The Media, Accountability and Civic Engagement in Africa

human development, democracy

The WISDOM Study: breaking the deadlock in the breast cancer screening debate.

There are few medical issues that have generated as much controversy as screening for breast cancer. In science, controversy often stimulates innovation; however, the intensely divisive debate over mammographic screening has had the opposite effect and has stifled progress. The same two questions-whether it is better to screen annually or bi-annually, and whether women are best served by beginning screening at 40 or some later age-have been debated for 20 years, based on data generated three to four decades ago. The controversy has continued largely because our current approach to screening assumes all women have the same risk for the same type of breast cancer. In fact, we now know that cancers vary tremendously in terms of timing of onset, rate of growth, and probability of metastasis. In an era of personalized medicine, we have the opportunity to investigate tailored screening based on a woman's specific risk for a specific tumor type, generating new data that can inform best practices rather than to continue the rancorous debate. It is time to move from debate to wisdom by asking new questions and generating new knowledge. The WISDOM Study (Women Informed to Screen Depending On Measures of risk) is a pragmatic, adaptive, randomized clinical trial comparing a comprehensive risk-based, or personalized approach to traditional annual breast cancer screening. The multicenter trial will enroll 100,000 women, powered for a primary endpoint of non-inferiority with respect to the number of late stage cancers detected. The trial will determine whether screening based on personalized risk is as safe, less morbid, preferred by women, will facilitate prevention for those most likely to benefit, and adapt as we learn who is at risk for what kind of cancer. Funded by the Patient Centered Outcomes Research Institute, WISDOM is the product of a multi-year stakeholder engagement process that has brought together consumers, advocates, primary care physicians, specialists, policy makers, technology companies and payers to help break the deadlock in this debate and advance towards a new, dynamic approach to breast cancer screening

Variational Integrators for Almost-Integrable Systems

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These integrators exploit that epsilon << 1 to increase their accuracy by constructing discrete Lagrangians based on the assumption that the integrator trajectory is close to that of the integrable system. Several of the integrators we present are equivalent to well-known symplectic integrators for the equivalent perturbed Hamiltonian systems, but their construction and error analysis is significantly simpler in the variational framework. One novel method we present, involving a weighted time-averaging of the perturbing terms, removes all errors from the integration at O(epsilon). This last method is implicit, and involves evaluating a potentially expensive time-integral, but for some systems and some error tolerances it can significantly outperform traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as accepted by Celestial Mechanics and Dynamical Astronom

Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error in predictor equation. ApJ, in pres

Meta-Didactical Slippages: A Qualitative Case Study of Didactical Situations in a Ninth Grade Mathematics Classroom

Research on the mathematical behavior of children over the past forty decades has considerably renewed and augmented the body of evaluative tests of the results of learning (Lester, 2007). Research however, has provided very little knowledge about the means of improving students’ performance on these tests. Nevertheless teachers, students, and others are being pressured to improve students’ performance, but in order to concentrate on basic skills, the learning itself is made more difficult and slower. The combination of requirements has led to a variety of uncontrolled phenomena such as meta-didactical slippage (Brousseau, 2008). The purpose of this study was to: (a) understand the nature of meta-didactical slippage that occurred in a ninth grade predominantly African American mathematics classroom; and (b) describe how these meta-didactical slippages affect students conceptual understanding on a unit of study of ninth grade mathematics. The study was a descriptive, qualitative, case study that employed ethnographic techniques of data collection and analysis. The theory of didactical situations in mathematics (Brousseau, 1997) served as the theoretical lens that grounded the interpretation of the data, because it enabled the researcher to isolate moments of instruction, action, formulation, validation, and institutionalization in the mathematics teaching and learning process. The study was conducted over a period of 15 weeks in one, ninth grade class of 23 predominantly African American students at a high school in a southeastern state. Data was crystalized using multiple data collection techniques: (a) collection of document artifacts, which included student work samples and teacher lesson plans; (b) interviews conducted with the teacher; (c) researcher introspection; and (d) direct observation. Data was analyzed using ethnographic and discourse analysis techniques, including domain analysis, coding, situated meaning, and the big “D” discourse tool. The study found four themes, which illustrated the nature meta-didactical slippages: (a) over-teaching, (b) situational bypass, (c) language and symbolic representation, and (d) the design of didactical situations

Meta-didactical Slippages in a Ninth Grade Mathematics Classroom: A Paradox of Teaching

This paper examines (a) the nature of meta-didactical slippages that occurred in a ninth grade predominantly African American mathematics classroom; and (b) how these meta-didactical slippages affect students’ conceptual understanding on a unit of ninth grade mathematics. A qualitative case study that employed ethnographic techniques of data collection and analysis was conducted. The theory of didactical situations in mathematics (Brousseau, 1997) served as the lens that grounded the interpretation of the data. The study found four themes, which illustrated the nature meta-didactical slippages: (a) over-teaching, (b) situational bypass, (c) language and symbolic representation, and (d) the design of didactical situations

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed