Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Species of ground beetle (Coleoptera: Carabidae) in organic apple orchards of British Columbia

In a two year study, 14 genera of Carabidae (Agonum Bonelli, Amara Bonelli, Anisodactylus Dejean, Bembidion Latreille, Carabus Linné, Harpalus Latreille, Lebia Latreille, Loricera Latreille, Poecilus Bonelli, Pterostichus Bonelli, Scaphinotus Dejean, Stenolophus Stephens, Syntomus Hope and Trechus Clairville) represented by 44 species were identified from six commercial organic apple orchards in the southern Similkameen valley in British Columbia, Canada; 13 of these species were not native to the area. The 4,299 specimens were caught in 'ramp' pitfall traps, with the genera Pterostichus and Harpalus comprising 56% and 43%, respectively. Numbers of Carabidae ranged from 11-21 species per orchard, with their presence detected throughout the collection period

Fluctuations for the Ginzburg-Landau ∇ϕ\nabla \phi Interface Model on a Bounded Domain

We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian \CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed to be symmetric and uniformly convex. This is a general model for a $(2+1)$-dimensional effective interface where $h$ represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: $h(x) = n x \cdot u + f(x)$ for $x \in \partial D_n$, $u \in \R^2$, and $f \colon \R^2 \to \R$ continuous. We prove that the fluctuations of linear functionals of $h(x)$ about the tilt converge in the limit to a Gaussian free field on $D$, the standard Gaussian with respect to the weighted Dirichlet inner product $(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i$ for some explicit $\beta = \beta(u)$. In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of $h$ are asymptotically described by $SLE(4)$, a conformally invariant random curve.Comment: 58 page

A simple method for finite range decomposition of quadratic forms and Gaussian fields

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagation speed of the wave equation and Chebyshev polynomials. It improves several existing results and also gives simpler proofs.Comment: minor correction for t<

A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in \mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al. In particular, all $K$'s are nowhere differentiable with derivatives singular distributions. $\mathcal{K}$ furnishes explicit realizations of the functional analytic result of Berezhnoi. Recently, the author and simulteously others laid the foundations of Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of $L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence form Aronsson PDE with as special case the $\infty$-Laplacian. Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the scalar case, we partially answered the open $C^1$ regularity problem of Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the solutions can not be rigorously interpreted by existing PDE theories and justify our new theory of Contact solutions for fully nonlinear systems (Katzourakis). Validity of arguments of our new theory and failure of classical approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

Identifying and Characterizing Regulatory Sequences in the Human Genome with Chromatin Accessibility Assays

After finishing a human genome reference sequence in 2002, the genomics community has turned to the task of interpreting it. A primary focus is to identify and characterize not only protein-coding genes, but all functional elements in the genome. The effort includes both individual investigators and large-scale projects like the Encyclopedia of DNA Elements (ENCODE) project. As part of the ENCODE project, several groups have identified millions of regulatory elements in hundreds of human cell-types using DNase-seq and FAIRE-seq experiments that detect regions of nucleosome-free open chromatin. ChIP-seq experiments have also been used to discover transcription factor binding sites and map histone modifications. Nearly all identified elements are found in non-coding DNA, hypothesizing a function for previously unannotated sequence. In this review, we provide an overview of the ENCODE effort to define regulatory elements, summarize the main results, and discuss implications of the millions of regulatory elements distributed throughout the genome

Fern spore extracts can damage DNA

The carcinogenicity of the vegetative tissues of bracken fern (Pteridium) has long been established. More recently, the carcinogenic effects of the spores of bracken have also been recognized. Both vegetative tissues and spores of bracken can induce adducts in DNA in animal tissues, but the possible genotoxic or carcinogenic effects of spores from fern species other than bracken are unknown. The single-cell gel electrophoresis (‘comet’) assay was used to investigate whether fern spores can cause DNA damage in vitro. Extracts of spores from six fern species were administered to cultured human premyeloid leukaemia (K562) cells. Spore extracts of five fern species: Anemia phyllitidis, Dicksonia antarctica, Pteridium aquilinum, Pteris vittata and Sadleria pallida, induced significantly more DNA strand breaks than those in the control groups. Only in one species, Osmunda regalis, was the effect no different from that in the control groups. Using extracts from A. phyllitidis and P. vittata, the extent of DNA damage was increased by increasing the original dose 10 times, whereas an experiment in which exposure times were varied suggested that the highest levels of strand breaks appear after 2 h exposure. Simultaneous incubation with human S9 liver enzyme mix ablated the damaging effect of the extracts. Our data show that fern spore extracts can cause DNA damage in human cells in vitro. Considering the strong correlation between DNA damage and carcinogenic events, the observations made in this report may well have some implications for human health. © 2000 Cancer Research Campaig

Locomotor loading mechanics in the hindlimbs of tegu lizards (Tupinambis merinae): comparitive and evolutionary implications

Skeletal elements are usually able to withstand several times their usual load before they yield, and this ratio is known as the bone\u27s safety factor. Limited studies on amphibians and non-avian reptiles have shown that they have much higher limb bone safety factors than birds and mammals. It has been hypothesized that this difference is related to the difference in posture between upright birds and mammals and sprawling ectotherms; however, limb bone loading data from a wider range of sprawling species are needed in order to determine whether the higher safety factors seen in amphibians and non-avian reptiles are ancestral or derived conditions. Tegus (family Teiidae) are an ideal lineage with which to expand sampling of limb bone loading mechanics for sprawling taxa, particularly for lizards, because they are from a different clade than previously sampled iguanas and exhibit different foraging and locomotor habits (actively foraging carnivore versus burst-activity herbivore). We evaluated the mechanics of locomotor loading for the femur of the Argentine black and white tegu (Tupinambus merianae) using three-dimensional measurements of the ground reaction force and hindlimb kinematics, in vivo bone strains and femoral mechanical properties. Peak bending stresses experienced by the femur were low (tensile: 10.4±1.1 MPa; compressive: –17.4±0.9 MPa) and comparable to those in other reptiles, with moderate shear stresses and strains also present. Analyses of peak femoral stresses and strains led to estimated safety factor ranges of 8.8–18.6 in bending and 7.8–17.5 in torsion, both substantially higher than typical for birds and mammals but similar to other sprawling tetrapods. These results broaden the range of reptilian and amphibian taxa in which high femoral safety factors have been evaluated and further indicate a trend for the independent evolution of lower limb bone safety factors in endothermic taxa