Non-ancient solution of the Ricci flow

For any complete noncompact K$\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.Comment: seven pages, latex fil

Validation of the Alzheimer's disease-resemblance atrophy index in classifying and predicting progression in Alzheimer's disease

BACKGROUND: Automated tools for characterising dementia risk have the potential to aid in the diagnosis, prognosis, and treatment of Alzheimer’s disease (AD). Here, we examined a novel machine learning-based brain atrophy marker, the AD-resemblance atrophy index (AD-RAI), to assess its test-retest reliability and further validate its use in disease classification and prediction. METHODS: Age- and sex-matched 44 probable AD (Age: 69.13 ± 7.13; MMSE: 27–30) and 22 non-demented control (Age: 69.38 ± 7.21; MMSE: 27–30) participants were obtained from the Minimal Interval Resonance Imaging in Alzheimer’s Disease (MIRIAD) dataset. Serial T1-weighted images (n = 678) from up to nine time points over a 2-year period, including 179 pairs of back-to-back scans acquired on same participants on the same day and 40 pairs of scans acquired at 2-week intervals were included. All images were automatically processed with AccuBrain® to calculate the AD-RAI. Its same-day repeatability and 2-week reproducibility were first assessed. The discriminative performance of AD-RAI was evaluated using the receiver operating characteristic curve, where DeLong’s test was used to evaluate its performance against quantitative medial temporal lobe atrophy (QMTA) and hippocampal volume adjusted by intracranial volume (ICV)-proportions and ICV-residuals methods, respectively (HVR and HRV). Linear mixed-effects modelling was used to investigate longitudinal trajectories of AD-RAI and baseline AD-RAI prediction of cognitive decline. Finally, the longitudinal associations between AD-RAI and MMSE scores were assessed. RESULTS: AD-RAI had excellent same-day repeatability and excellent 2-week reproducibility. AD-RAI’s AUC (99.8%; 95%CI = [99.3%, 100%]) was equivalent to that of QMTA (96.8%; 95%CI = [92.9%, 100%]), and better than that of HVR (86.8%; 95%CI = [78.2%, 95.4%]) or HRV (90.3%; 95%CI = [83.0%, 97.6%]). While baseline AD-RAI was significantly higher in the AD group, it did not show detectable changes over 2 years. Baseline AD-RAI was negatively associated with MMSE scores and the rate of the change in MMSE scores over time. A negative longitudinal association was also found between AD-RAI values and the MMSE scores among AD patients CONCLUSIONS: The AD-RAI represents a potential biomarker that may support AD diagnosis and be used to predict the rate of future cognitive decline in AD patients

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

Safety and efficacy of human Wharton's Jelly-derived mesenchymal stem cells therapy for retinal degeneration

Purpose To investigate the safety and efficacy of subretinal injection of human Wharton’s Jelly-derived mesenchymal stem cells (hWJ-MSCs) on retinal structure and function in Royal College of Surgeons (RCS) rats. Methods RCS rats were divided into 2 groups: hWJ-MSCs treated group (n = 8) and placebo control group (n = 8). In the treatment group, hWJ-MSCs from healthy donors were injected into the subretinal space in one eye of each rat at day 21. Control group received saline injection of the same volume. Additional 3 animals were injected with nanogold-labelled stem cells for in vivo tracking of cells localisation using a micro-computed tomography (microCT). Retinal function was assessed by electroretinography (ERG) 3 days before the injection and repeated at days 15, 30 and 70 after the injection. Eyes were collected at day 70 for histology, cellular and molecular studies. Results No retinal tumor formation was detected by histology during the study period. MicroCT scans showed that hWJ-MSCs stayed localised in the eye with no systemic migration. Transmission electron microscopy showed that nanogold-labelled cells were located within the subretinal space. Histology showed preservation of the outer nuclear layer (ONL) in the treated group but not in the control group. However, there were no significant differences in the ERG responses between the groups. Confocal microscopy showed evidence of hWJ-MSCs expressing markers for photoreceptor, Müller cells and bipolar cells. Conclusions Subretinal injection of hWJ-MSCs delay the loss of the ONL in RCS rats. hWJ-MSCs appears to be safe and has potential to differentiate into retinal-like cells. The potential of this cell-based therapy for the treatment of retinal dystrophies warrants further studies

Changes in urinary metabolomic profile during relapsing renal vasculitis

Current biomarkers of renal disease in systemic vasculitis lack predictive value and are insensitive to early damage. To identify novel biomarkers of renal vasculitis flare, we analysed the longitudinal urinary metabolomic profile of a rat model of anti-neutrophil cytoplasmic antibody (ANCA) vasculitis. Wistar-Kyoto (WKY) rats were immunised with human myeloperoxidase (MPO). Urine was obtained at regular intervals for 181 days, after which relapse was induced by re-challenge with MPO. Urinary metabolites were assessed in an unbiased fashion using nuclear magnetic resonance (NMR) spectroscopy, and analysed using partial least squares discriminant analysis (PLS-DA) and partial least squares regression (PLS-R). At 56 days post-immunisation, we found that rats with vasculitis had a significantly different urinary metabolite profile than control animals; the observed PLS-DA clusters dissipated between 56 and 181 days, and re-emerged with relapse. The metabolites most altered in rats with active or relapsing vasculitis were trimethylamine N-oxide (TMAO), citrate and 2-oxoglutarate. Myo-inositol was also moderately predictive. The key urine metabolites identified in rats were confirmed in a large cohort of patients using liquid chromatography-mass spectrometry (LC-MS). Hypocitraturia and elevated urinary myo-inositol remained associated with active disease, with the urine myo-inositol:citrate ratio being tightly correlated with active renal vasculitis

Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder.

Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking

Phase 3 KEYNOTE-042 Study: Pembrolizumab vs Platinum-Based Chemotherapy as 1l Therapy for Advanced NSCLC with a PD-L1 TPS ≥1%

First-line (1L) therapy with pembrolizumab in patients with metastatic NSCLC without targetable aberrations and programmed death ligand 1 (PD-L1) tumor proportion score (TPS) ≥50% significantly improved the primary endpoint of PFS, and OS (secondary endpoint) compared to chemotherapy in the KEYNOTE-024 study. In KEYNOTE-042 (NCT02220894), we evaluated pembrolizumab vs chemotherapy at the lower PD-L1 TPS of ≥1%