An hp-Adaptive Sampling Algorithm on Dispersion Relation Reconstruction for 2D Photonic Crystals

Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose a novel hp-adaptive sampling scheme that can detect singular points via adaptive mesh refinement in the parameter domain, and meanwhile, allow for adaptively enriching the local polynomial spaces on the elements that do not contain singular points. In this way, we obtain an element-wise interpolation on an adaptive mesh. We derive an exponential convergence rate when the number of singular points is finite, and a first-order convergence rate otherwise. Numerical tests are provided to illustrate its performance

Dispersion relation reconstruction for 2D Photonic Crystals based on polynomial interpolation

Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on global polynomial interpolation for the approximation of 2D photonic band functions. Our method relies on the fact that the band functions are piecewise analytic with respect to the wave vector in the first Brillouin zone. We utilize suitable sampling points in the first Brillouin zone at which we solve the eigenvalue problem involved in the band function calculation, and then employ Lagrange interpolation to approximate the band functions on the whole first Brillouin zone. Numerical results show that our proposed methods can significantly improve the computational efficiency.Comment: 26 pages, 13 figure

Quantized Low-Rank Multivariate Regression with Random Dithering

Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized LRMR, a practical setting where the responses and/or the covariates are discretized to finite precision. We focus on the estimation of the underlying coefficient matrix. To make consistent estimator that could achieve arbitrarily small error possible, we employ uniform quantization with random dithering, i.e., we add appropriate random noise to the data before quantization. Specifically, uniform dither and triangular dither are used for responses and covariates, respectively. Based on the quantized data, we propose the constrained Lasso and regularized Lasso estimators, and derive the non-asymptotic error bounds. With the aid of dithering, the estimators achieve minimax optimal rate, while quantization only slightly worsens the multiplicative factor in the error rate. Moreover, we extend our results to a low-rank regression model with matrix responses. We corroborate and demonstrate our theoretical results via simulations on synthetic data or image restoration.Comment: 16 pages (Submitted

Anti Spoofing Attack Positioning Algorithm for Wireless Sensor Networks Based on Distance Verification

The precise location of sensor node is the premise of guaranteeing the effectiveness and validity of WSNS in its application and nodes positioning technology is a key technology of wireless sensor networks. For its inherent characteristics, such as limitation of the resources, insecurity and openness of the deployment environment, mechanism of location for wireless sensor networks has security problems. An effective approach to monitoring and detecting spoofing attacks based on distance verification are proposed. The detecting mechanism is based on the visualization of the consistency between the time of transmission and the loss of the power. Experimental studies are conducted to investigate the effect of the algorithm

Dynamics-aware Adversarial Attack of Adaptive Neural Networks

In this paper, we investigate the dynamics-aware adversarial attack problem of adaptive neural networks. Most existing adversarial attack algorithms are designed under a basic assumption -- the network architecture is fixed throughout the attack process. However, this assumption does not hold for many recently proposed adaptive neural networks, which adaptively deactivate unnecessary execution units based on inputs to improve computational efficiency. It results in a serious issue of lagged gradient, making the learned attack at the current step ineffective due to the architecture change afterward. To address this issue, we propose a Leaded Gradient Method (LGM) and show the significant effects of the lagged gradient. More specifically, we reformulate the gradients to be aware of the potential dynamic changes of network architectures, so that the learned attack better "leads" the next step than the dynamics-unaware methods when network architecture changes dynamically. Extensive experiments on representative types of adaptive neural networks for both 2D images and 3D point clouds show that our LGM achieves impressive adversarial attack performance compared with the dynamic-unaware attack methods

Effects of intensive scallop mariculture on macrobenthic assemblages in Sishili Bay, the northern Yellow Sea of China

To elucidate the effects of scallop mariculture on the macrobenthic community in a moderate energy system, bimonthly samples from four transects along a distance gradient in Sishili Bay, the northern Yellow Sea of China, were investigated. Differences in macrobenthic community structure along the distance gradient were evaluated using univariate and multivariate analyses. The AZTI's Marine Biotic Index (AMBI) and multivariate-AMBI analyses indicated that the macrobenthic community suffered little disturbance from the scallop culture. Consistently, the results of two-way analysis of similarities demonstrated that macrobenthic communities showed no difference along the distance gradient, but were significantly affected by the sampling months and transects. This conclusion was also confirmed by other univariate and multivariate analyses. The concentration of total organic carbon was 17.27 +/- A 6.05 mg g(-1), which is below the dangerous threshold of 35 mg g(-1) toxic to benthic fauna. Combined results revealed that no detectable effects on the macrobenthic community were caused by intensive and long-term scallop culture in this moderate energy system. This is likely due to the influence of local hydrodynamics and it is recommended that intensive scallop farming be located in areas with strong tidal or current flows

Whole exome sequencing and system biology analysis support the "two-hit" mechanism in the onset of Ameloblastoma

Ameloblastoma is the most frequent odontogenic tumor. Various evidence has highlighted the role of somatic mutations, including recurrent mutation BRAF V600E, in the tumorigenesis of Ameloblastoma, but the intact genetic pathology remains unknown. We sequenced the whole exome of both tumor tissue and healthy bone tissue from four mandibular ameloblastoma patients. The identified somatic mutations were integrated into Weighted Gene Co-expression Network Analysis on publicly available expression data of odontoblast, ameloblast, and Ameloblastoma. We identified a total of 70 rare and severe somatic mutations. We found BRAF V600E on all four patients, supporting previous discovery. HSAP4 was also hit by two missense mutations on two different patients. By applying Weighted Gene Co-expression Network Analysis on expression data of odontoblast, ameloblast, and Ameloblastoma, we found a proliferation-associated gene module that was significantly disrupted in tumor tissues. Each patient carried at least two rare, severe somatic mutations affecting genes within this module, including HSPA4, GNAS, CLTC, NES, and KMT2D. All these mutations had a ratio of variant-support reads lower than BRAF V600E, indicating that they occurred later than BRAF V600E. We suggest that a severe somatic mutation on the gene network of cell proliferation other than BRAF V600E, namely second hit, may contribute to the tumorigenesis of Ameloblastoma