A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Queer community archives in California since 1950

Purpose: This study provides insight into the histories and current statuses of queer community archives in California and explores what the archives profession can learn from the queer community archives and archivists. Through the construction of histories of three community archives (GLBT Historical Society; Lavender Library, Archives, and Cultural Exchange of Sacramento, Inc.; and ONE National Gay & Lesbian Archives), the study discovered why these independent, community-based archives were created, the issues that influenced their evolution, and the similarities and differences among them. Additionally, it compared the community archives to institutional archives which collect queer materials to explore the similarities and differences among the archives and determine possible implications for the archives profession. Significance: The study contributes to the literature in several significant ways: it is the first in-depth comparative history of the queer community archives; it adds to the cross-disciplinary research in archives and history; it contributes to the current debates on the nature of the archives and the role of the professional archivist; and it has implications for changing archival practice. Methodology: This study used social constructionism for epistemological positioning and new social history theory for theoretical framework. Information was gathered through seven oral history interviews with community archivists and volunteers and from materials in the archives’ collections. This evidence was used to construct the histories of the archives and determine their current statuses. The institutional archives used in the comparisons are the: University of California, Berkeley’s Bancroft Library; University of California, Santa Cruz’s Special Collections and University Archives; and San Francisco Public Library’s James C. Hormel Gay and Lesbian Center. The collection policies, finding aids, and archival collections related to the queer communities at the institutional and community archives were compared to determine commonalities and differences among the archives. Findings: The findings revealed striking similarities in the histories of the community archives and important implications for the archives’ survival and their relevancy to the archives profession. Each archives was started by an individual or small group collecting materials to preserve history that would otherwise have been lost as institutional archives were not collecting queer materials. These private collections grew and became the basis for the community archives. The community archives differ in their staffing models, circulation policies, and descriptive practices. The community archives have grown to incorporate more public programming functions than most institutional archives. While in the past, the community archives had little connection to institutional archives, today they have varying degrees of partnerships. However, the historical lack of collecting queer materials by institutional archives makes some members of the communities reluctant to donate materials to institutional archives or collaborate with them. All three queer community archives are currently managed by professionally trained and educated archivists and face financial issues impacting their continued survival. The similarities and differences between the community and institutional archives include differences in collection policies, language differences in the finding aids, and differing levels of relationships between the archives. However, they share similar sensitivity in the use of language in describing the queer communities and overlap in the types of materials collected. Implications: This study supports previous research on community archives showing that communities take the preservation of history into their own hands when ignored by mainstream archives (Flinn, 2007; Flinn & Stevens, 2009; Nestle, 1990). Based on the study’s findings, institutional archivists could learn from their community archivist counterparts better ways to become involved in and relevant to the communities whose records they possess. This study also expands the understanding of history of the queer communities to include in-depth research into the archives which preserve and make available material for constructing history. Furthermore, this study supports reflective practice for archivists, especially in terms of descriptions used in finding aids. It also supports changes in graduate education for archives students to enable archivists in the United States to be more fully cognizant of community archives and able to engage in collaborative, international projects. Through this more activist role of the archivists, partnerships between the community and institutional archives would be built to establish more collaborative, respectful relationships with the communities in this post-custodial age of the archives (Stevens, Flinn, & Shepherd, 2010). Including community archives in discussions of archival practice and theory is one way of ensuring archives represent and serve a diversity of voices.

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.