Minimal matchings of point processes

Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider limits as gamma approaches 0, 1-, 1+ and infinity. We focus on dimension d = 1. We prove that almost surely no such matching has unmatched points. (This question is open for higher d). For each gamma < 1 we establish that there is almost surely a unique such matching, and that it can be expressed as a finitary factor of the points. Moreover, its typical edge length has finite rth moment if and only if r < 1 /2. In contrast, for gamma = 1 there are uncountably many matchings, while for gamma > 1 there are countably many, but it is impossible to choose one in a translation-invariant way. We obtain existence results in higher dimensions (covering many but not all cases). We address analogous questions for one-colour matchings also

Removal of deaminated cytosines and detection of in vivo methylation in ancient DNA

DNA sequences determined from ancient organisms have high error rates, primarily due to uracil bases created by cytosine deamination. We use synthetic oligonucleotides, as well as DNA extracted from mammoth and Neandertal remains, to show that treatment with uracil–DNA–glycosylase and endonuclease VIII removes uracil residues from ancient DNA and repairs most of the resulting abasic sites, leaving undamaged parts of the DNA fragments intact. Neandertal DNA sequences determined with this protocol have greatly increased accuracy. In addition, our results demonstrate that Neandertal DNA retains in vivo patterns of CpG methylation, potentially allowing future studies of gene inactivation and imprinting in ancient organisms

Targeted Fused Ridge Estimation of Inverse Covariance Matrices from Multiple High-Dimensional Data Classes

We consider the problem of jointly estimating multiple inverse covariance matrices from high-dimensional data consisting of distinct classes. An $\ell_2$-penalized maximum likelihood approach is employed. The suggested approach is flexible and generic, incorporating several other $\ell_2$-penalized estimators as special cases. In addition, the approach allows specification of target matrices through which prior knowledge may be incorporated and which can stabilize the estimation procedure in high-dimensional settings. The result is a targeted fused ridge estimator that is of use when the precision matrices of the constituent classes are believed to chiefly share the same structure while potentially differing in a number of locations of interest. It has many applications in (multi)factorial study designs. We focus on the graphical interpretation of precision matrices with the proposed estimator then serving as a basis for integrative or meta-analytic Gaussian graphical modeling. Situations are considered in which the classes are defined by data sets and subtypes of diseases. The performance of the proposed estimator in the graphical modeling setting is assessed through extensive simulation experiments. Its practical usability is illustrated by the differential network modeling of 12 large-scale gene expression data sets of diffuse large B-cell lymphoma subtypes. The estimator and its related procedures are incorporated into the R-package rags2ridges.Comment: 52 pages, 11 figure

Genetic Influences on Brain Gene Expression in Rats Selected for Tameness and Aggression

Inter-individual differences in many behaviors are partly due to genetic differences, but the identification of the genes and variants that influence behavior remains challenging. Here, we studied an F2 intercross of two outbred lines of rats selected for tame and aggressive behavior towards humans for more than 64 generations. By using a mapping approach that is able to identify genetic loci segregating within the lines, we identified four times more loci influencing tameness and aggression than by an approach that assumes fixation of causative alleles, suggesting that many causative loci were not driven to fixation by the selection. We used RNA sequencing in 150 F2 animals to identify hundreds of loci that influence brain gene expression. Several of these loci colocalize with tameness loci and may reflect the same genetic variants. Through analyses of correlations between allele effects on behavior and gene expression, differential expression between the tame and aggressive rat selection lines, and correlations between gene expression and tameness in F2 animals, we identify the genes Gltscr2, Lgi4, Zfp40 and Slc17a7 as candidate contributors to the strikingly different behavior of the tame and aggressive animals

Primer Extension Capture: Targeted Sequence Retrieval from Heavily Degraded DNA Sources

We present a method of targeted DNA sequence retrieval from DNA sources which are heavily degraded and contaminated with microbial DNA, as is typical of ancient bones. The method greatly reduces sample destruction and sequencing demands relative to direct PCR or shotgun sequencing approaches. We used this method to reconstruct the complete mitochondrial DNA (mtDNA) genomes of five Neandertals from across their geographic range. The mtDNA genetic diversity of the late Neandertals was approximately three times lower than that of contemporary modern humans. Together with analyses of mtDNA protein evolution, these data suggest that the long-term effective population size of Neandertals was smaller than that of modern humans and extant great apes

Native or Introduced? Fossil Pollen and Spores may Say. An Example from the Azores Islands

Aim: Among the various possible approaches to assess whether a species is native or introduced, the analysis of subfossil pollen and spores from natural archives is a valuable tool. Requirements include a sufficiently high taxonomic resolution of the pollen morphology, as well as sufficient temporal and spatial resolution. The aim of this study is to show the usefulness of this method in solving whether the taxon is native or introduced. Location: The results are derived from two islands of the Azores: Flores and Pico. Methods: Analysis of pollen and spores in lake sediments; radiocarbon dating of the studied sediments. Results: Selaginella kraussiana (Kunze) A. Braun has occurred on the Azores Islands at least for the last 6000 years. Main conclusions: Different authors had assigned three different types of status to Selaginella kraussiana: native, introduced (invasive), or uncertain. High numbers of spores of this taxon were present in the sediment cores from the two studied lakes already several thousand years before the Portuguese discovery and the Flemish settlement in the 15th century. This proves that the species is native on the Azores Islands. Pollen and spore analysis can therefore contribute to historical biogeography not only regarding questions about pre-Quaternary plate tectonics but also about early human impact

The Neandertal genome and ancient DNA authenticity

Recent advances in high-thoughput DNA sequencing have made genome-scale analyses of genomes of extinct organisms possible. With these new opportunities come new difficulties in assessing the authenticity of the DNA sequences retrieved. We discuss how these difficulties can be addressed, particularly with regard to analyses of the Neandertal genome. We argue that only direct assays of DNA sequence positions in which Neandertals differ from all contemporary humans can serve as a reliable means to estimate human contamination. Indirect measures, such as the extent of DNA fragmentation, nucleotide misincorporations, or comparison of derived allele frequencies in different fragment size classes, are unreliable. Fortunately, interim approaches based on mtDNA differences between Neandertals and current humans, detection of male contamination through Y chromosomal sequences, and repeated sequencing from the same fossil to detect autosomal contamination allow initial large-scale sequencing of Neandertal genomes. This will result in the discovery of fixed differences in the nuclear genome between Neandertals and current humans that can serve as future direct assays for contamination. For analyses of other fossil hominins, which may become possible in the future, we suggest a similar ‘boot-strap' approach in which interim approaches are applied until sufficient data for more definitive direct assays are acquired

Metabolic changes in schizophrenia and human brain evolution.

BACKGROUND: Despite decades of research, the molecular changes responsible for the evolution of human cognitive abilities remain unknown. Comparative evolutionary studies provide detailed information about DNA sequence and mRNA expression differences between humans and other primates but, in the absence of other information, it has proved very difficult to identify molecular pathways relevant to human cognition. RESULTS: Here, we compare changes in gene expression and metabolite concentrations in the human brain and compare them to the changes seen in a disorder known to affect human cognitive abilities, schizophrenia. We find that both genes and metabolites relating to energy metabolism and energy-expensive brain functions are altered in schizophrenia and, at the same time, appear to have changed rapidly during recent human evolution, probably as a result of positive selection. CONCLUSION: Our findings, along with several previous studies, suggest that the evolution of human cognitive abilities was accompanied by adaptive changes in brain metabolism, potentially pushing the human brain to the limit of its metabolic capabilities.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page