Classification of bicovariant differential calculi on quantum groups of type A, B, C and D

We present the MRI findings for 39 Wassel Type IV duplicated thumbs in 38 patients. We found that MRI revealed the morphology of the cartilaginous connection between the thumb anlages and the location of the deviation corresponding to the classification of Horii, which allowed precise preoperative planning of corrective osteotomies. All 39 thumbs were available for follow-up after surgical reconstruction at a mean of 29 months (range 25 to 39). Four out of nine Horii Type A cases and all 12 Type B, as well as the six Type C and the six Type D cases, achieved good results according to the Tada scoring system. Five Type A cases achieved fair results with residual stiffness of the interphalangeal joint. No secondary operations were needed. We conclude that MRI proved useful in subclassifying Wassel Type IV duplicated thumbs and may aid in planning the osteotomies needed for their reconstruction. Level of evidence: IV

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On the classification of easy quantum groups

Advances in Mathematics ◽

10.1016/j.aim.2013.06.019 ◽

2013 ◽

Vol 245 ◽

pp. 500-533 ◽

Cited By ~ 15

Author(s):

Moritz Weber

Keyword(s):

Quantum Groups

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The Center of Small Quantum Groups I: The Principal Block in Type A

International Mathematics Research Notices ◽

10.1093/imrn/rnx062 ◽

2017 ◽

Vol 2018 (20) ◽

pp. 6349-6405 ◽

Cited By ~ 1

Author(s):

Anna Lachowska ◽

You Qi

Keyword(s):

Quantum Groups ◽

Type A ◽

Principal Block ◽

Small Quantum

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PBW-type filtration on quantum groups of type A

Journal of Algebra ◽

10.1016/j.jalgebra.2015.09.054 ◽

2016 ◽

Vol 449 ◽

pp. 321-345 ◽

Cited By ~ 5

Author(s):

Xin Fang ◽

Ghislain Fourier ◽

Markus Reineke

Keyword(s):

Quantum Groups ◽

Type A

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Classification Of Uniform Flag Triangulations Of The Boundary Of The Full Root Polytope Of Type A

Acta Mathematica Hungarica ◽

10.1007/s10474-020-01099-2 ◽

2020 ◽

Author(s):

R. Ehrenborg ◽

G. Hetyei ◽

M. Readdy

Keyword(s):

Type A ◽

Root Polytope

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A New Classification of Cochleovestibular Malformations and Implications for Predicting Speech Perception Ability after Cochlear Implantation

Audiology and Neurotology ◽

10.1159/000365584 ◽

2015 ◽

Vol 20 (2) ◽

pp. 90-101 ◽

Cited By ~ 12

Author(s):

Sung-Wook Jeong ◽

Lee-Suk Kim

Keyword(s):

Speech Perception ◽

Cochlear Implantation ◽

Test Scores ◽

Type A ◽

Cochlear Nerve ◽

Type B ◽

New Classification ◽

Type D ◽

Type C

Objectives: The aims of this study were to introduce a new classification of cochleovestibular malformation (CVM) and to investigate how well this classification can predict speech perception ability after cochlear implantation in children with CVM. Methods: Fifty-nine children with CVM who had used a cochlear implant for more than 3 years were included. CVM was classified into 4 subtypes based on the morphology of the cochlea and the modiolus on temporal bone computed tomography (TBCT): normal cochlea and normal modiolus (type A, n = 16), malformed cochlea and partial modiolus (type B, n = 31), malformed cochlea and no modiolus (type C, n = 6), and no cochlea and no modiolus (type D, n = 6). Speech perception test scores were compared between the subtypes of CVM using analysis of covariance with post hoc Bonferroni test. Univariate and multivariate regression analyses were used to identify the significant predictors of the speech perception test scores. Results: The speech perception test scores after implantation were significantly better in children with CVM type A or type B than in children with CVM type C or type D. The test scores did not differ significantly between the implanted children with CVM type A or type B and those without CVM. In univariate regression analysis, the type of CVM was a significant predictor of the speech perception test scores in implanted children with CVM. Multivariate regression analysis revealed that the age at cochlear implantation, cochlear nerve size and preimplantation speech perception test scores were significant predictors of the postimplantation speech perception test scores. The chance of cochlear nerve deficiency increased progressively from CVM type A to type D. Conclusion: The new classification of CVM based on the morphology of the cochlea and the modiolus is simple and easy to use, and correlated well with postimplantation speech perception ability and cochlear nerve status. This simple classification of CVM using TBCT with cochlear nerve assessment by magnetic resonance imaging is helpful in the preoperative evaluation of children with CVM.

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Classification of Quantum Groups via Galois Cohomology

Communications in Mathematical Physics ◽

10.1007/s00220-019-03597-z ◽

2019 ◽

Vol 377 (2) ◽

pp. 1099-1129

Author(s):

Eugene Karolinsky ◽

Arturo Pianzola ◽

Alexander Stolin

Keyword(s):

Quantum Groups ◽

Galois Cohomology

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Classification of osteonecrosis of the femoral head

Bone and Joint Research ◽

10.1302/2046-3758.810.bjr-2019-0022.r1 ◽

2019 ◽

Vol 8 (10) ◽

pp. 451-458 ◽

Cited By ~ 3

Author(s):

Yutaka Kuroda ◽

Takeyuki Tanaka ◽

Takaki Miyagawa ◽

Toshiyuki Kawai ◽

Koji Goto ◽

...

Keyword(s):

Femoral Head ◽

Treatment Guidelines ◽

Type A ◽

Type B ◽

Kaplan Meier ◽

Joint Preserving Surgery ◽

Asymptomatic Patients ◽

Study Results ◽

Collapse Rate

Objectives Using a simple classification method, we aimed to estimate the collapse rate due to osteonecrosis of the femoral head (ONFH) in order to develop treatment guidelines for joint-preserving surgeries. Methods We retrospectively analyzed 505 hips from 310 patients (141 men, 169 women; mean age 45.5 years (sd 14.9; 15 to 86)) diagnosed with ONFH and classified them using the Japanese Investigation Committee (JIC) classification. The JIC system includes four visualized types based on the location and size of osteonecrotic lesions on weightbearing surfaces (types A, B, C1, and C2) and the stage of ONFH. The collapse rate due to ONFH was calculated using Kaplan–Meier survival analysis, with radiological collapse/arthroplasty as endpoints. Results Bilateral cases accounted for 390 hips, while unilateral cases accounted for 115. According to the JIC types, 21 hips were type A, 34 were type B, 173 were type C1, and 277 were type C2. At initial diagnosis, 238/505 hips (47.0%) had already collapsed. Further, the cumulative survival rate was analyzed in 212 precollapsed hips, and the two-year and five-year collapse rates were found to be 0% and 0%, 7.9% and 7.9%, 23.2% and 36.6%, and 57.8% and 84.8% for types A, B, C1, and C2, respectively. Conclusion Type A ONFH needs no further treatment, but precollapse type C2 ONFH warrants immediate treatment with joint-preserving surgery. Considering the high collapse rate, our study results justify the importance of early diagnosis and intervention in asymptomatic patients with type C2 ONFH. Cite this article: Y. Kuroda, T. Tanaka, T. Miyagawa, T. Kawai, K. Goto, S. Tanaka, S. Matsuda, H. Akiyama. Classification of osteonecrosis of the femoral head: Who should have surgery?. Bone Joint Res 2019;8:451–458. DOI: 10.1302/2046-3758.810.BJR-2019-0022.R1.

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