A unified fused Lasso approach for sparse and blocky feature selection in regression and classification

In many applications, sparse and blocky coefficients often occur in regression and classification problems. The fused Lasso was designed to recover these sparse structured features especially when the design matrix encounters the situation of ultrahigh dimension. Quantile loss is well known as a robust loss function in regression and classification. In this paper, we combine quantile loss and fused Lasso penalty together to produce quantile fused Lasso which can achieve sparse and blocky feature selection in both regression and classification. Interestingly, our proposed model has the unified optimization formula for regression and classification. For ultrahigh dimensional collected data, we derive multi-block linearized alternating direction method of multipliers (LADMM) to deal with it. Moreover, we prove convergence and derive convergence rates of the proposed LADMM algorithm through an elegant method. Note that the algorithm can be easily extended to solve many existing fused Lasso models. Finally, we present some numerical results for several synthetic and real world examples, which illustrate the robustness, scalability, and accuracy of the proposed method

The Study on the Curriculum Setting and Characteristics of Cambridge Undergraduate Philosophy Major

Education of philosophy is both an old and new topic. It is an important approach for human thoughts propagation and theoretical studies. At theUniversityofCambridge, philosophy teaching and learning activities have been existed for 804 years, born at the same time with the university. . This thesis aims to examine the developmental process  of philosophy education at the undergraduate level,, to  investigate the curriculum of philosophy education of the latest ten years, and to summarize the characteristics of philosophy education  at the University of Cambridge

Soil phosphorus budget in global grasslands and implications for management

Grasslands, accounting for one third of the world terrestrial land surface, are important in determining phosphorus (P) cycle at a global scale. Understanding the impacts of management on P inputs and outputs in grassland ecosystem is crucial for environmental management since a large amount of P is transported through rivers and groundwater and detained by the sea reservoir every year. To better understand P cycle in global grasslands, we mapped the distribution of different grassland types around the world and calculated the corresponding P inputs and outputs for each grassland type using data from literature. The distribution map of P input and output revealed a non-equilibrium condition in many grassland ecosystems, with: (i) a greater extent of input than output in most managed grasslands, but (ii) a more balanced amount between input and output in the majority of natural grasslands. Based on the mass balance between P input and output, we developed a framework to achieve sustainable P management in grasslands and discussed the measures targeting a more balanced P budget. Greater challenge is usually found in heavily-managed than natural grasslands to establish the optimum amount of P for grass and livestock production while minimizing the adverse impacts on surface waters. This study provided a comprehensive assessment of P budget in global grasslands and such information will be critical in determining the appropriate P management measures for various grassland types across the globe

Quantum-inspired Complex Convolutional Neural Networks

Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are mainly used for three-layer feedforward neural networks. In this work, we improve the quantum-inspired neurons by exploiting the complex-valued weights which have richer representational capacity and better non-linearity. We then extend the method of implementing the quantum-inspired neurons to the convolutional operations, and naturally draw the models of quantum-inspired convolutional neural networks (QICNNs) capable of processing high-dimensional data. Five specific structures of QICNNs are discussed which are different in the way of implementing the convolutional and fully connected layers. The performance of classification accuracy of the five QICNNs are tested on the MNIST and CIFAR-10 datasets. The results show that the QICNNs can perform better in classification accuracy on MNIST dataset than the classical CNN. More learning tasks that our QICNN can outperform the classical counterparts will be found.Comment: 12pages, 6 figure

Context-Aware Block Net for Small Object Detection.

State-of-the-art object detectors usually progressively downsample the input image until it is represented by small feature maps, which loses the spatial information and compromises the representation of small objects. In this article, we propose a context-aware block net (CAB Net) to improve small object detection by building high-resolution and strong semantic feature maps. To internally enhance the representation capacity of feature maps with high spatial resolution, we delicately design the context-aware block (CAB). CAB exploits pyramidal dilated convolutions to incorporate multilevel contextual information without losing the original resolution of feature maps. Then, we assemble CAB to the end of the truncated backbone network (e.g., VGG16) with a relatively small downsampling factor (e.g., 8) and cast off all following layers. CAB Net can capture both basic visual patterns as well as semantical information of small objects, thus improving the performance of small object detection. Experiments conducted on the benchmark Tsinghua-Tencent 100K and the Airport dataset show that CAB Net outperforms other top-performing detectors by a large margin while keeping real-time speed, which demonstrates the effectiveness of CAB Net for small object detection

Optimization and Noise Analysis of the Quantum Algorithm for Solving One-Dimensional Poisson Equation

Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic or Hamiltonian simulation. In this letter, we further develop this algorithm to make it closer to the real application on the noisy intermediate-scale quantum (NISQ) devices. To this end, we first develop a new way of performing the sine transformation, and based on it the algorithm is optimized by reducing the depth of the circuit from n2 to n. Then, we analyze the effect of common noise existing in the real quantum devices on our algorithm using the IBM Qiskit toolkit. We find that the phase damping noise has little effect on our algorithm, while the bit flip noise has the greatest impact. In addition, threshold errors of the quantum gates are obtained to make the fidelity of the circuit output being greater than 90%. The results of noise analysis will provide a good guidance for the subsequent work of error mitigation and error correction for our algorithm. The noise-analysis method developed in this work can be used for other algorithms to be executed on the NISQ devices.Comment: 20 pages, 9 figure