Angle sums on polytopes and polytopal complexes

We will study the angle sums of polytopes, listed in the $\alpha$-vector, working to exploit the analogy between the f-vector of faces in each dimension and the alpha-vector of angle sums. The Gram and Perles relations on the $\alpha$-vector are analogous to the Euler and Dehn-Sommerville relations on the f-vector. First we describe the spaces spanned by the the alpha-vector and the $\alpha$-f-vectors of certain classes of polytopes. Families of polytopes are constructed whose angle sums span the spaces of polytopes defined by the Gram and Perles equations. This shows that the dimension of the affine span of the space of angle sums of simplices is floor[(d-1)/2], and that of the combined angle sums and face numbers of simplicial polytopes and general polytopes are d-1 and 2d-3, respectively. Next we consider angle sums of polytopal complexes. We define the angle characteristic on the alpha-vector in analogy to the Euler characteristic. We show that the changes in the two correspond and that, in the case of certain odd-dimensional polytopal complexes, the angle characteristic is half the Euler characteristic. Finally, we consider spherical and hyperbolic polytopes and polytopal complexes. Spherical and hyperbolic analogs of the Gram relation and a spherical analog of the Perles relation are known, and we show the hyperbolic analog of the Perles relations in a number of cases. Proving this relation for simplices of dimension greater than 3 would finish the proof of this result. Also, we show how constructions on spherical and hyperbolic polytopes lead to corresponding changes in the angle characteristic and Euler characteristic.Comment: Ph.D. Dissertatio

U.S. adolescent and adult women\u27s experiences accessing and using toilets in schools, workplaces, and public spaces: A multi-site focus group study to inform future research in bladder health

The World Health Organization recognizes access to clean and safe toilets as crucial for public health. This study explored U.S. adolescent and adult cisgender women\u27s lived experiences accessing toilets in schools, workplaces, and public spaces. As part of the Prevention of Lower Urinary Tract Symptoms (PLUS) Research Consortium, we conducted 44 focus groups with female participants (n = 360; ages 11-93). Focus groups were stratified by age (11-14, 15-17, 18-25, 26-44, 45-64, 65+) and conducted across 7 geographically diverse U.S. sites from July 2017-April 2018. Using a transdisciplinary approach, we conducted conventional qualitative coding informed by our PLUS conceptual framework and used content analysis processes to identify salient themes. Across settings, toilet access was restricted by gatekeepers (i.e., individuals who control access to toilets). In contrast, self-restricting toilet use (deciding not to use the toilet despite biologic need to urinate) was based on internalized norms to prioritize school and job responsibilities over urination. In public spaces, self-restricting use was largely in response to lack of cleanliness. Across the life course, participants perceived gender disparities in the ability to easily access public toilets. Further research is needed to determine if and how these factors impact bladder health across the life course

Adolescent awareness and use of electronic cigarettes: A review of emerging trends and findings

Adult electronic cigarette (e-cigarette) use is increasing globally, and early studies have suggested that similar trends may be observed among the adolescent population, albeit at lower levels. The current literature review presents data collected since 2014 from 21 cross-sectional studies and one cohort study that were all published in English. In particular, it focuses on awareness, ever use, past 30-day use, and regular use of e-cigarettes. The article suggests that adolescents are nearing complete awareness of e-cigarettes. Furthermore, in relation to ever use and past 30-day use, higher prevalence rates continue to be reported across time, especially in the United States. Nonetheless, reported regular use of e-cigarettes remains much lower than past 30-day use, although conclusions are limited due to inconsistencies with measurement and consequent lack of cross-cultural applicability. The majority of studies do not report whether adolescents use non-nicotine e-cigarettes. There is a current absence of longitudinal studies that explore any association between e-cigarettes and tobacco use and little qualitative data that may illuminate how and why adolescents use e-cigarettes. Through addressing these methodological limitations, future research will be able to inform health care and policy more effectively

Prevention of Lower Urinary Tract Symptoms Research Consortium focus group Study of Habits, Attitudes, Realities, and Experiences of Bladder health

