Assume that S is an nth-order complex sign pattern.If for every nth degree complex coefficient polynomial f(λ)with a leading coefficient of 1,there exists a complex matrix C∈Q(S)such that the characteristic polynomi...Assume that S is an nth-order complex sign pattern.If for every nth degree complex coefficient polynomial f(λ)with a leading coefficient of 1,there exists a complex matrix C∈Q(S)such that the characteristic polynomial of C is f(λ),then S is called a spectrally arbitrary complex sign pattern.That is,if the spectrum of nth-order complex sign pattern S is a set comprised of all spectra of nth-order complex matrices,then S is called a spectrally arbitrary complex sign pattern.This paper presents a class of spectrally arbitrary complex sign pattern with only 3n nonzero elements by adopting the method of Schur complement and row reduction.展开更多
This paper examines the noise and rotation resistance capacity of Hopfield Neural Network （HNN） given four corrupted traffic sign images. In the study, Signal-to-Noise Ratio （SNR）, recall rate and pattern complexi...This paper examines the noise and rotation resistance capacity of Hopfield Neural Network （HNN） given four corrupted traffic sign images. In the study, Signal-to-Noise Ratio （SNR）, recall rate and pattern complexity are defined and employed to evaluate the recall performance. The experimental results indicate that the HNN possesses significant recall capacity against the strong noise corruption, and certain restoring competence to the rotation. It is also found that combining noise with rotation does not further challenge the HNN corruption resistance capability as the noise or rotation alone does.展开更多
An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern ...An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern class （ray pattern class） of 3 such that its characteristic polynomial is f（λ）. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns （sign pattern, complex sign pattern, ray pattern） are the same in form.展开更多
文摘Assume that S is an nth-order complex sign pattern.If for every nth degree complex coefficient polynomial f(λ)with a leading coefficient of 1,there exists a complex matrix C∈Q(S)such that the characteristic polynomial of C is f(λ),then S is called a spectrally arbitrary complex sign pattern.That is,if the spectrum of nth-order complex sign pattern S is a set comprised of all spectra of nth-order complex matrices,then S is called a spectrally arbitrary complex sign pattern.This paper presents a class of spectrally arbitrary complex sign pattern with only 3n nonzero elements by adopting the method of Schur complement and row reduction.
基金Supported by the Natural Science Foundation of Zhejiang Province(No.2010A610105)
文摘This paper examines the noise and rotation resistance capacity of Hopfield Neural Network （HNN） given four corrupted traffic sign images. In the study, Signal-to-Noise Ratio （SNR）, recall rate and pattern complexity are defined and employed to evaluate the recall performance. The experimental results indicate that the HNN possesses significant recall capacity against the strong noise corruption, and certain restoring competence to the rotation. It is also found that combining noise with rotation does not further challenge the HNN corruption resistance capability as the noise or rotation alone does.
基金National Natural Science Foundation of China(Grant No.11071227)Shanxi Scholarship Councilof China(Grant No.12-070)
文摘An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern class （ray pattern class） of 3 such that its characteristic polynomial is f（λ）. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns （sign pattern, complex sign pattern, ray pattern） are the same in form.
