Affine hypersurfaces admitting a pointwise symmetry

An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. In this paper, we deal with positive definite affine hypersurfaces of dimension three. First we solve an algebraic problem. We determine the non-trivial stabilizers G of the pair (K,S) under the action of SO(3) on an Euclidean vectorspace (V,h) and find a representative (canonical form of K and S) of each (SO(3)/G)-orbit. Then, we classify hypersurfaces admitting a pointwise G-symmetry for all non-trivial stabilizers G (apart of Z_2). Besides well-known hypersurfaces we obtain e.g. warped product structures of two-dimensional affine spheres (resp. quadrics) and curves.Comment: 27 pages, AMSTeX, submitted to Results in Mat

How to Host a Data Competition: Statistical Advice for Design and Analysis of a Data Competition

Data competitions rely on real-time leaderboards to rank competitor entries and stimulate algorithm improvement. While such competitions have become quite popular and prevalent, particularly in supervised learning formats, their implementations by the host are highly variable. Without careful planning, a supervised learning competition is vulnerable to overfitting, where the winning solutions are so closely tuned to the particular set of provided data that they cannot generalize to the underlying problem of interest to the host. This paper outlines some important considerations for strategically designing relevant and informative data sets to maximize the learning outcome from hosting a competition based on our experience. It also describes a post-competition analysis that enables robust and efficient assessment of the strengths and weaknesses of solutions from different competitors, as well as greater understanding of the regions of the input space that are well-solved. The post-competition analysis, which complements the leaderboard, uses exploratory data analysis and generalized linear models (GLMs). The GLMs not only expand the range of results we can explore, they also provide more detailed analysis of individual sub-questions including similarities and differences between algorithms across different types of scenarios, universally easy or hard regions of the input space, and different learning objectives. When coupled with a strategically planned data generation approach, the methods provide richer and more informative summaries to enhance the interpretation of results beyond just the rankings on the leaderboard. The methods are illustrated with a recently completed competition to evaluate algorithms capable of detecting, identifying, and locating radioactive materials in an urban environment.Comment: 36 page

Can Zipf's law be adapted to normalize microarrays?

BACKGROUND: Normalization is the process of removing non-biological sources of variation between array experiments. Recent investigations of data in gene expression databases for varying organisms and tissues have shown that the majority of expressed genes exhibit a power-law distribution with an exponent close to -1 (i.e. obey Zipf's law). Based on the observation that our single channel and two channel microarray data sets also followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. A computationally simple and intuitively appealing technique based on this observation is presented. RESULTS: Using pairwise comparisons using MA plots (log ratio vs. log intensity), we compared this novel method to previously published normalization techniques, namely global normalization to the mean, the quantile method, and a variation on the loess normalization method designed specifically for boutique microarrays. Results indicated that, for single channel microarrays, the quantile method was superior with regard to eliminating intensity-dependent effects (banana curves), but Zipf's law normalization does minimize this effect by rotating the data distribution such that the maximal number of data points lie on the zero of the log ratio axis. For two channel boutique microarrays, the Zipf's law normalizations performed as well as, or better than existing techniques. CONCLUSION: Zipf's law normalization is a useful tool where the Quantile method cannot be applied, as is the case with microarrays containing functionally specific gene sets (boutique arrays)

A MULTI-SLICE MODEL OBSERVER FOR MEDICAL IMAGE QUALITY ASSESSMENT

International audienc

Use and outcomes of targeted therapies in early and metastatic HER2-positive breast cancer in Australia: Protocol detailing observations in a whole of population cohort

