Lesley Ward

Modifications of Kleinberg's HITS algorithm using matrix exponentiation and web log records

Kleinberg’s HITS algorithm, a method of link analysis, uses the link structure of a network of webpages to assign authority and hub weights to each page. These weights are used to rank sources on a particular topic. We have found that certain tree-like web structures can lead the HITS algorithm to return either arbitrary or non-intuitive results. We give a characterization of these web structures. We present two modifications to the adjacency matrix input to the HITS algorithm. Exponentiated Input, our first modification, includes information not only on direct links but also on longer paths between pages. It resolves both limitations mentioned above. Usage Weighted Input, our second modification, weights links according to how often they were followed by users in a given time period; it incorporates user feedback without requiring direct user querying.

Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization

Algorithms such as Kleinbergs HITS algorithm, the PageRank algorithm of Brin and Page, and the SALSA algorithm of Lempel and Moran use the link structure of a network of web pages to assign weights to each page in the network. The weights can then be used to rank the pages as authoritative sources. These algorithms share a common underpinning; they find a dominant eigenvector of a nonnegative matrix that describes the link structure of the given network and use the entries of this eigenvector as the page weights. We use this commonality to give a unified treatment, proving the existence of the required eigenvector for the PageRank, HITS, and SALSA algorithms, the uniqueness of the PageRank eigenvector, and the convergence of the algorithms to these eigenvectors. However, we show that the HITS and SALSA eigenvectors need not be unique. We examine how the initialization of the algorithms affects the final weightings produced. We give examples of networks that lead the HITS and SALSA algorithms to return nonunique or nonintuitive rankings. We characterize all such networks in terms of the connectivity of the related HITS authority graph. We propose a modification, Exponentiated Input to HITS, to the adjacency matrix input to the HITS algorithm. We prove that Exponentiated Input to HITS returns a unique ranking, provided that the network is weakly connected. Our examples also show that SALSA can give inconsistent hub and authority weights, due to nonuniqueness. We also mention a small modification to the SALSA initialization which makes the hub and authority weights consistent.

Prevalence, Patterns, and Predictors of Yoga Use: Results of a U.S. Nationally Representative Survey.

INTRODUCTION The purpose of this study was to investigate the prevalence, patterns, and predictors of yoga use in the U.S. general population. METHODS Using cross-sectional data from the 2012 National Health Interview Survey Family Core, Sample Adult Core, and Adult Complementary and Alternative Medicine questionnaires (N=34,525), weighted frequencies for lifetime and 12-month prevalence of yoga use and patterns of yoga practice were analyzed. Using logistic regression analyses, sociodemographic predictors of lifetime yoga use were analyzed. Analyses were conducted in 2015. RESULTS Lifetime and 12-month prevalence of yoga use were 13.2% and 8.9%, respectively. Compared with nonpractitioners, lifetime yoga practitioners were more likely female, younger, non-Hispanic white, college educated, higher earners, living in the West, and of better health status. Among those who had practiced in the past 12 months, 51.2% attended yoga classes, 89.9% used breathing exercises, and 54.9% used meditation. Yoga was practiced for general wellness or disease prevention (78.4%), to improve energy (66.1%), or to improve immune function (49.7%). Back pain (19.7%), stress (6.4%), and arthritis (6.4%) were the main specific health problems for which people practiced yoga. CONCLUSIONS About 31 million U.S. adults have ever used yoga, and about 21 million practiced yoga in the past 12 months. Disease prevention and back pain relief were the most important health reasons for yoga practice. Yoga practice is associated with age, gender, ethnicity, SES, and health status.

