scholarly journals Moments of the Critical Values of Families of Elliptic Curves, with Applications

2010 ◽  
Vol 62 (5) ◽  
pp. 1155-1181 ◽  
Author(s):  
Matthew P. Young
Keyword(s):  
Elliptic Curves ◽  
Large Family ◽  
Critical Values ◽  
Central Values ◽  
The Family ◽  
Order Of Magnitude ◽  
Rank 2 ◽  
Family Based ◽  
First Moment ◽  
Positive Rank

AbstractWe make conjectures on the moments of the central values of the family of all elliptic curves and on themoments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of L-functions. Notably, we predict that the critical values of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves in the positive rank family.Furthermore, as arithmetical applications, we make a conjecture on the distribution of ap's amongst all rank 2 elliptic curves and show how the Riemann hypothesis can be deduced from sufficient knowledge of the first moment of the positive rank family (based on an idea of Iwaniec).

scholarly journals Amicable pairs and aliquot cycles on average

2015 ◽  
Vol 11 (06) ◽  
pp. 1751-1790 ◽  
Author(s):  
James Parks
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Upper Bound ◽  
The Family ◽  
Order Of Magnitude

Silverman and Stange defined the notion of an aliquot cycle of length L for a fixed elliptic curve E/ℚ, and conjectured an order of magnitude for the function that counts such aliquot cycles. We show that the conjectured upper bound holds for the number of aliquot cycles on average over the family of all elliptic curves with short bounds on the size of the parameters in the family.

scholarly journals An Efficient Approach to Point-Counting on Elliptic Curves from a Prominent Family over the Prime Field Fp

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1431
Author(s):  
Yuri Borissov ◽  
Miroslav Markov
Keyword(s):  
Elliptic Curves ◽  
Prime Number ◽  
Explicit Formula ◽  
Point Counting ◽  
Prime Field ◽  
Algorithmic Solution ◽  
The Family ◽  
Order Of Magnitude ◽  
Modulo P ◽  
Quantities Of Interest

Here, we elaborate an approach for determining the number of points on elliptic curves from the family Ep={Ea:y2=x3+a(modp),a≠0}, where p is a prime number >3. The essence of this approach consists in combining the well-known Hasse bound with an explicit formula for the quantities of interest-reduced modulo p. It allows to advance an efficient technique to compute the six cardinalities associated with the family Ep, for p≡1(mod3), whose complexity is O˜(log2p), thus improving the best-known algorithmic solution with almost an order of magnitude.

scholarly journals An asymptotic for the average number of amicable pairs for elliptic curves

2017 ◽  
Vol 166 (1) ◽  
pp. 33-59 ◽  
Author(s):  
JAMES PARKS
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Upper Bound ◽  
Asymptotic Constant ◽  
The Family ◽  
Order Of Magnitude ◽  
Precise Asymptotic

AbstractAmicable pairs for a fixed elliptic curve defined over ℚ were first considered by Silverman and Stange where they conjectured an order of magnitude for the function that counts such amicable pairs. This was later refined by Jones to give a precise asymptotic constant. The author previously proved an upper bound for the average number of amicable pairs over the family of all elliptic curves. In this paper we improve this result to an asymptotic for the average number of amicable pairs for a family of elliptic curves.

scholarly journals Outlier concepts auditing methodology for a large family of biomedical ontologies

2020 ◽  
Vol 20 (S10) ◽  
Author(s):  
Ling Zheng ◽  
Hua Min ◽  
Yan Chen ◽  
Vipina Keloth ◽  
James Geller ◽  
...  
Keyword(s):  
Quality Assurance ◽  
Large Family ◽  
Structural Features ◽  
Biomedical Ontologies ◽  
Partial Area ◽  
The Family ◽  
Big Picture ◽  
Family Based

Abstract Background Summarization networks are compact summaries of ontologies. The “Big Picture” view offered by summarization networks enables to identify sets of concepts that are more likely to have errors than control concepts. For ontologies that have outgoing lateral relationships, we have developed the "partial-area taxonomy" summarization network. Prior research has identified one kind of outlier concepts, concepts of small partials-areas within partial-area taxonomies. Previously we have shown that the small partial-area technique works successfully for four ontologies (or their hierarchies). Methods To improve the Quality Assurance (QA) scalability, a family-based QA framework, where one QA technique is potentially applicable to a whole family of ontologies with similar structural features, was developed. The 373 ontologies hosted at the NCBO BioPortal in 2015 were classified into a collection of families based on structural features. A meta-ontology represents this family collection, including one family of ontologies having outgoing lateral relationships. The process of updating the current meta-ontology is described. To conclude that one QA technique is applicable for at least half of the members for a family F, this technique should be demonstrated as successful for six out of six ontologies in F. We describe a hypothesis setting the condition required for a technique to be successful for a given ontology. The process of a study to demonstrate such success is described. This paper intends to prove the scalability of the small partial-area technique. Results We first updated the meta-ontology classifying 566 BioPortal ontologies. There were 371 ontologies in the family with outgoing lateral relationships. We demonstrated the success of the small partial-area technique for two ontology hierarchies which belong to this family, SNOMED CT’s Specimen hierarchy and NCIt’s Gene hierarchy. Together with the four previous ontologies from the same family, we fulfilled the “six out of six” condition required to show the scalability for the whole family. Conclusions We have shown that the small partial-area technique can be potentially successful for the family of ontologies with outgoing lateral relationships in BioPortal, thus improve the scalability of this QA technique.

