More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant

Principles and symmetries of complexity in quantum field theory

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems. Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry. Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems. We clarify why the bi-invariance is relevant in quantum field theoretic systems. After comparing our results with discrete qubit systems we show most results in $k$-local right-invariant metric can also appear in our framework. Based on the bi-invariance of our formalism, we propose a new interpretation for the Schr\"{o}dinger's equation in isolated systems - the quantum state evolves by the process of minimizing "computational cost."Comment: Published version; added a short introduction on Finsler geometr

Deep Autoencoder Neural Networks for Short-Term Traffic Congestion Prediction of Transportation Networks

Traffic congestion prediction is critical for implementing intelligent transportation systems for improving the efficiency and capacity of transportation networks. However, despite its importance, traffic congestion prediction is severely less investigated compared to traffic flow prediction, which is partially due to the severe lack of large-scale high-quality traffic congestion data and advanced algorithms. This paper proposes an accessible and general workflow to acquire large-scale traffic congestion data and to create traffic congestion datasets based on image analysis. With this workflow we create a dataset named Seattle Area Traffic Congestion Status (SATCS) based on traffic congestion map snapshots from a publicly available online traffic service provider Washington State Department of Transportation. We then propose a deep autoencoder-based neural network model with symmetrical layers for the encoder and the decoder to learn temporal correlations of a transportation network and predicting traffic congestion. Our experimental results on the SATCS dataset show that the proposed DCPN model can efficiently and effectively learn temporal relationships of congestion levels of the transportation network for traffic congestion forecasting. Our method outperforms two other state-of-the-art neural network models in prediction performance, generalization capability, and computation efficiency

Tentative Plan of Pneumatic Silt Scouring on Yellow River

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Discriminative Elastic-Net Regularized Linear Regression

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zeroone matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of theses methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available datasets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html

Representation of Traffic Congestion Data for Urban Road Traffic Networks Based on Pooling Operations

In order to improve the efficiency of transportation networks, it is critical to forecast traffic congestion. Large-scale traffic congestion data have become available and accessible, yet they need to be properly represented in order to avoid overfitting, reduce the requirements of computational resources, and be utilized effectively by various methodologies and models. Inspired by pooling operations in deep learning, we propose a representation framework for traffic congestion data in urban road traffic networks. This framework consists of grid-based partition of urban road traffic networks and a pooling operation to reduce multiple values into an aggregated one. We also propose using a pooling operation to calculate the maximum value in each grid (MAV). Raw snapshots of traffic congestion maps are transformed and represented as a series of matrices which are used as inputs to a spatiotemporal congestion prediction network (STCN) to evaluate the effectiveness of representation when predicting traffic congestion. STCN combines convolutional neural networks (CNNs) and long short-term memory neural network (LSTMs) for their spatiotemporal capability. CNNs can extract spatial features and dependencies of traffic congestion between roads, and LSTMs can learn their temporal evolution patterns and correlations. An empirical experiment on an urban road traffic network shows that when incorporated into our proposed representation framework, MAV outperforms other pooling operations in the effectiveness of the representation of traffic congestion data for traffic congestion prediction, and that the framework is cost-efficient in terms of computational resources. Document type: Articl

Deep Autoencoder Neural Networks for Short-Term Traffic Congestion Prediction of Transportation Networks

Traffic congestion prediction is critical for implementing intelligent transportation systems for improving the efficiency and capacity of transportation networks. However, despite its importance, traffic congestion prediction is severely less investigated compared to traffic flow prediction, which is partially due to the severe lack of large-scale high-quality traffic congestion data and advanced algorithms. This paper proposes an accessible and general workflow to acquire large-scale traffic congestion data and to create traffic congestion datasets based on image analysis. With this workflow we create a dataset named Seattle Area Traffic Congestion Status (SATCS) based on traffic congestion map snapshots from a publicly available online traffic service provider Washington State Department of Transportation. We then propose a deep autoencoder-based neural network model with symmetrical layers for the encoder and the decoder to learn temporal correlations of a transportation network and predicting traffic congestion. Our experimental results on the SATCS dataset show that the proposed DCPN model can efficiently and effectively learn temporal relationships of congestion levels of the transportation network for traffic congestion forecasting. Our method outperforms two other state-of-the-art neural network models in prediction performance, generalization capability, and computation efficiency