Background: The management of human epidermal growth factor receptor 2 (HER2)-positive breast cancer (BC) has changed dramatically with the introduction and widespread use of HER2-targeted therapies. However, there is relatively limited real-world information on patterns of use, effectiveness and safety in whole of population cohorts. The research programme detailed in this protocol will generate evidence on the prescribing patterns, safety monitoring and outcomes of patients with BC treated with HER2- targeted therapies in Australia. Methods/design: Our ongoing research programme will involve a series of retrospective cohort studies that include every patient accessing Commonwealth-funded HER2-targeted therapies for the treatment of early BC and advanced BC in Australia. At the time of writing, our cohorts consist of 11 406 patients with early BC and 5631 with advanced BC who accessed trastuzumab and lapatinib between 2001 and 2014. Pertuzumab and trastuzumab emtansine were publicly funded for metastatic BC in 2015, and future data updates will include patients accessing these medicines. We will use dispensing claims for cancer and other medicines, medical service claims and demographics data for each patient accessing HER2- targeted therapies to undertake this research. Ethics and dissemination: Ethics approval has been granted by the Population Health Service Research Ethics Committee and data access approval has been granted by the Australian Department of Human Services (DHS) External Review Evaluation Committee. Our findings will be reported in peer-reviewed publications, conference presentations and policy forums. By providing detailed information on the use and outcomes associated with HER2-targeted therapies in a national cohort treated in routine clinical care, our research programme will better inform clinicians and patients about the real-world use of these treatments and will assist third-party payers to better understand the use and economic costs of these treatments

Numerical Stability issues on Channelized Hotelling Observer under different background assumptions

International audienceThis paper addresses the numerical stability issue on the channelized Hotelling observer (CHO). The CHO is a well-known approach in the medical image quality assessment domain. Many researchers have found that the detection performance of the CHO does not increase with the number of channels, contrary to expectation. And to our knowledge, nobody in this domain has found the reason. We illustrated that this is due to the ill-posed problem of the scatter matrix and proposed a solution based on Tikhonov regularization. Although Tikhonov regularization has been used in many other domains, we show in this paper another important application of Tikhonov regularization. This is very important for researchers to continue the CHO (and other channelized model observer) investigation with a reliable detection performance calculation

Bringing high-grade arteriovenous malformations under control: clinical outcomes following multimodality treatment in children.

OBJECTIVE:Brain arteriovenous malformations (AVMs) consist of dysplastic blood vessels with direct arteriovenous shunts that can hemorrhage spontaneously. In children, a higher lifetime hemorrhage risk must be balanced with treatment-related morbidity. The authors describe a collaborative, multimodal strategy resulting in effective and safe treatment of pediatric AVMs. METHODS:A retrospective analysis of a prospectively maintained database was performed in children with treated and nontreated pediatric AVMs at the University of California, San Francisco, from 1998 to 2017. Inclusion criteria were age ≤ 18 years at time of diagnosis and an AVM confirmed by a catheter angiogram. RESULTS:The authors evaluated 189 pediatric patients with AVMs over the study period, including 119 ruptured (63%) and 70 unruptured (37%) AVMs. The mean age at diagnosis was 11.6 ± 4.3 years. With respect to Spetzler-Martin (SM) grade, there were 38 (20.1%) grade I, 40 (21.2%) grade II, 62 (32.8%) grade III, 40 (21.2%) grade IV, and 9 (4.8%) grade V lesions. Six patients were managed conservatively, and 183 patients underwent treatment, including 120 resections, 82 stereotactic radiosurgery (SRS), and 37 endovascular embolizations. Forty-four of 49 (89.8%) high-grade AVMs (SM grade IV or V) were treated. Multiple treatment modalities were used in 29.5% of low-grade and 27.3% of high-grade AVMs. Complete angiographic obliteration was obtained in 73.4% of low-grade lesions (SM grade I-III) and in 45.2% of high-grade lesions. A periprocedural stroke occurred in a single patient (0.5%), and there was 1 treatment-related death. The mean clinical follow-up for the cohort was 4.1 ± 4.6 years, and 96.6% and 84.3% of patients neurologically improved or remained unchanged in the ruptured and unruptured AVM groups following treatment, respectively. There were 16 bleeding events following initiation of AVM treatment (annual rate: 0.02 events per person-year). CONCLUSIONS:Coordinated multidisciplinary evaluation and individualized planning can result in safe and effective treatment of children with AVMs. In particular, it is possible to treat the majority of high-grade AVMs with an acceptable safety profile. Judicious use of multimodality therapy should be limited to appropriately selected patients after thorough team-based discussions to avoid additive morbidity. Future multicenter studies are required to better design predictive models to aid with patient selection for multimodal pediatric care, especially with high-grade AVMs