Electrophilic aromatic substitution reactions of compounds with Craig-Möbius aromaticity.

Electrophilic aromatic substitution (EAS) reactions are widely regarded as characteristic reactions of aromatic species, but no comparable reaction has been reported for molecules with Craig-Möbius aromaticity. Here, we demonstrate successful EAS reactions of Craig-Möbius aromatics, osmapentalenes, and fused osmapentalenes. The highly reactive nature of osmapentalene makes it susceptible to electrophilic attack by halogens, thus osmapentalene, osmafuran-fused osmapentalene, and osmabenzene-fused osmapentalene can undergo typical EAS reactions. In addition, the selective formation of a series of halogen substituted metalla-aromatics via EAS reactions has revealed an unprecedented approach to otherwise elusive compounds such as the unsaturated cyclic chlorirenium ions. Density functional theory calculations were conducted to study the electronic effect on the regioselectivity of the EAS reactions.

Is it still necessary to perform measured based pre-treatment patient-specific QA for SRS HyperArc treatments?

PURPOSE: The Mobius3D system was validated as a modern secondary check dosimetry system. In particular, our objective has been to assess the suitability of the M3D as pre-treatment patient-specific Quality Assurance (QA) tool for Stereotactic Radiosurgery (SRS) HyperArc (HA) treatments. We aimed to determine whether Mobius3D could safely replace the measurements-based patient-specific QA for this type of treatment. METHODS: 30 SRS HA treatment plans for brain were selected. The dose distributions, calculated by Mobius and our routinely used algorithm (AcurosXB v.15.6), were compared using gamma analysis index and DVH parameters based on the patient's CT dataset. All 30 plans were then delivered across the ionization chamber in a homogeneous phantom and the measured dose was compared with both M3D and TPS calculated one. The plans were delivered and verified in terms of PSQA using the electronic portal imaging device (EPID) with Portal Dosimetry (PD) and myQA SRS (IBA Dosimetry) detector. Plans that achieved a global gamma passing rate (GPR) ≥ 97% based on 2%/2 mm criteria, with both Mobius3D and the conventional methods were evaluated acceptable. Finally, we assessed the capability of the M3D system to detect errors related to the position of the Multi-Leaf Collimator (MLC) in comparison to the analyzed measurement-based systems. RESULTS: No relevant differences were observed in the comparison between the dose calculated on the CT-dataset by M3D and the TPS. Observed discrepancies are imputable to different used algorithms, but no discrepancies related to goodness of plans have been found. Average differences between calculated (M3D and TPS) vs measured dose with ionization chamber were 2.5% (from 0.41% to 3.2%) and 1.81% (from 0.66% to 2.65%), for M3D and TPS, respectively. All plans passed with a gamma passing rate > 97% using conventional PSQA methods with a gamma criterion of 2% dose difference and 2 mm distance-to-agreement. The average gamma passing rate for the M3D system was determined to be 99.4% (from 97.3% to 100%). Results from this study also demonstrated Mobius has better error detectability than conventional measurement-based systems. CONCLUSION: Our study shows Mobius3D could be a suitable alternative to conventional measured based QA methods for SRS HyperArc treatments.

Commissioning of Mobius3D/FX for patient-specific quality assurance: The CUIMC-NewYork Presbyterian Hospital experience.

PURPOSE: To present the process undertaken by our institute in commissioning Mobius3D (M3D) for patient-specific quality assurance. METHOD: 168 plans were randomly selected to compare dose distribution measured with ArcCheck and dose calculated from M3D, both compared against the treatment planning system (TPS). The gamma criteria for measurement and M3D are 3%/2 mm with 10% and 50% dose thresholds, respectively. The effect of tissue inhomogeneity was investigated on 11 plans by recalculating the dose in M3D on a homogeneous phantom. Tolerance and action limits were established following the AAPM Task Group 218 recommendations. RESULTS: The M3D showed high variability in gamma passing rate compared to the measurement. Twenty-three out of 168 plans had false negative dose comparisons. These plans fall under high tissue inhomogeneity like lung and metal implants, small field targets, and breast plans planned with high energy. One false negative case (0.6%) was observed. A single tolerance limit of 91% and 92% gamma passing rate for the M3D and measurement-based PSQA were established, respectively. Against the expectation, recalculating plans on the homogeneous phantom in M3D did not necessarily increase the gamma passing rate. These plans have a duty cycle >4.2, and the small field sizes combined with differences in slice thickness contributed to observed dose differences in the homogeneous phantom comparisons. CONCLUSION: Following the commissioning, M3D is adopted in our institute. Currently, the gamma criteria used for measurement and M3D are 3%/2 mm, 40% dose threshold, with gamma passing rates of 92% and 95%, respectively. A higher passing rate for M3D is adopted until more data is available. The combined effect of plan modulation, the field sizes, the tissue inhomogeneity, the dose algorithm, and the volume averaging effect from differences in slice thickness can contribute to the differences in dose in M3D and TPS.

