We study the dynamics of tumor cell growth with time-delayed feedback driven by multiplicative noise in an asymmetrical bistable potential well. For a small delay time, the analytical solutions of the probability dist...We study the dynamics of tumor cell growth with time-delayed feedback driven by multiplicative noise in an asymmetrical bistable potential well. For a small delay time, the analytical solutions of the probability distribution and the first passage time show that, with the increasing delay time, the peak of the probability distribution in a lower population state would increase, but in a higher population state it decreases. It is shown that the multiplicative noise and the time delay play opposite roles in the tumor cell growth.展开更多
Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing nee...Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing need for this,as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data.Results:In this review we provide an overview of some tensor analysis methods for biological systems.Conclusions:Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics,mathematics and many other areas.Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10975063, and the Fundamental Research Pund for Physics and Mathematics of Lanzhou University.
文摘We study the dynamics of tumor cell growth with time-delayed feedback driven by multiplicative noise in an asymmetrical bistable potential well. For a small delay time, the analytical solutions of the probability distribution and the first passage time show that, with the increasing delay time, the peak of the probability distribution in a lower population state would increase, but in a higher population state it decreases. It is shown that the multiplicative noise and the time delay play opposite roles in the tumor cell growth.
文摘Background:Since biological systems are complex and often involve multiple types of genomic relationships,tensor analysis methods can be utilized to elucidate these hidden complex relationships.There is a pressing need for this,as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data.Results:In this review we provide an overview of some tensor analysis methods for biological systems.Conclusions:Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics,mathematics and many other areas.Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.