The Safety of Yoga: A Systematic Review and Meta-Analysis of Randomized Controlled Trials

As yoga has gained popularity as a therapeutic intervention, its safety has been questioned in the lay press. Thus, this review aimed to systematically assess and meta-analyze the frequency of adverse events in randomized controlled trials of yoga. MEDLINE/PubMed, Scopus, the Cochrane Library, and IndMED were screened through February 2014. Of 301 identified randomized controlled trials of yoga, 94 (1975-2014; total of 8,430 participants) reported on adverse events. Life-threatening, disabling adverse events or those requiring intensive treatment were defined as serious and all other events as nonserious. No differences in the frequency of intervention-related, nonserious, or serious adverse events and of dropouts due to adverse events were found when comparing yoga with usual care or exercise. Compared with psychological or educational interventions (e.g., health education), more intervention-related adverse events (odds ratio = 4.21, 95% confidence interval: 1.01, 17.67; P = 0.05) and more nonserious adverse events (odds ratio = 7.30, 95% confidence interval: 1.91, 27.92; P < 0.01) occurred in the yoga group; serious adverse events and dropouts due to adverse events were comparable between groups. Findings from this review indicate that yoga appears as safe as usual care and exercise. The adequate reporting of safety data in future randomized trials of yoga is crucial to conclusively judge its safety.

Yoga for Functional Ability, Pain and Psychosocial Outcomes in Musculoskeletal Conditions: A Systematic Review and Meta-Analysis

OBJECTIVES Musculoskeletal conditions (MSCs) are the leading cause of disability and chronic pain in the developed world, impacting both functional ability and psychosocial health. The current review investigates the effectiveness of yoga on primary outcomes of functional ability, pain and psychosocial outcomes across a range of MSCs. METHODS A comprehensive search of 20 databases was conducted for full-text, randomized controlled trials of yoga in clinically diagnosed MSCs. RESULT Seventeen studies met the inclusion criteria, involving 1,626 participants with low back pain (LBP), osteoarthritis (OA), rheumatoid arthritis (RA), kyphosis or fibromyalgia. Studies were quality rated, and analysed for the effect of yoga on primary outcomes, immediately post-intervention. Twelve studies were rated as good quality. Yoga interventions resulted in a clinically significant improvement in functional outcomes in mild-to-moderate LBP and fibromyalgia, and showed a trend to improvement in kyphosis. Yoga significantly improved pain in OA, RA and mild-to-severe LBP. Psychosocial outcomes were significantly improved in mild-to-moderate LBP and OA. Meta-analysis of good-quality studies showed a moderate treatment effect for yoga of -0.64 (95%CI -0.89 to -0.39) for functional outcomes and -0.61 (95%CI -0.97 to -0.26) for pain outcomes. CONCLUSIONS Evidence suggests that yoga is an acceptable and safe intervention, which may result in clinically relevant improvements in pain and functional outcomes associated with a range of MSCs. Future analysis of outcomes which take into account the amount of yoga received by participants may provide insight into any putative duration or dosage effects of yoga interventions for MSCs.

Consensus on Exercise Reporting Template (CERT): Modified Delphi Study.

Background Exercise interventions are often incompletely described in reports of clinical trials, hampering evaluation of results and replication and implementation into practice. Objective The aim of this study was to develop a standardized method for reporting exercise programs in clinical trials: the Consensus on Exercise Reporting Template (CERT). Design and Methods Using the EQUATOR Networks methodological framework, 137 exercise experts were invited to participate in a Delphi consensus study. A list of 41 items was identified from a meta-epidemiologic study of 73 systematic reviews of exercise. For each item, participants indicated agreement on an 11-point rating scale. Consensus for item inclusion was defined a priori as greater than 70% agreement of respondents rating an item 7 or above. Three sequential rounds of anonymous online questionnaires and a Delphi workshop were used. Results There were 57 (response rate=42%), 54 (response rate=95%), and 49 (response rate=91%) respondents to rounds 1 through 3, respectively, from 11 countries and a range of disciplines. In round 1, 2 items were excluded; 24 items reached consensus for inclusion (8 items accepted in original format), and 16 items were revised in response to participant suggestions. Of 14 items in round 2, 3 were excluded, 11 reached consensus for inclusion (4 items accepted in original format), and 7 were reworded. Sixteen items were included in round 3, and all items reached greater than 70% consensus for inclusion. Limitations The views of included Delphi panelists may differ from those of experts who declined participation and may not fully represent the views of all exercise experts. Conclusions The CERT, a 16-item checklist developed by an international panel of exercise experts, is designed to improve the reporting of exercise programs in all evaluative study designs and contains 7 categories: materials, provider, delivery, location, dosage, tailoring, and compliance. The CERT will encourage transparency, improve trial interpretation and replication, and facilitate implementation of effective exercise interventions into practice.

