On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information

This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a group of agents. A cluster is viewed as a virtual noncooperative player that aims to minimize its local payoff function and the agents in a cluster are the actual players that cooperate within the cluster to optimize the payoff function of the cluster through communication via a connected graph. In our setting, agents have only partial-decision information, that is, they only know local information and cannot have full access to opponents' decisions. To solve the NE seeking problem of this formulated game, a discrete-time distributed algorithm, called distributed gradient tracking algorithm (DGT), is devised based on the inter- and intra-communication of clusters. In the designed algorithm, each agent is equipped with strategy variables including its own strategy and estimates of other clusters' strategies. With the help of a weighted Fronbenius norm and a weighted Euclidean norm, theoretical analysis is presented to rigorously show the linear convergence of the algorithm. Finally, a numerical example is given to illustrate the proposed algorithm

Tetra-μ-acetato-bis­{[9-(pyrazin-2-yl)-9H-carbazole]copper(II)}

The title complex, [Cu2(CH3COO)4(C16H11N3)2], lies on an inversion centre, with four acetate ligands bridging two symmetry-related CuII ions and two monodentate 9-(pyrazin-2-yl)-9H-carbazole ligands coordinating each CuII ion via the N atoms of the pyrazine rings, forming slightly distorted square-pyramidal geometries. There are weak π–π stacking inter­actions between the pyrrole rings of symmetry-related mol­ecules, with a centroid-to-centroid distance of 3.692 (2) Å

Diversity of Woodland Communities and Plant Species along an Altitudinal Gradient in the Guancen Mountains, China

Study on plant diversity is the base of woodland conservation. The Guancen Mountains are the northern end of Luliang mountain range in North China. Fifty-three quadrats of 10 m × 20 m of woodland communities were randomly established along an altitudinal gradient. Data for species composition and environmental variables were measured and recorded in each quadrat. To investigate the variation of woodland communities, a Two-Way Indicator Species Analysis (TWINSPAN) and a Canonical Correspondence Analysis (CCA) were conducted, while species diversity indices were used to analyse the relationships between species diversity and environmental variables in this study. The results showed that there were eight communities of woodland vegetation; each of them had their own characteristics in composition, structure, and environment. The variation of woodland communities was significantly related to elevation and also related to slope, slope aspect, and litter thickness. The cumulative percentage variance of species-environment relation for the first three CCA axes was 93.5%. Elevation was revealed as the factor which most influenced community distribution and species diversity. Species diversity was negatively correlated with elevation, slope aspect, and litter thickness, but positively with slope. Species richness and heterogeneity increased first and then decreased but evenness decreased significantly with increasing elevation. Species diversity was correlated with slope, slope aspect, and litter thickness