The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Genome-Wide Analysis of the Response of Dickeya dadantii 3937 to Plant Antimicrobial Peptides

Antimicrobial peptides constitute an important factor in the defense of plants against pathogens, and bacterial resistance to these peptides have previously been shown to be an important virulence factor in Dickeya dadantii, the causal agent of soft-rot disease of vegetables. In order to understand the bacterial response to antimicrobial pep- tides, a transcriptional microarray analysis was performed upon treatment with sub-lethal concentration of thionins, a widespread plant peptide. In all, 36 genes were found to be overexpressed, and were classified according to their deduced function as i) transcriptional regulators, ii) transport, and iii) modification of the bacterial membrane. One gene encoding a uricase was found to be repressed. The majority of these genes are known to be under the control of the PhoP/PhoQ system. Five genes representing the different functions induced were selected for further analysis. The results obtained indicate that the presence of antimicrobial peptides induces a complex response which includes peptide-specific elements and general stress-response elements contributing differentially to the virulence in different hosts.

The role of secretion systems and small molecules in soft-rot enterobacteriaceae pathogenicity

Soft-rot Enterobacteriaceae (SRE), which belong to the genera Pectobacterium and Dickeya, consist mainly of broad host-range pathogens that cause wilt, rot, and blackleg diseases on a wide range of plants. They are found in plants, insects, soil, and water in agricultural regions worldwide. SRE encode all six known protein secretion systems present in gram-negative bacteria, and these systems are involved in attacking host plants and competing bacteria. They also produce and detect multiple types of small molecules to coordinate pathogenesis, modify the plant environment, attack competing microbes, and perhaps to attract insect vectors. This review integrates new information about the role protein secretion and detection and production of ions and small molecules play in soft-rot pathogenicity.

Guidelines for Physical Activity During Pregnancy: Comparisons From Around the World

Guías de actividad física durante el embarazo