Obvious natural morphisms of sheaves are unique

We prove that a large class of natural transformations (consisting roughly of those constructed via composition from the "functorial" or "base change" transformations) between two functors of the form $\cdots f^* g_* \cdots$ actually has only one element, and thus that any diagram of such maps necessarily commutes. We identify the precise axioms defining what we call a "geofibered category" that ensure that such a coherence theorem exists. Our results apply to all the usual sheaf-theoretic contexts of algebraic geometry. The analogous result that would include any other of the six functors remains unknown.Comment: 52 pages. Final draft, version accepted to TA

On the homology of the space of knots

Consider the space of `long knots' in R^n, K_{n,1}. This is the space of knots as studied by V. Vassiliev. Based on previous work of the authors, it follows that the rational homology of K_{3,1} is free Gerstenhaber-Poisson algebra. A partial description of a basis is given here. In addition, the mod-p homology of this space is a `free, restricted Gerstenhaber-Poisson algebra'. Recursive application of this theorem allows us to deduce that there is p-torsion of all orders in the integral homology of K_{3,1}. This leads to some natural questions about the homotopy type of the space of long knots in R^n for n>3, as well as consequences for the space of smooth embeddings of S^1 in S^3.Comment: 36 pages, 6 figures. v3: small revisions before publicatio

Star Formation and Relaxation in 379 Nearby Galaxy Clusters

We investigate the relationship between star formation (SF) and level of relaxation in a sample of 379 galaxy clusters at z < 0.2. We use data from the Sloan Digital Sky Survey to measure cluster membership and level of relaxation, and to select star-forming galaxies based on mid-infrared emission detected with the Wide-Field Infrared Survey Explorer. For galaxies with absolute magnitudes M_r < -19.5, we find an inverse correlation between SF fraction and cluster relaxation: as a cluster becomes less relaxed, its SF fraction increases. Furthermore, in general, the subtracted SF fraction in all unrelaxed clusters (0.117 +/- 0.003) is higher than that in all relaxed clusters (0.097 +/- 0.005). We verify the validity of our SF calculation methods and membership criteria through analysis of previous work. Our results agree with previous findings that a weak correlation exists between cluster SF and dynamical state, possibly because unrelaxed clusters are less evolved relative to relaxed clusters.Comment: 6 pages, 4 figures, accepted for publication in Ap

Trauma Early Mortality Prediction Tool (TEMPT) for assessing 28-day mortality.

Background:Prior mortality prediction models have incorporated severity of anatomic injury quantified by Abbreviated Injury Severity Score (AIS). Using a prospective cohort, a new score independent of AIS was developed using clinical and laboratory markers present on emergency department presentation to predict 28-day mortality. Methods:All patients (n=1427) enrolled in an ongoing prospective cohort study were included. Demographic, laboratory, and clinical data were recorded on admission. True random number generator technique divided the cohort into derivation (n=707) and validation groups (n=720). Using Youden indices, threshold values were selected for each potential predictor in the derivation cohort. Logistic regression was used to identify independent predictors. Significant variables were equally weighted to create a new mortality prediction score, the Trauma Early Mortality Prediction Tool (TEMPT) score. Area under the curve (AUC) was tested in the validation group. Pairwise comparison of Trauma Injury Severity Score (TRISS), Revised Trauma Score, Glasgow Coma Scale, and Injury Severity Score were tested against the TEMPT score. Results:There was no difference between baseline characteristics between derivation and validation groups. In multiple logistic regression, a model with presence of traumatic brain injury, increased age, elevated systolic blood pressure, decreased base excess, prolonged partial thromboplastin time, increased international normalized ratio (INR), and decreased temperature accurately predicted mortality at 28 days (AUC 0.93, 95% CI 0.90 to 0.96, P&lt;0.001). In the validation cohort, this score, termed TEMPT, predicted 28-day mortality with an AUC 0.94 (95% CI 0.92 to 0.97). The TEMPT score preformed similarly to the revised TRISS score for severely injured patients and was highly predictive in those having mild to moderate injury. Discussion:TEMPT is a simple AIS-independent mortality prediction tool applicable very early following injury. TEMPT provides an AIS-independent score that could be used for early identification of those at risk of doing poorly following even minor injury. Level of evidence:Level II

GUI Design for Android Apps

GUI Design for Android Apps is the perfect—and concise—introduction for mobile app developers and designers. Through easy-to-follow tutorials, code samples, and case studies, the book shows the must-know principles for user-interface design for Android apps running on the Intel platform, including smartphones, tablets and embedded devices. This book is jointly developed for individual learning by Intel Software College and China Shanghai JiaoTong University, and is excerpted from Android Application Development for the Intel® Platform

Made in the Shade: Promoting Solar Over Water Projects

One rarely mentioned impact of global climate change is that higher temperatures are causing water in reservoirs and canals to evaporate at faster rates. This increased evaporation is placing additional pressure on already limited water supplies in some arid regions of the world. Finding ways to reduce evaporative water losses is thus becoming an increasingly important policy challenge in certain areas across the globe. Of course, generating more carbon-free energy also continues to be an important policy focus in the face of global warming and its threatening effects as well. One relatively new renewable energy strategy that can simultaneously help to address both challenges is to install solar panels over water. “Solar over water” projects are installations of photovoltaic solar panels on a water body’s surface or just above the surface of canals or other waterways. The panels generate carbon-free electricity, and the shade that they create also reduces evaporation rates so that more of a region’s precious water reaches end-users. Unfortunately, existing policies in many jurisdictions create unjustifiable obstacles to solar over water development. This Article uses the ongoing effort to install solar panels above portions of the Central Arizona Project’s canal system as a case study to highlight the significant potential benefits of solar over water development. The Article then identifies specific policy changes capable of better facilitating and promoting these innovative and uniquely valuable renewable energy projects