Lp⃗−Lq⃗L^{\vec{p}}-L^{\vec{q}} Boundedness of Multiparameter Forelli-Rudin Type Operators on the Product of Unit Balls of Cn\mathbb{C}^n

In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli-Rudin type operators from one mixed-norm Lebesgue space $L^{\vec p}$ to another space $L^{\vec q}$, when $1\leq \vec{p}\leq \vec q<\infty$, equipped with possibly different weights. Using these characterizations, we establish the necessary and sufficient conditions for both $L^{\vec p}-L^{\vec q}$ boundedness of the weighted multiparameter Berezin transform and $L^{\vec p}-A^{\vec q}$ boundedness of the weighted multiparameter Bergman projection, where $A^{\vec q}$ denotes the mixed-norm Bergman space. Our approach presents several novelties. Firstly, we conduct refined integral estimates of holomorphic functions on the unit ball in $\mathbb{C}^n$. Secondly, we adapt the classical Schur's test to different weighted mixed-norm Lebesgue spaces. These improvements are crucial in our proofs and allow us to establish the desired characterization and sharp conditions.Comment: 42 page

Bounded, compact and Schatten class Hankel operators on Fock-type spaces

In this paper, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are $C^3$-logarithmic growth functions with mild smoothness conditions. It is shown that a Hankel operator is bounded on such a Fock space if and only if its symbol function has bounded distance to analytic functions BDA which is initiated by Luecking(J. Funct. Anal. 110:247-271, 1992). We also characterize the compactness and Schatten class membership of Hankel operators. Besides, we give characterizations of the Schatten class membership of Toeplitz operators with positive measure symbols for the small exponent $0<p<1$. Our proofs depend strongly on the technique of H\"{o}mander's $L^2$ estimates for the $\overline{\partial}$ operator and the decomposition theory of BDA spaces as well as integral estimates involving the reproducing kernel

SiGeC/Si superlattice microcoolers

Monolithically integrated active cooling is an attractive way for thermal management and temperature stabilization of microelectronic and optoelectronic devices. SiGeC can be lattice matched to Si and is a promising material for integrated coolers. SiGeC/Si superlattice structures were grown on Si substrates by molecular beam epitaxy. Thermal conductivity was measured by the 3omega method. SiGeC/Si superlattice microcoolers with dimensions as small as 40×40 µm^2 were fabricated and characterized. Cooling by as much as 2.8 and 6.9 K was measured at 25 °C and 100 °C, respectively, corresponding to maximum spot cooling power densities on the order of 1000 W/cm^2

Over-expression of HO-1 on mesenchymal stem cells promotes angiogenesis and improves myocardial function in infarcted myocardium

Heme oxygenase-1 (HO-1) is a stress-inducible enzyme with diverse cytoprotective effects, and reported to have an important role in angiogenesis recently. Here we investigated whether HO-1 transduced by mesenchymal stem cells (MSCs) can induce angiogenic effects in infarcted myocardium. HO-1 was transfected into cultured MSCs using an adenoviral vector. 1 × 106 Ad-HO-1-transfected MSCs (HO-1-MSCs) or Ad-Null-transfected MSCs (Null-MSCs) or PBS was respectively injected into rat hearts intramyocardially at 1 h post-myocardial infarction. The results showed that HO-1-MSCs were able to induce stable expression of HO-1 in vitro and in vivo. The capillary density and expression of angiogenic growth factors, VEGF and FGF2 were significantly enhanced in HO-1-MSCs-treated hearts compared with Null-MSCs-treated and PBS-treated hearts. However, the angiogenic effects of HO-1 were abolished by treating the animals with HO inhibitor, zinc protoporphyrin. The myocardial apoptosis was marked reduced with significantly reduced fibrotic area in HO-1-MSCs-treated hearts; Furthermore, the cardiac function and remodeling were also significantly improved in HO-1-MSCs-treated hearts. Our current findings support the premise that HO-1 transduced by MSCs can induce angiogenic effects and improve heart function after acute myocardial infarction

Better Representations via Adversarial Training in Pre-Training: A Theoretical Perspective

