scholarly journals Optimal extension of Lipschitz embeddings in the plane

2019 ◽  
Vol 51 (4) ◽  
pp. 622-632
Author(s):  
Leonid V. Kovalev
Keyword(s):  
Optimal Extension ◽  
Lipschitz Embeddings

scholarly journals Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces

2020 ◽  
Vol 45 (2) ◽  
pp. 931-955
Author(s):  
Vasileios Chousionis ◽  
Sean Li ◽  
Vyron Vellis ◽  
Scott Zimmerman
Keyword(s):  
Euclidean Spaces ◽  
Lipschitz Embeddings

Optimal Extension Fields (OEFs)

2012 ◽  
Keyword(s):  
Optimal Extension

scholarly journals Hamiltonian Systems Admitting a Runge–Lenz Vector and an Optimal Extension of Bertrand’s Theorem to Curved Manifolds

2009 ◽  
Vol 290 (3) ◽  
pp. 1033-1049 ◽  
Author(s):  
Ángel Ballesteros ◽  
Alberto Enciso ◽  
Francisco J. Herranz ◽  
Orlando Ragnisco
Keyword(s):  
Hamiltonian Systems ◽  
Curved Manifolds ◽  
Optimal Extension

Optimal extension of the Hausdorff-Young inequality

2008 ◽  
Vol 2008 (620) ◽  
Author(s):  
G. Mockenhaupt ◽  
W. J. Ricker
Keyword(s):  
Young Inequality ◽  
Optimal Extension

ON ASYMPTOTIC UNIFORM SMOOTHNESS AND NONLINEAR GEOMETRY OF BANACH SPACES

2019 ◽  
pp. 1-38
Author(s):  
B. M. Braga
Keyword(s):  
Banach Spaces ◽  
Open Problem ◽  
Concentration Inequalities ◽  
Uniformly Smooth ◽  
Uniform Smoothness ◽  
Weakly Sequentially Continuous ◽  
Nonlinear Geometry ◽  
Lipschitz Embeddings ◽  
Uniformly Smooth Banach Spaces ◽  
Descriptive Set

These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach–Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.

scholarly journals Multiplex analysis of mitochondrial DNA pathogenic and polymorphic sequence variants

2010 ◽  
Vol 391 (10) ◽  
Author(s):  
Jason C. Poole ◽  
Vincent Procaccio ◽  
Martin C. Brandon ◽  
Greg Merrick ◽  
Douglas C. Wallace
Keyword(s):  
Mitochondrial Dna ◽  
Pcr Amplification ◽  
Integrated System ◽  
Sequence Variants ◽  
Coding Region ◽  
Single Nucleotide Variants ◽  
Standard Curve ◽  
Mtdna Mutations ◽  
Pathogenic Mutations ◽  
Optimal Extension

Abstract The mitochondrial DNA (mtDNA) encompasses two classes of functionally important sequence variants: recent pathogenic mutations and ancient adaptive polymorphisms. To rapidly and cheaply evaluate both classes of single nucleotide variants (SNVs), we have developed an integrated system in which mtDNA SNVs are analyzed by multiplex primer extension using the SNaPshot system. A multiplex PCR amplification strategy was used to amplify the entire mtDNA, a computer program identifies optimal extension primers, and a complete global haplotyping system is also proposed. This system genotypes SNVs on multiplexed mtDNA PCR products or directly from enriched mtDNA samples and can quantify heteroplasmic variants down to 0.8% using a standard curve. With this system, we have developed assays for testing the common pathogenic mutations in four multiplex panels: two genotype the 13 most common pathogenic mtDNA mutations and two genotype the 10 most common Leber Hereditary Optic Neuropathy mutations along with haplogroups J and T. We use a hierarchal system of 140 SNVs to delineate the major global mtDNA haplogroups based on a global phylogenetic tree of coding region polymorphisms. This system should permit rapid and inexpensive genotyping of pathogenic and lineage-specific mtDNA SNVs by clinical and research laboratories.

Sign in / Sign up

Export Citation Format

Share Document