Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration

AMS subject classification: 60J80, 62F12, 62P10.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

One-year outcome of bevacizumab therapy for chronic macular edema in central and branch retinal vein occlusions in real-world clinical practice in the UK

Background: The purpose of this study was to investigate the 12-month outcome of macular edema secondary to both chronic and new central and branch retinal vein occlusions treated with intravitreal bevacizumab in the real-life clinical setting in the UK. Methods: Retrospective case notes analysis of consecutive patients with retinal vein occlusions treated with bevacizumab in 2010 to 2012. Outcome measures were visual acuity (measured with Snellen, converted into logMAR [logarithm of the minimum angle of resolution] for statistical calculation) and central retinal thickness at baseline, 4 weeks post-loading phase, and at 1 year. Results: There were 56 and 100 patients with central and branch retinal vein occlusions, respectively, of whom 62% had chronic edema and received prior therapies and another 32% required additional laser treatments post-baseline bevacizumab. Baseline median visual acuity was 0.78 (interquartile range [IQR] 0.48–1.22) in the central group and 0.6 (IQR 0.3–0.78) in the branch group. In both groups, visual improvement was statistically significant from baseline compared to post-loading (P,0.001 and P=0.03, respectively), but was not significant by month 12 (P=0.058 and P=0.166, respectively); 30% improved by at least three lines and 44% improved by at least one line by month 12. Baseline median central retinal thickness was 449 μm (IQR 388–553) in the central group and 441 µm (IQR 357–501) in the branch group. However, the mean reduction in thickness was statistically significant at post-loading (P,0.001) and at the 12-month time point (P,0.001) for both groups. The average number of injections in 1 year was 4.2 in the central group and 3.3 in the branch group. Conclusion: Our large real-world cohort results indicate that bevacizumab introduced to patients with either new or chronic edema due to retinal vein occlusion can result in resolution of edema and stabilization of vision in the first year.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

On the shoulders of a giant:his legacy will live on

Editorial

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.

Crevalle jack, Rookery Branch, Shark River

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Blue tilapia, Rookery Branch, Shark River

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Waking the sleeping giant: Beliefs of Brazilian and *American teachers concerning liberation curriculum

The school curriculum is a matter mandated by the educational system rather than determined by the school stakeholders of a community, as Freire (1993) suggests. At the present time, one significant vision of school is challenging the current order of curriculum practice. It focuses on school as a liberating agency grounded on the belief that the abilities to access information and to think critically about it will educate an individual capable of making independent decisions. This dissertation investigates teacher's beliefs concerning curriculum. It was assumed that there is a discrepancy between what has been the position proposed by critical theorists including Freire (1998a, 1993); Apple (1979); Giroux (1998), and the position on curriculum which school systems are typically advancing. ^ There were four purposes of this study. The major purpose of this study was to determine whether or not Brazilian and American Teachers believe that a school curriculum based on Freirean principles could be implemented in the schools in which they worked. Also, this study sought to determine the differences found between teachers' beliefs in the Brazilian and American contexts. Another purpose was to determine how Brazilian and American teachers justify their beliefs and actions when these may represent conflicting values. Finally, this study sought to determine if these teachers believe that the curriculum is in need of change or if they accept the current curriculum as adequate. This study consisted of quantitative and qualitative data collection through multiple methods involving surveys and interviews. The study involved 171 teachers (88 Brazilian and 83 American) from multiple settings with the majority working for public systems. Overall, it seems that Brazilian and American teachers believe that a curriculum based on Freirean principles of education can be implemented in their schools, if ongoing education is provided. The majority of Brazilian teachers believe a curriculum change is necessary while half of the American teachers believe a curriculum change is needed and the other half seems to believe curriculum is adequate. Teachers explain that it is hard to implement a curriculum they believe to be most appropriate for students because the current curriculum is mandated by the school system or by national guidelines. The majority of Brazilian teachers and those American teachers who believed a curriculum change is necessary explained their rationale for change in terms of social justice, problem-solving, collective work, student-centered and context-based curriculum. American teachers, who believed that the curriculum is adequate, explained that they are satisfied with their student's achievements. They stated that their students are doing well on tests and are learning what is required. ^