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摘要： Y Manipulating multiphysical fields with metamaterials has received enormous attention recently because of the high functional integration and extensive practical applicability. However, coupled multi-field systems such as thermoelectric fields, where heat and electric fluxes are coupled via the Seebeck coefficients, still lack efficient control with artificial structures. Here, we theoretically design a category of bilayer thermoelectric metamaterials based on the generalized scattering-cancellation method. By solving the governing equations directly, we formulate the specific parameter requirements for the desired functionalities beyond existing single-field or decoupled multi-field Laplacian metamaterials. Compared with the recently reported transformation optics for thermoelectric flows, bilayer schemes do not require inhomogeneity and anisotropy in constitutive materials. Finite-element simulations confirm the analytical results and show robustness under various exterior conditions. A feasible experimental design with naturally occuring materials is also proposed for further proof-of-principle verification. Our theoretical method and device design may be extended to other coupled multiphysical systems such as thermo-optics, thermomagnetics, optomechanics, etc. Copyright (C) 2021 EPLA

关键词： color distortion   convolutional neural networks   image contrast   local Laplacian pyramid   medical image fusion  

摘要： Medical image fusion technology makes clinical diagnosis and treatment more accurate. This technique can solve the existing problem that single mode medical images conveying insufficient information. Therefore, the key to this technology is to retain as much as possible information in the original medical image of multiple modes. However, the existing methods often lose source image detail with a low contrast and cause color distortion. This article proposed a novel multi-modal medical image fusion framework. Our framework has four key steps. First, extracting the super-resolution images from anatomical images via a deep neural network is performed. Second, decomposing the source images into detail-enhanced approximate and residual images, and then processing by local Laplacian filtering. Third, a convolution neural network is used to complete the mapping of the source image to the feature map and the local energy-based strategy is used to integrate the coefficients. Finally, the inversed local Laplacian pyramid is adopted to reconstruct the fused image. The experimental results prove that the fused image via the proposed method has the characteristics of high contrast, high brightness, and high color saturation and great advantages in retaining the color and structural information.

关键词： EGFR   extracellular vesicles   liquid biopsy   NSCLC   RNA  

摘要： The mutational status of the epidermal growth factor receptor (EGFR) guides the stratification of non-small cell lung cancer (NSCLC) patients for treatment with tyrosine kinase inhibitors (TKIs). A liquid biopsy test on cell-free DNA is recommended as a clinical decision-supporting tool, although it has limited sensitivity. Here, we comparatively investigated the extracellular vesicle (EV)-RNA as an independent source for multidimensional and longitudinal EGFR profiling in a cohort of 27 NSCLC patients. We introduced and validated a new rapid, highly specific EV-RNA test with wild-type (WT) and mutant-sensitive probes (E746-A750del, L858R, and T790M). We included a cohort of 20 NSCLC patients with EGFR WT tumor tissues and systematically performed molecular EV-RNA and circulating tumor DNA analyses with clinical data statistics and biophysical profiles of EVs. At the single-patient level, we detected variegated tumor heterogeneity dynamics supported by combinations of driver EGFR mutations. EV-RNA-based mutation analysis showed an unprecedented sensitivity of over 90%. The resistance-associated mutation T790M frequently pre-existed at baseline with a gained EV-transcript copy number at progression, while the general mutational burden was mostly decreasing during the intermediate follow-up. The biophysical profile of EVs and the quantitative assessment of T790M revealed an association with tumor size determined by the sum of the longest diameters in target lesions. Vesicular RNA provides a validated tool suitable for use in clinical practice to investigate the dynamics of common driver EGFR mutations in NSCLC patients receiving TKIs.

关键词： Mathematics   general  

摘要： Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function G(s) (z(1), z(2)) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable z(1) over all CM points of a fixed discriminant d(1) (twisted by a genus character), and allow in the second variable the evaluation at individual CM points of discriminant d(2). This result is deduced from more general statements for automorphic Green functions on Shimura varieties associated with the group GSpin(n, 2). We also use our approach to prove a Gross-Kohnen-Zagier theorem for higher Heegner divisors on Kuga-Sato varieties over modular curves.

