A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lat...A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations. The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations, the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinskii gasket are calculated.展开更多
This paper investigates the statistical behaviors of fluctuations of price changes in a stock market.The Sierpinski carpet lattice fractal and the percolation system are applied to develop a new random stock price for...This paper investigates the statistical behaviors of fluctuations of price changes in a stock market.The Sierpinski carpet lattice fractal and the percolation system are applied to develop a new random stock price for the financial market.The Sierpinski carpet is an infinitely ramified fractal and the percolation theory is usually used to describe the behavior of connected clusters in a random graph.The authors investigate and analyze the statistical behaviors of returns of the price model by some analysis methods,including multifractal analysis,autocorrelation analysis,scaled return interval analysis.Moreover,the authors consider the daily returns of Shanghai Stock Exchange Composite Index,and the comparisons of return behaviors between the actual data and the simulation data are exhibited.展开更多
基金Supported by the National Natural Foundation of China (79970121).
文摘A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations. The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations, the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinskii gasket are calculated.
基金supported by the National Natural Science Foundation of China Grant Nos.71271026 and 10971010
文摘This paper investigates the statistical behaviors of fluctuations of price changes in a stock market.The Sierpinski carpet lattice fractal and the percolation system are applied to develop a new random stock price for the financial market.The Sierpinski carpet is an infinitely ramified fractal and the percolation theory is usually used to describe the behavior of connected clusters in a random graph.The authors investigate and analyze the statistical behaviors of returns of the price model by some analysis methods,including multifractal analysis,autocorrelation analysis,scaled return interval analysis.Moreover,the authors consider the daily returns of Shanghai Stock Exchange Composite Index,and the comparisons of return behaviors between the actual data and the simulation data are exhibited.
