Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used....Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used. Results The distribution range of the data setsinfluences the sensitivity of Pearson product-moment correlation coefficient. Weighted Pearsonproduct-moment correlation coefficient is more sensitive when the range of the data set is large.Conclusion Weighted Pearson product-moment correlation coefficient is necessary when the range ofthe data set is large.展开更多
In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biol...In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz (1963) model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures (sensitivity functions) to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.展开更多
The author studies the effect of uncertain conductivity on the electroencephalography (EEG) forward problem. A three-layer spherical head model with different and random layer conductivities is considered. Polynomia...The author studies the effect of uncertain conductivity on the electroencephalography (EEG) forward problem. A three-layer spherical head model with different and random layer conductivities is considered. Polynomial Chaos (PC) is used to model the randomness. The author performs a sensitivity and correlation analysis of EEG sensors influenced by uncertain conductivity. The author addressed the sensitivity analysis at three stages: dipole location and moment averaged out, only the dipole moment averaged out, and both fixed. On average, the author observes the least influenced electrodes along the great longitudinal fissure. Also, sensors located closer to a dipole source, are of greater influence to a change in conductivity. The highly influenced sensors were on average located temporal. This was also the case in the correlation analysis. Sensors in the temporal parts of the brain are highly correlated. Whereas the sensors in the occipital and lower frontal region, though they are close together, are not so highly correlated as in the temporal regions. This study clearly shows that intrinsic sensor correlation exists, and therefore cannot be discarded, especially in the inverse problem. In the latter it makes it possible not to specify the conductivities. It also offers an easy but rigorous modeling of the stochastic propagation of uncertain conductivity to sensorial potentials (e.g., making it suited for research on optimal placing of these sensors).展开更多
In this short review, I discuss the sensitivity of the generation of the light and the life-relevant elements such as carbon and oxygen under changes of the parame- ters of the Standard Model pertinent to nuclear phys...In this short review, I discuss the sensitivity of the generation of the light and the life-relevant elements such as carbon and oxygen under changes of the parame- ters of the Standard Model pertinent to nuclear physics. Chiral effective field theory allows for a systematic and precise description of the forces between two, three and four nucleons. In this framework, variations under the light quark masses and the electromagnetic fine-structure constant can also be consistently calculated. Combining chiral nuclear effective field theory with Monte Carlo simulations allows to further calculate the properties of nuclei, in particular of the Hoyle state in carbon, that plays a crucial role in the gener- ation of the life-relevant elements in hot, old stars. The dependence of the triple-alpha process on the fundamental constants of nature is calculated, and some implications for our anthropic view of the Universe are discussed.展开更多
文摘Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used. Results The distribution range of the data setsinfluences the sensitivity of Pearson product-moment correlation coefficient. Weighted Pearsonproduct-moment correlation coefficient is more sensitive when the range of the data set is large.Conclusion Weighted Pearson product-moment correlation coefficient is necessary when the range ofthe data set is large.
文摘In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz (1963) model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures (sensitivity functions) to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.
文摘The author studies the effect of uncertain conductivity on the electroencephalography (EEG) forward problem. A three-layer spherical head model with different and random layer conductivities is considered. Polynomial Chaos (PC) is used to model the randomness. The author performs a sensitivity and correlation analysis of EEG sensors influenced by uncertain conductivity. The author addressed the sensitivity analysis at three stages: dipole location and moment averaged out, only the dipole moment averaged out, and both fixed. On average, the author observes the least influenced electrodes along the great longitudinal fissure. Also, sensors located closer to a dipole source, are of greater influence to a change in conductivity. The highly influenced sensors were on average located temporal. This was also the case in the correlation analysis. Sensors in the temporal parts of the brain are highly correlated. Whereas the sensors in the occipital and lower frontal region, though they are close together, are not so highly correlated as in the temporal regions. This study clearly shows that intrinsic sensor correlation exists, and therefore cannot be discarded, especially in the inverse problem. In the latter it makes it possible not to specify the conductivities. It also offers an easy but rigorous modeling of the stochastic propagation of uncertain conductivity to sensorial potentials (e.g., making it suited for research on optimal placing of these sensors).
基金supported in part by DFG and NSFC (Sino-German CRC 110)Helmholtz Association (contract VHVI-417)+2 种基金BMBF (grant 05P12PDFTE)the EU (Hadron Physics3 project)LENPIC (DEC-2103/10/M/ST2/00420)
文摘In this short review, I discuss the sensitivity of the generation of the light and the life-relevant elements such as carbon and oxygen under changes of the parame- ters of the Standard Model pertinent to nuclear physics. Chiral effective field theory allows for a systematic and precise description of the forces between two, three and four nucleons. In this framework, variations under the light quark masses and the electromagnetic fine-structure constant can also be consistently calculated. Combining chiral nuclear effective field theory with Monte Carlo simulations allows to further calculate the properties of nuclei, in particular of the Hoyle state in carbon, that plays a crucial role in the gener- ation of the life-relevant elements in hot, old stars. The dependence of the triple-alpha process on the fundamental constants of nature is calculated, and some implications for our anthropic view of the Universe are discussed.