Optoelectronic Properties of Triply Twisted Möbius Carbon Nanobelt and the Design of Its Isomeric Nanomaterials.

The triply twisted Möbius carbon nanobelt (TMCNB) possesses an extremely distinctive geometric and electronic structure and therefore is anticipated to demonstrate outstanding optical properties. In this paper, through integrating quantum chemical calculations and wave function analysis approaches, in-depth studies are conducted on the one-photon absorption (OPA) and two-photon absorption (TPA) characteristics, aromaticity, and circular dichroism of the TMCNB. Inspired by this structure, we further deform it to construct a novel structure, MCNB2, and verify the stability of this structure, thereby confirming its rationality. Since variations in structure will result in dissimilar optical properties, we also undertake theoretical analyses on the absorption properties and circular dichroism of MCNB2. The outcomes of this study offer a significant theoretical foundation for the design and construction of chiral optoelectronic materials.

Circumcenter extension maps for non-positively curved spaces.

We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditions. We describe regions on which this map is Hölder-continuous. Furthermore, we show that this map is a rough isometry, whenever the manifolds admit cocompact group actions by isometries and we improve previously known quasi-isometry constants, provided by Biswas, in the case of 2-dimensional CAT(-1) manifolds. Finally, we provide a sufficient condition for this map to be an isometry in the case of Hadamard surfaces.

Unveiling Möbius/Hückel Topology and Aromaticity in A Core-Expanded [10]Annulene at Different Oxidation States.

The exploration of annulene's conformation, electronic properties and aromaticity has generated enduring interest over the years, yet it continues to present formidable challenges for annulenes with more than ten carbon atoms. In this study, we present the synthesis of a stable [10]cyclo-para-phenylmethine derivative (1), which bears a resemblance to [10]annulene. 1 can be readily oxidized into its respective cations, wherein electrons are effectively delocalized along the backbone, resulting in different conformations and aromaticity. Both 1 and its tetracation (14+ ⋅ 4SbF6 - ) exhibit a nearly planar conformation with a rectangular shape, akin to the E,Z,E,Z,Z-[10]annulene. In contrast, the radical cation (1⋅+ ⋅ SbCl6 - ) possesses a doubly twisted Hückel topology. Furthermore, the dication (12+ ⋅ 2SbCl6 - ) displays conformational flexibility in solution and crystalizes with the simultaneous presence of Möbius-twisted (1a2+ ⋅ 2SbCl6 - ) and Hückel-planar (1b2+ ⋅ 2SbCl6 - ) isomers in its unit cell. Detailed experimental measurements and theoretical calculations reveal that: (1) 1 demonstrates localized aromaticity with an alternating benzenoid/quinoid structure; (2) 1a2+ ⋅ 2SbCl6 - and 1b2+ ⋅ 2SbCl6 - with 48π electrons are weakly Möbius aromatic and Hückel antiaromatic, respectively; (3) 14+ ⋅ 4SbF6 - exhibits Hückel aromaticity (46π) and open-shell diradical character.

[5]Helicene Based π-Conjugated Macrocycles with Persistent Figure-Eight and Möbius Shapes: Efficient Synthesis, Chiral Resolution and Bright Circularly Polarized Luminescence.

π-Conjugated chiral shape-persistent molecular nanocarbons hold great potential as chiroptical materials, though their synthesis remains a considerable challenge. Here, we present a simple approach using Suzuki coupling of a [5]helicene building block with various aromatic units, enabling the one-pot synthesis of a series of chiral macrocycles with persistent figure-eight and Möbius shapes. Single-crystal structures of 7 compounds were solved, and 22 enantiomers were separated by preparative chiral HPLC. A notable pyrene-bridged figure-eight macrocycle, with its rigid, fully π-conjugated and overcrowded structure, exhibited pure excimer emission and outstanding circularly polarized luminescence (CPL) properties, including a large dissymmetric factor (|glum| = 3.8 × 10-2) and significant CPL brightness (BCPL = 710.5 M-1cm-1). This method provides a versatile synthetic platform for producing various chiral D2-symmetric figure-eight macrocycles and singly or triply twisted Möbius macrocycles with C2 and D3 symmetry, offering tunable chiroptical properties for CPL applications.

