Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Understanding drivers of domestic public expenditure on reproductive, maternal, neonatal and child health in Peru at district level:an ecological study

Background Peru has increased substantially its domestic public expenditure in maternal and child health. Peruvian departments are heterogeneous in contextual and geographic factors, underlining the importance of disaggregated expenditure analysis up to the district level. We aimed to assess possible district level factors influencing public expenditure on reproductive, maternal, neonatal and child health (RMNCH) in Peru. Methods We performed an ecological study in 24 departments, with specific RMNCH expenditure indicators as outcomes, and covariates of different hierarchical dimensions as predictors. To account for the influence of variables included in the different dimensions over time and across departments, we chose a stepwise multilevel mixed-effects regression model, with department-year as the unit of analysis. Results Public expenditure increased in all departments, particularly for maternal-neonatal and child health activities, with a different pace across departments. The multilevel analysis did not reveal consistently influential factors, except for previous year expenditure on reproductive and maternal-neonatal health. Our findings may be explained by a combination of inertial expenditure, a results-based budgeting approach to increase expenditure efficiency and effectiveness, and by a mixed-effects decentralization process. Sample size, interactions and collinearity cannot be ruled out completely. Conclusions Public district-level RMNCH expenditure has increased remarkably in Peru. Evidence on underlying factors influencing such trends warrants further research, most likely through a combination of quantitative and qualitative approaches

Long-term resightings of humpback whales off Ecuador

This paper reports on the long-term re-sight histories of fifteen photo-identified humpback whales encountered to date transiting Ecuadorian waters. It also provides information about connections to feeding area destinations. Whale EC1261 has been resighted over a 26 year span and provides insight into age and potential longevity of this species in the stock G. The resighting of whale EC1261 provides the earliest connection from Ecuador to Antarctica. and supports previous findings that Antarctic Peninsula is the main feeding area of humpback whales migrating to Ecuadorian waters. Although there are only a low percentage of re-sighted animals between Ecuador and the Strait of Magellan, two records represent long-term observations of 17 and 21 years. Resightings of these whales previously confirmed the Straits of Magellan as a feeding area (Gibbons et al, 1998; Gibbons et al, 2003; Acevedo et al. 2007; Capella et al. 2008). These results are based on the individual identification of the ventral surface of humpback whale tails. This method has been used extensively by researchers, NGO’s and government institutions in Antarctica, Chile, and Colombi

Nitric oxide releasing-dendrimers: an overview

Platforms able to storage, release or scavenge NO in a controlled and specific manner is interesting for biological applications. Among the possible matrices for these purposes, dendrimers are excellent candidates for that. These molecules have been used as drug delivery systems and exhibit interesting properties, like the possibility to perform chemical modifications on dendrimers surface, the capacity of storage high concentrations of compounds of interest in the same molecule and the ability to improve the solubility and the biocompatibility of the compounds bonded to it. This review emphasizes the recent progress in the development and in the biological applications of different NO-releasing dendrimers and the nitric oxide release pathways in these compounds

Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel

A major use of the 1000 Genomes Project (1000GP) data is genotype imputation in genome-wide association studies (GWAS). Here we develop a method to estimate haplotypes from low-coverage sequencing data that can take advantage of single-nucleotide polymorphism (SNP) microarray genotypes on the same samples. First the SNP array data are phased to build a backbone (or 'scaffold') of haplotypes across each chromosome. We then phase the sequence data 'onto' this haplotype scaffold. This approach can take advantage of relatedness between sequenced and non-sequenced samples to improve accuracy. We use this method to create a new 1000GP haplotype reference set for use by the human genetic community. Using a set of validation genotypes at SNP and bi-allelic indels we show that these haplotypes have lower genotype discordance and improved imputation performance into downstream GWAS samples, especially at low-frequency variants. © 2014 Macmillan Publishers Limited. All rights reserved