Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) \le l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page

Hypercomplex Integrable Systems

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one of which is in Cauchy-Kovaleskaya form which enables a formal general solution to be given. Various other properties of the field equations and their solutions are studied, such as their symmetry properties and the associated hierarchy of conservation laws.Comment: Latex file, 19 page

On Self-Dual Gravity I

(One typo corrected and one incorrect statement removed. Extra details on conserved quantities and symmetry algebras added).Comment: 17 pages, Latex, DAMTP-R92/4

Choriocapillaris and Choroidal Microvasculature Imaging with Ultrahigh Speed OCT Angiography

We demonstrate in vivo choriocapillaris and choroidal microvasculature imaging in normal human subjects using optical coherence tomography (OCT). An ultrahigh speed swept source OCT prototype at 1060 nm wavelengths with a 400 kHz A-scan rate is developed for three-dimensional ultrahigh speed imaging of the posterior eye. OCT angiography is used to image three-dimensional vascular structure without the need for exogenous fluorophores by detecting erythrocyte motion contrast between OCT intensity cross-sectional images acquired rapidly and repeatedly from the same location on the retina. En face OCT angiograms of the choriocapillaris and choroidal vasculature are visualized by acquiring cross-sectional OCT angiograms volumetrically via raster scanning and segmenting the three-dimensional angiographic data at multiple depths below the retinal pigment epithelium (RPE). Fine microvasculature of the choriocapillaris, as well as tightly packed networks of feeding arterioles and draining venules, can be visualized at different en face depths. Panoramic ultra-wide field stitched OCT angiograms of the choriocapillaris spanning ~32 mm on the retina show distinct vascular structures at different fundus locations. Isolated smaller fields at the central fovea and ~6 mm nasal to the fovea at the depths of the choriocapillaris and Sattler's layer show vasculature structures consistent with established architectural morphology from histological and electron micrograph corrosion casting studies. Choriocapillaris imaging was performed in eight healthy volunteers with OCT angiograms successfully acquired from all subjects. These results demonstrate the feasibility of ultrahigh speed OCT for in vivo dye-free choriocapillaris and choroidal vasculature imaging, in addition to conventional structural imaging.National Institutes of Health (U.S.) (NIH R01-EY011289-27)National Institutes of Health (U.S.) (NIH R01-EY013178-12)National Institutes of Health (U.S.) (NIH R44-EY022864-01)National Institutes of Health (U.S.) (NIH R01-CA075289-16)United States. Air Force Office of Scientific Research (AFOSR FA9550-10-1-0551)United States. Air Force Office of Scientific Research (AFOSR FA9550-12-1-0499

Common variation near CDKN1A, POLD3 and SHROOM2 influences colorectal cancer risk

We performed a meta-analysis of five genome-wide association studies to identify common variants influencing colorectal cancer (CRC) risk comprising 8,682 cases and 9,649 controls. Replication analysis was performed in case-control sets totaling 21,096 cases and 19,555 controls. We identified three new CRC risk loci at 6p21 (rs1321311, near CDKN1A; P = 1.14 × 10(-10)), 11q13.4 (rs3824999, intronic to POLD3; P = 3.65 × 10(-10)) and Xp22.2 (rs5934683, near SHROOM2; P = 7.30 × 10(-10)) This brings the number of independent loci associated with CRC risk to 20 and provides further insight into the genetic architecture of inherited susceptibility to CRC.Swedish Research Council et al.Manuscrip

Multiple Common Susceptibility Variants near BMP Pathway Loci GREM1, BMP4, and BMP2 Explain Part of the Missing Heritability of Colorectal Cancer

Peer reviewe

Empirical Models of Manufacturer-Retailer Interaction: A Review and Agenda for Future Research

The nature of the interaction between manufacturers and retailers has received a great deal of empirical attention in the last 15 years. One major line of empirical research examines the balance of power between them and ranges from reduced form models quantifying aggregate profit and other related trends for manufacturers and retailers to structural models that test alternative forms of manufacturer-retailer pricing interaction. A second line of research addresses the sources of leverage for each party, e.g., trade promotions and their pass-through, customer information from loyalty programs, manufacturer advertising, productassortment in general, and private label assortment in particular. The purpose of this article is to synthesize what has been learnt about the nature of the interaction between manufacturers and retailers and the effectiveness of each party’s sources of leverage and to highlight gaps in our knowledge that future research should attempt to fill

Phase I dose intensification study of 2-weekly epirubicin with GM-CSF in advanced cancer

This study investigated dose intensification of epirubicin administered as a 2-weekly regimen with granulocyte-macrophage colony-stimulating factor (GM-CSF) support. The aim was to define the maximally tolerated dose of epirubicin and to assess the efficacy of GM-CSF to ameliorate its toxicity. Patients with anthracycline-responsive advanced malignancies were eligible. Six dose levels, commencing at 90 mg/m2, of epirubicin administered every 2 weeks for four courses were planned with GM-CSF 10 µg/kg/day administered for 10 days from the second day of each course. Six patients were to be entered at each dose level, and escalation to the next level was based upon toxicity criteria. Twelve patients were entered, six at dose level 1 (90 mg/m2) and six at dose level 2 (120 mg/m2). Prospectively defined haematological dose-limiting toxicities were noted in one patient at dose level 1 and in five patients at dose level 2. Further dose escalation was not attempted. Significant nonhaematological toxicities included febrile neutropenia in two and four patients at dose levels 1 and 2, respectively. This study has demonstrated that epirubicin can be safely administered at 2 week intervals with GM-CSF at a dose of 90 mg/m2, equivalent to the previously reported maximum tolerated dose intensity of 45 mg/m2/week. Neutropenia was dose-limiting despite the use of GM-CSF

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows