Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Principal component analysis of dietary and lifestyle patterns in relation to risk of subtypes of esophageal and gastric cancer

Purpose To carry out pattern analyses of dietary and lifestyle factors in relation to risk of esophageal and gastric cancers. Methods We evaluated risk factors for esophageal adenocarcinoma (EA), esophageal squamous cell carcinoma (ESCC), gastric cardia adenocarcinoma (GCA), and other gastric cancers (OGA) using data from a population-based case-control study conducted in Connecticut, New Jersey, and western Washington state. Dietary/lifestyle patterns were created using principal component analysis (PCA). The impact of the resultant scores on cancer risk was estimated through logistic regression. Results PCA identified six patterns: meat/nitrite, fruit/vegetable, smoking/alcohol, legume/meat alternate, GERD/BMI, and fish/vitamin C. Risk of each cancer under study increased with rising meat/nitrite score. The risk of EA increased with increasing GERD/BMI score, and the risk of ESCC rose with increasing smoking/alcohol score and decreasing gastroesophageal reflux disease (GERD)/body mass index (BMI) score. Fruit/vegetable scores were inversely associated with EA, ESCC, and GCA. Conclusions PCA may provide a useful approach for summarizing extensive dietary/lifestyle data into fewer interpretable combinations that discriminate between cancer cases and controls. The analyses suggest that meat/nitrite intake is associated with an elevated risk of each cancer under study, whereas fruit/vegetable intake reduces the risk of EA, ESCC, and GCA. GERD/obesity was confirmed as risk factors for EA and smoking/alcohol as risk factors for ESCC

Food group intake and risk of subtypes of esophageal and gastric cancer

Incidence rates for adenocarcinomas of the esophagus and gastric cardia have been increasing rapidly, while rates for non‐cardia gastric adenocarcinoma and esophageal squamous cell carcinoma have declined. We examined food group intake as a risk factor for subtypes of esophageal and gastric cancers in a multicenter, population‐based case–control study in Connecticut, New Jersey and western Washington state. Associations between food groups and risk were estimated using adjusted odds ratios (OR), based on increasing intake of one serving per day. Total vegetable intake was associated with decreased risk of esophageal adenocarcinoma (OR = 0.85, 95% CI = 0.75, 0.96). Conversely, total meat intake was associated with increased risk of esophageal adenocarcinoma (OR = 1.43, 95% CI = 1.11, 1.83), gastric cardia adenocarcinoma (OR = 1.37, 95% CI = 1.08, 1.73) and noncardia gastric adenocarcinoma (OR = 1.39, 95% CI = 1.12, 1.71), with red meat most strongly associated with esophageal adenocarcinoma risk (OR = 2.49, 95% CI = 1.39, 4.46). Poultry was most strongly associated with gastric cardia adenocarcinoma (OR = 1.89, 95% CI = 1.15, 3.11) and noncardia gastric adenocarcinoma (OR = 1.90, 95% CI = 1.19, 3.03). High‐fat dairy was associated with increased risk of both esophageal and gastric cardia adenocarcinoma. Higher intake of meats, particularly red meats, and lower intake of vegetables were associated with an increased risk of esophageal adenocarcinoma, while higher intake of meats, particularly poultry, and high‐fat dairy was associated with increased risk of gastric cardia adenocarcinoma

Food group intake and risk of subtypes of esophageal and gastric cancer

Incidence rates for adenocarcinomas of the esophagus and gastric cardia have been increasing rapidly, while rates for non‐cardia gastric adenocarcinoma and esophageal squamous cell carcinoma have declined. We examined food group intake as a risk factor for subtypes of esophageal and gastric cancers in a multicenter, population‐based case–control study in Connecticut, New Jersey and western Washington state. Associations between food groups and risk were estimated using adjusted odds ratios (OR), based on increasing intake of one serving per day. Total vegetable intake was associated with decreased risk of esophageal adenocarcinoma (OR = 0.85, 95% CI = 0.75, 0.96). Conversely, total meat intake was associated with increased risk of esophageal adenocarcinoma (OR = 1.43, 95% CI = 1.11, 1.83), gastric cardia adenocarcinoma (OR = 1.37, 95% CI = 1.08, 1.73) and noncardia gastric adenocarcinoma (OR = 1.39, 95% CI = 1.12, 1.71), with red meat most strongly associated with esophageal adenocarcinoma risk (OR = 2.49, 95% CI = 1.39, 4.46). Poultry was most strongly associated with gastric cardia adenocarcinoma (OR = 1.89, 95% CI = 1.15, 3.11) and noncardia gastric adenocarcinoma (OR = 1.90, 95% CI = 1.19, 3.03). High‐fat dairy was associated with increased risk of both esophageal and gastric cardia adenocarcinoma. Higher intake of meats, particularly red meats, and lower intake of vegetables were associated with an increased risk of esophageal adenocarcinoma, while higher intake of meats, particularly poultry, and high‐fat dairy was associated with increased risk of gastric cardia adenocarcinoma

The Treasured Hunt: Collecting Medieval and Renaissance Manuscripts, Past, Present, and Future

Welcome and Opening Remarks: E. Ann Matter, University of Pennsylvania, and Lynn Ransom, Free Library of Philadelphia Session 1. Beginnings: Collecting in the Middle Ages and Renaissance Session Chair: Emily Steiner, Department of English, University of Pennsylvania Claire Richter Sherman, Center for Advanced Study in the Visual Arts at the National Gallery of Art, The Manuscript Collection of King Charles V of France: The Personal and the Political David Rundle, History Faculty and Corpus Christi College, Oxford University, The Butcher of England and the Renaissance Arts of Book-Collecting Session 2: Civic Service: The Legacies of Philadelphia-Area Collectors Chair: Peter Stallybrass, Department of English, University of Pennsylvania James Tanis, Director of Libraries and Professor of History Emeritus, Bryn Mawr College, Migrating Manuscripts Derick Dreher, Director, The Rosenbach Museum & Library, Of Private Collectors and Public Libraries: Dr. A. S. W. Rosenbach and John Frederick Lewis Session 3: Keynote address Welcome: H. Carton Rogers, Vice Provost & Director of Libraries, University of Pennsylvania Chair: Robert Maxwell, Department of the History of Art, University of Pennsylvania Christopher de Hamel, Gaylord Donnelley Fellow Librarian, Corpus Christi College, Cambridge University, The Manuscript Collection of C. L. Ricketts (1859-1941) Session 4: The Hunters and the Hunted: A Roundtable Discussion with Private and Institutional Collectors Chair: David Wallace, Department of English, University of Pennsylvania Moderator: Richard Linenthal, Bernard Quaritch Ltd. Panelists: Lawrence J. Schoenberg, Private Collector Gifford Combs, Private Collector Toshiyuki Takamiya, Private Collector, Keio University Consuelo Dutschke, Curator of Medieval and Renaissance Manuscripts, Columbia University William Noel, Curator of Manuscripts and Rare Books, The Walters Art Museu

Principal Component Analysis of Dietary and Lifestyle Patterns in Relation to Risk of Subtypes of Esophageal and Gastric Cancer

To perform pattern analyses of dietary and lifestyle factors in relation to risk of esophageal and gastric cancers

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Enterocyte Shedding and Epithelial Lining Repair Following Ischemia of the Human Small Intestine Attenuate Inflammation

BACKGROUND: Recently, we observed that small-intestinal ischemia and reperfusion was found to entail a rapid loss of apoptotic and necrotic cells. This study was conducted to investigate whether the observed shedding of ischemically damaged epithelial cells affects IR induced inflammation in the human small gut. METHODS AND FINDINGS: Using a newly developed IR model of the human small intestine, the inflammatory response was studied on cellular, protein and mRNA level. Thirty patients were consecutively included. Part of the jejunum was subjected to 30 minutes of ischemia and variable reperfusion periods (mean reperfusion time 120 (+/-11) minutes). Ethical approval and informed consent were obtained. Increased plasma intestinal fatty acid binding protein (I-FABP) levels indicated loss in epithelial cell integrity in response to ischemia and reperfusion (p<0.001 vs healthy). HIF-1alpha gene expression doubled (p = 0.02) and C3 gene expression increased 4-fold (p = 0.01) over the course of IR. Gut barrier failure, assessed as LPS concentration in small bowel venous effluent blood, was not observed (p = 0.18). Additionally, mRNA expression of HO-1, IL-6, IL-8 did not alter. No increased expression of endothelial adhesion molecules, TNFalpha release, increased numbers of inflammatory cells (p = 0.71) or complement activation, assessed as activated C3 (p = 0.14), were detected in the reperfused tissue. CONCLUSIONS: In the human small intestine, thirty minutes of ischemia followed by up to 4 hours of reperfusion, does not seem to lead to an explicit inflammatory response. This may be explained by a unique mechanism of shedding of damaged enterocytes, reported for the first time by our group

Measuring Five Dimensions of Religiosity Across Adolescence

This paper theorizes and tests a latent variable model of adolescent religiosity in which five dimensions of religiosity are interrelated: religious beliefs, religious exclusivity, external religiosity, private practice, and religious salience. Research often theorizes overlapping and independent influences of single items or dimensions of religiosity on outcomes such as adolescent sexual behavior, but rarely operationalizes the dimensions in a measurement model accounting for their associations with each other and across time. We use longitudinal structural equation modeling (SEM) with latent variables to analyze data from two waves of the National Study of Youth and Religion. We test our hypothesized measurement model as compared to four alternate measurement models and find that our proposed model maintains superior fit. We then discuss the associations between the five dimensions of religiosity we measure and how these change over time. Our findings suggest how future research might better operationalize multiple dimensions of religiosity in studies of the influence of religion in adolescence