On the estimation of a support curve of indeterminate sharpness

We propose nonparametric methods for estimating the support curve of a bivariate density, when the density decreases at a rate which might vary along the curve. Attention is focussed on cases where the rate of decrease is relatively fast this, being the most difficult setting. It demands the use of a relatively large number of bivariate order statistics. By way of comparison, support curve estimation in the context of slow rates of decrease of the density may be addressed using methods that use only a relatively small number of order statistics at the extremities of the point cloud. In this paper we suggest a new type of estimator, based on projecting onto an axis those data values lying within a thin rectangular strip. Adaptive univariate methods are then applied to the problem of estimating an endpoint of the distribution on the axis. The new method is shown to have theoretically optimal performance in a range of settings. Its numerical properties are explored in a simulation study

Morning concurrent track 2: Creation and correction of myths about global warming

MORNING CONCURRENT TRACK 2: CREATION AND CORRECTION OF MYTHS ABOUT GLOBAL WARMING Moderator Robert Futrell Student Union Room 211 Matthew Lachniet – Global Warming Misconceptions and Myths: Barriers and Opportunities for Communicating Climate Change Science to a Non-scientific Audience Abstract: Opinions on an anthropogenic influence in global warming abound. Within the non-scientific public, the strength of one’s opinion commonly seems to be in inverse proportion to their knowledge of climate science. One reason for this disconnect between reality and opinion is the persistence of many climate change myths in popular knowledge of global warming. These myths are regularly propagated in popular media and internet blogs, some of which appear to be driven more by ideology than a quest for truth about Nature. In the past, the desire to provide balance in media coverage of global warming at the expense of scientific accuracy has handed the soapbox to many with minority viewpoints that are not supported by all of the available scientific evidence. However, many of these myths contain an element of but have been misunderstood (at best) by the general public and misappropriated (at worst) by interest groups on all sides of ideological spectrum. This presentation will outline some of the common myths on global warming and how they can be used as opportunities in a teaching environment to enhance students’ understanding of global warming and climate science. Gale Sinatra, CarolAnne Kardash, Gita Taasoobshirazi, Doug Lombardi – College Students’ Understanding of and Reactions to Global Warming Abstract: The principles underlying global climate change involve a complex interconnection between many scientific concepts that are difficult for students to understand. This study examined whether persuasive texts would impact readers’ willingness to take mitigative action to reduce the impacts of human-induced climate change. College students participating in the study were randomly assigned to read a persuasive text about global warming or the same text accompanied by a persuasive image. Both groups showed statistically significant increases in their knowledge about global warming and their willingness to take action to reduce its effects. This research demonstrates that persuasive text can produce not only change in students’ thinking about a controversial topic like global climate change, but may also promote a willingness to take action. This is significant because in the case of this topic, a change in students’ knowledge may not be a sufficient criterion for successful learning. It may be as important to promote willingness in future generations to take efforts to reduce their individual impact on the environment. E. Michael Nussbaum – Global Warming and Middle School: An Argument-Based Intervention Abstract: As part of a semester-long intervention to teach middle school students to critically evaluate arguments, 60 sixth- and seventh- graders from a Las Vegas charter school in the Clark County School District discussed issues surrounding global climate change. The presentation will first describe the argument-based intervention used with the students and its effect on attitude change. Most students became accepting of the existence of global climate change and the need to develop alternative modes of transportation. The intervention also provided students with some opportunity to learn about science, political, geography, and economics in an integrated way, as well as an opportunity to develop critical and creative thinking. Second, the overall findings of the research study will be presented, concluding that the skill of “weighing values” may be a productive one to teach to middle school students. Third, some misconceptions that students retained will be described so that future instructional efforts may address them. Doug Lombardi – Students’ Perceptions about the Plausibility of Human Induced Climate Change Abstract: Students can develop robust misconceptions when encountering complex phenomena such as global climate change. For example, students cite short0term and local weather events as evidence to support or refute long‐term changes, and thereby display a fundamental misunderstanding about the distinctions between weather and climate. This confusion may impact perceptions of plausibility about scientific statements that implicate humans in worldwide increases in global temperatures and widespread melting of snow and ice. Additionally, the confusion between weather and climate may be related to a fundamental lack of understanding about deep time, a concept that spans several scientific content areas. This presentation will describe an ongoing study involving undergraduate students enrolled in introductory geoscience and geography courses. Currently, students are completing three surveys examining the relationships between student understanding of deep time and their confusion about the distinctions between weather and climate, as well as how these levels of understanding influence perceptions about the plausibility of human‐induced global climate change. This presentation will highlight preliminary results

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

Evaluation of polygenic risk scores for breast and ovarian cancer risk prediction in BRCA1 and BRCA2 mutation carriers

