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Jingfei Jiang, Dengqing Cao and Huatao Chen

Abstract

In this paper, we study the two-point boundary value problems for fractional differential equation with causal operator. By lower and upper solution method and the monotone iterative technique, some results for the extremal solution and quasisolutions are obtained. At last, an example is given to demonstrate the validity of assumptions and theoretical results.

Open access

Jingfei Jiang, Rongdong Hu, Fei Zhang and Yong Dou

Abstract

The Sparse Coding (SC) model has been proved to be among the best neural networks which are mainly used in unsupervised feature learning for many applications. Running a sparse coding algorithm is a time-consuming task due to its large scale and processing characteristics, which naturally leads to investigating FPGA acceleration. Fixed-point arithmetic can be used when implementing SC in FPGAs to reduce the execution time, but the implications for accuracy are not clear. Previous studies have focused only on accelerators using some fixed bitwidths on other neural networks models. Our work gives a comprehensive evaluation to demonstrate the bit-width effect on SCs, achieving the best performance and area efficiency. The method of data format conversion and the matrix blocking are the main factors considered according to the situation of hardware implementation. The simulation method of the simple truncation, the representation of the domain constraint and the matrix blocking with different parallelism were evaluated in this paper. The results have shown that the fixedpoint bit-width did have effect on the performance of SC. We must limit the representation domain of the data carefully and select an available bit-width according to the computation parallelism. The result has also shown that using a fixed-point arithmetic can guarantee the precision of the SC algorithm and get acceptable convergence speed.

Open access

H. Chen, Jingfei Jiang, Dengqing Cao and Xiaoming Fan

Abstract

In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable coefficient are investigated numerically. It is shown that global 𝒟-bifurcation, secondary global 𝒟-bifurcation and complex dynamical behavior occur in motion of the system with increasing the intensity of linear component in the heat source. Furthermore, the results obtained here indicate that Hasudorff dimension which is relevant to global Lyapunov exponent can be used to describe global dynamics of the associated system qualitatively.