Identifying spatial agglomeration and driving forces of land use by green industries: a case study of Jiangsu Province, China.

In response to China's aims of becoming "carbon-neutral," the development of green industries such as renewable energy and recycling has flourished. Based on 2015 and 2019 data, this study uses spatial autocorrelation to analyze the evolution of land use by the green industries in Jiangsu Province. The Geodetector model was also applied to identify the driving factors underlying these spatial patterns. The spatial variability of green industrial land use in Jiangsu Province is significant, with the land-use area gradually decreasing from Southern to Northern Jiangsu. In terms of spatial-temporal changes, there is an increase in land use and a trend of expansion in the central and northern regions of Jiangsu. Land use by green industries in the province exhibits a more significant spatial clustering pattern but with a weakened clustering effect. The clustering types are mainly H-H and L-L, with the H-H type distributed mainly in the Su-Xi-Chang region and the L-L type distributed mainly in the Northern Jiangsu region. The levels of technology, economic development, industrialization, and industrial diversification are important individual driving factors, and the interaction among the different factors enhances their driving forces. This study suggests that spatial spillover effects should be focused to promote the coordinated development of regional energy-saving and environmental protection industries. At the same time, joint efforts should be made from the aspects of resources, government, economy, and related industries to promote the agglomeration of land for energy-saving and environmental protection industries.

Non-divergence of stochastic discrete time algorithms for PCA neural networks.

Learning algorithms play an important role in the practical application of neural networks based on principal component analysis, often determining the success, or otherwise, of these applications. These algorithms cannot be divergent, but it is very difficult to directly study their convergence properties, because they are described by stochastic discrete time (SDT) algorithms. This brief analyzes the original SDT algorithms directly, and derives some invariant sets that guarantee the nondivergence of these algorithms in a stochastic environment by selecting proper learning parameters. Our theoretical results are verified by a series of simulation examples.

Determination of the number of principal directions in a biologically plausible PCA model.

Adaptively determining an appropriate number of principal directions for principal component analysis (PCA) neural networks is an important problem to address when one uses PCA neural networks for online feature extraction. In this letter, inspired from biological neural networks, a single-layer neural network model with lateral connections is proposed which uses an improved generalized Hebbian algorithm (GHA) to address this problem. In the proposed model, the number of principal directions can be adaptively determined to approximate the intrinsic dimensionality of the given data set so that the dimensionality of the data set can be reduced to approach the intrinsic dimensionality to any required precision through the network.

Output convergence analysis for a class of delayed recurrent neural networks with time-varying inputs.

This paper studies the output convergence of a class of recurrent neural networks with time-varying inputs. The model of the studied neural networks has different dynamic structure from that in the well known Hopfield model, it does not contain linear terms. Since different structures of differential equations usually result in quite different dynamic behaviors, the convergence of this model is quite different from that of Hopfield model. This class of neural networks has been found many successful applications in solving some optimization problems. Some sufficient conditions to guarantee output convergence of the networks are derived.

Convergence analysis of a deterministic discrete time system of Oja's PCA learning algorithm.

The convergence of Oja's principal component analysis (PCA) learning algorithms is a difficult topic for direct study and analysis. Traditionally, the convergence of these algorithms is indirectly analyzed via certain deterministic continuous time (DCT) systems. Such a method will require the learning rate to converge to zero, which is not a reasonable requirement to impose in many practical applications. Recently, deterministic discrete time (DDT) systems have been proposed instead to indirectly interpret the dynamics of the learning algorithms. Unlike DCT systems, DDT systems allow learning rates to be constant (which can be a nonzero). This paper will provide some important results relating to the convergence of a DDT system of Oja's PCA learning algorithm. It has the following contributions: 1) A number of invariant sets are obtained, based on which we can show that any trajectory starting from a point in the invariant set will remain in the set forever. Thus, the nondivergence of the trajectories is guaranteed. 2) The convergence of the DDT system is analyzed rigorously. It is proven, in the paper, that almost all trajectories of the system starting from points in an invariant set will converge exponentially to the unit eigenvector associated with the largest eigenvalue of the correlation matrix. In addition, exponential convergence rate are obtained, providing useful guidelines for the selection of fast convergence learning rate. 3) Since the trajectories may diverge, the careful choice of initial vectors is an important issue. This paper suggests to use the domain of unit hyper sphere as initial vectors to guarantee convergence. 4) Simulation results will be furnished to illustrate the theoretical results achieved.