Cosmetic operations and Khovanov multicurves.

We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants Kh~ and BN~. We apply the same techniques to reprove a result of Wang about the Cosmetic Crossing Conjecture and split links. Along the way, we show that Kh~ and BN~ detect if a Conway tangle is split.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2Te4.

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN, though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex) and its spatial fluctuation in the QAH insulator 5-layer MnBi2Te4. Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Prevalence of symptoms, comorbidities, fibrin amyloid microclots and platelet pathology in individuals with Long COVID/Post-Acute Sequelae of COVID-19 (PASC).

BACKGROUND: Fibrin(ogen) amyloid microclots and platelet hyperactivation previously reported as a novel finding in South African patients with the coronavirus 2019 disease (COVID-19) and Long COVID/Post-Acute Sequelae of COVID-19 (PASC), might form a suitable set of foci for the clinical treatment of the symptoms of Long COVID/PASC. A Long COVID/PASC Registry was subsequently established as an online platform where patients can report Long COVID/PASC symptoms and previous comorbidities. METHODS: In this study, we report on the comorbidities and persistent symptoms, using data obtained from 845 South African Long COVID/PASC patients. By using a previously published scoring system for fibrin amyloid microclots and platelet pathology, we also analysed blood samples from 80 patients, and report the presence of significant fibrin amyloid microclots and platelet pathology in all cases. RESULTS: Hypertension, high cholesterol levels (dyslipidaemia), cardiovascular disease and type 2 diabetes mellitus (T2DM) were found to be the most important comorbidities. The gender balance (70% female) and the most commonly reported Long COVID/PASC symptoms (fatigue, brain fog, loss of concentration and forgetfulness, shortness of breath, as well as joint and muscle pains) were comparable to those reported elsewhere. These findings confirmed that our sample was not atypical. Microclot and platelet pathologies were associated with Long COVID/PASC symptoms that persisted after the recovery from acute COVID-19. CONCLUSIONS: Fibrin amyloid microclots that block capillaries and inhibit the transport of O2 to tissues, accompanied by platelet hyperactivation, provide a ready explanation for the symptoms of Long COVID/PASC. Removal and reversal of these underlying endotheliopathies provide an important treatment option that urgently warrants controlled clinical studies to determine efficacy in patients with a diversity of comorbidities impacting on SARS-CoV-2 infection and COVID-19 severity. We suggest that our platelet and clotting grading system provides a simple and cost-effective diagnostic method for early detection of Long COVID/PASC as a major determinant of effective treatment, including those focusing on reducing clot burden and platelet hyperactivation.

Defects, band bending and ionization rings in MoS2.

Chalcogen vacancies in transition metal dichalcogenides are widely acknowledged as both donor dopants and as a source of disorder. The electronic structure of sulphur vacancies in MoS2however is still controversial, with discrepancies in the literature pertaining to the origin of the in-gap features observed via scanning tunneling spectroscopy (STS) on single sulphur vacancies. Here we use a combination of scanning tunnelling microscopy and STS to study embedded sulphur vacancies in bulk MoS2crystals. We observe spectroscopic features dispersing in real space and in energy, which we interpret as tip position- and bias-dependent ionization of the sulphur vacancy donor due to tip induced band bending. The observations indicate that care must be taken in interpreting defect spectra as reflecting in-gap density of states, and may explain discrepancies in the literature.

Heegaard Floer homology for manifolds with torus boundary: properties and examples.

This is a companion paper to earlier work of the authors (Preprint, arXiv:1604.03466, 2016), which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We establish a variety of properties of this invariant, paying particular attention to its relation to knot Floer homology, the Thurston norm, and the Turaev torsion. We also give a geometric description of the gradings package from bordered Heegaard Floer homology and establish a symmetry under Spin c conjugation; this symmetry gives rise to genus one mutation invariance in Heegaard Floer homology for closed three-manifolds. Finally, we include more speculative discussions on relationships with Seiberg-Witten theory, Khovanov homology, and HF ± . Many examples are included.

Neurodisability with Severe Restriction of Mobility Is Associated with Reduced Serum Creatinine Values.

INTRODUCTION: We investigated whether reduced mobility is associated with a reduction in serum creatinine in otherwise well children with neurodisability. MATERIALS AND METHODS: This was a record based retrospective study and creatinine levels of children in groups with Gross Motor Function Classification System (GMFCS) category 1, 2, or 3 (group I); GMFCS 4 or 5 (group II); and age matched controls (group III) were compared. RESULTS: Creatinine values were significantly different (p=0.002) between patients with neurodisability (mean 32.0 (SD 9.3), n=88) compared to patients without (mean 36.5 SD (9.8), n=88). There was no significant difference in creatinine levels (p=0.684) between group I (mean 35.6 (9.1), n=23) and group III (mean 36.5 (9.8), n=88). A significantly lower creatinine level (p<0.001) was found in group II (mean 30.7 (9.1), n=65) compared to group III and group I compared to group II (p=0.034). Creatinine levels were with a mean (SD) of 25.7 (4.1) micromol/l significantly lower in patients with GMFCS 4 or 5 who died (n=4) compared to survivors (31.1 (3.6)), (p=0.04, n=61). CONCLUSIONS: Children with neurodisability with severe mobility restriction had a significantly lower serum creatinine compared to controls with less severe or no neurodisability. Death in severe neurodisability may be associated with lower creatinine levels.