On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Genotype imputation using the Positional Burrows Wheeler Transform.

Genotype imputation is the process of predicting unobserved genotypes in a sample of individuals using a reference panel of haplotypes. In the last 10 years reference panels have increased in size by more than 100 fold. Increasing reference panel size improves accuracy of markers with low minor allele frequencies but poses ever increasing computational challenges for imputation methods. Here we present IMPUTE5, a genotype imputation method that can scale to reference panels with millions of samples. This method continues to refine the observation made in the IMPUTE2 method, that accuracy is optimized via use of a custom subset of haplotypes when imputing each individual. It achieves fast, accurate, and memory-efficient imputation by selecting haplotypes using the Positional Burrows Wheeler Transform (PBWT). By using the PBWT data structure at genotyped markers, IMPUTE5 identifies locally best matching haplotypes and long identical by state segments. The method then uses the selected haplotypes as conditioning states within the IMPUTE model. Using the HRC reference panel, which has ∼65,000 haplotypes, we show that IMPUTE5 is up to 30x faster than MINIMAC4 and up to 3x faster than BEAGLE5.1, and uses less memory than both these methods. Using simulated reference panels we show that IMPUTE5 scales sub-linearly with reference panel size. For example, keeping the number of imputed markers constant, increasing the reference panel size from 10,000 to 1 million haplotypes requires less than twice the computation time. As the reference panel increases in size IMPUTE5 is able to utilize a smaller number of reference haplotypes, thus reducing computational cost

Lexis Nexus Complexus: Comparative Contract Law and International Accounting Collide in the IASB-FASB Revenue Recognition Exposure Draft

U.S. and international accounting-standard setters plan to launch a new, global revenue accounting standard, Revenue from Contracts with Customers, in 2013. Poised at the nexus of comparative contract law and international accounting, the proposal\u27s contract-based revenue recognition model creates new legal risks and opportunities for accountants, lawyers, clients, and financial statement users. Despite its focus on legally enforceable contracts, the proposed standard was drafted without input from the legal community. This Article models the proposal\u27s complex contract-analysis process, demonstrating that its revenue outcomes may vary materially because of seemingly minor interjurisdictional differences in law applicable to open-price contracts; offers practice pointers for attorneys, accountants, and auditors; recommends changes to the proposal, including the substitution of self-enforcing Nash equilibria for legally enforceable contracts; and encourages more collaboration between the legal and accounting professions in the joint deployment of legal and accounting expertise for better value creation, value allocation, and risk mitigation

Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure has been determined, whereby 25 x 25 graphene unit cells lie on 23 x 23 unit cells of Ru. Each supercell contains 2 x 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers, and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C-C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.Comment: 9 pages, 3 figures, paper submitted to peer reviewed journa

Characterization of nanometer-sized, mechanically exfoliated graphene on the H-passivated Si(100) surface using scanning tunnelling microscopy

We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.Comment: Accepted for publication in Nanotechnolog

Synthesis, Structure, Photophysics, and Singlet Oxygen Sensitization by a Platinum(II) Complex of Meso-Tetra-Acenaphthyl Porphyrin

A new platinum(II) porphyrin complex has been synthesized and characterized via various spectroscopic techniques. Single-crystal XRD analysis reveals that the geometry around the Pt(II) center is near the perfect square planar geometry. The Pt(II)−N bond distances are in the ranges of 2.005 Å–2.020 Å. The platinum(II) porphyrin derivative exhibited one reversible oxidative couple at +1.10 V and a reversible reductive couple at −1.47 V versus Ag/AgCl. In deaerated dichloromethane solution at 298 K, a strong phosphorescence is observed at 660 nm, with emission quantum yield of 35 % and lifetime of 75 μs. Upon excitation of the acenaphthene chromophores at 300 nm, sensitised phosphorescence of the Pt(II) porphyrin is observed with a unitary efficient energy transfer, demonstrating that this system behaves as a light harvesting antenna. The red phosphorescence is strongly quenched by oxygen, resulting in singlet oxygen production with a very high quantum yield of 88 %. This result indicates that this Pt(II) porphyrin is an excellent photosensitizer for the production of singlet oxygen and will have potential applications in the field of photodynamic therapy as well as oxygen sensors