Differences between Male and Female Consumers of Complementary and Alternative Medicine in a National US Population: A Secondary Analysis of 2012 NIHS Data

We examined the National Health Interview Survey (NHIS) 2012 to explore how US adult consumers of CAM differ by gender in terms of their sociodemographic characteristics, current health conditions, and perceived benefits of CAM. All individuals who completed the adults core interviews (N = 34,525) were included. CAM use, major sociodemographic variables, perceived benefits of using CAM, and top ten reported health conditions for which CAM was used were selected and analyzed by Stata. Findings revealed that 29.6% (n = 10,181) reported having used at least one form of CAM in the previous 12 months. Compared to male CAM users, female CAM users were more likely to have a bachelor degree, to be divorced/separated or widowed, and less likely to earn

Establishing key components of yoga interventions for musculoskeletal conditions: a Delphi survey

75,000 or more. Back pain/problem was the most common problem reported by both male and female CAM users (32.2% and 22.6%, resp.). A higher proportion of female CAM users reported using CAM for perceived benefits such as general wellness or general disease prevention. This paper provides foundation information regarding gender differences in CAM use and is a platform for further in-depth examination into how and why males and females differ in their reasons for CAM use.

Harmonic analysis : from Fourier to wavelets

BackgroundEvidence suggests yoga is a safe and effective intervention for the management of physical and psychosocial symptoms associated with musculoskeletal conditions. However, heterogeneity in the components and reporting of clinical yoga trials impedes both the generalization of study results and the replication of study protocols. The aim of this Delphi survey was to address these issues of heterogeneity, by developing a list of recommendations of key components for the design and reporting of yoga interventions for musculoskeletal conditions.MethodsRecognised experts involved in the design, conduct, and teaching of yoga for musculoskeletal conditions were identified from a systematic review, and invited to contribute to the Delphi survey. Forty-one of the 58 experts contacted, representing six countries, agreed to participate. A three-round Delphi was conducted via electronic surveys. Round 1 presented an open-ended question, allowing panellists to individually identify components they considered key to the design and reporting of yoga interventions for musculoskeletal conditions. Thematic analysis of Round 1 identified items for quantitative rating in Round 2; items not reaching consensus were forwarded to Round 3 for re-rating.ResultsThirty-six panellists (36/41; 88%) completed the three rounds of the Delphi survey. Panellists provided 348 comments to the Round 1 question. These comments were reduced to 49 items, grouped under five themes, for rating in subsequent rounds. A priori group consensus of ≥80% was reached on 28 items related to five themes concerning defining the yoga intervention, types of yoga practices to include in an intervention, delivery of the yoga protocol, domains of outcome measures, and reporting of yoga interventions for musculoskeletal conditions. Additionally, a priori consensus of ≥50% was reached on five items relating to minimum values for intervention parameters.ConclusionsExpert consensus has provided a non-prescriptive reference list for the design and reporting of yoga interventions for musculoskeletal conditions. It is anticipated future research incorporating the Delphi guidelines will facilitate high quality international research in this field, increase homogeneity of intervention components and parameters, and enhance the comparison and reproducibility of research into the use of yoga for the management of musculoskeletal conditions.

The effectiveness of complementary manual therapies for pregnancy-related back and pelvic pain: A systematic review with meta-analysis.

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fouriers study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues. The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently. This book is published in cooperation with IAS/Park City Mathematics Institute.