Absolute continuity of Brownian bridges under certain gauge transformations

We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure for the periodic derivative nonlinear Schr\"odinger equation obtained by Nahmod, Oh, Rey-Bellet and Staffilani in [20], and with respect to which they proved almost surely global well-posedness, coincides with the weighted Wiener measure constructed by Thomann and Tzvetkov [24]. Thus, in particular we prove the invariance of the measure constructed in [24].Comment: 12 pages. Submitte

Fixation for Distributed Clustering Processes

We study a discrete-time resource flow in $Z^d$, where wealthier vertices attract the resources of their less rich neighbors. For any translation-invariant probability distribution of initial resource quantities, we prove that the flow at each vertex terminates after finitely many steps. This answers (a generalized version of) a question posed by van den Berg and Meester in 1991. The proof uses the mass-transport principle and extends to other graphs

Wolbachia and DNA barcoding insects: patterns, potential and problems

Wolbachia is a genus of bacterial endosymbionts that impacts the breeding systems of their hosts. Wolbachia can confuse the patterns of mitochondrial variation, including DNA barcodes, because it influences the pathways through which mitochondria are inherited. We examined the extent to which these endosymbionts are detected in routine DNA barcoding, assessed their impact upon the insect sequence divergence and identification accuracy, and considered the variation present in Wolbachia COI. Using both standard PCR assays (Wolbachia surface coding protein – wsp), and bacterial COI fragments we found evidence of Wolbachia in insect total genomic extracts created for DNA barcoding library construction. When >2 million insect COI trace files were examined on the Barcode of Life Datasystem (BOLD) Wolbachia COI was present in 0.16% of the cases. It is possible to generate Wolbachia COI using standard insect primers; however, that amplicon was never confused with the COI of the host. Wolbachia alleles recovered were predominantly Supergroup A and were broadly distributed geographically and phylogenetically. We conclude that the presence of the Wolbachia DNA in total genomic extracts made from insects is unlikely to compromise the accuracy of the DNA barcode library; in fact, the ability to query this DNA library (the database and the extracts) for endosymbionts is one of the ancillary benefits of such a large scale endeavor – for which we provide several examples. It is our conclusion that regular assays for Wolbachia presence and type can, and should, be adopted by large scale insect barcoding initiatives. While COI is one of the five multi-locus sequence typing (MLST) genes used for categorizing Wolbachia, there is limited overlap with the eukaryotic DNA barcode region

Requirement of the CXXC Motif of Novel Francisella Infectivity Potentiator Protein B FipB, and FipA in Virulence of F. tularensis subsp. tularensis

The lipoprotein encoded by the Francisella tularensis subsp. tularensis locus FTT1103 is essential for virulence; an FTT1103 deletion mutant is defective in uptake and intracellular survival, and mice survive high dose challenges of greater than 108 bacteria. This protein has two conserved domains; one is found in a class of virulence proteins called macrophage infectivity potentiator (Mip) proteins, and the other in oxidoreductase Disulfide Bond formation protein A (DsbA)-related proteins. We have designated the protein encoded by FTT1103 as FipB for Francisella infectivity potentiator protein B. The locus FTT1102 (fipA), which is upstream of fipB, also has similarity to same conserved Mip domain. Deletion and site-specific mutants of fipA and fipB were constructed in the Schu S4 strain, and characterized with respect to intracellular replication and in vivo virulence. A nonpolar fipA mutant demonstrated reduced survival in host cells, but was only slightly attenuated in vivo. Although FipB protein was present in a fipA mutant, the abundance of the three isoforms of FipB was altered, suggesting that FipA has a role in post-translational modification of FipB. Similar to many DsbA homologues, FipB contains a cysteine-any amino acid-any amino acid-cysteine (CXXC) motif. This motif was found to be important for FipB's role in virulence; a deletion mutant complemented with a gene encoding a FipB protein in which the first cysteine was changed to an alanine residue (AXXC) failed to restore intracellular survival or in vivo virulence. Complementation with a gene that encoded a CXXA containing FipB protein was significantly defective in intracellular growth; however, only slightly attenuated in vivo

The accessible chromatin landscape of the human genome

DNaseI hypersensitive sites (DHSs) are markers of regulatory DNA and have underpinned the discovery of all classes of cis-regulatory elements including enhancers, promoters, insulators, silencers, and locus control regions. Here we present the first extensive map of human DHSs identified through genome-wide profiling in 125 diverse cell and tissue types. We identify ~2.9 million DHSs that encompass virtually all known experimentally-validated cis-regulatory sequences and expose a vast trove of novel elements, most with highly cell-selective regulation. Annotating these elements using ENCODE data reveals novel relationships between chromatin accessibility, transcription, DNA methylation, and regulatory factor occupancy patterns. We connect ~580,000 distal DHSs with their target promoters, revealing systematic pairing of different classes of distal DHSs and specific promoter types. Patterning of chromatin accessibility at many regulatory regions is choreographed with dozens to hundreds of co-activated elements, and the trans-cellular DNaseI sensitivity pattern at a given region can predict cell type-specific functional behaviors. The DHS landscape shows signatures of recent functional evolutionary constraint. However, the DHS compartment in pluripotent and immortalized cells exhibits higher mutation rates than that in highly differentiated cells, exposing an unexpected link between chromatin accessibility, proliferative potential and patterns of human variation