Ordering dynamics of the driven lattice gas model

The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus, depending on this parameter, the resulting state could be either single or multi striped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L_y, becoming infinitely long in the thermodynamic limit. This implies that the multi striped state is thermodynamically stable. The results put previous studies of the model in a more general framework

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra"

A Qualitative Analysis of Factors Influencing HPV Vaccine Uptake in Soweto, South Africa among Adolescents and Their Caregivers

Background: In South Africa, the prevalence of oncogenic Human Papillomavirus (HPV) may be as high as 64%, and cervical cancer is the leading cause of cancer-related death among women. The development of efficacious prophylactic vaccines has provided an opportunity for primary prevention. Given the importance of psycho-social forces in vaccine uptake, we sought to elucidate factors influencing HPV vaccination among a sample of low-income South African adolescents receiving the vaccine for the first time in Soweto. Methods: The HPV vaccine was introduced to adolescents in low-income townships throughout South Africa as part of a nationwide trial to understand adolescent involvement in future vaccine research targeting human immunodeficiency virus (HIV). We performed in-depth semi-structured interviews with purposively-sampled adolescents and their care providers to understand what forces shaped HPV vaccine uptake. Interviews were recorded, transcribed, translated, and examined using thematic analysis. Results: Of 224 adolescents recruited, 201 initiated the vaccine; 192 (95.5%) received a second immunization; and 164 (81.6%) completed three doses. In our qualitative study of 39 adolescent-caregiver dyads, we found that factors driving vaccine uptake reflected a socio-cultural backdrop of high HIV endemnicity, sexual violence, poverty, and an abundance of female-headed households. Adolescents exercised a high level of autonomy and often initiated decision-making. Healthcare providers and peers provided support and guidance that was absent at home. The impact of the HIV epidemic on decision-making was substantial, leading participants to mistakenly conflate HPV and HIV. Conclusions: In a setting of perceived rampant sexual violence and epidemic levels of HIV, adolescents and caregivers sought to decrease harm by seeking a vaccine targeting a sexually transmitted infection (STI). Despite careful consenting, there was confusion regarding the vaccine’s target. Future interventions promoting STI vaccines will need to provide substantial information for participants, particularly adolescents who may exercise a significant level of autonomy in decision-making

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint