scholarly journals Optimal extension of Lipschitz embeddings in the plane

2019 ◽  
Vol 51 (4) ◽  
pp. 622-632
Author(s):  
Leonid V. Kovalev
2020 ◽  
Vol 45 (2) ◽  
pp. 931-955
Author(s):  
Vasileios Chousionis ◽  
Sean Li ◽  
Vyron Vellis ◽  
Scott Zimmerman

2009 ◽  
Vol 290 (3) ◽  
pp. 1033-1049 ◽  
Author(s):  
Ángel Ballesteros ◽  
Alberto Enciso ◽  
Francisco J. Herranz ◽  
Orlando Ragnisco

Author(s):  
B. M. Braga

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.


2010 ◽  
Vol 391 (10) ◽  
Author(s):  
Jason C. Poole ◽  
Vincent Procaccio ◽  
Martin C. Brandon ◽  
Greg Merrick ◽  
Douglas C. Wallace

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.


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