Trilogy on Computing Maximal Eigenpair

The eigenpair here means the twins consist of eigenvalue and its eigenvector. This paper introduces the three steps of our study on computing the maximal eigenpair. In the first two steps, we construct efficient initials for a known but dangerous algorithm, first for tridiagonal matrices and then for irreducible matrices, having nonnegative off-diagonal elements. In the third step, we present two global algorithms which are still efficient and work well for a quite large class of matrices, even complex for instance.Comment: Updated versio

Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde

Investigation of spray characteristics for flashing injection of fuels containing dissolved air and superheated fuels

The flow, atomization and spreading of flashing injector flowing liquids containing dissolved gases (jet/air) as well as superheated liquids (Freon II) were considered. The use of a two stage expansion process separated by an expansion chamber, ws found to be beneficial for flashing injection particularly for dissolved gas systems. Both locally homogeneous and separated flow models provided good predictions of injector flow properties. Conventional correlations for drop sizes from pressure atomized and airblast injectors were successfully modified, using the separated flow model to prescribe injector exit conditions, to correlate drop size measurements. Additional experimental results are provided for spray angle and combustion properties of sprays from flashing injectors

Quantifying pelagic primary production and respiration via automated in-situ incubation system

We developed and validated a novel automated water incubator that measures in-situ rates of photosynthesis and respiration. This dataset includes raw data, Monte-Carlo simulation method, and processed results from field deployments in Summer, 2021. Deployment of the incubator was conducted near Ucantena Island, Massachusetts, USA. The dataset includes timeseries of automated incubation experiments, reporting dissolved oxygen concentration (DO), temperature, and photosynthetically active radiation (PAR). There are four deployments spanning from late august to early October, 2021. Each deployment lasted approximately 72 hours. Hourly DO fluxes from photosynthesis/respiration are calculated and reported for each deployment respectively. Data of derivative analysis are also included for various validation on the automated incubator and data analysis techniques.National Science Foundation OTIC 184109

Hyperoctahedral Chen calculus for effective Hamiltonians

The algebraic structure of iterated integrals has been encoded by Chen. Formally, it identifies with the shuffle and Lie calculus of Lyndon, Ree and Sch\"utzenberger. It is mostly incorporated in the modern theory of free Lie algebras. Here, we tackle the problem of unraveling the algebraic structure of computations of effective Hamiltonians. This is an important subject in view of applications to chemistry, solid state physics, quantum field theory or engineering. We show, among others, that the correct framework for these computations is provided by the hyperoctahedral group algebras. We define several structures on these algebras and give various applications. For example, we show that the adiabatic evolution operator (in the time-dependent interaction representation of an effective Hamiltonian) can be written naturally as a Picard-type series and has a natural exponential expansion.Comment: Minor corrections. Some misleading notations and typos in the first version have been fixe

Strategic Monitoring and Resilience Training in the Ala Wai Watershed, Oʻahu: Seasonal and Episodic Variability

OCN 499 - Undergraduate Thesi

Changes in Outcome and Complication Rates of Very-low-birth-weight Infants in One Tertiary Center in Southern Taiwan Between 2003 and 2010

BackgroundNeonatal intensive care has changed dramatically over the past few decades and the survival of infants has generally improved in many countries. The purpose of this study was to explore the recent evolution of mortality and morbidities among very-low-birth-weight (VLBW) infants in southern Taiwan.MethodsWe retrospectively reviewed the medical records of VLBW (birth weight <1500 g) infants who were admitted to a neonatal intensive care unit at a tertiary medical center in southern Taiwan from 2003 to 2010. The study period was divided into two cohorts: the first cohort of 2003–2006 and the second cohort of 2007–2010. Demographic profiles and complications were recorded, including the following information: sex, birth body weight (BBW), gestational age (GA), Apgar score, patent ductus arteriosus (PDA), necrotizing enterocolitis, retinopathy, chronic lung disease (CLD), inguinal hernia, and sepsis. The length of stay (LOS) in hospital was compared between the two cohorts.ResultsA total of 420 (212 male) VLBW infants were enrolled with 52 (12.4%) deaths. Compared to surviving infants, deceased infants had significantly lower GA, Apgar scores, and BBW. The mortality of VLBW infants remained static between the two birth cohorts, but the incidence of major morbidities generally decreased. The LOS for overall surviving infants and the proportion of LOS > 60 days were both reduced in the period of 2007–2010. With further stratification by BBW, the major reduction of long LOS was only found in the group of BBW ≥ 1000 g. The multivariate logistic regression model found PDA, CLD, and BBW < 1000 g were major complications to be associated with long LOS among surviving infants.ConclusionPeriodic evaluation of the mortality and morbidity of preterm infants can help to understand the changes and trends of our neonatal care. Further study using the national dataset to provide more representative information is warranted