A one line factoring algorithm

We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package

Class invariants from a new kind of Weber-like modular equation

A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method. They are obtained by means of specialising certain modular equations related to Weber's modular equations of `irrational type'. The technique works for certain eta quotients evaluated at points in an imaginary quadratic field with discriminant d1 (mod 8)

A New Class of Theta Function Identities in Two Variables

Copyright © 2010 Nova Science PublishersWe describe a new class of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan

Estimating the Costs of Revenue Assurance

Using a formula to estimate per acre costs at 70, 75, and 80 percent levels of coverage, this study provides estimates of the government cost of the revenue assurance plan, one of the alternative proposals for the 1995 Farm Bill. These costs are compared with results from previous studies and with crop insurance premiums. The authors conclude that a revenue assurance program would result in substantial budget savings over the current program

Cave-adapted evolution in the North American amblyopsid fishes inferred using phylogenomics and geometric morphometrics

© 2020 The Authors. Evolution © 2020 The Society for the Study of Evolution. Cave adaptation has evolved repeatedly across the Tree of Life, famously leading to pigmentation and eye degeneration and loss, yet its macroevolutionary implications remain poorly understood. We use the North American amblyopsid fishes, a family spanning a wide degree of cave adaptation, to examine the impact of cave specialization on the modes and tempo of evolution. We reconstruct evolutionary relationships using ultraconserved element loci, estimate the ancestral histories of eye-state, and examine the impact of cave adaptation on body shape evolution. Our phylogenomic analyses provide a well-supported hypothesis for amblyopsid evolutionary relationships. The obligate blind cavefishes form a clade and the cave-facultative eyed spring cavefishes are nested within the obligate cavefishes. Using ancestral state reconstruction, we find support for at least two independent subterranean colonization events within the Amblyopsidae. Eyed and blind fishes have different body shapes, but not different rates of body shape evolution. North American amblyopsids highlight the complex nature of cave-adaptive evolution and the necessity to include multiple lines of evidence to uncover the underlying processes involved in the loss of complex traits

A checklist for clinical trials in rare disease: Obstacles and anticipatory actions-lessons learned from the FOR-DMD trial

Background: Trials in rare diseases have many challenges, among which are the need to set up multiple sites in different countries to achieve recruitment targets and the divergent landscape of clinical trial regulations in those countries. Over the past years, there have been initiatives to facilitate the process of international study set-up, but the fruits of these deliberations require time to be operationally in place. FOR-DMD (Finding the Optimum Steroid Regimen for Duchenne Muscular Dystrophy) is an academic-led clinical trial which aims to find the optimum steroid regimen for Duchenne muscular dystrophy, funded by the National Institutes of Health (NIH) for 5 years (July 2010 to June 2015), anticipating that all sites (40 across the USA, Canada, the UK, Germany and Italy) would be open to recruitment from July 2011. However, study start-up was significantly delayed and recruitment did not start until January 2013. Method: The FOR-DMD study is used as an example to identify systematic problems in the set-up of international, multi-centre clinical trials. The full timeline of the FOR-DMD study, from funding approval to site activation, was collated and reviewed. Systematic issues were identified and grouped into (1) study set-up, e.g. drug procurement; (2) country set-up, e.g. competent authority applications; and (3) site set-up, e.g. contracts, to identify the main causes of delay and suggest areas where anticipatory action could overcome these obstacles in future studies. Results: Time from the first contact to site activation across countries ranged from 6 to 24 months. Reasons of delay were universal (sponsor agreement, drug procurement, budgetary constraints), country specific (complexity and diversity of regulatory processes, indemnity requirements) and site specific (contracting and approvals). The main identified obstacles included (1) issues related to drug supply, (2) NIH requirements regarding contracting with non-US sites, (3) differing regulatory requirements in the five participating countries, (4) lack of national harmonisation with contracting and the requirement to negotiate terms and contract individually with each site and (5) diversity of languages needed for study materials. Additionally, as with many academic-led studies, the FOR-DMD study did not have access to the infrastructure and expertise that a contracted research organisation could provide, organisations often employed in pharmaceutical-sponsored studies. This delay impacted recruitment, challenged the clinical relevance of the study outcomes and potentially delayed the delivery of the best treatment to patients. Conclusion: Based on the FOR-DMD experience, and as an interim solution, we have devised a checklist of steps to not only anticipate and minimise delays in academic international trial initiation but also identify obstacles that will require a concerted effort on the part of many stakeholders to mitigate

Mabel Engineering Flights, 2010-2013: Flight Report

In December 2010, NASA deployed for the first time the Multiple Altimeter Beam Experimental Lidar (MABEL), an airborne simulator for Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) algorithm development. Between 2010 and 2013, engineering flights were conducted in the continental United States, to ready the instrument for deployments to Alaska and Iceland, where flight lines could be designed and flown over sea ice and grounded ice. Ultimately, MABEL engineering missions included: 1) flights based out of NASA Armstrong Flight Research Center (California, formerly Dryden Flight Research Center) in 2010, 2011, and 2012; flights based out of NASA Wallops Flight Facility (Virginia) in 2012; flights based out of NASA Langley Research Center (Virginia) in 2013; and flights based out of the Mojave Air and Space Port (California) in 2013