Precedence thinness in graphs

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of $k$ interval graphs, by splitting the graph in some special way. As a recent example of such an approach, the classes of $k$-thin and proper $k$-thin graphs have been introduced generalizing interval and proper interval graphs, respectively. The complexity of the recognition of each of these classes is still open, even for fixed $k \geq 2$. In this work, we introduce a subclass of $k$-thin graphs (resp. proper $k$-thin graphs), called precedence $k$-thin graphs (resp. precedence proper $k$-thin graphs). Concerning partitioned precedence $k$-thin graphs, we present a polynomial time recognition algorithm based on $PQ$-trees. With respect to partitioned precedence proper $k$-thin graphs, we prove that the related recognition problem is \NP-complete for an arbitrary $k$ and polynomial-time solvable when $k$ is fixed. Moreover, we present a characterization for these classes based on threshold graphs.Comment: 33 page

Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings

This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a `convex polyhedral pseudomanifold'. We prove that S has a polyhedral nonoverlapping unfolding into R^d, so the metric space S is obtained from a closed (usually nonconvex) polyhedral ball in R^d by identifying pairs of boundary faces isometrically. Our existence proof exploits geodesic flow away from a source point v in S, which is the exponential map to S from the tangent space at v. We characterize the `cut locus' (the closure of the set of points in S with more than one shortest path to v) as a polyhedral complex in terms of Voronoi diagrams on facets. Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v on S produces an algorithmic method for constructing Voronoi diagrams in each facet, and hence the unfolding of S. The algorithm, for which we provide pseudocode, solves the discrete geodesic problem. Its main construction generalizes the source unfolding for boundaries of 3-polytopes into R^2. We present conjectures concerning the number of shortest paths on the boundaries of convex polyhedra, and concerning continuous unfolding of convex polyhedra. We also comment on the intrinsic non-polynomial complexity of nonconvex polyhedral manifolds.Comment: 47 pages; 21 PostScript (.eps) figures, most in colo

Normative body image development: A longitudinal meta-analysis of mean-level change

This meta-analysis synthesized longitudinal data on mean-level change in body image, focusing on the constructs of body satisfaction and dissatisfaction, body esteem, perceived attractiveness, valuation, self-objectification, and body shame. We searched five databases and accessed unpublished data to identify studies that assessed body image at two or more time points over six months or longer. Analyses were based on data from 142 samples representing a total of 128,254 participants. The age associated with the midpoint of measurement intervals ranged from 6 to 54 years. Multilevel metaregression models examined standardized yearly mean change, and the potential moderators of body image construct, gender, birth cohort, attrition rate, age, and time lag. Boys and men showed fluctuations in overall body image with net-improvements between ages 10 and 24. Girls and women showed worsening body image between ages 10 and 16, but improvements between ages 16 and 24. Change was greatest between ages 10 and 14, and stabilized around age 24. We found no effect of construct, birth cohort, or attrition rate. Results suggest a need to revise understandings of normative body image development: sensitive periods may occur somewhat earlier than previously believed, and body image may show mean-level improvements during certain age ranges

Body image perceptions and symptoms of disturbed eating behavior among children and adolescents in Germany

Abstract Theoretical background Body image distortions such as perception biases are assumed to be precursors of eating disorders (ED). This study aims to investigate body image perceptions and symptoms of disturbed eating behavior among a sample of 11–17 year-old students in Germany. Methods A cross-sectional survey study was carried out among 1524 students of twelve secondary schools from all school types in North Rhine-Westphalia (Germany). A naturalistic photograph-rating consisting of photographs of young women’s bodies was used to examine children’s perceptions of female bodies (i.e., perceived average body size and perceived ideal body size of young women). Also, symptoms of disturbed eating behavior were examined. Results Compared to statistical data, children and adolescents underestimated the average body size of young women by more than two BMI-points (estimated average BMI = 20), with no differences between boys and girls. Also, girls and boys generally held a slim female thin-ideal (perceived ideal BMI = 19.5), which is nearly three BMI-points below the average body size in the young female population. Girls showed a slightly stronger female thin-ideal than boys. Among all subgroups, early-adolescent girls (13–14 years) displayed the strongest thin-ideal internalization. Nearly one-third of this group perceived a BMI below 18 as ideal female body size. Symptoms of disturbed eating behavior were common among youth and most frequent among adolescent girls (15–17 years). Girls who displayed a bias towards underestimation of female body size and girls who displayed an underweight female thin-ideal were more likely to report harmful dieting behaviors and psychological distress associated with eating, body, and weight. Conclusions This study found that 11–17 year-old girls and boys do not show accurate judgements regarding the average body size of young women. Instead, there is systematic and significant underestimation, indicating considerable perception biases, which may constitute a risk factor for the development and maintenance of ED. Symptoms of disturbed eating behavior were common, especially among girls, and associated with body-related perceptions. Future research will need to clarify the severity and course of these symptoms

