for the questionnaires, like the Facility Index, the Standard Deviation, the Discrimination Index and the Discrimination Coefficient. Derived from these parameters, the educational performances are inferred, identified and predicted. The conclusions of this work, permit to modify deficient knowledge-evaluation practices, to identify needs for specific groups or for students with particular requirements; being, in this way, feasible to apply these parameters with guarantee of success in similar evaluation processesPostprint (published version

Species Diversity and Distribution in Presence‐Absence Matrices: Mathematical Relationships and Biological Implications

The diversity of sites and the distribution of species are fundamental pieces in the analysis of biogeographic and macroecological questions. A link between these two variables is the correlation between the species diversity of sites and the mean range size of species occurring there. Alternatively, one could correlate the range sizes of species and the mean species diversity within those ranges. Here we show that both approaches are mirror images of the same patterns, reflecting fundamental mathematical and biological relationships. We develop a theory and analyze data for North American mammals to interpret range‐diversity plots in which the species diversity of sites and the geographic range of species can be depicted simultaneously. We show that such plots contain much more information than traditional correlative approaches do, and we demonstrate that the positions of points in the plots are determined to a large extent by the average, minimum, and maximum values of range and diversity but that the dispersion of points depends on the association among species and the similitude among sites. These generalizations can be applied to biogeographic studies of diversity and distribution and in the identification of hotspots of diversity and endemism

Cutting the same fraction of several measures

We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure

Interactive redescription mining

Exploratory data analysis consists of multiple iterated steps: a data mining method is run on the data, the results are interpreted, new insights are formed, and the resulting knowl- edge is utilized when executing the method in a next round, and so on until satisfactory results are obtained. We focus on redescription mining, a powerful data analysis method that aims at finding alternative descriptions of the same entities, for example, ways to characterize geographical regions in terms of both the fauna that inhabits them and their bioclimatic conditions, so-called bioclimatic niches. We present Siren, a tool for interactive redescription min- ing. It is designed to facilitate the exploratory analysis of data by providing a seamless environment for mining, visu- alizing and editing redescriptions in an interactive fashion, supporting the analysis process in all its stages. We demon- strate its use for exploratory data mining. Simultaneously, Siren exemplifies the power of the various visualizations and means of interaction integrated into it; Techniques that reach beyond the task of redescription mining considered here, to other analysis methods