scholarly journals Exome sequencing reveals a novel variant in NFX1 causing intracranial aneurysm in a Chinese family

2019 ◽  
Vol 12 (2) ◽  
pp. 221-226 ◽  
Author(s):  
Xinghuan Ding ◽  
Sen Zhao ◽  
Qianqian Zhang ◽  
Zihui Yan ◽  
Yang Wang ◽  
...  
Keyword(s):  
Exome Sequencing ◽  
Intracranial Aneurysms ◽  
Molecular Mechanisms ◽  
Large Family ◽  
Missense Variant ◽  
Chinese Family ◽  
Zinc Finger Domain ◽  
The Family ◽  
Novel Variant ◽  
Family Based

BackgroundGenetic risk factors play an important role in the pathogenesis of familial intracranial aneurysms (FIAs); however, the molecular mechanisms remain largely unknown.ObjectiveTo investigate potential FIA-causing genetic variants by rare variant interrogation and a family-based genomics approach in a large family with an extensive multigenerational pedigree with FIAs.MethodExome sequencing (ES) was performed in a dominant likely family with intracranial aneurysms (IAs). Variants were analyzed by an in-house developed pipeline and prioritized using various filtering strategies, including population frequency, variant type, and predicted variant pathogenicity. Sanger sequencing was also performed to evaluate the segregation of the variants with the phenotype.ResultsBased on the ES data obtained from five individuals from a family with 7/21 living members affected with IAs, a total of 14 variants were prioritized as candidate variants. Familial segregation analysis revealed that NFX1 c.2519T>C (p.Leu840Pro) segregated in accordance with Mendelian expectations with the phenotype within the family—that is, present in all IA-affected cases and absent from all unaffected members of the second generation. This missense variant is absent from public databases (1000genome, ExAC, gnomAD, ESP5400), and has damaging predictions by bioinformatics tools (Gerp ++ score = 5.88, CADD score = 16.43, MutationTaster score = 1, LRT score = 0). In addition, 840Leu in NFX1 is robustly conserved in mammals and maps in a region before the RING-type zinc finger domain.ConclusionNFX1 c.2519T>C (p.Leu840Pro) may contribute to the pathogenetics of a subset of FIAs.

scholarly journals Chemerin, A Novel Adipokine in the Regulation of Angiogenesis

2010 ◽  
Vol 24 (4) ◽  
pp. 874-874
Author(s):  
Kiymet Bozaoglu ◽  
Joanne E. Curran ◽  
Claire J. Stocker ◽  
Mohamed S. Zaibi ◽  
David Segal ◽  
...  
Keyword(s):  
Endothelial Cells ◽  
Mexican American ◽  
Large Family ◽  
Disease Status ◽  
Human Endothelial Cells ◽  
Gene Encoding ◽  
The Metabolic Syndrome ◽  
Heart Study ◽  
A Genome ◽  
Family Based

Abstract Context: Chemerin is a new adipokine associated with obesity and the metabolic syndrome. Gene expression levels of chemerin were elevated in the adipose depots of obese compared with lean animals and was markedly elevated during differentiation of fibroblasts into mature adipocytes. Objective: To identify factors that affect the regulation and potential function of chemerin using a genetics approach. Design, setting, patients and intervention: Plasma chemerin levels were measured in subjects from the San Antonio Family Heart Study (SAFHS), a large family-based genetic epidemiological study including 1354 Mexican American individuals. Individuals were randomly sampled without regard to phenotype or disease status. Main Outcome Measures: A genome wide association analysis using 542,944 SNPs in a subset of 523 of the same subjects was undertaken. The effect of chemerin on angiogenesis was measured using human endothelial cells and interstitial cells in co-culture in a specially formulated medium. Results: Serum chemerin levels were found to be highly heritable (h2 = 0.25; P = 1.4 x 10−9). The SNP showing strongest evidence of association (rs347344; P = 1.4 x 10−6) was located within the gene encoding EDIL3, which has a known role in angiogenesis. Functional angiogenesis assays in human endothelial cells confirmed that chemerin significantly mediated the formation of blood vessels to a similar extent as VEGF. Conclusion: Here we demonstrate for the first time that plasma chemerin levels are significantly heritable and identified a novel role for chemerin as a stimulator of angiogenesis.

Separating the Contributions in Localization Methods: A Technique to Enhance Identification of Damping Related Parameters

1999 ◽  
Author(s):  
Hervé Algrain ◽  
Calogero Conti ◽  
Pierre Dehombreux
Keyword(s):  
Finite Element ◽  
Model Updating ◽  
Element Model ◽  
Dynamic Responses ◽  
Finite Element Model Updating ◽  
Global Localization ◽  
Localization Method ◽  
The Family ◽  
Family Based ◽  
The Stability

Abstract Finite Element Model Updating has for objective to increase the correlation between the experimental dynamic responses of a structure and the predictions from a model. Among different initial choices, these procedures need to establish a set of representative parameters to be updated in which some are in real error and some are not. It is therefore important to select the correct properties that have to be updated to ensure that no marginal corrections are introduced. In this paper the standard localization criteria are presented and a technique to separate the global localization criteria in family-based criteria for damped structures is introduced. The methods are analyzed and applied to both numerical and experimental examples; a clear enhancement of the results is noticed using the family-based criteria. A simple way to qualify the stability of a localization method to noise is presented.

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