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

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

Intensification of hydrological drought in California by human water management

We analyze the contribution of human water management to the intensification and mitigation of hydrological drought over California using the PCR-GLOBWB hydrological model for the period 1979-2014. We demonstrate that considering water management results in more accurate discharge representation. During the severe 2014 drought, water management alleviated the drought deficit by ∼50% in Southern California through reservoir operation during low flow periods. However, human water consumption (mostly irrigation) in the Central Valley increased drought duration and deficit by 50% and 50-100%, respectively. Return level analysis indicates that there is more than 50% chance that the probability of occurrence of an extreme 2014-magnitude drought event was at least doubled under the influence of human activities compared to natural variability. This impact is most significant over the San Joaquin Drainage basin with a 50% and 75% likelihood that the return period is more than 3.5 and 1.5 times larger, respectively, because of human activities

Calculus on manifolds of conformal maps and CFT

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis of the powerful techniques of CFT. Conformal maps of simply connected domains naturally have the structure of an infinite-dimensional groupoid, which generalizes the finite-dimensional group of self-maps. We put a topological structure on the space of conformal maps on simply connected domains, which makes it into a topological groupoid. Further, we (almost) extend this to a local manifold structure based on the infinite-dimensional Frechet topological vector space of holomorphic functions on a given domain A. From this, we develop the notion of conformal A-differentiability at the identity. Our main conclusion is that quadratic differentials characterizing cotangent elements on the local manifold enjoy properties similar to those of the holomorphic stress-energy tensor of CFT; these properties underpin the local symmetries of CFT. Applying the general formalism to CFT correlation functions, we show that the stress-energy tensor is exactly such a quadratic differential. This is at the basis of constructing the stress-energy tensor in conformal loop ensembles. It also clarifies the relation between Cardy's boundary conditions for CFT on simply connected domains, and the expression of the stress-energy tensor in terms of metric variations.Comment: v1: 51 pages, 5 figures. v2: 56 pages, corrections and clarifications. v3: 53 pages, one substantial addition (groupoid structure), discussion further clarified and simplified. v4: 59 pages, introduction improved, with a discussion on the relations with previous works. Published versio

Thomson scattering from high-temperature high-density plasmas revisited

The theory of Thomson scattering from high-temperature high-density plasmas is revisited from the view point of plasma fluctuation theory. Three subtle effects are addressed with a unified theory. The first is the correction of the first order of $v/c$, where $v$ is the particle velocity and $c$ is the light speed, the second is the plasma dielectric effect, and the third is the finite scattering volume effect. When the plasma density is high, the first effect is very significant in inferring plasma parameters from the scattering spectra off electron plasma waves. The second is also be notable but less significant. When the size of the scattering volume is much larger than the probe wavelength, the third is negligible.Comment: 16 pages, 2 figures, submitted to Plasma Physics and Controlled Fusio

A genome-wide scan for common alleles affecting risk for autism

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10−8. When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10−8 threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C

Таксононімія логічних девіацій у нормативно-правових актах

Розглянуто особливості логічних девіацій у текстах нормативно-правових актів, які є складовою частиною офіційно-ділового стилю української літературної мови. Запропоновано власний підхід до класифікації виявлених у текстах чинних кодексів логічно аномальних уживань.The features of the logical deviations in the texts of laws which belong to the official style of Ukrainian literary language is under consideration. The taxonomy for the notion above in Ukrainian laws is proposed