Hybrid tri-memristor hyperchaotic map and application in Wasserstein Generative Adversarial Nets

Inspired by basic circuit connection methods,memristors can also be utilized in the construction of complex discrete chaotic systems.To investigate the dynamical effects of hybrid memristors,we propose two hybrid tri-memristor hyperchaotic(HTMH)mapping structures based on the hybrid parallel/cascade and cascade/parallel operations,respectively.Taking the HTMH mapping structure with hybrid parallel/cascade operation as an example,this map possesses a spatial invariant set whose stability is closely related to the initial states of the memristors.Dynamics distributions and bifurcation behaviours dependent on the control parameters are explored with numerical tools.Specifically,the memristor initial offset-boosting mechanism is theoretically demonstrated,and memristor initial offset-boosting behaviours are numerically verified.The results clarify that the HTMH map can exhibit hyperchaotic behaviours and extreme multistability with homogeneous coexisting infinite attractors.In addition,an FPGA hardware platform is fabricated to implement the HTMH map and generate pseudorandom numbers(PRNs)with high randomness.Notably,the generated PRNs can be applied in Wasserstein generative adversarial nets(WGANs)to enhance training stability and generation capability.

Top-k probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions： 1） the concept of the top-k prob- abilistic prevalent co-locations based on a possible world model is defined; 2） a framework for discovering the top- k probabilistic prevalent co-locations is set up; 3） a matrix method is proposed to improve the computation of the preva- lence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for ex- act solutions; 4） a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5） an ap- proximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.