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In this paper, we consider networks with topologies described by some connected undirected graph G = (V , E) and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and optimization problem min x ⁡ { F (x) = ∑ i ∈ V f i (x) } with local objective functions f i depending only on neighboring variables of the vertex i ∈ V. We introduce a divide-and-conquer algorithm to solve the above optimization problem in a distributed and decentralized manner. The proposed divide-and-conquer algorithm has exponential convergence, its computational cost is almost linear with respect to the size of the network, and it can be fully implemented at fusion centers of the network. In addition, our numerical demonstrations indicate that the proposed divide-and-conquer algorithm has superior performance than popular decentralized optimization methods in solving the least squares problem, both with and without the ℓ 1 penalty, and exhibits great performance on networks equipped with asynchronous local peer-to-peer communication. [ABSTRACT FROM AUTHOR]

Distributedly training models across diverse clients with heterogeneous data samples can significantly impact the convergence of federated learning. Various novel federated learning methods address these challenges but often require significant communication resources and local computational capacity, leading to reduced global inference accuracy in scenarios with imbalanced label data distribution and quantity skew. To tackle these challenges, we propose FedVGL, a Federated Variational Generative Learning method that directly trains a local generative model to learn the distribution of local features and improve global target model inference accuracy during aggregation, particularly under conditions of severe data heterogeneity. FedVGL facilitates distributed learning by sharing generators and latent vectors with the global server, aiding in global target model training from mapping local data distribution to the variational latent space for feature reconstruction. Additionally, FedVGL implements anonymization and encryption techniques to bolster privacy during generative model transmission and aggregation. In comparison to vanilla federated learning, FedVGL minimizes communication overhead, demonstrating superior accuracy even with minimal communication rounds. It effectively mitigates model drift in scenarios with heterogeneous data, delivering improved target model training outcomes. Empirical results establish FedVGL's superiority over baseline federated learning methods under severe label imbalance and data skew condition. In a Label-based Dirichlet Distribution setting with α =0.01 and 10 clients using the MNIST dataset, FedVGL achieved an exceptional accuracy over 97% with the VGG-9 target model. • FedVGL reduces model drift with imbalanced data using variational generative models to train globally while preserving privacy. • FedVGL applies Privacy Preserving techniques to secure data, enhance underrepresented classes, and boost global model accuracy. • FedVGL demonstrates great potential for secure, efficient distributed learning in imbalanced data scenarios. [ABSTRACT FROM AUTHOR]

Abstract: This study considered a model for species abundance dynamics in two local community (or islands) connected to a regional metacommunity. The model was analyzed using continuous probabilistic technique that employs Kolmogorov–Fokker–Planck forward equation to derive the probability density of the species abundance in the two local communities. Using this technique, we proposed a classification for the species abundance dynamics in the local communities. This classification was made based on such characteristics as immigration intensity, species representation in the metacommunity and the size of local communities. We further distinguished several different scenarios for species abundance dynamics using different ecological characteristics such as species persistence, extinction and monodominance in one or both local communities. The similarity of the species abundance distributions between the two local communities was studied using the correlation coefficient between species abundances in two local communities. The correlation is a function of migration rates between local communities and between local and metacommunity. Immigration between local communities drives the homogenization of the local communities, while immigration from the metacommunity will differentiate them. This community subdivision model provides useful insights for studying the effect of landscape fragmentation on species diversity. [Copyright &y& Elsevier]