关键词： Registration   B-splines   Laplacian commutators  

摘要： It is highly desirable that the complementary information of computed tomography (CT) for dose planning and magnetic resonance imaging (MRI) for accurate organ delineation should be merged in oncology. In this paper, we propose a hierarchical method based on B-splines and Laplacian commutators for registration between MR and CT brain images. Firstly, we apply histogram equalization on the CT image for intensifying its local details. Then, the principal component analysis (PCA) is adopted to align MR and CT images roughly. We use PCA to find the centroid and orientation of these two images to initialize the translation and rotation. Next, registration is refined via a free-form deformation which is based on B-splines for describing local deformations. Here we adopt Laplacian commutators as a similarity metric in both stages of registration, and the limited memory Broyden-Fletcher-Goldfarb-Shannon (L-BFGS) optimization method has been applied for optimization process. Experimental results have shown that the performances of the obtained images are improved by comparing with the state-of-the-art methods, demonstrating potentials of the proposed method to be applied for brain tumor radiation therapy.

关键词： Signless Laplacian matrix   Largest eigenvalue   Hamiltonian graph   Spectral inequalities  

摘要： We give an upper (resp. a lower) bound on the largest (resp. the least) eigenvalue of the signless Laplacian matrix of a Hamiltonian graph. These bounds are applied to obtain sufficient spectral conditions for the non-existence of Hamiltonian cycles. Under certain additional assumptions we provide a polynomial time decisive spectral criterion for the Hamiltonicity of a given graph with sufficiently large minimum vertex degree.

关键词： Laser trapping   Optical confinement and manipulation   Particles  

摘要： For an ellipsoid suspended in a dual-fiber optic trap with transverse offset, the optical force, torque and posture are theoretically analyzed. When importing a transverse offset between two fibers, in the water environment, the azimuthal angle between the long axis and the optical axis increases with the offset distance. In the vacuum environment, the ellipsoid will spin in the trap center. When the offset is great than the threshold, the ellipsoid will move around the trap center along an elliptic trajectory, accompanied with the spin motion. The results will contribute to better understanding of the spin motion in the transversely misaligned dual-beam fiber-optic trap.

关键词： 经济数学  

ISBN: (纸本)9787312053030

摘要： 本书利用量子理论的思想与方法，系统地研究了金融市场不确定性的本质和作用，开辟了金融市场的一个新的研究方向，可简称为“不确定性市场”原理，这项成果属于自然科学与社会科学的交叉学科领域，不但是发展金融理论的一个新的生长点，而且对于提高金融系统演化规律的预测能力方面，有着广阔的应用前景。

关键词： Fractional Laplacians   Dirichlet problems   Singularity nonlinearities   The sub-sup ersolution method   Uniqueness  

摘要： In this paper we prove the existence and uniqueness of positive classical solutions of fractional Laplacians with singular nonlinearities in a smooth bounded domain with zero Dirichlet boundary conditions. By the sub-sup ersolution method, we derive the existence of positive classical solutions to the approximation problems. In order to obtain the regularity, we first establish the existence of weak solutions for the fraction Laplacians. Thanks to Xia and Yang (2013), the regularity follows from the boundedness of weak solutions. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Population biological system   General variational inequality principle   Demicontinuous strongly pseudo-contractive and    p-Laplacian operator   Generalized duality mapping with normalization function   Approximation-solvability  

摘要： The aim of this paper is to investigate existence, uniqueness and convergence of approximants of nonzero positive weak solutions for a class of population biology systems, which are models of one species based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators and in-volved logistic growth and harvesting rates. Toward this end, we foremost develop a kind of new general variational inequality principles with generalized duality mappings in reflexive Banach spaces. Then, we employ the new principle to obtain our main results for a general p-Laplacian elliptic inequality and the population biology systems. We note that the results are different from those relevant work of p- Laplacian elliptic inequalities in the literature, it is because a pseudo-contractive operator may not be an S-contractive operator and vice versa. (c) 2021 Elsevier Ltd. All rights reserved.