Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation.Mathematics Subject Classification (MSC2000): 35R30, 35C20.

Although successful detection of malignant tumors from histopathological images largely depends on the long-term experience of radiologists, experts sometimes disagree with their decisions. Computer-aided diagnosis provides a second option for image diagnosis, which can improve the reliability of experts’ decision-making. Automatic and precision classification for breast cancer histopathological image is of great importance in clinical application for identifying malignant tumors from histopathological images. Advanced convolution neural network technology has achieved great success in natural image classification, and it has been used widely in biomedical image processing. In this paper, we design a novel convolutional neural network, which includes a convolutional layer, small SE-ResNet module, and fully connected layer. We propose a small SE-ResNet module which is an improvement on the combination of residual module and Squeeze-and-Excitation block, and achieves the similar performance with fewer parameters. In addition, we propose a new learning rate scheduler which can get excellent performance without complicatedly fine-tuning the learning rate. We use our model for the automatic classification of breast cancer histology images (BreakHis dataset) into benign and malignant and eight subtypes. The results show that our model achieves the accuracy between 98.87% and 99.34% for the binary classification and achieve the accuracy between 90.66% and 93.81% for the multi-class classification.

A t . f . I ccura e segmentation o retma vessels 1s a basic step in Diabetic retinopathy(DR) detection. Most methods based on deep convolutional neural network (DCNN) have small receptive fields, and hence they are unable to capture global context information of larger regions, with difficult to identify lesions. The final segmented retina vessels contain more noise with low classificaiton accuracy. Therefore, in this paper, we propose a DCNN structure named as D-Net. In the proposed D-Net, the dilation convolution is used in the backbone network to obtain a larger receptive field without losing spatial resolution, so as to reduce the loss of feature information and to reduce the difficulty of tiny thin vessels segmentation. The large receptive field can better distinguished between the lesion area and the blood vessel area. In the proposed Multi-Scale Information Fusion module (MSIF), parallel convolution layers with different dilation rates are used, so that the model can obtain more dense feature information and better capture retinal vessel information of different sizes. In the decoding module, the skip layer connection is used to propagate context information to higher resolution layers, so as to prevent low-level information from passing the entire network structure. Finally, our method was verified on DRIVE, STARE and CHASE dataset. The experimental results show that our network structure outperforms some state-of-art method, such as N 4 -fields, U-Net, and DRIU in terms of accuracy, sensitivity, specificity, and AUG Roe-Particularly, D-Net outperforms U-Net by 1.04 %, 1.23 % and 2.79 % in DR画，STARE, and CHASE three dataset, respectively. : INDEX TERMS Multi-scale, retinal vessel segmentation, deep convolutional neural network, dilationconvolutions, residual module.

This is the second part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. In this part, we explore the scattering problem in the homogenization regimes, where the size of the period is much smaller than the incident wavelength. In particular, two homogenization regimes are investigated, where the size of the pattered slits has the same order as the size of the period in the first configuration, and the size of the slit is much smaller than the size of the period in the second configuration. By presenting rigorous asymptotic analysis, we demonstrate that surface plasmonic effect mimicking that of plasmonic metals occurs in the first homogenization regime. The corresponding dispersion curve lies below the light line and the associated eigenmodes are surface bound sates. In addition, for the incident plane wave, we discover and justify a novel phenomenon of total transmission which occurs either at certain frequencies for all incident angles, or at a special incident angle but for all frequencies. For the second homogenization regime, the non-resonant field enhancement is investigated, and it is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement. Moreover, the enhancement becomes stronger when the coupling of the slits is weaker.

A schematic illustration of CuS@BSA-RGD nanoparticle synthesis and the application of photoacoustic imaging in an orthotopic HCC model.

Automatic breast lesion segmentation in ultrasound helps to diagnose breast cancer, which is one of the dreadful diseases that affect women globally. Segmenting breast regions accurately from ultrasound image is a challenging task due to the inherent speckle artifacts, blurry breast lesion boundaries, and inhomogeneous intensity distributions inside the breast lesion regions. Recently, convolutional neural networks (CNNs) have demonstrated remarkable results in medical image segmentation tasks. However, the convolutional operations in a CNN often focus on local regions, which suffer from limited capabilities in capturing long-range dependencies of the input ultrasound image, resulting in degraded breast lesion segmentation accuracy. In this paper, we develop a deep convolutional neural network equipped with a global guidance block (GGB) and breast lesion boundary detection (BD) modules for boosting the breast ultrasound lesion segmentation. The GGB utilizes the multi-layer integrated feature map as a guidance information to learn the long-range non-local dependencies from both spatial and channel domains. The BD modules learn additional breast lesion boundary map to enhance the boundary quality of a segmentation result refinement. Experimental results on a public dataset and a collected dataset show that our network outperforms other medical image segmentation methods and the recent semantic segmentation methods on breast ultrasound lesion segmentation. Moreover, we also show the application of our network on the ultrasound prostate segmentation, in which our method better identifies prostate regions than state-of-the-art networks.

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