Monozygotic twins discordant for a congenital cranial dysinnervation disorder with features of Moebius syndrome.

Moebius syndrome is a congenital cranial dysinnervation disorder (CCDD) that presents with nonprogressive cranial nerve (CN) VI and VII palsies resulting in facial weakness and inability to abduct the eye(s). While many CCDDs have an underlying genetic cause, the etiology of Moebius syndrome remains unclear as most cases are sporadic. Here, we describe a pair of monochorionic, diamniotic twin girls; one with normal growth and development, and one with micrognathia, reduced facial expression, and poor feeding. Magnetic resonance imaging of the brain performed on the affected twin at 19 months of age showed severely hypoplastic or absent CN IV bilaterally, left CN VI smaller than right, and bilateral hypoplastic CN VII and IX, consistent with a diagnosis of a CCDD, most similar to that of Moebius syndrome. Genomic sequencing was performed on each twin and data was assessed for discordant variants, as well as variants in novel and CCDD-associated genes. No pathogenic, likely pathogenic, or variants of uncertain significance were identified in genes known to be associated with CCDDs or other congenital facial weakness conditions. This family provides further evidence in favor of a stochastic event as the etiology in Moebius syndrome, rather than a monogenic condition.

Optical Physical Mechanisms of Helicene Carbon Nanohoop with Möbius Topology.

Optical and spectral properties of carbon nanohoop with Möbius topology is of great interest in nano-science and nano-technology. And it can be imagined that it has a lot of unexpected potential application prospects. However, theoretical calculations based on some figure-of-eight helicene carbon nanohoop with Möbius topology are still insufficient. Therefore, in this paper, we theoretically study the optical and spectral properties of figure-of-eight helicene carbon nanohoop with Möbius topology. Optical and spectral properties are analyzed with visualization method of transition density matrix and charge density difference, which reveal the unique characterization of carbon nanohoop with Möbius topology. Our results can not only deepen the understanding of the optical physical mechanisms of the nanorings with mobius carbons, but also provide deeper insight on optical properties and potential design on optical nanodevices.

Scale-up analysis of geometrically dissimilar single-use bioreactors.

Cell culture scale-up is a challenging task due to the simultaneous change of multiple hydrodynamic process characteristics and their different dependencies on the bioreactor size as well as variation in the requirements of individual cell lines. Conventionally, the volumetric power input is the most common parameter to select the impeller speed for scale-up, however, it is well reported that this approach fails when there are huge differences in bioreactor scales. In this study, different scale-up criteria are evaluated. At first, different hydrodynamic characteristics are assessed using computational fluid dynamics data for four single-use bioreactors, the Mobius® CellReady 3 L, the Xcellerex™ XDR-10, the Xcellerex™ XDR-200, and the Xcellerex™ XDR-2000. On the basis of this numerical data, several potential scale-up criteria such as volumetric power input, impeller tip speed, mixing time, maximum hydrodynamic stress, and average strain rate in the impeller zone are evaluated. Out of all these criteria, the latter is found to be most appropriate, and the successful scale-up from 3 to 10 L bioreactor and to 200 L bioreactor is confirmed with cell culture experiments using Chinese Hamster Ovary cell cultivation.

Prenatal diagnosis of Poland-Möbius syndrome by multimodality fetal imaging.

We describe prenatal diagnosis of Poland-Möbius syndrome using a combination of ultrasound and MRI. Poland syndrome was diagnosed based on absence of the pectoralis muscles associated with dextroposition of the fetal heart and elevation of the left diaphragm. Associated brain anomalies that led to the diagnosis of Poland-Möbius syndrome, included ventriculomegaly, hypoplastic cerebellum, tectal beaking, and a peculiar flattening of the posterior aspect of the pons and medulla oblongata, which has been reported by postnatal diffusion tensor imaging studies as a reliable neuroimaging marker for Möbius syndrome. Since abnormalities of cranial nerves VI and VII may be difficult to detect prenatally, careful attention to the appearance of the brain stem as illustrated in the current report may aid in the prenatal diagnosis of Möbius syndrome.

Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information.

Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies while leaving certain fundamentally different systems indistinguishable. Furthermore, there is no consensus on the correct higher-order generalisation of mutual information (MI). In this manuscript, we show that a recently proposed model-free definition of higher-order interactions among binary variables (MFIs), such as mutual information, is a Möbius inversion on a Boolean algebra, except of surprisal instead of entropy. This provides an information-theoretic interpretation to the MFIs, and by extension to Ising interactions. We study the objects dual to mutual information and the MFIs on the order-reversed lattices. We find that dual MI is related to the previously studied differential mutual information, while dual interactions are interactions with respect to a different background state. Unlike (dual) mutual information, interactions and their duals uniquely identify all six 2-input logic gates, the dy- and triadic distributions, and different causal dynamics that are identical in terms of their Shannon information content.

Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map.

In encryption technology, image scrambling is a common processing operation. This paper proposes a quantum version of the 3D Mobius scrambling transform based on the QRCI model, which changes not only the position of pixels but also the gray values. The corresponding quantum circuits are devised. Furthermore, an encryption scheme combining the quantum 3D Mobius transform with the 3D hyper-chaotic Henon map is suggested to protect the security of image information. To facilitate subsequent processing, the RGB color image is first represented with QRCI. Then, to achieve the pixel-level permutation effect, the quantum 3D Mobius transform is applied to scramble bit-planes and pixel positions. Ultimately, to increase the diffusion effect, the scrambled image is XORed with a key image created by the 3D hyper-chaotic Henon map to produce the encrypted image. Numerical simulations and result analyses indicate that our designed encryption scheme is secure and reliable. It offers better performance in the aspect of key space, histogram variance, and correlation coefficient than some of the latest algorithms.

Synthesis of Twisted [n]Cycloparaphenylene by Alkene Insertion.

Mono-alkene-inserted [n]cycloparaphenylenes 1 [(ene)-[n]CPP] with n=6, 8, and 10, mono-ortho-phenylene-inserted [6]CPP 2, and di-alkene-insertved [n]CPP 3 [(ene)2 -[n]CPP] with n=4, 6, and 8 were synthesized by fusing CPP precursors and alkene or ortho- phenylene groups through coupling reactions. Single-crystal X-ray diffraction analyses reveal that the strips formed by the π-surfaces of 1 and 2 exhibited a Möbius topology in the solid state. While the Möbius topology in the parent 1 and 2 in solution was lost due to the free rotation of the paraphenylene unit even at low temperatures, ene-[6]CPP 4 with eight 1-pyrrolyl groups preserved the Möbius topology even in solution. Despite a twist, 1 has in-plane conjugation and possesses a unique size dependence of the electronic properties: namely, the opposite size dependency of the HOMO-LUMO energy relative to conventional π-conjugated molecules.

3D-Printed Möbius Microring Lasers: Topology Engineering in Photonic Microstructures.

Manipulating photons in artificially structured materials is highly desired in modern photonic technology. Nontrivial topological structures are rapidly emerging as a state-of-art platform for achieving unprecedented fascinating phenomena of photon manipulation. However, the current studies mainly focus on planar structures, and the fabrication of photonic microstructures with specific topological geometric features still remains a great challenge. Extending the topological photonics to 3D microarchitectures is expected to enrich the photon manipulation capabilities and further advance the topological photonic devices. Here, a femtosecond laser direct writing technique is employed to fabricate 3D topological Möbius microring resonators from dye-doped polymer. The high-quality-factor Möbius microring resonator supports a unique spin-orbit coupled lasing at very low threshold. Due to the spin-orbit coupling induced geometric/Berry phase, the Möbius microrings, in striking contrast with ordinary microrings, output laser signals with all polarization states. The manipulation of miniaturized coherent light sources in the fabricated Möbius microrings represents a significant step forward toward 3D topological photonics that offers a novel design philosophy for functional photonic and optoelectronic devices.

A Fully Conjugated Porphyrin-[36]Octaphyrin-Porphyrin Hybrid Tape Exhibiting Möbius Aromaticity.

Directly meso-meso linked porphyrin-tetrabromo[36]octaphyrin-porphyrin hybrid trimer 10 was successfully synthesized via acid-catalyzed condensation reaction and subsequent oxidation. ZnII -metalation of 10 induced transannular meso-meso bond formation to give Möbius aromatic bis-ZnII octaphyrin 11, which was oxidized by DDQ/Sc(OTf)3 to provide fully conjugated porphyrin-[36]octaphyrin-porphyrin hybrid tape 12 as the first example of porphyrin tape exhibiting Möbius aromaticity. Hybrid tape 12 displays significantly red-shifted absorption and small electrochemical HOMO-LUMO gap, indicating the effective conjugation through the whole chromophores.

Poland-Möbius syndrome: a case report implicating a novel mutation of the PLXND1 gene and literature review.

