Conjugate gradient method for finding fundamental solitary waves

The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves of nonlinear Hamiltonian equations. The main obstacle that such a modified CGM overcomes is that the operator of the equation linearized about a solitary wave is not sign definite. Instead, it has a finite number of eigenvalues on the opposite side of zero than the rest of its spectrum. We present versions of the modified CGM that can find solitary waves with prescribed values of either the propagation constant or power. We also extend these methods to handle multi-component nonlinear wave equations. Convergence conditions of the proposed methods are given, and their practical implications are discussed. We demonstrate that our modified CGMs converge much faster than, say, Petviashvili's or similar methods, especially when the latter converge slowly.Comment: 44 pages, submitted to Physica

Following Design Justice Perspectives to Lay the Groundwork for a Digital Archive of Oxford College’s Muslim Students Association

Born out of conversations around the thirtieth anniversary of Oxford College\u27s Muslim Students Association (MSA), this project uses digital tools to uncover and preserve the many ways MSA and its members have actively participated in and shaped the life of our college and the wider community. To that end, REL383 Islam in America students began conducting oral history interviews in the spring of 2022 with MSA alumni about their experiences and memories. The project has continued as an undergraduate research project to preserve and share these important stories through Emory University\u27s digital tools, such as Aviary, OHMS, and Omeka. Taking cues from design justice practitioners, our work-in-progress presentation focuses on the ethical responsibilities of digital scholarship collaborations with marginalized communities. It spells out how we ensure that community members are included in meaningful ways throughout the design and research process. Attendees will learn about the steps we have taken in cooperation with the library\u27s Digital Projects Team to meet the ethical responsibilities for digital scholarship at the intersection of community collaboration and social justice. These include early collaborative efforts with MSA stakeholders during conceptualization, communication protocols and outreach to potential interview subjects, and a customized consent process resulting in different levels of accessibility for individual archival items. Finally, we will address future directions, such as formalizing MSA stakeholders\u27 participation by creating an advisory board

Comparing Transactional eHealth Literacy of Individuals With Cancer and Surrogate Information Seekers: Mixed Methods Study

BackgroundThe number of adults entering higher-risk age groups for receiving a cancer diagnosis is rising, with predicted numbers of cancer cases expected to increase by nearly 50% by 2050. Living with cancer puts exceptional burdens on individuals and families during treatment and survivorship, including how they navigate their relationships with one another. One role that a member of a support network may enact is that of a surrogate seeker, who seeks information in an informal capacity on behalf of others. Individuals with cancer and surrogate seekers often use the internet to learn about cancer, but differences in their skills and strategies have received little empirical attention. ObjectiveThis study aimed to examine the eHealth literacy of individuals with cancer and surrogate information seekers, including an investigation of how each group evaluates the credibility of web-based cancer information. As a secondary aim, we sought to explore the differences that exist between individuals with cancer and surrogate seekers pertaining to eHealth literacies and sociodemographic contexts. MethodsBetween October 2019 and January 2020, we conducted a web-based survey of 282 individuals with cancer (n=185) and surrogate seekers (n=97). We used hierarchical linear regression analyses to explore differences in functional, communicative, critical, and translational eHealth literacy between individuals with cancer and surrogate seekers using the Transactional eHealth Literacy Instrument. Using a convergent, parallel mixed methods design, we also conducted a thematic content analysis of an open-ended survey response to qualitatively examine how each group evaluates web-based cancer information. ResultseHealth literacy scores did not differ between individuals with cancer and surrogate seekers, even after adjusting for sociodemographic variables. Individuals with cancer and surrogate seekers consider the credibility of web-based cancer information based on its channel (eg, National Institutes of Health). However, in evaluating web-based information, surrogate seekers were more likely than individuals with cancer to consider the presence and quality of scientific references supporting the information. Individuals with cancer were more likely than surrogate seekers to cross-reference other websites and web-based sources to establish consensus. ConclusionsWeb-based cancer information accessibility and evaluation procedures differ among individuals with cancer and surrogate seekers and should be considered in future efforts to design web-based cancer education interventions. Future studies may also benefit from more stratified recruitment approaches and account for additional contextual factors to better understand the unique circumstances experienced within this population