Most robust and fragile two-qubit entangled states under depolarizing channels

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad et al. [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region [1/2,1]. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.Comment: 10 pages, 9 figs. to appear in Quantum Information & Computation (QIC

Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler (LTPE) scheme, which also admits an invariant measure, to handle the potential influence of the linear stiffness. Under certain assumptions, both the SDE and the corresponding LTPE method are shown to converge exponentially to the underlying invariant measures, respectively. Moreover, with time-independent regularity estimates for the corresponding Kolmogorov equation, the weak error between the numerical invariant measure and the original one can be guaranteed with an order one. Numerical experiments are provided to verify our theoretical findings.Comment: 45 pages, 7 figure

Guangzhou as livable city: Its origin, inheritance, and development

This article intends to explore the ideas and concepts that dominate the landmark versions of planning in a historical survey on the development of urban planning for the construction of Guangzhou. From the Late 17th C. to the Mid-19th C. Xiguan in Guangzhou witnessed the booming of the Thirteen-hong characterized by gardens and buildings in Western architectural styles. These characteristics constituted the architectural features and urban spatial patterns on both sides of the Pearl River, and caused the moving westward of the ancient city center to the Thirteen-hong Business District. After The Second Opium War Western merchants began their planning and construction of Shameen with Western planning techniques, which, together with the model of the Thirteen-hong, led to the urban modernization of Guangzhou urban planning. During the years from 1911 to 1948, the urban planning and construction in Guangzhou underwent a sequence of processes from simplicity to complexity, and from part to whole. There was also a process from the simple imitation of Western ideas and concepts of urban planning in Dashatou Island to the renovation of Guangzhou urban planning marked with road and park construction, This process includes the dismantle of the city walls for road construction in 1912, the prelude of modern urban planning of Guangzhou in 1914, the planning for network and city-round road and park construction in 1918, the idea of “Traffic First” in 1921, the regional studies and planning in 1923, the concept of functional division in 1932, the idea of implementing urban function division in 1920s and 1930s, and the transference from the initial techniques and measures to land management in 1937. After that there was the adoption of the "zonal cluster layout" along the Pearl River in 1984, the idea of the Planning of Urban Agglomeration of the Pearl River Delta in 1995, and the continuation of the “four land usage modes” in 2003. The idea and concept of urban planning for Guangzhou, thus derived localized from the practice of Western urban planning in the Thirteen-hong and Shameen, later underwent the municipal planning of Dashatou, the idyllic residential districts. The innovated regional green space in 2006, followed by the livable urban and rural planning in 2016, and up to the lately ecological city in 2018, all bear the marks of the early ideas and concepts realized in the Thirteen-hong, Shameen, and Dashatou. Therefore, it can be further concluded that the urban planning of Guangzhou, developed from the initial function of landscape beautification to the regulation of regional green environment of the Pearl River Delta, underwent finally a full process of imitation, learning, transformation, and innovation, resulting in an idea of green, open, and shared urban construction

LSTM Pose Machines

We observed that recent state-of-the-art results on single image human pose estimation were achieved by multi-stage Convolution Neural Networks (CNN). Notwithstanding the superior performance on static images, the application of these models on videos is not only computationally intensive, it also suffers from performance degeneration and flicking. Such suboptimal results are mainly attributed to the inability of imposing sequential geometric consistency, handling severe image quality degradation (e.g. motion blur and occlusion) as well as the inability of capturing the temporal correlation among video frames. In this paper, we proposed a novel recurrent network to tackle these problems. We showed that if we were to impose the weight sharing scheme to the multi-stage CNN, it could be re-written as a Recurrent Neural Network (RNN). This property decouples the relationship among multiple network stages and results in significantly faster speed in invoking the network for videos. It also enables the adoption of Long Short-Term Memory (LSTM) units between video frames. We found such memory augmented RNN is very effective in imposing geometric consistency among frames. It also well handles input quality degradation in videos while successfully stabilizes the sequential outputs. The experiments showed that our approach significantly outperformed current state-of-the-art methods on two large-scale video pose estimation benchmarks. We also explored the memory cells inside the LSTM and provided insights on why such mechanism would benefit the prediction for video-based pose estimations.Comment: Poster in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 201

The Knowledge Graph for Macroeconomic Analysis with Alternative Big Data

The current knowledge system of macroeconomics is built on interactions among a small number of variables, since traditional macroeconomic models can mostly handle a handful of inputs. Recent work using big data suggests that a much larger number of variables are active in driving the dynamics of the aggregate economy. In this paper, we introduce a knowledge graph (KG) that consists of not only linkages between traditional economic variables but also new alternative big data variables. We extract these new variables and the linkages by applying advanced natural language processing (NLP) tools on the massive textual data of academic literature and research reports. As an example of potential applications, we use it as the prior knowledge to select variables for economic forecasting models in macroeconomics. Compared to statistical variable selection methods, KG-based methods achieve significantly higher forecasting accuracy, especially for long run forecasts

A TOU Pricing Mechanism to Promote Renewable Energy Consumption: The Case of the Western Inner Mongolia Grid in China

The curtailment of wind power and photovoltaic power is becoming increasingly serious from the year 2012 to present in China. And the small installed capacity captive coal-fired power plants have been developed rapidly aiming to cut production costs. Therefore, by the substitution of renewable energy for captive coal-fired power plants, this paper establishes a time-of-use (TOU) pricing mechanism with a linkage between the supply side and the demand side to promote renewable energy consumption, which is applied to the Western Inner Mongolia grid in China. The results show that the benefits to the grid company, electricity users, renewable energy producers, and social environment are influenced by the quantity of renewable energy purchased in the market, the market price for renewable energy, the quantity of electricity from grid to peak shaving, the carbon price, and the quantity of electricity generated by captive coal-fired power plants shifting to grid, in which the first factor has the greatest influence on the benefits of stakeholders. Furthermore, improving the accuracy of renewable energy generation forecast and optimizing using electricity behaviors by considering the renewable energy generation characteristics could ensure the TOU mechanism implementation successfully