Neural networks with integer weights are more suited for embedded systems and hardware implementations than those with real weights. However, many learning algorithms, which have been proposed for training neural netw...Neural networks with integer weights are more suited for embedded systems and hardware implementations than those with real weights. However, many learning algorithms, which have been proposed for training neural networks with float weights, are inefficient and difficult to train for neural networks with integer weights. In this paper, a novel regeneratable dynamic differential evolution algorithm (RDDE) is presented. This algorithm is efficient for training networks with integer weights. In comparison with the conventional differential evolution algorithm (DE), RDDE has introduced three new strategies: (1) A regeneratable strategy is introduced to ensure further evolution, when all the individuals are the same after several iterations such that they cannot evolve further. In other words, there is an escape from the local minima. (2) A dynamic strategy is designed to speed up convergence and simplify the algorithm by updating its population dynamically. (3) A local greedy strategy is introduced to improve local searching ability when the population approaches the global optimal solution. In comparison with other gradient based algorithms, RDDE does not need the gradient information, which has been the main obstacle for training networks with integer weights. The experiment results show that RDDE can train integer-weight networks more efficiently.展开更多
Embryonic Array(EA) with different configuration methods will directly affect its reliability and hardware consumption. At present, EA configuration design is lack of quantitative analysis method. In order to reasonab...Embryonic Array(EA) with different configuration methods will directly affect its reliability and hardware consumption. At present, EA configuration design is lack of quantitative analysis method. In order to reasonably optimize EA configuration design, an EA configuration optimization design method is proposed, which is based on the constraints of EA hardware consumption and reliability. Through the analysis of EA working process and composition, quantitative analysis of EA reliability and hardware consumption are completed. Based on the constraints of EA hardware consumption and reliability, the mathematical model of EA configuration optimization design is established, which transfers EA configuration optimization design into an integer nonlinear programming model problem. According to the difference of the fitness value of individual waiting for mutation in population, adaptive mutation operator and crossover operator are selected, and a novel Modified Adaptive Differential Evolution(MADE) algorithm is proposed,which is used to solve EA configuration optimization design problem. Simulation experiments and analysis indicate that the MADE is able to effectively improve the speed, accuracy and stability of algorithm. Moreover, the proposed EA configuration optimization design method can select the most reasonable EA configuration design, and play an important guiding role in EA optimization design.展开更多
The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and he...The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and hence the features of the Logistic model,such as subcritical and supercritical harvesting,have been investigated in a view of fractional calculus.The positive auxiliary parameter,σ,with dimension of time is implemented to maintain the dimensionality of the system.The significant information of such parameter to the population has been discussed.The population expressions,obtained by conformable description,are compared with the expressions of the classical derivative.This comparison shows that the non-integer expressions are in a parallel line with that of the classical one.展开更多
To improve the classical lossless compression of low efficiency,a method of image lossless compression with high efficiency is presented.Its theory and the algorithm implementation are introduced.The basic approach of...To improve the classical lossless compression of low efficiency,a method of image lossless compression with high efficiency is presented.Its theory and the algorithm implementation are introduced.The basic approach of medical image lossless compression is then briefly described.After analyzing and implementing differential plus code modulation(DPCM)in lossless compression,a new method of combining an integer wavelet transform with DPCM to compress medical images is discussed.The analysis and simulation results show that this new method is simpler and useful.Moreover,it has high compression ratio in medical image lossless compression.展开更多
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
文摘Neural networks with integer weights are more suited for embedded systems and hardware implementations than those with real weights. However, many learning algorithms, which have been proposed for training neural networks with float weights, are inefficient and difficult to train for neural networks with integer weights. In this paper, a novel regeneratable dynamic differential evolution algorithm (RDDE) is presented. This algorithm is efficient for training networks with integer weights. In comparison with the conventional differential evolution algorithm (DE), RDDE has introduced three new strategies: (1) A regeneratable strategy is introduced to ensure further evolution, when all the individuals are the same after several iterations such that they cannot evolve further. In other words, there is an escape from the local minima. (2) A dynamic strategy is designed to speed up convergence and simplify the algorithm by updating its population dynamically. (3) A local greedy strategy is introduced to improve local searching ability when the population approaches the global optimal solution. In comparison with other gradient based algorithms, RDDE does not need the gradient information, which has been the main obstacle for training networks with integer weights. The experiment results show that RDDE can train integer-weight networks more efficiently.
基金supported by the National Natural Science Foundation of China(Nos.61372039 and 61601495)
文摘Embryonic Array(EA) with different configuration methods will directly affect its reliability and hardware consumption. At present, EA configuration design is lack of quantitative analysis method. In order to reasonably optimize EA configuration design, an EA configuration optimization design method is proposed, which is based on the constraints of EA hardware consumption and reliability. Through the analysis of EA working process and composition, quantitative analysis of EA reliability and hardware consumption are completed. Based on the constraints of EA hardware consumption and reliability, the mathematical model of EA configuration optimization design is established, which transfers EA configuration optimization design into an integer nonlinear programming model problem. According to the difference of the fitness value of individual waiting for mutation in population, adaptive mutation operator and crossover operator are selected, and a novel Modified Adaptive Differential Evolution(MADE) algorithm is proposed,which is used to solve EA configuration optimization design problem. Simulation experiments and analysis indicate that the MADE is able to effectively improve the speed, accuracy and stability of algorithm. Moreover, the proposed EA configuration optimization design method can select the most reasonable EA configuration design, and play an important guiding role in EA optimization design.
文摘The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and hence the features of the Logistic model,such as subcritical and supercritical harvesting,have been investigated in a view of fractional calculus.The positive auxiliary parameter,σ,with dimension of time is implemented to maintain the dimensionality of the system.The significant information of such parameter to the population has been discussed.The population expressions,obtained by conformable description,are compared with the expressions of the classical derivative.This comparison shows that the non-integer expressions are in a parallel line with that of the classical one.
基金supported by the National Natural Science Foundation of China (Grant No.60475036).
文摘To improve the classical lossless compression of low efficiency,a method of image lossless compression with high efficiency is presented.Its theory and the algorithm implementation are introduced.The basic approach of medical image lossless compression is then briefly described.After analyzing and implementing differential plus code modulation(DPCM)in lossless compression,a new method of combining an integer wavelet transform with DPCM to compress medical images is discussed.The analysis and simulation results show that this new method is simpler and useful.Moreover,it has high compression ratio in medical image lossless compression.
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
