Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Let $\mu_{\Omega,\vec{b}}$ be the multilinear commutator generalized by $\mu_{\Omega}$, the $n$-dimensional Marcinkiewicz integral with the bounded kernel, and b_{j}\in \Osc_{\exp L^{r_{j}}}(1\le j\le m). In this paper, the following weighted inequalities are proved for $\omega\in A_{\infty}$ and $0<p<\infty$, $$\|\mu_{\Omega}(f)\|_{L^{p}(\omega)}\leq C\|M(f)\|_{L^{p}(\omega)}, \ \ \|\mu_{\Omega,\vec{b}}(f)\|_{L^{p}(\omega)}\leq C\|M_{L(\log L)^{1/r}}(f)\|_{L^{p}(\omega)}.$$ The weighted weak $L(\log L)^{1/r}$ -type estimate is also established when $p=1$ and $\omega\in A_{1}$.Comment: In 2012, it is accepted by Ukrainian Mathematical Journal. And there are 13 page

Weighted estimates for multilinear commutators of Marcinkiewicz integrals with bounded kernel

Let μΩ,b→ be a multilinear commutator generalized by the n-dimensional Marcinkiewicz integral with bounded kernel μ Ώ and let bj ∈OscexpLrj , 1 ≤ j ≤ m. We prove the following weighted inequalities for ω ∈ A ∞ and 0 < p < ∞: The weighted weak L(log L)1/r -type estimate is also established for p =1 and ω ∈ A.Нехай μΩ,b→ — мультилінійний комутатор, що узагальнює μΏ, n-вимірний iнтеграл Марцинкевича з обмеженим ядром, та нехай bj∈OscexpLrj(1≤j≤m). Доведено такі зважені нерівності для ω∈A∞ та 0<p<∞: Зважену слабку оцінку L(log L)1/r -типу також встановлено для p=1 та ω∈A

Low complexity Reed–Solomon-based low-density parity-check design for software defined optical transmission system based on adaptive puncturing decoding algorithm

AbstractWe propose and demonstrate a low complexity Reed–Solomon-based low-density parity-check (RS-LDPC) code with adaptive puncturing decoding algorithm for elastic optical transmission system. Partial received codes and the relevant column in parity-check matrix can be punctured to reduce the calculation complexity by adaptive parity-check matrix during decoding process. The results show that the complexity of the proposed decoding algorithm is reduced by 30% compared with the regular RS-LDPC system. The optimized code rate of the RS-LDPC code can be obtained after five times iteration

Large datasets of water vapor sorption, mass diffusion immersed in water, hygroscopic expansion and mechanical properties of flax fibre/shape memory epoxy hygromorph composites

This data article presents four experimental sets of results related to flax fibre composites with epoxy shape memory polymer matrix: water vapor absorption, mass diffusion immersed in water, hygroscopic expansion, mechanical properties. The water vapor absorption tests are described in raw data related to four types of laminates with weights measured at different relative humidity (0%, 9%, 33%, 44%,75%, 85% and 100%). The mass diffusion experiments are related to weights of immersed samples over time. The unidirectional composite hygroscopic expansion is also measured along the fibre longitude and transverse directions. The mechanical properties of flax composite at various temperatures (20°C, 40°C, 60°C, 80°C and 100°C) and humidity environments (50% and immersed) are also described. Load-displacement diagrams of the hygromorph composites are converted into stress-strain diagrams via a compliance calibration, from which the tensile moduli are extracted. The data presented in this article can provide a benchmark for the development of new models, or for the determination of other properties via post processing. The detailed interpretation of the data can be found in [1]. The data is available in the Mendeley Data repository at [2]

Biobased and Programmable Electroadhesive Metasurfaces

[Image: see text] Electroadhesion has shown the potential to deliver versatile handling devices because of its simplicity of actuation and rapid response. Current electroadhesion systems have, however, significant difficulties in adapting to external objects with complex shapes. Here, a novel concept of metasurface is proposed by combining the use of natural fibers (flax) and shape memory epoxy polymers in a hygromorphic and thermally actuated composite (HyTemC). The biobased material composite can be used to manipulate adhesive surfaces with high precision and controlled environmental actuation. The HyTemC concept is preprogrammed to store controllable moisture and autonomous desorption when exposed to the operational environment, and can reach predesigned bending curvatures up to 31.9 m(–1) for concave and 29.6 m(–1) for convex shapes. The actuated adhesive surface shapes are generated via the architected metasurface structure, incorporating an electroadhesive component integrated with the programmable biobased materials. This biobased metasurface stimulated by the external environment provides a large taxonomy of shapes—from flat, circular, single/double concave, and wavy, to piecewise, polynomial, trigonometric, and airfoil configurations. The objects handled by the biobased metasurface can be fragile because of the high conformal matching between contacting surfaces and the absence of compressive adhesion. These natural fiber-based and environmentally friendly electroadhesive metasurfaces can significantly improve the design of programmable object handling technologies, and also provide a sustainable route to lower the carbon and emission footprint of smart structures and robotics

