Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates

Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, an

Higher-quality tetrahedral mesh generation for domains with small angles by constrained Delaunay refinement

Algorithms for generating Delaunay tetrahedral meshes have difficulty with domains whose boundary polygons meet at small angles. The requirement that all tetrahedra be Delaunay often forces mesh generators to overrefine near small domain angles---that is, to produce too many tetrahedra, making them too small. We describe a provably good algorithm that generates meshes that are constrained Delaunay triangulations, rather than purely Delaunay. Given a piecewise linear domain free of small angles, our algorithm is guaranteed to construct a mesh in which every tetrahedron has a radius-edge ratio of $2 \sqrt{2 / 3} \doteq 1.63$ or better. This is a substantial improvement over the usual bound of $2$; it is obtained by relaxing the conditions in which boundary triangles are subdivided. Given a domain with small angles, our algorithm produces a mesh in which the quality guarantee is compromised only in specific places near small domain angles. We prove that most mesh edges have lengths proportional to the domain's minimum local feature size; the exceptions span small domain angles. Our algorithm tends to generate meshes with fewer tetrahedra than purely Delaunay methods because it uses the constrained Delaunay property, rather than vertex insertions, to enforce the conformity of the mesh to the domain boundaries. An implementation demonstrates that our algorithm does not overrefine near small domain angles

Restricted Constrained Delaunay Triangulations

We introduce the restricted constrained Delaunay triangulation (restricted CDT), a generalization of both the restricted Delaunay triangulation and the constrained Delaunay triangulation. The restricted CDT is a triangulation of a surface whose edges include a set of user-specified constraining segments. We define the restricted CDT to be the dual of a restricted Voronoi diagram defined on a surface that we have extended by topological surgery. We prove several properties of restricted CDTs, including sampling conditions under which the restricted CDT contains every constraining segment and is homeomorphic to the underlying surface

Minorities with lupus nephritis and medications: a study of facilitators to medication decision-making

Prioritized facilitators in AA2 (UAB, Birmingham, AA, 6 low SES, 1 high SES). This table provides a list of prioritized facilitators to help patients make decisions about treatment choices in African-American patients in nominal group 2. AA African-American, SES socioeconomic status, UAB University of Alabama at Birmingham (DOC 43 kb

Associations among parental feeding styles and children's food intake in families with limited incomes

<p>Abstract</p> <p>Background</p> <p>Although general parenting styles and restrictive parental feeding practices have been associated with children's weight status, few studies have examined the association between feeding styles and proximal outcomes such as children's food intake, especially in multi-ethnic families with limited incomes. The purpose of this study was to evaluate the association of parental feeding styles and young children's evening food intake in a multiethnic sample of families in Head Start.</p> <p>Methods</p> <p>Participants were 715 Head Start children and their parents from Texas and Alabama representing three ethnic groups: African-American (43%), Hispanic (29%), and White (28%). The Caregivers Feeding Styles Questionnaire (Hughes) was used to characterize authoritative, authoritarian (referent), indulgent or uninvolved feeding styles. Food intake in several food groups was calculated from 3 days of dietary recalls for the child for evening food intakes from 3 PM until bedtime.</p> <p>Results</p> <p>Compared to children of authoritarian parents, intakes of fruits, juice and vegetables were lowest among children of indulgent or uninvolved parents (1.77 ± 0.09 vs 1.45 ± 0.09 and 1.42 ± 0.11 cups) as were intakes of dairy foods (0.84 ± 0.05 vs 0.67 ± 0.05 and 0.63+0.06 cups), respectively.</p> <p>Conclusion</p> <p>Findings suggest that permissive parent feeding styles like indulgent or uninvolved relate negatively to children's intake of nutrient-rich foods fruit, 100% fruit juice, vegetables and dairy foods from 3 PM until bedtime.</p

Emotional Climate, Feeding Practices, and Feeding Styles: An Observational Analysis of the Dinner Meal in Head Start Families