Background: Genome-wide association studies (GWAS) have identified 94 common single-nucleotide polymorphisms (SNPs) associated with breast cancer (BC) risk and 18 associated with ovarian cancer (OC) risk. Several of these are also associated with risk of BC or OC for women who carry a pathogenic mutation in the high-risk BC and OC genes BRCA1 or BRCA2. The combined effects of these variants on BC or OC risk for BRCA1 and BRCA2 mutation carriers have not yet been assessed while their clinical management could benefit from improved personalized risk estimates. Methods: We constructed polygenic risk scores (PRS) using BC and OC susceptibility SNPs identified through population-based GWAS: for BC (overall, estrogen receptor [ER]-positive, and ER-negative) and for OC. Using data from 15 252 female BRCA1 and 8211 BRCA2 carriers, the association of each PRS with BC or OC risk was evaluated using a weighted cohort approach, with time to diagnosis as the outcome and estimation of the hazard ratios (HRs) per standard deviation increase in the PRS. Results: The PRS for ER-negative BC displayed the strongest association with BC risk in BRCA1 carriers (HR = 1.27, 95% confidence interval [CI] = 1.23 to 1.31, P = 8.2 x 10(53)). In BRCA2 carriers, the strongest association with BC risk was seen for the overall BC PRS (HR = 1.22, 95% CI = 1.17 to 1.28, P = 7.2 x 10(-20)). The OC PRS was strongly associated with OC risk for both BRCA1 and BRCA2 carriers. These translate to differences in absolute risks (more than 10% in each case) between the top and bottom deciles of the PRS distribution; for example, the OC risk was 6% by age 80 years for BRCA2 carriers at the 10th percentile of the OC PRS compared with 19% risk for those at the 90th percentile of PRS. Conclusions: BC and OC PRS are predictive of cancer risk in BRCA1 and BRCA2 carriers. Incorporation of the PRS into risk prediction models has promise to better inform decisions on cancer risk management

BRCA2 polymorphic stop codon K3326X and the risk of breast, prostate, and ovarian cancers

Background: The K3326X variant in BRCA2 (BRCA2*c.9976A>T; p.Lys3326*; rs11571833) has been found to be associated with small increased risks of breast cancer. However, it is not clear to what extent linkage disequilibrium with fully pathogenic mutations might account for this association. There is scant information about the effect of K3326X in other hormone-related cancers. Methods: Using weighted logistic regression, we analyzed data from the large iCOGS study including 76 637 cancer case patients and 83 796 control patients to estimate odds ratios (ORw) and 95% confidence intervals (CIs) for K3326X variant carriers in relation to breast, ovarian, and prostate cancer risks, with weights defined as probability of not having a pathogenic BRCA2 variant. Using Cox proportional hazards modeling, we also examined the associations of K3326X with breast and ovarian cancer risks among 7183 BRCA1 variant carriers. All statistical tests were two-sided. Results: The K3326X variant was associated with breast (ORw = 1.28, 95% CI = 1.17 to 1.40, P = 5.9x10- 6) and invasive ovarian cancer (ORw = 1.26, 95% CI = 1.10 to 1.43, P = 3.8x10-3). These associations were stronger for serous ovarian cancer and for estrogen receptor–negative breast cancer (ORw = 1.46, 95% CI = 1.2 to 1.70, P = 3.4x10-5 and ORw = 1.50, 95% CI = 1.28 to 1.76, P = 4.1x10-5, respectively). For BRCA1 mutation carriers, there was a statistically significant inverse association of the K3326X variant with risk of ovarian cancer (HR = 0.43, 95% CI = 0.22 to 0.84, P = .013) but no association with breast cancer. No association with prostate cancer was observed. Conclusions: Our study provides evidence that the K3326X variant is associated with risk of developing breast and ovarian cancers independent of other pathogenic variants in BRCA2. Further studies are needed to determine the biological mechanism of action responsible for these associations

α-Synuclein in human cerebrospinal fluid is principally derived from neurons of the central nervous system

The source of Parkinson disease-linked α-synuclein (aSyn) in human cerebrospinal fluid (CSF) remains unknown. We decided to measure the concentration of aSyn and its gradient in human CSF specimens and compared it with serum to explore its origin. We correlated aSyn concentrations in CSF versus serum (QaSyn) to the albumin quotient (Qalbumin) to evaluate its relation to blood–CSF barrier function. We also compared aSyn with several other CSF constituents of either central or peripheral sources (or both) including albumin, neuron-specific enolase, β-trace protein and total protein content. Finally, we examined whether aSyn is present within the structures of the choroid plexus (CP). We observed that QaSyn did not rise or fall with Qalbumin values, a relative measure of blood–CSF barrier integrity. In our CSF gradient analyses, aSyn levels decreased slightly from rostral to caudal fractions, in parallel to the recorded changes for neuron-specific enolase; the opposite trend was recorded for total protein, albumin and β-trace protein. The latter showed higher concentrations in caudal CSF fractions due to the diffusion-mediated transfer of proteins from blood and leptomeninges into CSF in the lower regions of the spine. In postmortem sections of human brain, we detected highly variable aSyn reactivity within the epithelial cell layer of CP in patients diagnosed with a range of neurological diseases; however, in sections of mice that express only human SNCA alleles (and in those without any Snca gene expression), we detected no aSyn signal in the epithelial cells of the CP. We conclude from these complementary results that despite its higher levels in peripheral blood products, neurons of the brain and spinal cord represent the principal source of aSyn in human CSF