A Network-Based Approach to Investigate the Pattern of Syndrome in Depression

In Traditional Chinese Medicine theory, syndrome is essential to diagnose diseases and treat patients, and symptom is the foundation of syndrome differentiation. Thus the combination and interaction between symptoms represent the pattern of syndrome at phenotypic level, which can be modeled and analyzed using complex network. At first, we collected inquiry information of 364 depression patients from 2007 to 2009. Next, we learned classification models for 7 syndromes in depression using naïve Bayes, Bayes network, support vector machine (SVM), and C4.5. Among them, SVM achieves the highest accuracies larger than 0.9 except for Yin deficiency. Besides, Bayes network outperforms naïve Bayes for all 7 syndromes. Then key symptoms for each syndrome were selected using Fisher&apos;s score. Based on these key symptoms, symptom networks for 7 syndromes as well as a global network for depression were constructed through weighted mutual information. Finally, we employed permutation test to discover dynamic symptom interactions, in order to investigate the difference between syndromes from the perspective of symptom network. As a result, significant dynamic interactions were quite different for 7 syndromes. Therefore, symptom networks could facilitate our understanding of the pattern of syndrome and further the improvement of syndrome differentiation in depression

Ancient and recent collisions revealed by phosphate minerals in the Chelyabinsk meteorite

AbstractThe collision history of asteroids is an important archive of inner Solar System evolution. Evidence for these collisions is brought to Earth by meteorites. However, as meteorites often preserve numerous impact-reset mineral ages, interpretation of their collision histories is controversial. Here, we combine analysis of phosphate U-Pb ages and microtextures to interpret the collision history of Chelyabinsk—a highly shocked meteorite. We show that phosphate U-Pb ages correlate with phosphate microtextural state. Pristine phosphate domain U-Pb compositions are generally concordant, whereas fracture-damaged domains universally display discordance. Combining both populations best constrains upper (4473 ± 11 Ma) and lower intercept (−9 ± 55 Ma, i.e., within error of present) U-Pb ages. All phosphate U-Pb ages were completely reset during an ancient high energy collision, whilst fracture-damaged domains experienced further Pb-loss during mild and recent collisional re-heating. Targeting textural sub-populations of phosphate grains permits more robust reconstruction of asteroidal collision histories.</jats:p

Multiple Angle Observations Would Benefit Visible Band Remote Sensing Using Night Lights

The spatial and angular emission patterns of artificial and natural light emitted, scattered, and reflected from the Earth at night are far more complex than those for scattered and reflected solar radiation during daytime. In this commentary, we use examples to show that there is additional information contained in the angular distribution of emitted light. We argue that this information could be used to improve existing remote sensing retrievals based on night lights, and in some cases could make entirely new remote sensing analyses possible. This work will be challenging, so we hope this article will encourage researchers and funding agencies to pursue further study of how multi‐angle views can be analyzed or acquired

Prediction of recurrence of ischemic stroke within 1 year of discharge based on machine learning MRI radiomics

PurposeThis study aimed to investigate the value of a machine learning-based magnetic resonance imaging (MRI) radiomics model in predicting the risk of recurrence within 1 year following an acute ischemic stroke (AIS).MethodsThe MRI and clinical data of 612 patients diagnosed with AIS at the Second Affiliated Hospital of Nanchang University from March 1, 2019, to March 5, 2021, were obtained. The patients were divided into recurrence and non-recurrence groups according to whether they had a recurrent stroke within 1 year after discharge. Randomized splitting was used to divide the data into training and validation sets using a ratio of 7:3. Two radiologists used the 3D-slicer software to label the lesions on brain diffusion-weighted (DWI) MRI sequences. Radiomics features were extracted from the annotated images using the pyradiomics software package, and the features were filtered using the Least Absolute Shrinkage and Selection Operator (LASSO) regression analysis. Four machine learning algorithms, logistic regression (LR), Support Vector Classification (SVC), LightGBM, and Random forest (RF), were used to construct a recurrence prediction model. For each algorithm, three models were constructed based on the MRI radiomics features, clinical features, and combined MRI radiomics and clinical features. The sensitivity, specificity, and area under the receiver operating characteristic (ROC) curve (AUC) were used to compare the predictive efficacy of the models.ResultsTwenty features were selected from 1,037 radiomics features extracted from DWI images. The LightGBM model based on data with three different features achieved the best prediction accuracy from all 4 models in the validation set. The LightGBM model based solely on radiomics features achieved a sensitivity, specificity, and AUC of 0.65, 0.671, and 0.647, respectively, and the model based on clinical data achieved a sensitivity, specificity, and AUC of 0.7, 0.799, 0.735, respectively. The sensitivity, specificity, and AUC of the LightGBM model base on both radiomics and clinical features achieved the best performance with a sensitivity, specificity, and AUC of 0.85, 0.805, 0.789, respectively.ConclusionThe ischemic stroke recurrence prediction model based on LightGBM achieved the best prediction of recurrence within 1 year following an AIS. The combination of MRI radiomics features and clinical data improved the prediction performance of the model