Some counterexamples to Donaldson's four-six question

We prove that the examples of Smith and McMullen-Taubes provide infinitely many counterexamples to one direction of the Donaldson four-six question and the closely related Stabilising Conjecture. Moreover, we show that in both examples the symplectic forms remain deformation inequivalent after taking products with arbitrarily many copies of $(S^2,\omega_{\text{std}})$.Comment: 8 pages, no figures, comments welcom

Infinitely many monotone Lagrangian tori in higher projective spaces

Vianna constructed infinitely many exotic Lagrangian tori in the complex projective plane. We lift these tori to higher-dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula by Pascaleff-Tonkonog.Comment: 11 pages, 1 figure. Comments welcome

Quasi maximum likelihood estimation for simultaneous spatial autoregressive models

This paper considers the problem of estimating a simultaneous spatial autoregressive model (SSAR). We propose using the quasi maximum likelihood method to estimate the model. The asymptotic properties of the maximum likelihood estimator including consistency and limiting distribution are investigated. We also run Monte Carlo simulations to examine the finite sample performance of the maximum likelihood estimator

Quasi maximum likelihood estimation for simultaneous spatial autoregressive models

This paper considers the problem of estimating a simultaneous spatial autoregressive model (SSAR). We propose using the quasi maximum likelihood method to estimate the model. The asymptotic properties of the maximum likelihood estimator including consistency and limiting distribution are investigated. We also run Monte Carlo simulations to examine the finite sample performance of the maximum likelihood estimator

Legendrian embedded contact homology

We give a construction of embedded contact homology (ECH) for a contact $3$-manifold $Y$ with convex sutured boundary and a pair of Legendrians $\Lambda_+$ and $\Lambda_-$ contained in $\partial Y$ satisfying an exactness condition. The chain complex is generated by certain configurations of closed Reeb orbits of $Y$ and Reeb chords of $\Lambda_+$ to $\Lambda_-$. The main ingredients include: a general Legendrian adjunction formula for curves in $\mathbb{R} \times Y$ with boundary on $\mathbb{R} \times \Lambda$; a relative writhe bound for curves in contact $3$-manifolds asymptotic to Reeb chords; and a Legendrian ECH index with an accompanying ECH index inequality. The (action filtered) Legendrian ECH of any pair $(Y,\Lambda)$ of a closed contact $3$-manifold $Y$ and a Legendrian link $\Lambda$ can also be defined using this machinery after passing to a sutured link complement. This work builds on ideas present in Colin-Ghiggini-Honda's proof of the equivalence of Heegaard-Floer homology and ECH. The independence of our construction of choices of almost complex structure and contact form should require a new flavor of monopole Floer homology. It is beyond the scope of this paper.Comment: 78 pages, comments welcome! v2 corrected a few typos in the arXiv submission of v

The Effects of Jiang-Zhi-Ning and Its Main Components on Cholesterol Metabolism

To examine how Jiang-Zhi-Ning (JZN) regulates cholesterol metabolism and compare the role of its four main components. We established a beagle model of hyperlipidemia, fed with JZN extract and collected JZN-containing serum 0, 1, 2, 4, and 6 h later. Human liver cells Bel-7402 were stimulated with 10% JZN-containing serum as well as the four main components of JZN and Atorvastatin. The mRNA expression of LDL receptor (LDL-R), 3-hydroxy-3-methyl-glutaryl-CoA reductase (HMG-CoAR), cytochrome P450 7A1 (CYP7A1), and acetyl-Coenzyme A acetyltransferase 2 (ACAT2) was measured by real-time PCR. LDL-R surface expression and LDL-binding and internalization were examined by flow cytometry. The results showed that JZN-containing serum significantly increased the mRNA expression of LDL-R, HMG-CoAR, and CYP7A1 in Bel-7402 cells. All the four components significantly increased the mRNA and protein expression of LDL-R and HMG-CoAR and decreased the mRNA and protein expression of ACAT2 in Bel-7402 cells. Hyperinand chrysophanol also markedly increased the mRNA expression of CYP7A1. Stimulation with stilbene glycosidesignificantly increased the surface expression of LDL-R and the binding and internalization of LDL. In conclusion, JZN and its four components have close relationship with the process of cholesterol metabolism, emphasizing their promising application as new drug candidates in the treatment of hyperlipidemia

Effect of Pyrolysis Temperature on the Characterisation of Dissolved Organic Matter from Pyroligneous Acid