Pre-training is known to generate universal representations for downstream tasks in large-scale deep learning such as large language models. Existing literature, e.g., \cite{kim2020adversarial}, empirically observe that the downstream tasks can inherit the adversarial robustness of the pre-trained model. We provide theoretical justifications for this robustness inheritance phenomenon. Our theoretical results reveal that feature purification plays an important role in connecting the adversarial robustness of the pre-trained model and the downstream tasks in two-layer neural networks. Specifically, we show that (i) with adversarial training, each hidden node tends to pick only one (or a few) feature; (ii) without adversarial training, the hidden nodes can be vulnerable to attacks. This observation is valid for both supervised pre-training and contrastive learning. With purified nodes, it turns out that clean training is enough to achieve adversarial robustness in downstream tasks.Comment: To appear in AISTATS202

Plasma vascular endothelial growth factor B is elevated in non-alcoholic fatty liver disease patients and associated with blood pressure and renal dysfunction

Vascular endothelial growth factor B (VEGF-B) is a critical metabolic regulator in insulin resistance, and lipid distribution. We intended to ascertain the relationship between circulating VEGF-B and non-alcoholic fatty liver disease (NAFLD) in the general public. We recruited a total of 194 general participants for a routine physical health examination; of these, 84 participants were identified with NAFLD and 110 without NAFLD based on ultrasonographic findings. Homeostasis model assessment of insulin resistance (HOMA-IR), body mass index (BMI), HbA1c, liver function, kidney function, plasma VEGF-B levels and indexes of metabolic syndrome (blood pressure, fasting plasma glucose, fasting lipids) were evaluated. Plasma VEGF-B values were significantly higher in individuals with NAFLD compared to those without NAFLD (P = 0.022), and analysis of covariance confirmed this result. VEGF-B showed a positive correlation with γ-glutamyl transpeptidase (γ-GT) and HOMA-IR in univariate analysis (q = 0.242; P = 0.001; q =0.174; P = 0.019, respectively). Multiple linear regression analysis showed that γ-GT and ALT were independently correlated with VEGF-B even after adjusted for gender and age (q = 0.286; P = 0.01; q =0.237; P = 0.033, respectively). Moreover, plasma VEGF-B showed a powerful correlation with blood pressure and renal dysfunction. Plasma VEGF-B might be a new clinical variable related to NAFLD and could be a proper biomarker for the early detection of hypertension and renal dysfunction. However, further studies with large cohorts’ size are warranted to validate our findings

Rheumatoid meningitis: a rare neurological complication of rheumatoid arthritis

ObjectiveTo describe the clinical and neuroimaging characteristics of rheumatoid meningitis (RM) in Chinese patients. MethodsThe patients admitted to our hospital with the diagnosis of RM in the past 8 years were retrospectively analyzed. ResultsSix patients with RM were identified among 933 patients admitted with rheumatoid arthritis (RA). The symptoms of meningitis occurred after onset of arthritis in five patients and before onset in one. Headache (n=6), hyperacute focal neurological deficits (n=4) and seizures (n=3) were the most prevalent symptoms. The nadir modified Rankin Scale score was ≥3 in five patients. Rheumatoid factor was elevated in all patients, and interleukin-6 levels in cerebrospinal fluid were dramatically elevated in three of four tested patients. Magnetic resonance imaging of the brain revealed that the meninges were affected in all patients and the cerebral parenchyma was affected in one patient. The lesions were generally located in the frontoparietal region and showed restricted diffusion along the adjacent subarachnoid space. RM occurred during disease-modifying therapy in four patients. In the acute episode, three patients improved on tocilizumab and the other three improved on pulse corticosteroids. For maintenance therapy, two patients received combined therapy of tocilizumab and other immunosuppressive agents, one received adalimumab and methotrexate, and two received low-dose oral corticosteroids with an immunosuppressive agent. Five patients had a good outcome, and one died of Pneumocystis jirovecii pneumonia after stabilization of his neurologic conditions. No relapse of RM occurred on immunotherapy during follow-up. ConclusionsChinese patients with RM share some remarkable clinical and neuroimaging features and respond well to appropriate immunotherapy. Tocilizumab could be a treatment option for this severe complication of RA