The use of singular functions for the approximate conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly- connected domain onto a circular annulus. We consider the use of two closely related methods for determining approximations to f of the form fn (z) = z exp, ⎪⎩⎪⎨⎧⎭⎬⎫Σ−(z)uan1jjj where {uj} is a set of basis functions. The two methods are respectively a variational method, based on an extremum property of the function H(z) = f′(z)/f(z) - 1/z, and an orthononnalization method, based on approximating the function H by a finite Fourier series sum. The main purpose of the paper is to consider the use of the two methods for the mapping of domains having sharp corners, where corner singularities occur. We show, by means of numerical examples, that both methods are capable of producing approximations of high accuracy for the mapping of such "difficult" doubly-connected domains. The essential requirement for this is that the basis set {uj} contains singular functions that reflect the asymptotic behaviour of the function H in the neighbourhood of each "singular" corner

Numerical conformal mapping of exterior domains

The work of the present paper is closely related to the two numerical procedures described in [11], for determining approximations to the function which maps conformally a bounded simply-connected domain Ω1 , with boundary ∂Ω, onto the unit disc. Here, we consider the use of these procedures for the solution of the corresponding exterior problem, i.e. the problem of determining approximations to the mapping function which maps conformally the exterior domain Ω = compl(ΩI⋃∂Ω) onto the unit disc

Numerical techniques for conformal mapping onto a rectangle

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In particular, we study the following two classes of methods for the mapping of domains of the form . (i) Methods which approximate where f is an approximation to the conformal map of Q onto the unit disc, and S is a simple Schwarz-Christoffel transformation. (ii) Methods based on approximating the conformal map of a certain symmetric doubly-connected domain onto a circular annulus. Keywords: Conforma

An orthonormalization method for the approximate conformal mapping of multiply-connected domains

We consider the use of an orthonormalization method for constructing approximations to one of the standard conformal maps for multiply-connected domains. The method has been used successfully in [12], but only for the mapping of doubly-connected domains. Our purpose here is to consider its application to the mapping of domains whose connectivity is greater than two

Object Detection Through Exploration With A Foveated Visual Field

We present a foveated object detector (FOD) as a biologically-inspired alternative to the sliding window (SW) approach which is the dominant method of search in computer vision object detection. Similar to the human visual system, the FOD has higher resolution at the fovea and lower resolution at the visual periphery. Consequently, more computational resources are allocated at the fovea and relatively fewer at the periphery. The FOD processes the entire scene, uses retino-specific object detection classifiers to guide eye movements, aligns its fovea with regions of interest in the input image and integrates observations across multiple fixations. Our approach combines modern object detectors from computer vision with a recent model of peripheral pooling regions found at the V1 layer of the human visual system. We assessed various eye movement strategies on the PASCAL VOC 2007 dataset and show that the FOD performs on par with the SW detector while bringing significant computational cost savings.Comment: An extended version of this manuscript was published in PLOS Computational Biology (October 2017) at https://doi.org/10.1371/journal.pcbi.100574

High-intensity exercise to promote accelerated improvements in cardiorespiratory fitness (HI-PACE): study protocol for a randomized controlled trial

Background: African Americans have a disproportionate prevalence and incidence of type 2 diabetes compared with Caucasians. Recent evidence indicates that low cardiorespiratory fitness (CRF) level, an independent risk factor for type 2 diabetes, is also more prevalent in African Americans than Caucasians. Numerous studies in Caucasian populations suggest that vigorous exercise intensity may promote greater improvements in CRF and other type 2 diabetes risk factors (e.g., reduction of glucose/insulin levels, pulse wave velocity, and body fat) than moderate intensity. However, current evidence comparing health benefits of different aerobic exercise intensities on type 2 diabetes risk factors in African Americans is negligible. This is clinically important as African Americans have a greater risk for type 2 diabetes and are less likely to meet public health recommendations for physical activity than Caucasians. The purpose of the HI-PACE (High-Intensity exercise to Promote Accelerated improvements in CardiorEspiratory fitness) study is to evaluate whether high-intensity aerobic exercise elicits greater improvements in CRF, insulin action, and arterial stiffness than moderate-intensity exercise in African Americans. Methods/Design: A randomized controlled trial will be performed on overweight and obese (body mass index of 25–45 kg/m2) African Americans (35–65 years) (n = 60). Participants will be randomly assigned to moderate-intensity (MOD-INT) or high-intensity (HIGH-INT) aerobic exercise training or a non-exercise control group (CON) for 24 weeks. Supervised exercise will be performed at a heart rate associated with 45–55% and 70–80% of VO2 max in the MOD-INT and HIGH-INT groups, respectively, for an exercise dose of 600 metabolic equivalents of task (MET)-minutes per week (consistent with public health recommendations). The primary outcome is change in CRF. Secondary outcomes include change in insulin sensitivity (measured via an intravenous glucose tolerance test), skeletal muscle mitochondrial oxidative capacity (via near-infrared spectroscopy), skeletal muscle measurements (i.e., citrate synthase, COX IV, GLUT-4, CPT-1, and PGC1-α), arterial stiffness (via carotid-femoral pulse wave velocity), body fat, C-reactive protein, and psychological outcomes (quality of life/exercise enjoyment). Discussion: The anticipated results of the HI-PACE study will provide vital information on the health effects of high-intensity exercise in African Americans. This study will advance health disparity research and has the potential to influence future public health guidelines for physical activity

Randomized trial of a phone- and web-based weight loss program for women at elevated breast cancer risk: the HELP study

Excess weight and physical inactivity are modifiable risk factors for breast cancer. Behavioral intervention is particularly important among women with an elevated risk profile. This trial tested an intervention that trained women to use a self-monitoring website to increase activity and lose weight. Women with BMI≥27.5 kg/m(2) at elevated breast cancer risk were randomized to the intervention (N=71) or usual care (N=34). The intervention group received telephone-based coaching and used web-based self-monitoring tools. At 6 months, significant weight loss was observed in the intervention group (4.7% loss from starting weight; SD=4.7%) relative to usual care (0.4% gain; SD=3.0%) (p<.0001). By 12 months, the intervention group had lost 3.7% of weight (SD=5.4%), compared to 1.3% (SD=4.2) for usual care (p=.003). At 12 months, accelerometer-measured moderate-to-vigorous physical activity increased by 12 min/day (SD=24) compared to no change in usual care (p=.04. In summary, this web- and phone-based approach produced modest but significant improvements in weight and physical activity for women at elevated breast cancer risk