(1R*,2R*)‐1,2‐(2,3‐Di­methoxy­butane‐2,3‐dioxy)cyclo­hexane

The title compound, 2,3‐di­methoxy‐2,3‐di­methyl‐5,6,7,8‐tetra­hydro‐4‐oxa­chroman, C₁₂H₂₂O₄, was synthesized as a model compound for substituted diequatorial fixed vicinal trans‐cyclo­hexane­diols.     

Glaucoma classification based on visual pathway analysis using diffusion tensor imaging

Most of the existing methods for diagnosing glaucoma analyze the eye with a main focus on the retina, despite the transsynaptic nature of the fiber degeneration caused by glaucoma. Thus, they ignore a significant part of the visual system represented by the visual pathway in the brain. The advances in neuroimaging, especially diffusion tensor imaging (DTI), enable the identification and characterization of white matter fibers. In this work, we propose a system based on DTI analysis of the visual pathway fibers in the optic radiation for detecting and discriminating different glaucoma entities. The optic radiation is identified semi-automatically. DTI provides information about the fiber orientation as well as a set of derived parameters describing the degree of diffusion anisotropy and diffusivity. Features for each DTI derived measure are extracted from a specified region of interest on the optic radiation. The features are grouped into three sets: Histogram, co-occurrence matrices, and Laws features. For feature selection, the features are ranked using a support vector machine classifier. The highest ranked features are used for classification. A support vector machine classifier is used for classification in a 10-fold cross validation setup. The system is applied to three age-matched subjects’ categories containing 27 healthy, 39 primary open angle glaucoma (POAG), and 18 normal tension glaucoma (NTG) subjects. The discrimination accuracy between healthy and glaucoma (POAG and NTG) subjects is 94.1% with an area under the ROC of 0.97. Classification accuracy of 92.4% is obtained for the normal and the POAG groups while it increased to 100% in case of healthy and NTG groups. In addition, the system could differentiate between glaucoma types (POAG and NTG) with an accuracy of 98.3%. A complementary analysis was performed to estimate the selection bias in the obtained accuracy. The bias ranged from 10% to 20% depending on the group pair under consideration. The classification results indicate the high performance of the system compared to retina-based glaucoma detection systems. The proposed approach utilizes visual pathway analysis rather than the conventional eye analysis which presents a new trend in glaucoma detection. Analyzing the entire visual system could provide significant information that can improve the glaucoma examination flow and treatment.     

Electronic Structures and Chiroptical Properties of Post‐functionalized Helicene Quinones

The synthesis of redox‐active p‐ and o‐quinones 2‐phenylamino‐4‐phenylimino[6]helicene‐1‐one 1 , 2‐phenylamino[6]‐helicene‐1,4‐dione 2 , and 4‐phenyl[6]helicene‐1,2‐dione 3 in their enantiopure forms by post‐functionalization of (P)‐ and (M)‐1,2‐dimethoxy[6]helicene is presented. Structural characterization in solution and in the solid state was accomplished by 2D NMR spectroscopy methods and X‐ray diffraction analysis, respectively. Interpretation of electrochemical redox data was accompanied by a detailed orbital picture, derived from DFT calculations. The electronic structures of compounds 1 – 3 were investigated by UV/Vis and electronic circular dichroism (ECD) spectroscopy, complemented by TD‐DFT calculations. Quinones 1 – 3 were chemically reduced to study the EPR signatures of their respective radical anions. DFT methods were used for the atom assignment of the hyperfine coupling constants. The results are discussed within the context of electrochromic chiral switches and molecular recognition.     

Push–Pull Buta‐1,2,3‐trienes: Exceptionally Low Rotational Barriers of Cumulenic CC Bonds and Proacetylenic Reactivity

A variety of asymmetrically donor–acceptor‐substituted [3]cumulenes (buta‐1,2,3‐trienes) were synthesized by developed procedures. The activation barriers to rotation ΔG^≠ were measured by variable temperature NMR spectroscopy and found to be as low as 11.8 kcal mol^?1, in the range of the barriers for rotation around sterically hindered single bonds. The central C?C bond of the push–pull‐substituted [3]cumulene moiety is shortened down to 1.22 Å as measured by X‐ray crystallography, leading to a substantial bond length alternation (BLA) of up to 0.17 Å. All the experimental results are supported by DFT calculations. Zwitterionic transition states (TS) of bond rotation confirm the postulated proacetylenic character of donor–acceptor [3]cumulenes. Additional support for the proacetylenic character of these chromophores is provided by their reaction with tetracyanoethene (TCNE) in a cycloaddition‐retroelectrocyclization (CA–RE) cascade characteristic of donor‐polarized acetylenes.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

NHC→SiCl4: An Ambivalent Carbene‐Transfer Reagent

The addition of BCl₃ to the carbene‐transfer reagent NHC→SiCl₄ (NHC=1,3‐dimethylimidazolidin‐2‐ylidene) gave the tetra‐ and pentacoordinate trichlorosilicon(IV) cations [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ with tetrachloroborate as counterion. This is in contrast to previous reactions, in which NHC→SiCl₄ served as a transfer reagent for the NHC ligand. The addition of BF₃ ? OEt₂, on the other hand, gave NHC→BF₃ as the product of NHC transfer. In addition, the highly Lewis acidic bis(pentafluoroethyl)silane (C₂F₅)₂SiCl₂ was treated with NHC→SiCl₄. In acetonitrile, the cationic silicon(IV) complexes [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ were detected with [(C₂F₅)SiCl₃]^? as counterion. A similar result was already reported for the reaction of NHC→SiCl₄ with (C₂F₅)₂SiH₂, which gave [(NHC)₂SiCl₂H][(C₂F₅)SiCl₃]. If the reaction medium was changed to dichloromethane, the products of carbene transfer, NHC→Si(C₂F₅)₂Cl₂ and NHC→Si(C₂F₅)₂ClH, respectively, were obtained instead. The formation of the latter species is a result of chloride/hydride metathesis. These compounds may serve as valuable precursors for electron‐poor silylenes. Furthermore, the reactivity of NHC→SiCl₄ towards phosphines is discussed. The carbene complex NHC→PCl₃ shows similar reactivity to NHC→SiCl₄, and may even serve as a carbene‐transfer reagent as well.