Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

STRUCTURAL INTERDEPENDENCE AMONG COLOMBIAN DEPARTMENTS

This paper analyzes structural interdependence among Colombian departments. The results show that Bogota has a large influence on the other regional economies through the power of its purchases. Additionally, a center-periphery pattern emerges in the spatial concentration of the effects of the hypothetical extraction of any territory. From a policy point of view, the main findings reaffirm the role played by Bogota in the recent polarization process observed in the regional economies in Colombia. Any policy action oriented to reduce these regional disparities should take into account that, given the structural interdependence among Colombian departments, the effects of new investment in the lagged regions would flow through Bogota and the major regional economies.

Spatial aspects of trade liberalization in Colombia: A general equilibrium approach

This paper offers some preliminary steps in the marriage of some of the theoretical foundations of new economic geography with spatial computable general equilibrium models. Modelling the spatial economy of Colombia using the traditional assumptions of computable general equilibrium (CGE) models makes little sense when one territorial unit, Bogota, accounts for over one quarter of GDP and where transportation costs are high and accessibility low compared to European or North American standards. Hence, handling market imperfections becomes imperative as does the need to address internal spatial issues from the perspective of Colombia`s increasing involvement with external markets. The paper builds on the Centro de Estudios de Economia Regional (CEER) model, a spatial CGE model of the Colombian economy; non-constant returns and non-iceberg transportation costs are introduced and some simulation exercises carried out. The results confirm the asymmetric impacts that trade liberalization has on a spatial economy in which one region, Bogota, is able to more fully exploit scale economies vis--vis the rest of Colombia. The analysis also reveals the importance of different hypotheses on factor mobility and the role of price effects to better understand the consequences of trade opening in a developing economy.

Reliability of short comparative genomic hybridization in fibroblasts and blastomeres for a comprehensive aneuploidy screening: first clinical application

BACKGROUND: Comparative genomic hybridization (CGH) is a valuable alternative to fluorescence in situ hybridization (FISH) for preimplantation genetic screening (PGS) because it allows full karyotype analysis. However, this approach requires the cryopreservation of biopsied embryos until results are available. The aim of this study is to reduce the hybridization period of CGH, in order to make this short-CGH technique suitable for PGS of Day-3 embryos, avoiding the cryopreservation step. METHODS: Thirty-two fibroblasts from six aneuploid cell lines (Coriell) and 48 blastomeres from 10 Day-4 embryos, discarded after PGS by FISH with 9 probes (9-chr-FISH), were analysed by short-CGH. A reanalysis by the standard 72 h-CGH and FISH using telomeric probes was performed when no concordant results between short-CGH and FISH diagnosis were observed. The short-CGH was subsequently applied in a clinical case of advanced maternal age. RESULTS: In 100% of the fibroblasts analysed, the characteristic aneuploidies of each cell line were detected by short-CGH. The results of the 48 blastomeres screened by short-CGH were supported by both 72 h-CGH results and FISH reanalysis. The chromosomes most frequently involved in aneuploidy were 22 and 16, but aneuploidies for the other chromosomes, excepting 1, 10 and 13, were also detected. Forty-one of the 94 aneuploid events observed (43.6%) corresponded to chromosomes which are not analysed by 9-chr-FISH. CONCLUSIONS: We have performed a preliminary validation of the short-CGH technique, including one clinical case, suggesting this approach may be applied to Day-3 aneuploidy analysis, thereby avoiding embryo cryopreservation and perhaps helping to improve implantation rate after PGS.