Buyers, sellers and middlemen: variations in search theory

We study bilateral exchange, both direct trade and indirect trade that happens through chains of intermediaries or middlemen. We develop a model of this activity and present applications. This illustrates how, and how many, intermediaries get involved, and how the terms of trade are determined. Bargaining with intermediaries depends on how they bargain with downstream intermediaries, leading to interesting holdup problems. We discuss the roles of buyers and sellers in bilateral exchange, and how to interpret prices. We develop a particular bargaining solution and relate it to other solutions. We also illustrate how bubbles can emerge in the value of inventories.

REST: Integrating Term Rewriting with Program Verification (Extended Version)

We introduce REST, a novel term rewriting technique for theorem proving that uses online termination checking and can be integrated with existing program verifiers. REST enables flexible but terminating term rewriting for theorem proving by: (1) exploiting newly-introduced term orderings that are more permissive than standard rewrite simplification orderings; (2) dynamically and iteratively selecting orderings based on the path of rewrites taken so far; and (3) integrating external oracles that allow steps that cannot be justified with rewrite rules. Our REST approach is designed around an easily implementable core algorithm, parameterizable by choices of term orderings and their implementations; in this way our approach can be easily integrated into existing tools. We implemented REST as a Haskell library and incorporated it into Liquid Haskell's evaluation strategy, extending Liquid Haskell with rewriting rules. We evaluated our REST implementation by comparing it against both existing rewriting techniques and E-matching and by showing that it can be used to supplant manual lemma application in many existing Liquid Haskell proofs

A Cross-Cultural Study of Body Dissatisfaction among Mexican and Mexican-American Women

abstract: ABSTRACT While the cross-cultural literature on body dissatisfaction among Mexican and Mexican-American women has continued to grow, the traditional Latino female gender role of marianismo, sociocultural factors related to ethnic culture and mainstream/American culture ideal perceived discrepancies in body size, and one’s romantic relationship have not been explored with this population in relationship to body satisfaction. The current study included 227 female participants predominantly from a large southwestern university in the United States and a large university in northern Mexico. The study examined differences in marianismo and body satisfaction between 120 Mexican and 107 Mexican-American women, investigated the role of marianismo as a mediator between weight-related teasing and body satisfaction, and explored the relationship between marianismo, Partner Ideal Discrepancy, Ethnic Culture Ideal Discrepancy, Mainstream/American Culture Ideal Discrepancy, Perceived Weight-Related Criticism/Teasing, Relationship Support, Relationship Depth, and Relationship Conflict to overall body satisfaction. Results indicated Mexican-American women endorsed less overall body satisfaction than did their Mexican counterparts suggesting that Mexican American women may be more influenced by societal messages about thinness and beauty than are Mexican women. The findings also revealed a possible trend for marianismo as a mediator between weight-related criticism and body satisfaction. Marianismo and weight-related teasing were found to have a negative relationship with body satisfaction. Multiple regression analyses revealed that Partner Ideal and Mainstream/American Culture Ideal discrepancies accounted for significant variance in body satisfaction. Relationship Conflict accounted for a smaller but still significant amount of the variance in body satisfaction. Ethnic Culture Discrepancy, Relationship Support, and Relationship Depth were not significant predictors. These findings from this study suggest that both cultural variables and romantic relationship variables are related to the body image of Mexican American and Mexican women. These findings have important implications for the adaptation of current etiological models explaining body satisfaction among Mexican and Mexican-American women as well as highlighting the need to consider the role of both cultural and relationship variables in designing clinical interventions for Mexican American and Mexican women coping with body image concerns.Dissertation/ThesisDoctoral Dissertation Counseling Psychology 201

Logical Reasoning for Higher-Order Functions with Local State

We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higher-order datum and quantifiers over hidden references. We explore the logic's descriptive and reasoning power with non-trivial programming examples combining higher-order procedures and dynamically generated local state. Axioms for reachability and local invariant play a central role for reasoning about the examples.Comment: 68 page