Non-smooth or even abrupt state changes exist during many biological processes, e.g., cell differentiation processes, proliferation processes, or even disease deterioration processes. Such dynamics generally signals t...Non-smooth or even abrupt state changes exist during many biological processes, e.g., cell differentiation processes, proliferation processes, or even disease deterioration processes. Such dynamics generally signals the emergence of critical transition phenomena, which result in drastic changes of system states or eventually qualitative changes of phenotypes. Hence, it is of great importance to detect such transitions and further reveal their molecular mechanisms at network level. Here, we review the recent advances on dynamical network biomarkers （DNBs） as well as the related theoretical foundation, which can identify not only early signals of the critical transitions but also their leading networks, which drive the whole system to initiate such transitions. In order to demonstrate the effectiveness of this novel approach, examples of complex diseases are also provided to detect pre-disease stage, for which traditional methods or biomarkers failed.展开更多
The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and ...The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP scheme.Some numerical tests are given to verify the accuracy of the proposed method.展开更多
We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regu...We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.展开更多
文摘Non-smooth or even abrupt state changes exist during many biological processes, e.g., cell differentiation processes, proliferation processes, or even disease deterioration processes. Such dynamics generally signals the emergence of critical transition phenomena, which result in drastic changes of system states or eventually qualitative changes of phenotypes. Hence, it is of great importance to detect such transitions and further reveal their molecular mechanisms at network level. Here, we review the recent advances on dynamical network biomarkers （DNBs） as well as the related theoretical foundation, which can identify not only early signals of the critical transitions but also their leading networks, which drive the whole system to initiate such transitions. In order to demonstrate the effectiveness of this novel approach, examples of complex diseases are also provided to detect pre-disease stage, for which traditional methods or biomarkers failed.
基金the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308-MA,and US-AFSOR grant FA9550-06-1-0241.
文摘The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP scheme.Some numerical tests are given to verify the accuracy of the proposed method.
基金supported by the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308MA and US-AFSOR grant FA9550-06-1-0241
文摘We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.
