Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics

The Conformal Vega Disk

Abstract The relationship between square and circle has intrigued humans since antiquity. Computer visualizations of the conformal equivalence between the two shapes double as mathematical illustrations and as op art after Vasarely. Victor Vasarely created a series of Vega compositions, which explored possibilities for filling a disc with distorted squares, usually creating the illusion of a hemispherical bulge in a planar grid. Inspired by Vasarely (and presumably also Escher), Douglas Dunham [1] recently introduced a non-Euclidean version, in which infinitely many 'hyperbolic squares' fill the Poincare disk (the exterior of which is left blank). The mathematical tool for producin

A Network Analysis of Developmental Change in ADHD Symptom Structure from Preschool to Adulthood

Although there is substantial support for the validity of the diagnosis of attention-deficit/hyperactivity disorder (ADHD), there is considerable disagreement about how to best capture developmental changes in the expression of ADHD symptomatology. This article examines the associations among the 18 individual ADHD symptoms using a novel network analysis approach, from preschool to adulthood. The 1,420 participants were grouped into four age brackets: preschool (ages 3–6, n = 109), childhood (ages 6–12, n = 548), adolescence (ages 13–17, n = 357), and young adulthood (ages 18–36, n = 406). All participants completed a multistage, multi-informant diagnostic process, and self and informant symptom ratings were obtained. Network analysis indicated ADHD symptom structure became more differentiated over development. Two symptoms, often easily distracted and difficulty sustaining attention, appeared as central, or core, symptoms across all age groups. Thus, a small number of core symptoms may warrant extra weighting in future diagnostic systems

Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.Comment: To appear in PRE, figures available on reques

Phase Separation of Crystal Surfaces: A Lattice Gas Approach

We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic crystal with nearest--neighbor attractive interactions and weak next--nearest--neighbor repulsive interactions. It is likely applicable to alkali halides with the sodium chloride structure. Emphasis is placed on the fact that the equilibrium crystal shape can be interpreted as a phase diagram and that the details of its structure tell us into which surface orientations an unstable surface will decompose. We find that, depending on the temperature and growth conditions, a number of interesting behaviors are expected. For a crystal in equilibrium with its vapor, these include a low temperature regime with logarithmically--slow separation into three symmetrically--equivalent facets, and a higher temperature regime where separation proceeds as a power law in time into an entire one--parameter family of surface orientations. For a crystal slightly out of equilibrium with its vapor (slow crystal growth or etching), power--law growth should be the rule at late enough times. However, in the low temperature regime, the rate of separation rapidly decreases as the chemical potential difference between crystal and vapor phases goes to zero.Comment: 16 pages (RevTex 3.0); 12 postscript figures available on request ([email protected]). Submitted to Physical Review E. SFU-JDSDJB-94-0

Profiling Critical Cancer Gene Mutations in Clinical Tumor Samples

Background: Detection of critical cancer gene mutations in clinical tumor specimens may predict patient outcomes and inform treatment options; however, high-throughput mutation profiling remains underdeveloped as a diagnostic approach. We report the implementation of a genotyping and validation algorithm that enables robust tumor mutation profiling in the clinical setting. Methodology: We developed and implemented an optimized mutation profiling platform (“OncoMap”) to interrogate ∼400 mutations in 33 known oncogenes and tumor suppressors, many of which are known to predict response or resistance to targeted therapies. The performance of OncoMap was analyzed using DNA derived from both frozen and FFPE clinical material in a diverse set of cancer types. A subsequent in-depth analysis was conducted on histologically and clinically annotated pediatric gliomas. The sensitivity and specificity of OncoMap were 93.8% and 100% in fresh frozen tissue; and 89.3% and 99.4% in FFPE-derived DNA. We detected known mutations at the expected frequencies in common cancers, as well as novel mutations in adult and pediatric cancers that are likely to predict heightened response or resistance to existing or developmental cancer therapies. OncoMap profiles also support a new molecular stratification of pediatric low-grade gliomas based on BRAF mutations that may have immediate clinical impact. Conclusions: Our results demonstrate the clinical feasibility of high-throughput mutation profiling to query a large panel of “actionable” cancer gene mutations. In the future, this type of approach may be incorporated into both cancer epidemiologic studies and clinical decision making to specify the use of many targeted anticancer agents

Spitzer mapping of molecular hydrogen pure rotational lines in NGC 1333: A detailed study of feedback in star formation

We present mid-infrared spectral maps of the NGC 1333 star forming region, obtained with the the Infrared Spectrometer on board the Spitzer Space Telescope. Eight pure H2 rotational lines, from S (0) to S (7), are detected and mapped. The H2 emission appears to be associated with the warm gas shocked by the multiple outflows present in the region. A comparison between the observed intensities and the predictions of detailed shock models indicates that the emission arises in both slow (12 - 24 km/s) and fast (36 - 53 km/s) C-type shocks with an initial ortho-to-para ratio of ~ 1. The present H2 ortho-to-para ratio exhibits a large degree of spatial variations. In the post-shocked gas, it is usually about 2, i.e. close to the equilibrium value (~ 3). However, around at least two outflows, we observe a region with a much lower (~ 0.5) ortho-to-para ratio. This region probably corresponds to gas which has been heated-up recently by the passage of a shock front, but whose ortho-to-para has not reached equilibrium yet. This, together with the low initial ortho-to-para ratio needed to reproduce the observed emission, provide strong evidence that H2 is mostly in para form in cold molecular clouds. The H2 lines are found to contribute to 25 - 50% of the total outflow luminosity, and thus can be used to ascertain the importance of star formation feedback on the natal cloud. From these lines, we determine the outflow mass loss rate and, indirectly, the stellar infall rate, the outflow momentum and the kinetic energy injected into the cloud over the embedded phase. The latter is found to exceed the binding energy of individual cores, suggesting that outflows could be the main mechanism for core disruption.Comment: Accepted for publication in the Astrophysical Journa