Roses of Beautiful Memories

https://digitalcommons.library.umaine.edu/mmb-vp/6151/thumbnail.jp

Hydraulic flow through a channel contraction: multiple steady states

We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upstream steady and moving bores/shocks, and oblique waves in the contraction, as single and multiple steady states, as well as a steady reservoir with a complex hydraulic jump in the contraction occurring in a small section of the $b_c/b_0$ and Froude number parameter plane. One-dimensional hydraulic theory provides a comprehensive leading-order approximation, in which a turbulent frictional parametrization is used to achieve quantitative agreement. An analytical and numerical analysis is given for two-dimensional supercritical shallow water flows. It shows that the one-dimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly well, even though the two-dimensional oblique hydraulic jump patterns can show large variations across the contraction channel

Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

The development and technology transfer of software engineering technology at NASA. Johnson Space Center

The United State's big space projects of the next decades, such as Space Station and the Human Exploration Initiative, will need the development of many millions of lines of mission critical software. NASA-Johnson (JSC) is identifying and developing some of the Computer Aided Software Engineering (CASE) technology that NASA will need to build these future software systems. The goal is to improve the quality and the productivity of large software development projects. New trends are outlined in CASE technology and how the Software Technology Branch (STB) at JSC is endeavoring to provide some of these CASE solutions for NASA is described. Key software technology components include knowledge-based systems, software reusability, user interface technology, reengineering environments, management systems for the software development process, software cost models, repository technology, and open, integrated CASE environment frameworks. The paper presents the status and long-term expectations for CASE products. The STB's Reengineering Application Project (REAP), Advanced Software Development Workstation (ASDW) project, and software development cost model (COSTMODL) project are then discussed. Some of the general difficulties of technology transfer are introduced, and a process developed by STB for CASE technology insertion is described

Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese Restaurant Process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.Comment: 10 Figures, 2 Table

Depression and self-harm from adolescence to young adulthood in sexual minorities compared to heterosexuals: a population-based cohort study

BACKGROUND: There are few population-based cohort studies of the emergence, development, and persistence of mental health problems in sexual minorities compared with heterosexuals. We compared trajectories of depressive symptoms in sexual-minority adolescents and heterosexual adolescents from when they were aged 10 years to 21 years, and examined self-harm at ages 16 years and 21 years. // METHODS: The study included 4828 adolescents born between April 1, 1991, and Dec 31, 1992, from the Avon Longitudinal Study of Parents and Children birth cohort (Bristol, UK) who reported their sexual orientation when aged 16 years. Depressive symptoms were assessed with the short Mood and Feelings Questionnaire (sMFQ) at seven timepoints between ages 10 years and 21 years. A self-harm questionnaire was completed at ages 16 years and 21 years. Analyses were linear multilevel models with growth curves (depressive symptoms), logistic multilevel models (self-harm in the previous year at ages 16 years and 21 years), and multinomial regression (lifetime self-harm with and without suicidal intent at age 21 years). // FINDINGS: At age 10 years, depressive symptoms were higher in sexual minorities (mean sMFQ 4·58 [SD 3·59]) than in heterosexuals (3·79 [3·36]) and increased with age to a larger extent. Depressive symptoms increased at each timepoint by 0·31 sMFQ points in hetereosexuals (95% CI 0·27–0·34), and by 0·49 sMFQ points in sexual minorities (0·40–0·59). Sexual-minority adolescents were more likely than heterosexual adolescents to report self-harm in the previous year at ages 16 years and 21 years (adjusted odds ratio 4·23, 95% CI 2·90–6·16), with no evidence that this estimate decreased with age (p=0·80). When aged 21 years, sexual minorities were 4·53 (95% CI 3·02 to 6·78) times more likely to report lifetime self-harm (ie, on at least one previous occasion) with suicidal intent than heterosexuals. // INTERPRETATION: Mental health disparities between heterosexuals and sexual minorities are present early in adolescence and increase throughout the school years, persisting to young adulthood. Prevention of these mental health problems and early intervention must be a priority. // FUNDING: Medical Research Council, Wellcome Trust

Generalized Bayesian Record Linkage and Regression with Exact Error Propagation

Record linkage (de-duplication or entity resolution) is the process of merging noisy databases to remove duplicate entities. While record linkage removes duplicate entities from such databases, the downstream task is any inferential, predictive, or post-linkage task on the linked data. One goal of the downstream task is obtaining a larger reference data set, allowing one to perform more accurate statistical analyses. In addition, there is inherent record linkage uncertainty passed to the downstream task. Motivated by the above, we propose a generalized Bayesian record linkage method and consider multiple regression analysis as the downstream task. Records are linked via a random partition model, which allows for a wide class to be considered. In addition, we jointly model the record linkage and downstream task, which allows one to account for the record linkage uncertainty exactly. Moreover, one is able to generate a feedback propagation mechanism of the information from the proposed Bayesian record linkage model into the downstream task. This feedback effect is essential to eliminate potential biases that can jeopardize resulting downstream task. We apply our methodology to multiple linear regression, and illustrate empirically that the "feedback effect" is able to improve the performance of record linkage.Comment: 18 pages, 5 figure

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page