Free actions of free groups on countable structures and property (T)

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Subequivalence Relations and Positive-Definite Functions

We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent co-inducing construction of Epstein to produce new kinds of mixing actions of an arbitrary infinite discrete group and it is also used to show that orbit equivalence of free, measure preserving, mixing actions of non-amenable groups is unclassifiable in a strong sense. Finally, in the case of property (T) groups we discuss connections with invariant percolation on Cayley graphs and the calculation of costs

Loss of DNA methyltransferase activity in primed human ES cells triggers increased cell-cell variability and transcriptional repression

Maintenance of pluripotency and specification towards a new cell fate are both dependent on precise interactions between extrinsic signals and transcriptional and epigenetic regulators. Directed methylation of cytosines by the de novo methyltransferases DNMT3A and DNMT3B plays an important role in facilitating proper differentiation, whereas DNMT1 is essential for maintaining global methylation levels in all cell types. Here, we generated single-cell mRNA expression data from wild-type, DNMT3A, DNMT3A/3B and DNMT1 knockout human embryonic stem cells and observed a widespread increase in cellular and transcriptional variability, even with limited changes in global methylation levels in the de novo knockouts. Furthermore, we found unexpected transcriptional repression upon either loss of the de novo methyltransferase DNMT3A or the double knockout of DNMT3A/3B that is further propagated upon differentiation to mesoderm and ectoderm. Taken together, our single-cell RNA-sequencing data provide a high-resolution view into the consequences of depleting the three catalytically active DNMTs in human pluripotent stem cells

Ultraweak excitations of the quantum vacuum as physical models of gravity

It has been argued by several authors that the space-time curvature observed in gravitational fields, and the same idea of forms of physical equivalence different from the Lorentz group, might emerge from the dynamical properties of the physical flat-space vacuum in a suitable hydrodynamic limit. To explore this idea, one could start by representing the physical vacuum as a Bose condensate of elementary quanta and look for vacuum excitations that, on a coarse grained scale, resemble the Newtonian potential. In this way, it is relatively easy to match the weak-field limit of classical General Relativity or of some of its possible variants. The idea that Bose condensates can provide various forms of gravitational dynamics is not new. Here, I want to emphasize some genuine quantum field theoretical aspects that can help to understand i) why infinitesimally weak, 1/r interactions can indeed arise from the same physical vacuum of electroweak and strong interactions and ii) why, on a coarse-grained scale, their dynamical effects can be re-absorbed into an effective curved metric structure.Comment: 30 pages, no figures, accepted by Classical and Quantum Gravit

YeTFaSCo: a database of evaluated yeast transcription factor sequence specificities

The yeast Saccharomyces cerevisiae is a prevalent system for the analysis of transcriptional networks. As a result, multiple DNA-binding sequence specificities (motifs) have been derived for most yeast transcription factors (TFs). However, motifs from different studies are often inconsistent with each other, making subsequent analyses complicated and confusing. Here, we have created YeTFaSCo (The Yeast Transcription Factor Specificity Compendium, http://yetfasco.ccbr.utoronto.ca/), an extensive collection of S. cerevisiae TF specificities. YeTFaSCo differs from related databases by being more comprehensive (including 1709 motifs for 256 proteins or protein complexes), and by evaluating the motifs using multiple objective quality metrics. The metrics include correlation between motif matches and ChIP-chip data, gene expression patterns, and GO terms, as well as motif agreement between different studies. YeTFaSCo also features an index of ‘expert-curated’ motifs, each associated with a confidence assessment. In addition, the database website features tools for motif analysis, including a sequence scanning function and precomputed genome-browser tracks of motif occurrences across the entire yeast genome. Users can also search the database for motifs that are similar to a query motif

Nucleosome-coupled expression differences in closely-related species

<p>Abstract</p> <p>Background</p> <p>Genome-wide nucleosome occupancy is negatively related to the average level of transcription factor motif binding based on studies in yeast and several other model organisms. The degree to which nucleosome-motif interactions relate to phenotypic changes across species is, however, unknown.</p> <p>Results</p> <p>We address this challenge by generating nucleosome positioning and cell cycle expression data for <it>Saccharomyces bayanus </it>and show that differences in nucleosome occupancy reflect cell cycle expression divergence between two yeast species, <it>S. bayanus </it>and <it>S. cerevisiae</it>. Specifically, genes with nucleosome-depleted MBP1 motifs upstream of their coding sequence show periodic expression during the cell cycle, whereas genes with nucleosome-shielded motifs do not. In addition, conserved cell cycle regulatory motifs across these two species are more nucleosome-depleted compared to those that are not conserved, suggesting that the degree of conservation of regulatory sites varies, and is reflected by nucleosome occupancy patterns. Finally, many changes in cell cycle gene expression patterns across species can be correlated to changes in nucleosome occupancy on motifs (rather than to the presence or absence of motifs).</p> <p>Conclusions</p> <p>Our observations suggest that alteration of nucleosome occupancy is a previously uncharacterized feature related to the divergence of cell cycle expression between species.</p

The PADME electromagnetic calorimeter

The PADME experiment, hosted at Laboratori Nazionali di Frascati in Italy, is going to start its data taking in September 2018. It is designed to search for the Dark Photon (indicated by the symbol A′), an hypothetical particle that can explain the Dark Matter elusiveness, possibly produced in the reaction e + e - → A′ γ. Together with the target, the segmented electromagnetic calorimeter is the most important component of the experiment, since it is needed to detect the recoil photon energy and position, in such a way to measure the A′ mass. It will consist of 616 2.1 × 2.1 × 23.0 cm3 BGO crystals arranged in a cylindrical shape and read by HZC photomultipliers with a diameter of 1.9 cm. Here we present the results obtained during the measurements performed on the scintillating units with a radioactive source and test beams, together with an overall description of the entire experiment

Generic representations of abelian groups and extreme amenability

If $G$ is a Polish group and $\Gamma$ is a countable group, denote by \Hom(\Gamma, G) the space of all homomorphisms $\Gamma \to G$. We study properties of the group \cl{\pi(\Gamma)} for the generic \pi \in \Hom(\Gamma, G), when $\Gamma$ is abelian and $G$ is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and the isometry group of the Urysohn metric space. Under mild assumptions on $\Gamma$, we prove that in the first case, there is (up to isomorphism of topological groups) a unique generic \cl{\pi(\Gamma)}; in the other two, we show that the generic \cl{\pi(\Gamma)} is extremely amenable. We also show that if $\Gamma$ is torsion-free, the centralizer of the generic $\pi$ is as small as possible, extending a result of King from ergodic theory.Comment: Version