Invertible Carnot Groups

Freeman, David

doi:10.2478/agms-2014-0009

Cited by 4 publications

(4 citation statements)

References 20 publications

(18 reference statements)

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“…In strains lacking CdtLoc, a unique 68-bp sequence is found inserted in the same genomic location [ 48 , 49 ]. In non-toxigenic strains, such as the recently discovered NTCD-035 by Maslanka et al [ 42 ], PaLoc is replaced by a conserved non-coding sequence of 115 bp [ 46 , 50 , 51 , 52 ]. Ongoing works on the comparative genomics of C. difficile are highlighting some important features on the evolution of these two pathogenic regions.…”

Section: Genetic Evolution Of C Difficile Virulencementioning

confidence: 99%

“…Several studies focusing on both human and animal isolates have suggested a possible role for animals as sources of C. difficile [ 38 , 39 , 40 , 41 , 42 , 43 ]. A small Italian study, conducted on 39 samples, identified 14 different C. difficile ribotypes (RTs, see paragraph “Molecular typing techniques for C. difficile strains”), of which four (i.e., RT020, RT078, RT106, RT126) were detected in both animal and human samples.…”

Section: Introductionmentioning

confidence: 99%

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Make It Less difficile: Understanding Genetic Evolution and Global Spread of Clostridioides difficile

Mengoli

Barone

Fabbrini

et al. 2022

Genes

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Clostridioides difficile is an obligate anaerobic pathogen among the most common causes of healthcare-associated infections. It poses a global threat due to the clinical outcomes of infection and resistance to antibiotics recommended by international guidelines for its eradication. In particular, C. difficile infection can lead to fulminant colitis associated with shock, hypotension, megacolon, and, in severe cases, death. It is therefore of the utmost urgency to fully characterize this pathogen and better understand its spread, in order to reduce infection rates and improve therapy success. This review aims to provide a state-of-the-art overview of the genetic variation of C. difficile, with particular regard to pathogenic genes and the correlation with clinical issues of its infection. We also summarize the current typing techniques and, based on them, the global distribution of the most common ribotypes. Finally, we discuss genomic surveillance actions and new genetic engineering strategies as future perspectives to make it less difficile.

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Section: Genetic Evolution Of C Difficile Virulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Make It Less difficile: Understanding Genetic Evolution and Global Spread of Clostridioides difficile

Mengoli

Barone

Fabbrini

et al. 2022

Genes

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“…While these share many properties with Möbius transformations in R n , see e.g. [14,28], there are important differences. To give some examples, the conformal group in our case is not transitive on the set of triples of distinct points [50], rotations are not transitive on ∂B, and unlike x → x |x| 2 , the Korányi inversion does not keep ∂B pointwise fixed.…”

Section: Carleson Measuresmentioning

confidence: 99%

Hardy spaces and quasiconformal maps in the Heisenberg group

Adamowicz¹,

Fässler²

2022

Preprint

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We define Hardy spaces H p , 0 < p < ∞, for quasiconformal mappings on the Korányi unit ball B in the first Heisenberg group H 1 . Our definition is stated in terms of the Heisenberg polar coordinates introduced by Korányi and Reimann, and Balogh and Tyson. First, we prove the existence of p0(K) > 0 such that every K-quasiconformal map f : B → f (B) ⊂ H 1 belongs to H p for all 0 < p < p0(K). Second, we give two equivalent conditions for the H p membership of a quasiconformal map f , one in terms of the radial limits of f , and one using a nontangential maximal function of f . As an application, we characterize Carleson measures on B via integral inequalities for quasiconformal mappings on B and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from R n to H 1 . A crucial difference between the proofs in R n and H 1 is caused by the nonisotropic nature of the Korányi unit sphere with its two characteristic points.

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“…Iwasawa N groups, the nilpotent groups that arise in the Iwasawa decomposition KAN of a semi-simple Lie group, are further examples of Carnot groups. This family of Carnot groups has been studied quite intensively; see, for instance, [4,5,7,15,27]. Other examples of Carnot groups which are reasonably well understood include H-type groups, filiform groups, free nilpotent groups and jet spaces; see, for instance, [16,19,21,23,22,26].…”

Section: Introductionmentioning

confidence: 99%