AimThe study purpose is to explore adolescent and adult women’s experiences, perceptions, beliefs, knowledge and behaviours related to bladder health across the life course using a socioecological perspective. Lower urinary tract symptoms affect between 20-40% of young adult to middle-aged women, with symptoms increasing in incidence and severity with aging. There is limited evidence to address bladder health promotion and prevention of dysfunction. This first study of the Prevention of Lower Urinary Tract Symptoms (PLUS) Research Consortium is designed to address gaps in existing qualitative research in this area.DesignThis focus group study will be implemented across seven geographically diverse United States research centres using a semi-structured focus group guide informed by a conceptual framework based on the socioecological model.MethodsThe study was approved in July 2017. A total of 44 focus groups composed of 6-8 participants representing six different age categories (ranging from 11 to over 65 years) will be completed. We aim to recruit participants with diverse demographic and personal characteristics including race, ethnicity, education, socioeconomic status, urban/rural residence, physical/health conditions, and urinary symptom experience. Six of the focus groups will be conducted in Spanish and translated into English. Focus group transcripts will undergo content analysis and data interpretation to identify and classify themes and articulate emerging themes.DiscussionThis foundational qualitative study seeks to develop an evidence base to inform future research on bladder health promotion in adolescent and adult women.ImpactThis study has the potential to provide new insights and understanding into adolescent and adult women’s lived experience of bladder health, the experience of lower urinary symptoms and knowledge and beliefs across the life course.ç ®ç æ ¬ç  ç©¶ç ç ®ç æ ¯ä» ç¤¾ä¼ ç æ å­¦ç è§ åº¦,æ ¢è®¨é å° å¹´å æ å¹´å¥³æ §å ¨äººç è¿ ç¨ ä¸­ä¸ è è ±å ¥åº·ç ¸å ³ç ç» éª ã è§ å¿µã 信念ã ç ¥è¯ å è¡ ä¸ºã ä¸ å°¿è·¯ç ç ¶å½±å 20-40%ç 中é å¹´å¥³æ §,é ç å¹´é¾ ç å¢ é ¿,ç ç ¶ç å ç ç å 严é ç¨ åº¦é ½å ¨å¢ é ¿ã å ³äº ä¿ è¿ è è ±å ¥åº·å é¢ é ²å è ½é ç¢ ç è¯ æ ®æ é ã æ ¬æ¬¡é¢ é ²ä¸ å°¿è·¯ç ç ¶(PLUS)ç  ç©¶è ç ç ç  ç©¶æ ¯é¦ ä¸ªå ³äº æ­¤æ ¹é ¢ç ç  ç©¶,æ ¨å ¨è§£å ³ç °æ ç å® æ §ç  ç©¶å ¨è¿ æ ¹é ¢ç å·®è· ã è®¾è®¡è¯¥é¡¹ç ¦ç ¹å° ç» ç  ç©¶å° å ¨ä¸ ä¸ªä¸ å ä½ ç½®ç ç¾ å ½ç  ç©¶ä¸­å¿ è¿ è¡ ,ä»¥å ºäº ç¤¾ä¼ ç æ 模å æ¦ å¿µæ¡ æ ¶ç å ç» æ å ç ç ¦ç ¹å° ç» æ å 为æ 导ã æ ¹æ³ è¯¥ç  ç©¶äº 2017å¹´7æ è ·å¾ æ ¹å ã ç ±6-8å 代表6ä¸ªä¸ å å¹´é¾ ç±»å «(ä» 11å² å °65å² ä»¥ä¸ )ç å ä¸ è ç» æ å ±44ä¸ªç ¦ç ¹å° ç» ã æ 们计å æ å ä¸ å äººå £å ä¸ªäººç ¹å¾ ç å ä¸ è ,ä¾ å¦ ç§ æ ã ç§ æ æ¸ æº ã æ è ²ç» å ã ç¤¾ä¼ ç» æµ å °ä½ ã å ä¹¡å± æ° ã èº«ä½ /å ¥åº·ç ¶å µå æ³ å°¿ç³»ç» ç ç ¶ç» å ã å ­ä¸ªç ¦ç ¹å° ç» ç ç  ç©¶å° ä»¥è¥¿ç ­ç è¯­è¿ è¡ ,å¹¶ç¿»è¯ æ è ±è¯­ã ç ¦ç ¹å° ç» ç èª æ ¬å° è¢«ç ¨äº å 容å æ å æ °æ ®è§£é ,ä»¥ç¡®å® å å ç±»ä¸»é¢ ,并é æ æ °å ºç °ç ä¸»é¢ ã è®¨è®ºè¿ é¡¹å ºç¡ æ §ç å® æ §ç  ç©¶æ ¨å ¨ä¸ºæ é« æ ªæ ¥é å° å¹´å æ å¹´å¦ å¥³ç è è ±å ¥åº·ç ç  ç©¶æ ä¾ è¯ æ ®å ºç¡ ã å½±å è¿ é¡¹ç  ç©¶æ å ¯è ½æ ä¾ å ³äº é å° å¹´å æ å¹´å¦ å¥³ç è è ±å ¥åº·ç ç æ´»ç» éª ,ç» éª ç ä¸ å°¿è·¯ç ç ¶å ç ¥è¯ å ç æ³ ç 人ç è¿ ç¨ ä¸­æ °ç è§ è§£å ç 解ãPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151981/1/jan14148_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151981/2/jan14148.pd

Review of the literature on negative health risks based interventions to guide anabolic steroid misuse prevention

Background. Despite the Internet and the WorldWideWeb providing ready access to information on the risks and health consequences of AS misuse for all ages, AS use remains a public health concern. The aim of this narrative review is to examine the ability of negative health consequences information (NHCI) to prevent adolescent AS misuse in the era of the Internet information revolution. Methods. A search of the literature published between January 2000 and March 2014 was conducted to identify studies that examined the effect of NHCI on AS use and other healthrelated social cognitive constructs and behavior in adolescent samples. Results. No empirical study was found that specifically investigated the isolated effect of NHCI on AS use. Other health-related intervention studies - involving adolescents - showed that the severity of the consequences tied to social disapproval can be more effective than the severity tied to health consequences. Relevance of NHCI can operate as a moderator or a mediator of the relationship between NHCI and social cognitive constructs and behavior change. Pre-existing knowledge about negative health consequences functions as a mediator of the relationship between NHCI and social cognitive constructs and outcomes. Conclusion. The best way to understand the effect of NHCI on social cognitive constructs and behavior is to consider it in a larger nomological network that includes perceived severity, vulnerability, relevance and pre-existing knowledge. The review highlights gaps in the literature and suggests directions for future research. Implications for prevention programs are discussed