Dissolved organic matter (DOM) greatly influences the transformation of nutrients and pollutants in the environment. To investigate the effects of pyrolysis temperatures on the composition and evolution of pyroligneous acid (PA)-derived DOM, DOM solutions extracted from a series of PA derived from eucalyptus at five pyrolysis temperature ranges (240–420 °C) were analysed with Fourier transform infrared spectroscopy, gas chromatography–mass spectroscopy, and fluorescence spectroscopy. Results showed that the dissolved organic carbon content sharply increased (p 370 °C). The results of two-dimensional correlation spectroscopic analysis suggested that with increasing pyrolysis temperatures, the humic-acid-like substances became more sensitive than other fluorescent components. This study provides valuable information on the characteristic evolution of PA-derived DOM

Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysis

A wireless federated learning system is investigated by allowing a server and workers to exchange uncoded information via orthogonal wireless channels. Since the workers frequently upload local gradients to the server via bandwidth-limited channels, the uplink transmission from the workers to the server becomes a communication bottleneck. Therefore, a one-shot distributed principle component analysis (PCA) is leveraged to reduce the dimension of uploaded gradients such that the communication bottleneck is relieved. A PCA-based wireless federated learning (PCA-WFL) algorithm and its accelerated version (i.e., PCA-AWFL) are proposed based on the low-dimensional gradients and the Nesterov's momentum. For the non-convex loss functions, a finite-time analysis is performed to quantify the impacts of system hyper-parameters on the convergence of the PCA-WFL and PCA-AWFL algorithms. The PCA-AWFL algorithm is theoretically certified to converge faster than the PCA-WFL algorithm. Besides, the convergence rates of PCA-WFL and PCA-AWFL algorithms quantitatively reveal the linear speedup with respect to the number of workers over the vanilla gradient descent algorithm. Numerical results are used to demonstrate the improved convergence rates of the proposed PCA-WFL and PCA-AWFL algorithms over the benchmarks

Familial hypercholesterolaemia in children and adolescents from 48 countries: a cross-sectional study

Background: Approximately 450 000 children are born with familial hypercholesterolaemia worldwide every year, yet only 2·1% of adults with familial hypercholesterolaemia were diagnosed before age 18 years via current diagnostic approaches, which are derived from observations in adults. We aimed to characterise children and adolescents with heterozygous familial hypercholesterolaemia (HeFH) and understand current approaches to the identification and management of familial hypercholesterolaemia to inform future public health strategies. Methods: For this cross-sectional study, we assessed children and adolescents younger than 18 years with a clinical or genetic diagnosis of HeFH at the time of entry into the Familial Hypercholesterolaemia Studies Collaboration (FHSC) registry between Oct 1, 2015, and Jan 31, 2021. Data in the registry were collected from 55 regional or national registries in 48 countries. Diagnoses relying on self-reported history of familial hypercholesterolaemia and suspected secondary hypercholesterolaemia were excluded from the registry; people with untreated LDL cholesterol (LDL-C) of at least 13·0 mmol/L were excluded from this study. Data were assessed overall and by WHO region, World Bank country income status, age, diagnostic criteria, and index-case status. The main outcome of this study was to assess current identification and management of children and adolescents with familial hypercholesterolaemia. Findings: Of 63 093 individuals in the FHSC registry, 11 848 (18·8%) were children or adolescents younger than 18 years with HeFH and were included in this study; 5756 (50·2%) of 11 476 included individuals were female and 5720 (49·8%) were male. Sex data were missing for 372 (3·1%) of 11 848 individuals. Median age at registry entry was 9·6 years (IQR 5·8-13·2). 10 099 (89·9%) of 11 235 included individuals had a final genetically confirmed diagnosis of familial hypercholesterolaemia and 1136 (10·1%) had a clinical diagnosis. Genetically confirmed diagnosis data or clinical diagnosis data were missing for 613 (5·2%) of 11 848 individuals. Genetic diagnosis was more common in children and adolescents from high-income countries (9427 [92·4%] of 10 202) than in children and adolescents from non-high-income countries (199 [48·0%] of 415). 3414 (31·6%) of 10 804 children or adolescents were index cases. Familial-hypercholesterolaemia-related physical signs, cardiovascular risk factors, and cardiovascular disease were uncommon, but were more common in non-high-income countries. 7557 (72·4%) of 10 428 included children or adolescents were not taking lipid-lowering medication (LLM) and had a median LDL-C of 5·00 mmol/L (IQR 4·05-6·08). Compared with genetic diagnosis, the use of unadapted clinical criteria intended for use in adults and reliant on more extreme phenotypes could result in 50-75% of children and adolescents with familial hypercholesterolaemia not being identified. Interpretation: Clinical characteristics observed in adults with familial hypercholesterolaemia are uncommon in children and adolescents with familial hypercholesterolaemia, hence detection in this age group relies on measurement of LDL-C and genetic confirmation. Where genetic testing is unavailable, increased availability and use of LDL-C measurements in the first few years of life could help reduce the current gap between prevalence and detection, enabling increased use of combination LLM to reach recommended LDL-C targets early in life