Largeness and SQ-universality of cyclically presented groups

Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contains, amongst others, the various generalizations of Fibonacci groups introduced by Campbell and Robertson

No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

A 1-D modelling of streaming potential dependence on water content during drainage experiment in sand

The understanding of electrokinetics for unsaturated conditions is crucial for numerous of geophysical data interpretation. Nevertheless, the behaviour of the streaming potential coefficient C as a function of the water saturation Sw is still discussed. We propose here to model both the Richards' equation for hydrodynamics and the Poisson's equation for electrical potential for unsaturated conditions using 1-D finite element method. The equations are first presented and the numerical scheme is then detailed for the Poisson's equation. Then, computed streaming potentials (SPs) are compared to recently published SP measurements carried out during drainage experiment in a sand column. We show that the apparent measurement of DV / DP for the dipoles can provide the SP coefficient in these conditions. Two tests have been performed using existing models for the SP coefficient and a third one using a new relation. The results show that existing models of unsaturated SP coefficients C(Sw) provide poor results in terms of SP magnitude and behaviour. We demonstrate that the unsaturated SP coefficient can be until one order of magnitude larger than Csat, its value at saturation. We finally prove that the SP coefficient follows a non-monotonous behaviour with respect to water saturation. Key words: Electrical properties; Electromagnetic theory; Hydrogeophysics; Hydrology; Permeability and porosity; electrokinetic; streaming potential; self-potential; water content; water saturation; unsaturated condition; finite element modelin

Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism

This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in defining the ensemble. Ensembles are obtained by dividing a huge rock sample into many mesoscopic volumes. Because rocks are a disordered collection of grains in cohesive contact, we expect that once shear strain is applied and cracks begin to arrive in the system, the mesoscopic volumes will have a wide distribution of different crack states. These mesoscopic volumes are the members of our ensembles. We determine the probability of observing a mesoscopic volume to be in a given crack state by maximizing Shannon's measure of the emergent crack disorder subject to constraints coming from the energy-balance of brittle fracture. The laws of thermodynamics, the partition function, and the quantification of temperature are obtained for such cracking systems.Comment: 11 pages, 2 figure

Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media

We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity were shown to be a good approximation of the simulation data. The dependence of the relative permeability coefficients on water saturation was investigated and showed good qualitative agreement with experimental data. Non-steady state invasion flows were investigated, with particular interest in the asymptotic residual oil saturation. The addition of surfactant to the invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.

Human oral viruses are personal, persistent and gender-consistent.

Viruses are the most abundant members of the human oral microbiome, yet relatively little is known about their biodiversity in humans. To improve our understanding of the DNA viruses that inhabit the human oral cavity, we examined saliva from a cohort of eight unrelated subjects over a 60-day period. Each subject was examined at 11 time points to characterize longitudinal differences in human oral viruses. Our primary goals were to determine whether oral viruses were specific to individuals and whether viral genotypes persisted over time. We found a subset of homologous viral genotypes across all subjects and time points studied, suggesting that certain genotypes may be ubiquitous among healthy human subjects. We also found significant associations between viral genotypes and individual subjects, indicating that viruses are a highly personalized feature of the healthy human oral microbiome. Many of these oral viruses were not transient members of the oral ecosystem, as demonstrated by the persistence of certain viruses throughout the entire 60-day study period. As has previously been demonstrated for bacteria and fungi, membership in the oral viral community was significantly associated with the sex of each subject. Similar characteristics of personalized, sex-specific microflora could not be identified for oral bacterial communities based on 16S rRNA. Our findings that many viruses are stable and individual-specific members of the oral ecosystem suggest that viruses have an important role in the human oral ecosystem

Diverse CRISPRs Evolving in Human Microbiomes

CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) loci, together with cas (CRISPR–associated) genes, form the CRISPR/Cas adaptive immune system, a primary defense strategy that eubacteria and archaea mobilize against foreign nucleic acids, including phages and conjugative plasmids. Short spacer sequences separated by the repeats are derived from foreign DNA and direct interference to future infections. The availability of hundreds of shotgun metagenomic datasets from the Human Microbiome Project (HMP) enables us to explore the distribution and diversity of known CRISPRs in human-associated microbial communities and to discover new CRISPRs. We propose a targeted assembly strategy to reconstruct CRISPR arrays, which whole-metagenome assemblies fail to identify. For each known CRISPR type (identified from reference genomes), we use its direct repeat consensus sequence to recruit reads from each HMP dataset and then assemble the recruited reads into CRISPR loci; the unique spacer sequences can then be extracted for analysis. We also identified novel CRISPRs or new CRISPR variants in contigs from whole-metagenome assemblies and used targeted assembly to more comprehensively identify these CRISPRs across samples. We observed that the distributions of CRISPRs (including 64 known and 86 novel ones) are largely body-site specific. We provide detailed analysis of several CRISPR loci, including novel CRISPRs. For example, known streptococcal CRISPRs were identified in most oral microbiomes, totaling ∼8,000 unique spacers: samples resampled from the same individual and oral site shared the most spacers; different oral sites from the same individual shared significantly fewer, while different individuals had almost no common spacers, indicating the impact of subtle niche differences on the evolution of CRISPR defenses. We further demonstrate potential applications of CRISPRs to the tracing of rare species and the virus exposure of individuals. This work indicates the importance of effective identification and characterization of CRISPR loci to the study of the dynamic ecology of microbiomes