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Finding the densest subgraph has tremendous potential in computer vision and social network research, among other domains. In computer vision, it can demonstrate essential structures, and in social network research, it aids in identifying closely associated communities. The densest subgraph problem is finding a subgraph with maximum mean density. However, most densest subgraph-finding algorithms are based on edge-weighted graphs, where edge weights can only represent a single value dimension, whereas practical applications involve multiple dimensions. To resolve the challenge, we propose two algorithms for resolving the densest subgraph problem in a vertex-weighted graph. First, we present an exact algorithm that builds upon Goldberg's original algorithm. Through theoretical exploration and analysis, we rigorously verify our proposed algorithm's correctness and confirm that it can efficiently run in polynomial time O(n(n + m)log2n) is its temporal complexity. Our approach can be applied to identify closely related subgroups demonstrating the maximum average density in real-life situations. Additionally, we consistently offer an approximation algorithm that guarantees an accurate approximation ratio of 2. In conclusion, our contributions enrich theoretical foundations for addressing the densest subgraph problem. [ABSTRACT FROM AUTHOR]

Based on nonlinear memory feedback, the robust admissibility problem of a class of singular nonlinear time-delay systems was investigated. First, an equivalent structural model of the system was created using the state decomposition approach. Then, sufficient criteria for the robust admissibility of the system were obtained in the form of linear matrix inequalities using the Lyapunov–Krasovskii theory and free weighted matrix method. Subsequently, the closed-loop robust admissibility of the system under nonlinear memory feedback control was investigated using similar research techniques as before, yielding corresponding results. The intended design controller was obtained by explicitly computing each component in the deconstructed structure of the nonlinear memory feedback controller. Importantly, the flexibility and viability of the planned control design could be enhanced by the algorithm for solving controller gain through this component decomposition. Finally, numerical examples confirmed the feasibility of the method. [ABSTRACT FROM AUTHOR]

In this study, model predictive control (MPC) was considered for a class of discrete time-delay systems with external disturbances. Equivalent input disturbance (EID) is a commonly utilized active disturbance rejection technique that enhances the rejection of system disturbances. Any disturbance can be effectively suppressed using the EID approach, leaving no traces of the disturbance. This paper proposes a novel MPC control approach that combines the EID method with the MPC principle. An MPC law with disturbance-rejection performance was presented after obtaining and combining the EID estimates with performance indicators using the EID method. Optimizing the performance index is then converted into a semi-definite problem comprising of an objective function and linear matrix inequality through building a Lyapunov function. Based on this basis, an MPC design algorithm is proposed. A numerical simulation was conducted to confirm superiority and efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

Biogenic volatile organic compounds (BVOCs) significantly contribute to atmospheric chemistry at both regional and global scales. The composition and intensity of BVOC emissions vary significantly among different plant species. Previous studies have focused on BVOC emissions from tree species, but the results of research on BVOC emissions from wetland plants are still limited. Therefore, in this study, BVOCs emitted by three aquatic plants (Phragmites australis, Typha angustifolia, and Iris pseudacorus) were sampled and analyzed using a dynamic headspace technique combined with GC-MS at daily scales. The diurnal observation data showed that the total BVOC emission rates of the three plants peaked with the increase in environmental factors (temperature, PAR, and water temperature). P. australis was the only of the three plants that emitted isoprene with a high rate of 48.34 μg·g−1Dw·h−1. Moreover, the peak emission rates of total BVOC (78.45 μg·g−1Dw·h−1) in P. australis were higher than most tree species. The emissions rates of volatile organic compounds, including monoterpenes, oxygenated volatile organic compounds, alkanes, and other volatile organic compounds, were statistically correlated across all species. The emission rates of isoprene from P. australis had significant associations with intercellular CO2 concentration (Ci) (0.58, p < 0.05) and transpiration rate (Tr) (−0.63, p < 0.01). The emission rates of monoterpenes from P. australis were found to have a significantly positive correlation with the net photosynthetic rate (Pn) (0.58, p < 0.05) while T. angustifolia (−0.59, p < 0.05) and I. pseudacorus (−0.47, p < 0.05) showed the opposite trend. Such findings hold significance for the refinement of localized emission inventories and the development of comprehensive emission process models in future research, as BVOC emissions from wetland plants were reported here for the first time. [ABSTRACT FROM AUTHOR]

The stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative. [ABSTRACT FROM AUTHOR]

Soil heavy metal contamination poses a significant threat to both environmental health and ecological safety. To investigate the influencing factors, ecological hazards, and sources analysis of heavy metals in purple soil, 27 sets of soil samples were collected from varying genetic horizons within Guang'an City, and the contents of As, Cd, Cu, Cr, Hg, Ni, Pb, and Zn were analyzed. The results indicated higher concentrations of heavy metals in soil A horizon, compared to that of C horizon. The relevance analysis indicated that the soil's heavy metals were strongly correlated with the soil's physicochemical properties. The enrichment factor, pollution load index, and potential risk index highlighted slightly to severely polluted levels of soil Cd and Hg, which significantly contribute to the ecological hazards posed by soil heavy metals. The potential source of heavy metals analyzed using the APCS-MLR model identified both anthropogenic inputs and natural sources as primary contributors to heavy metal presence in soils. The Cu, Cr, Ni, Pb, and Zn contents in the samples from different genetic horizons were chiefly influenced by natural sources, such as soil matrix erosion and weathering, while the concentrations of Cd and Hg were largely affected by anthropogenic activities, specifically coal combustion and agriculture. Conversely, the As content was found to be influenced by a combination of both factors. Anthropogenic activities greatly impacted soil heavy metals at various depths within the study area, thereby underscoring the importance of monitoring these heavy metals. The findings gained from this research can give a scientific basis for the potential utilization of purple soil. [ABSTRACT FROM AUTHOR]