Abstract.A collaborative filtering algorithm based on double clustering and user trust to solve data sparse and cold start problem is present. This algorithm uses user-clustering matrix to measure the user's degree of similarity, which could reduce the dimension of the user-item matrix. On the other hand it uses user level trust to perform predictions in rating predicting step. The experiments results show that this method could relieve the sparsity problem and improve the accuracy of the prediction results.
In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHugh–Nagumo model. The results of numerical experiments are consistent with the theoretical results of other scholars, which verifies the accuracy of the method. We show that stable spatio-temporal patterns can be sustained for a long time; these patterns are different from any previously obtained in numerical studies. Here, we show that behavior patterns can be described well by the fractional FitzHugh–Nagumo and Gray–Scott models, which have unique properties that integer models do not have. Results show that the Fourier spectral method has strong competitiveness, reliability, and solving ability for solving 2D and 3D fractional-in-space nonlinear reaction-diffusion models.
In this paper we provide a quantum public-key cryptosystem based on super dense coding technology. A user Alice shares a set of Einstein-Podolsky-Rosen (EPR) pairs with a key management center (KMC) in which the particles hold by Alice are the private key and the particle hold by KMC are the public key. By the help of the key management center any other user can send encrypted message to Alice. Any one including KMC except Alice can't recover the message. On the other hand digital signature can also be achieved by this public-key cryptosystem. In the cryptosystem one EPR pair can be used to encrypt two bits of the plain text. So it's efficient. Finally we prove that our cryptosystem is robust against possible attacks.
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