Aliquot Cycles for Elliptic Curves with Complex Multiplication

We review the history of elliptic curves and show that it is possible to form a group law using the points on an elliptic curve over some field L. We review various methods for computing the order of this group when L is finite, including the complex multiplication method. We then define and examine the properties of elliptic pairs, lists, and cycles, which are related to the notions of amicable pairs and aliquot cycles for elliptic curves, defined by Silverman and Stange. We then use the properties of elliptic pairs to prove that aliquot cycles of length greater than two exist for elliptic curves with complex multiplication, contrary to an assertion of Silverman and Stange, proving that such cycles only occur for elliptic curves of j-invariant equal to zero, and they always have length six. We explore the connection between elliptic pairs and several other conjectures, and propose limitations on the lengths of elliptic lists

Analysis of Observer Effect in Logbook Reporting Accuracy for U.S. Pelagic Longline Fishing Vessels in the Atlantic and Gulf of Mexico

Commercial pelagic longline fishers within the U.S. Atlantic, Gulf of Mexico, and Caribbean are required to report all fishing interactions per each gear deployment to NOAA’s Vessel Logbook Program of the Southeast Fisheries Science Center to quantify bycatch, increase conservation efforts, and avoid jeopardizing the existence of vulnerable species listed under the Endangered Species Act (ESA). To provide additional accuracy, the Pelagic Observer Program (POP) of the SEFSC deploys professionally trained observers on longline vessels to produce a statistically reliable subset of longline fisheries data. A comparison of self-reported (“unobserved”) datasets versus observer-collected (“observed”) datasets showed a general consistency for most target species but non-reporting or under-reporting for a number of bycatch species and “lesser-valued” target species. These discrepancies between catch compositions and abundancies regarding targeted species, species of bycatch concern, and species of minimum economic value can provide insight into increased fisheries regulations, stricter requirements, or additional observer coverage

Caltech Example Data Management Plan

The example data management plan describes data management for a microscopy project and uses general NSF template. Always refer to the specific guidance for your grant proposal when writing a data management plan, as requirements differ

Elliptic Reciprocity

The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman and Stange. Settling a matter left open by Silverman and Stange it is shown that for d=3 there are elliptic cycles of length 6. For d not equal to 3 the question of the existence of proper elliptic lists of length n over d is reduced to the the theory of prime producing quadratic polynomials. For d=163 a proper elliptic list of length 40 is exhibited. It is shown that for each d there is an upper bound on the length of a proper elliptic list over d. The final section of the paper contains heuristic arguments supporting conjectured asymptotics for the number of elliptic pairs below integer X. Finally, for d congruent to 3 modulo 8 the existence of infinitely many anomalous prime numbers is derived from Bunyakowski's Conjecture for quadratic polynomials.Comment: 17 pages, including one figure and two table

Real-time emotion detection technologies for potential health applications

PostprintPeer reviewe

Comparative genomics approaches accurately predict deleterious variants in plants

Recent advances in genome resequencing have led to increased interest in prediction of the functional consequences of genetic variants. Variants at phylogenetically conserved sites are of particular interest, because they are more likely than variants at phylogenetically variable sites to have deleterious effects on fitness and contribute to phenotypic variation. Numerous comparative genomic approaches have been developed to predict deleterious variants, but the approaches are nearly always assessed based on their ability to identify known disease-causing mutations in humans. Determining the accuracy of deleterious variant predictions in nonhuman species is important to understanding evolution, domestication, and potentially to improving crop quality and yield. To examine our ability to predict deleterious variants in plants we generated a curated database of 2,910 Arabidopsis thaliana mutants with known phenotypes. We evaluated seven approaches and found that while all performed well, their relative ranking differed from prior benchmarks in humans. We conclude that deleterious mutations can be reliably predicted in A. thaliana and likely other plant species, but that the relative performance of various approaches does not necessarily translate from one species to another

Launching a Researcher-Focused Data Repository at Caltech using the Invenio 3 platform

The vast majority of digital data associated with scientific research are not accessible online. While there are many challenges associated with making research data openly accessible, one significant challenge is usability and long term availability of storage services. Open institutional repositories have the potential to support data preservation and sharing of valuable raw and processed data from local research efforts. However, research data are inherently heterogeneous and requires researcher involvement to accurately describe the nature of the deposited data files. We used a researcher-focused design principle to develop a data repository on the Invenio 3 platform with TIND. These principles included automating the deposit process as much as possible, employing standard metadata to support discoverability and future applications, and providing API access so the repository can power other visualization and analysis services. The repository includes DOI minting to support data citation, ORCID identifiers to facilitate credit attribution, and Github integration to encourage software archiving. The newly launched repository captures research data that might otherwise be lost due to poor storage and organization practices, and enables researchers, the library, and the Caltech Archives to develop tools and preservation strategies around this valuable resource

ORCID iD Handout

A quick handout with information about ORCID iD