Control energy of complex networks towards distinct mixture states

Controlling complex networked systems is a real-world puzzle that remains largely unsolved. Despite recent progress in understanding the structural characteristics of network control energy, target state and system dynamics have not been explored. We examine how varying the final state mixture affects the control energy of canonical and conformity-incorporated dynamical systems. We find that the control energy required to drive a network to an identical final state is lower than that required to arrive a non-identical final state. We also demonstrate that it is easier to achieve full control in a conformity-based dynamical network. Finally we determine the optimal control strategy in terms of the network hierarchical structure. Our work offers a realistic understanding of the control energy within the final state mixture and sheds light on controlling complex systems.This work was funded by The National Natural Science Foundation of China (Grant Nos. 61763013, 61703159, 61403421), The Natural Science Foundation of Jiangxi Province (No. 20171BAB212017), The Measurement and Control of Aircraft at Sea Laboratory (No. FOM2016OF010), and China Scholarship Council (201708360048). The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, and by DTRA Grant HDTRA1-14-1-0017. (61763013 - National Natural Science Foundation of China; 61703159 - National Natural Science Foundation of China; 61403421 - National Natural Science Foundation of China; 20171BAB212017 - Natural Science Foundation of Jiangxi Province; FOM2016OF010 - Measurement and Control of Aircraft at Sea Laboratory; 201708360048 - China Scholarship Council; PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - DTRA)Published versio

Characteristics of typical pollutants in tannery site soil

Content: This paper briefly introduced the process of leather manufacture and the potential pollution sources of soil in tannery sites. Pollutants are mainly derived from the use of a large number of various chemicals and organic matter decomposed by raw skin. The characteristics of typical pollutants in tannery sites soil were summarized, including tannery site soil pH, organic and inorganic compounds, and heavy metals, etc., especially the status of chromium contamination were reviewed. The pH of soil in the tanning workshop (6.65-7.8) is generally lower than tannery sludge dumping site (7.94-8.40). The main organic pollutants contained in the tannery site soil include nitrogen compound, grease, petroleum hydrocarbon. In tannery sludge dumping site soil, the content of nitrogen compound (10cm depth) is 28400 mg/kg, which is similar to tannery sludge. The content of petroleum hydrocarbon is 5-700 mg/kg, which partially exceed the limits of China agricultural land quality standard(450mg/L), total dissolved solids (>1000mg/L), sulfate ions (>250mg/L), nitrite nitrogen (>0.02mg/L) partially exceed the limits of China groundwater quality standard, which are found in groundwater below the tannery site. Heavy metal pollutants in the tannery sites soil have many characteristics and large differences in content, due to the different tanning processes. Among them, chromium (Cr) is the most used heavy metal and the highest content of pollutants. Cr content in tanning process wastewater, dyeing process wastewater and chromiumcontaining sludge are about 2000-3000 mg/L, 30-40 mg/L and 8500-25800 mg/kg, respectively. Total Cr content in the partial tannery sites soil are higher than 800 mg/kg, which exceed the limits of China agricultural land quality standard(<150mg/kg). Surprisingly, Cr(VI) appears in tannery sites soil and the contents are partly higher than 40 mg/kg, which exceed the limits of China development land quality standard(<3.0mg/kg). Furthermore, the more effort needs to be directed toward the chemistry of chromium-organic complex pollutants, and an understanding of the speciation of Cr in highly organics contaminated tannery site soil is essential for the development of suitable remediation strategies for contaminated soil. Take-Away: 1. The pH of soil in the tanning workshop (6.65-7.8) is generally lower than tannery sludge dumping site(7.94-8.40). 2. Total Cr content in the partial tannery sites soil are higher than 800 mg/kg, which exceed the limits of China agricultural land quality standard(<150mg/kg). 3. Cr(VI) appears in tannery sites soil and the contents are partly higher than 40 mg/kg, which exceed the limits of China development land quality standard(<3.0mg/kg)

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under PolyakL jasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analysis for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the respective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications

Coupled effects of local movement and global interaction on contagion

By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the situation where only local movement or individual-based linkage exists, the coexistence of them leads to a wider spread of infectious disease. The roles of narrowing segregated spatial domain and reducing mobility in epidemic control are checked, these two measures are found to be conducive to curbing the spread of infectious disease. Considering heterogeneous time scales between local movement and global interaction, a log-log relation between the change in the number of infected individuals and the timescale $\tau$ is found. A theoretical analysis indicates that the evolutionary dynamics in the present model is related to the encounter probability and the encounter time. A functional relation between the epidemic threshold and the ratio of shortcuts, and a functional relation between the encounter time and the timescale $\tau$ are found

(E)-2-{3-[4-(Diphenyl­amino)styr­yl]-5,5-dimethyl­cyclo­hex-2-enyl­idene}­malono­nitrile

In the title compound, C31H27N3, the cyclo­hexene ring has an envelope configuration. In the crystal structure, there is an 34 Å3 void around the inversion center, but the low electron density (0.13 e Å−3) in the difference Fourier map suggests no solvent mol­ecule occupying this void. No hydrogen bonding is found in the crystal structure