SPECTRAL SPARSIFICATION IN THE SEMI-STREAMING SETTING

Abstract. Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than m edges. The strongest commonly-used notion of sparsification is spectral sparsification; H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate one another well. This notion is strictly stronger than the earlier concept of combinatorial sparsification. In this paper, we consider a semi-streaming setting, where we have only Õ(n) storage space, and we thus cannot keep all of G. In this case, maintaining a sparsifier instead gives us a useful approximation to G, allowing us to answer certain questions about the original graph without storing all of it. In this paper, we introduce an algorithm for constructing a spectral sparsifier of G with O(n log n/ɛ 2) edges (where ɛ is a parameter measuring the quality of the sparsifier), taking Õ(m) time and requiring only one pass over G. In addition, our algorithm has the property that it maintains at all times a valid sparsifier for the subgraph of G that we have received. Our algorithm is natural and conceptually simple. As we read edges of G, we add them to the sparsifier H. Whenever H gets too big, we re-sparsify it in Õ(n) time. Adding edges to a graph changes the structure of its sparsifier’s restriction to the already existing edges. It would thus seem that the above procedure would cause errors to compound each time that we re-sparsify, and that we should need to either retain significantly more information or reexamine previously discarded edges in order to construct the new sparsifier. However, we show how to use the information contained in H to perform this re-sparsification using only the edges retained by earlier steps in nearly linear time. 1

Medicinas alternativas e complementares: Uma metassíntese

O aumento do uso de Medicinas Alternativas e Complementares (MAC) motivou o crescimento do número de estudos qualitativos sobre o tema, justificando a realização de sínteses sobre esse material. Este artigo apresenta uma revisão sistemática de pesquisas qualitativas sobre MAC publicadas em periódicos internacionais. Esta revisão se orientou pela metodologia dos metaestudos. Foi realizada busca em revistas do Portal Periódicos da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior e foram selecionados 32 artigos para análise. Os estudos revisados apresentam questões que têm como foco: o paciente, suas experiências terapêuticas e seus contextos sociais e culturais; o profissional, as relações profissionais e o processo de profissionalização das MAC; a MAC e sua relação com a biomedicina. Conclui-se que as pesquisas qualitativas sobre as MAC ensejam um olhar exploratório sobre o tema, procurando identificar as experiências de pacientes e profissionais com essas terapêuticas, assim como buscam discutir as conseqüências desse uso para a Medicina Convencional ou biomedicina.<br>The growing use of Complementary and Alternative Medicines (CAM) has led to an increase in the number of qualitative studies on the subject, thus justifying a meta-synthesis of the resulting material. The current article presents a systematic review of qualitative studies on CAM published in international journals. The review was conducted according to the meta-synthesis methodology. A search was performed in journals through the Periodicals Periodical of CAPES, the National Agency for the Evaluation of Graduate Studies, and 32 articles were selected for analysis. The reviewed studies raise questions focusing on: patients, their therapeutic experiences, and their social and cultural contexts; professionals, professional relations, and the process of professionalization of CAM; and CAM and their relationship to biomedicine. The article concludes that qualitative studies on CAM call for an exploratory view of the theme, seeking to identify the experiences of patients and professionals with these therapies and discussing the impact of their use on conventional medicine or biomedicine

The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) Challenge: Results after 1 Year Follow-up

Accurate prediction of progression in subjects at risk of Alzheimer's disease is crucial for enrolling the right subjects in clinical trials. However, a prospective comparison of state-of-the-art algorithms for predicting disease onset and progression is currently lacking. We present the findings of "The Alzheimer's Disease Prediction Of Longitudinal Evolution" (TADPOLE) Challenge, which compared the performance of 92 algorithms from 33 international teams at predicting the future trajectory of 219 individuals at risk of Alzheimer's disease. Challenge participants were required to make a prediction, for each month of a 5-year future time period, of three key outcomes: clinical diagnosis, Alzheimer's Disease Assessment Scale Cognitive Subdomain (ADAS-Cog13), and total volume of the ventricles. The methods used by challenge participants included multivariate linear regression, machine learning methods such as support vector machines and deep neural networks, as well as disease progression models. No single submission was best at predicting all three outcomes. For clinical diagnosis and ventricle volume prediction, the best algorithms strongly outperform simple baselines in predictive ability. However, for ADAS-Cog13 no single submitted prediction method was significantly better than random guesswork. Two ensemble methods based on taking the mean and median over all predictions, obtained top scores on almost all tasks. Better than average performance at diagnosis prediction was generally associated with the additional inclusion of features from cerebrospinal fluid (CSF) samples and diffusion tensor imaging (DTI). On the other hand, better performance at ventricle volume prediction was associated with inclusion of summary statistics, such as the slope or maxima/minima of patient-specific biomarkers. On a limited, cross-sectional subset of the data emulating clinical trials, performance of the best algorithms at predicting clinical diagnosis decreased only slightly (2 percentage points) compared to the full longitudinal dataset. The submission system remains open via the website https://tadpole.grand-challenge.org, while TADPOLE SHARE (https://tadpole-share.github.io/) collates code for submissions. TADPOLE's unique results suggest that current prediction algorithms provide sufficient accuracy to exploit biomarkers related to clinical diagnosis and ventricle volume, for cohort refinement in clinical trials for Alzheimer's disease. However, results call into question the usage of cognitive test scores for patient selection and as a primary endpoint in clinical trials.</jats:p