BACKGROUND: Möbius (Moebius) and Poland's syndromes are two rare congenital syndromes characterized by non-progressive bilateral (and often asymmetric) dysfunction of the 6th and 7th cranial nerves and hypoplasia of the pectoral muscles associated with chest wall and upper limb anomalies respectively. Manifest simultaneously as Poland-Möbius (Poland-Moebius) syndrome, debate continues as to whether this is a distinct nosological entity or represents phenotypic variation as part of a spectrum of disorders of rhomboencephalic development. Etiological hypotheses implicate both genetic and environmental factors. The PLXND1 gene codes for a protein expressed in the fetal central nervous system and vascular endothelium and is thus involved in embryonic neurogenesis and vasculogenesis. It is located at chromosome region 3q21-q22, a locus of interest for Möbius syndrome. CASE PRESENTATION: We present the first report of a patient with Poland-Möbius syndrome and a mutation in the PLXND1 gene. A child with Poland-Möbius syndrome and a maternally inherited missense variant (NM_015103.2:ex14:c.2890G > Ap.V964M) in the PLXND1 gene is described. In order to contextualize these findings, the literature was examined to identify other confirmed cases of Poland-Möbius syndrome for which genetic data were available. Fourteen additional cases of Poland-Möbius syndrome with genetic studies are described in the literature. None implicated the PLXND1 gene which has previously been implicated in isolated Möbius syndrome. CONCLUSIONS: This report provides further evidence in support of a role for PLXND1 mutations in Möbius syndrome and reasserts the nosological link between Möbius and Poland's syndromes. LEVEL OF EVIDENCE: Level V, Descriptive Study.

Assessment of log-based fingerprinting system of Mobius3D with Elekta linear accelerators.

PURPOSE: The purpose of this study was to investigate the matching error that occurs when the Mobius3D fingerprinting system is applied in conjunction with an Elekta linear accelerator (LINAC) and to offer an acceptable and alternative method for circumventing this problem. MATERIAL AND METHODS: To avoid the multileaf collimator (MLC) conflicting error in the Mobius3D fingerprinting system, we developed an in-house program to move the MLC in the Digital Imaging and Communications in Medicine (DICOM) radiotherapy (RT)-Plan to pertinent positions, considering the relationship between log data and planned data. The re-delivered log files were calculated in the Mobius3D system, and the results were compared with those of corrected data (i.e., we analyzed a pair of re-collected log data and the previous DICOM RT-Plan data). The results were then evaluated by comparing several items, such as point dose errors, gamma index (GI) passing rates, and MLC root-mean-square (RMS) values. RESULTS: For the point dose error, the maximum difference found was below 2.0%. In the case of GI analysis of all plans, the maximum difference in the passing rates was below 1.4%. The statistical results obtained using a paired Student's t-test showed that there were no significant differences within the uncertainty. In the case of the RMS test, the maximum difference found was approximately 0.08 mm. CONCLUSIONS: Our results showed that all the mismatched log files were sufficiently acceptable within the uncertainty. We conclude that the matching error obtained when applying Mobius3D to an Elekta LINAC may be addressed using a simple modification of the fingerprinting system, and we expect that our study findings will help vendors resolve this issue in the near future.

Scalable OneM2M IoT Open-Source Platform Evaluated in an SDN Optical Network Controller Scenario.

Software Defined Networking represents a mature technology for the control of optical networks, though all open controller implementations present in the literature still lack the adequate level of maturity and completeness to be considered for (pre)-production network deployments. This work aims at experimenting on, assessing and discussing the use of the OneM2M open-source platform in the context of optical networks. Network elements and devices are implemented as IoT devices, and the control application is built on top of an OneM2M-compliant server. The work concretely addresses the scalability and flexibility performances of the proposed solution, accounting for the expected growth of optical networks. The two experiment scenarios show promising results and confirm that the OneM2M platform can be adopted in such a context, paving the way to other researches and studies.

Information Theoretic Methods for Variable Selection-A Review.

We review the principal information theoretic tools and their use for feature selection, with the main emphasis on classification problems with discrete features. Since it is known that empirical versions of conditional mutual information perform poorly for high-dimensional problems, we focus on various ways of constructing its counterparts and the properties and limitations of such methods. We present a unified way of constructing such measures based on truncation, or truncation and weighing, for the Möbius expansion of conditional mutual information. We also discuss the main approaches to feature selection which apply the introduced measures of conditional dependence, together with the ways of assessing the quality of the obtained vector of predictors. This involves discussion of recent results on asymptotic distributions of empirical counterparts of criteria, as well as advances in resampling.