BACKGROUND: A number of studies conducted with ethnically diverse, low-income samples have found that parents with indulgent feeding styles had children with a higher weight status. Indulgent parents are those who are responsive to their child\u27s emotional states but have problems setting appropriate boundaries with their child. Because the processes through which styles impact child weight are poorly understood, the aim of this study was to observe differences in the emotional climate created by parents (including affect, tone of voice, and gestures) and behavioral feeding practices among those reporting different feeding styles on the Caregiver\u27s Feeding Styles Questionnaire. A secondary aim was to examine differences on child weight status across the feeding styles. METHODS: Participants were 177 Head Start families from Houston, Texas (45% African-American; 55% Hispanic). Using an observational approach, the relationship between the observed emotional climate of the meal, behavioral feeding practices, and self-reported parent feeding styles were examined. Mean age of the children was 4.4 years (SD = 0.7) equally distributed across gender. Families were observed on 3 separate dinner occasions. Heights and weight were measured on the parents and children. RESULTS: Parents with self-reported indulgent feeding styles made fewer demands on their children to eat during dinner and showed lower levels of negative affect and intrusiveness. Surprisingly, these parents also showed higher levels of emotional detachment with their children during dinner. Hispanic boys with indulgent parents had significantly higher BMI z scores compared to Hispanic boys in the other three feeding style groups. No other differences were found on child weight status. CONCLUSIONS: Results suggest that the emotional climate created by indulgent parents during dinner and their lack of demands on their children to eat may play an important role in how young children become overweight. Numerous observed emotional climate and behavioral differences were found between the other self-reported feeding styles as well. Results suggest that parents\u27 self-reported feeding styles may be a proxy for the emotional climate of the dinner meal, which may in turn influence the child\u27s eating behaviors and weight status

What hispanic parents do to encourage and discourage 3-5 year old children to be active : a qualitative study using nominal group technique

Purpose : Hispanic preschoolers are less active than their non-Hispanic peers. As part of a feasibility study to assess environmental and parenting influences on preschooler physical activity (PA) (Ni&ntilde;os Activos), the aim of this study was to identify what parents do to encourage or discourage PA among Hispanic 3-5 year old children to inform the development of a new PA parenting practice instrument and future interventions to increase PA among Hispanic youth. Methods : Nominal Group Technique (NGT), a structured multi-step group procedure, was used to elicit and prioritize responses from 10 groups of Hispanic parents regarding what parents do to encourage (5 groups) or discourage (5 groups) preschool aged children to be active. Five groups consisted of parents with low education (less than high school) and 5 with high education (high school or greater) distributed between the two NGT questions. Results : Ten NGT groups (n&thinsp;=&thinsp;74, range 4-11/group) generated 20-46 and 42-69 responses/group for practices that encourage or discourage PA respectively. Eight to 18 responses/group were elected as the most likely to encourage or discourage PA. Parental engagement in child activities, modeling PA, and feeding the child well were identified as parenting practices that encourage child PA. Allowing TV and videogame use, psychological control, physical or emotional abuse, and lack of parental engagement emerged as parenting practices that discourage children from being active. There were few differences in the pattern of responses by education level. Conclusions : Parents identified ways they encourage and discourage 3-5 year-olds from PA, suggesting both are important targets for interventions. These will inform the development of a new PA parenting practice scale to be further evaluated. Further research should explore the role parents play in discouraging child PA, especially in using psychological control or submitting children to abuse, which were new findings in this study

Fixed Points of the Restricted Delaunay Triangulation Operator

The restricted Delaunay triangulation can be conceived as an operator that takes as input a k-manifold (typically smooth) embedded in R^d and a set of points sampled with sufficient density on that manifold, and produces as output a k-dimensional triangulation of the manifold, the input points serving as its vertices. What happens if we feed that triangulation back into the operator, replacing the original manifold, while retaining the same set of input points? If k = 2 and the sample points are sufficiently dense, we obtain another triangulation of the manifold. Iterating this process, we soon reach an iteration for which the input and output triangulations are the same. We call this triangulation a fixed point of the restricted Delaunay triangulation operator. With this observation, and a new test for distinguishing "critical points" near the manifold from those near its medial axis, we develop a provably good surface reconstruction algorithm for R^3 with unusually modest sampling requirements. We develop a similar algorithm for constructing a simplicial complex that models a 2-manifold embedded in a high-dimensional space R^d, also with modest sampling requirements (especially compared to algorithms that depend on sliver exudation). The latter algorithm builds a non-manifold representation similar to the flow complex, but made solely of Delaunay simplices. The algorithm avoids the curse of dimensionality: its running time is polynomial, not exponential, in d

Updating and Constructing Constrained Delaunay and Constrained Regular Triangulations by Flips

I discuss algorithms based on bistellar flips for inserting and deleting constraining (d − 1)-facets in d-dimensional constrained Delaunay triangulations (CDTs) and weighted CDTs, also known as constrained regular triangulations. The facet insertion algorithm is likely to outperform other known algorithms on most inputs. The facet deletion algorithm is the first proposed for d&gt; 2, short of recomputing the CDT from scratch. An incremental facet insertion algorithm that begins with an unconstrained Delaunay triangulation can construct the CDT of a ridge-protected piecewise linear log nv) time. Hence, in odd dimensions, CDT construction by incremental facet insertion is within a factor of log nv of worst-case optimal. Perhaps the most important feature of these algorithms is that they are relatively easy to implement. complex with nv vertices in O(n ⌊d/2⌋+1