Beijing International Center for Mathematical Research

Beijing, China

Beijing International Center for Mathematical Research

Beijing, China
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Guo Z.,Peking University | Nakanishi K.,Kyoto University | Wang S.,Peking University | Wang S.,Beijing International Center for Mathematical Research
Communications in Partial Differential Equations | Year: 2014

We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up. © 2014 Copyright Taylor & Francis Group, LLC.

Guo Z.,Peking University | Guo Z.,Beijing International Center for Mathematical Research | Nakanishi K.,Kyoto University | Wang S.,Peking University
Advances in Mathematics | Year: 2013

We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup. © 2013 Elsevier Ltd.

Jia C.,Peking University | Jia C.,Beijing International Center for Mathematical Research | Jiang D.,Peking University | Qian M.,Peking University
Physical Biology | Year: 2014

The inositol trisphosphate receptor (IPR) is a crucial ion channel that regulates the Ca2+ influx from the endoplasmic reticulum (ER) to the cytoplasm. A thorough study of the IPR channel contributes to a better understanding of calcium oscillations and waves. It has long been observed that the IPR channel is a typical biological system which performs adaptation. However, recent advances on the physical essence of adaptation show that adaptation systems with a negative feedback mechanism, such as the IPR channel, must break detailed balance and always operate out of equilibrium with energy dissipation. Almost all previous IPR models are equilibrium models assuming detailed balance and thus violate the dissipative nature of adaptation. In this article, we constructed a nonequilibrium allosteric model of single IPR channels based on the patch-clamp experimental data obtained from the IPR in the outer membranes of isolated nuclei of the Xenopus oocyte. It turns out that our model reproduces the patch-clamp experimental data reasonably well and produces both the correct steady-state and dynamic properties of the channel. Particularly, our model successfully describes the complicated bimodal [Ca2+] dependence of the mean open duration at high [IP3], a steady-state behavior which fails to be correctly described in previous IPR models. Finally, we used the patch-clamp experimental data to validate that the IPR channel indeed breaks detailed balance and thus is a nonequilibrium system which consumes energy. © 2014 IOP Publishing Ltd.

Jia C.,Peking University | Jia C.,Beijing International Center for Mathematical Research | Qian M.,Peking University | Jiang D.,Peking University
IET Systems Biology | Year: 2014

A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data. © The Institution of Engineering and Technology 2014.

Lv C.,Peking University | Li X.,Peking University | Li F.,Peking University | Li T.,Peking University | Li T.,Beijing International Center for Mathematical Research
PLoS ONE | Year: 2014

Genetic switching driven by noise is a fundamental cellular process in genetic regulatory networks. Quantitatively characterizing this switching and its fluctuation properties is a key problem in computational biology. With an autoregulatory dimer model as a specific example, we design a general methodology to quantitatively understand the metastability of gene regulatory system perturbed by intrinsic noise. Based on the large deviation theory, we develop new analytical techniques to describe and calculate the optimal transition paths between the on and off states. We also construct the global quasi-potential energy landscape for the dimer model. From the obtained quasi-potential, we can extract quantitative results such as the stationary distributions of mRNA, protein and dimer, the noise strength of the expression state, and the mean switching time starting from either stable state. In the final stage, we apply this procedure to a transcriptional cascades model. Our results suggest that the quasi-potential energy landscape and the proposed methodology are general to understand the metastability in other biological systems with intrinsic noise. © 2014 Lv et al.

