抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

https://digital.csic.es/bitstream/10261/108964/1/experiment%20at%20the%20LHC.pdf

Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differential equations to describe motion of such grain boundaries. Next, we relax curvature effect of the grain boundaries to isolate the effect of the dynamics of lattice misorientations and triple junctions drag, and we establish local well-posedness result for the considered model.

Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, various dynamic boundary conditions have been proposed in order to account for possible short-range interactions of the material with the solid wall. We propose a new class of dynamic boundary conditions for the Cahn-Hilliard equation in a rather general setting. The derivation is based on an energetic variational approach that combines the least action principle and Onsager's principle of maximum energy dissipation. One feature of our model is that it naturally fulfills important physical constraints such as conservation of mass, dissipation of energy and force balance relations. Then we investigate the resulting system of partial differential equations. Under suitable assumptions, we prove the existence and uniqueness of global weak/strong solutions to the initial boundary problem with or without surface diffusion. Furthermore, we establish the uniqueness of asymptotic limit as $t\to+\infty$ and characterize the stability of local energy minimizers for the system.

An Energetic Variational Approach for the Cahn-Hilliard Equation with Dynamic Boundary Conditions: Derivation and Analysis

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.

Numerical complete solution for random genetic drift by energetic variational approach

This chapter aims at the mathematical theory of incompressible viscoelastic fluids and related complex fluid models. An energetic variational approach is employed to derive the hydrodynamics of complex fluids which focuses on the competition and coupling between different physical effects. Such a framework also provides guides to the corresponding analysis. This chapter includes those X. Hu ( ) Department of Mathematics, City University of Hong Kong, Hong Kong, China e-mail: xianpehu@cityu.edu.hk F.-H. Lin Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY, USA e-mail: linf@cims.nyu.edu C. Liu Department of Mathematics, Pennsylvania State University, State College, PA, USA e-mail: liu@math.psu.edu © Springer International Publishing AG 2016 Y. Giga, A. Novotny (eds.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, DOI 10.1007/978-3-319-10151-4_25-1 1

Chun Liu

Papers

The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

An Energetic Variational Approach for the Cahn-Hilliard Equation with Dynamic Boundary Conditions: Derivation and Analysis

Numerical complete solution for random genetic drift by energetic variational approach

Equations for viscoelastic fluids