Li T.,Peking University | Li T.,Beijing International Center for Mathematical Research | Min B.,Peking University | Wang Z.,Peking University
Journal of Chemical Physics | Year: 2013

The stochastic integral ensuring the Newton-Leibnitz chain rule is essential in stochastic energetics. Marcus canonical integral has this property and can be understood as the Wong-Zakai type smoothing limit when the driving process is non-Gaussian. However, this important concept seems not well-known for physicists. In this paper, we discuss Marcus integral for non-Gaussian processes and its computation in the context of stochastic energetics. We give a comprehensive introduction to Marcus integral and compare three equivalent definitions in the literature. We introduce the exact pathwise simulation algorithm and give the error analysis. We show how to compute the thermodynamic quantities based on the pathwise simulation algorithm. We highlight the information hidden in the Marcus mapping, which plays the key role in determining thermodynamic quantities. We further propose the tau-leaping algorithm, which advance the process with deterministic time steps when tau-leaping condition is satisfied. The numerical experiments and its efficiency analysis show that it is very promising. © 2013 American Institute of Physics.

Yang J.,Peking University | Cong W.,Virginia Polytechnic Institute and State University | Jiang M.,Peking University | Jiang M.,Virginia Polytechnic Institute and State University | And 2 more authors.
Journal of X-Ray Science and Technology | Year: 2012

In this paper, we study a new type of high order interior problems characterized by high order differential phase shift measurement. This problem is encountered in local X-ray phase-contrast tomography. Here we extend our previous theoretical framework from interior CT to interior differential phase-contrast tomography, and establish the solution uniqueness in this context. We employ the analytic continuation method and high order total variation minimization which we developed in our previous work for interior CT, and prove that an image in a region of interest (ROI) can be uniquely reconstructed from truncated high order differential projection data if the image is known a priori in a sub-region of the ROI or the image is piecewise polynomial in the ROI. Preliminary numerical experiments support the theoretical finding. © 2012-IOS Press and the authors. All rights reserved.

Li T.,Peking University | Li T.,Beijing International Center for Mathematical Research | Zhang P.,Peking University | Zhang W.,Peking University
Multiscale Modeling and Simulation | Year: 2013

We focus on the nucleation rate calculation for diblock copolymers by studying the two-dimensional stochastic Cahn-Hilliard dynamics with a Landau-Brazovskii energy functional. To do this, we devise the string method to compute the minimal energy path of nucleation events and the gentlest ascent dynamics to locate the saddle point on the path in Fourier space. Both methods are combined with the semi-implicit spectral method and hence are very effective. We derive the nucleation rate formula in the infinite-dimensional case and prove the convergence under numerical discretizations. The computation of the determinant ratio is also discussed for obtaining the rate. The algorithm is successfully applied to investigate the nucleation from the lamellar phase to the cylinder phase in the mean field theory for diblock copolymer melts. The comparison with projected stochastic Allen-Cahn dynamics is also discussed. © 2013 Society for Industrial and Applied Mathematics.

Yang J.,Peking University | Yang J.,Virginia Polytechnic Institute and State University | Yu H.,Virginia Polytechnic Institute and State University | Yu H.,Wake forest University | And 5 more authors.
Inverse Problems | Year: 2012

Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues. © 2012 IOP Publishing Ltd.

Xu Z.,Shanghai JiaoTong University | Cai W.,University of North Carolina at Charlotte | Cai W.,Beijing International Center for Mathematical Research | Cheng X.,Oak Ridge National Laboratory
Communications in Computational Physics | Year: 2011

A multiple-image method is proposed to approximate the reaction-field potential of a source charge inside a finite length cylinder due to the electric polarization of the surrounding membrane and bulk water. When applied to a hybrid ion-channel model, this method allows a fast and accurate treatment of the electrostatic interactions of protein with membrane and solvent. To treat the channel/membrane interface boundary conditions of the electric potential, an optimization approach is used to derive image charges by fitting the reaction-field potential expressed in terms of cylindric harmonics. Meanwhile, additional image charges are introduced to satisfy the boundary conditions at the planar membrane interfaces. In the end, we convert the electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/water into one in a homogeneous free space embedded with discrete charges (the source charge and image charges). The accuracy of this method is then validated numerically in calculating the solvation self-energy of a point charge. © 2011 Global-Science Press.

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