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

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

The Structure and Function of Complex Networks

Certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. The criterion for this is the sign of the sub-Lyapunov exponents. We apply these ideas to a real set of synchronizing chaotic circuits.

Synchronization in chaotic systems

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

In this paper, we consider a class of mechanical models which consists of a linear chain of identical chaotic cells, each of which has two small lateral holes and contains a rotating disk at its center. Particles are injected at characteristic temperatures and rates from stochastic heat baths located at both ends of the chain. Once in the system, the particles move freely within the cells and will experience elastic collisions with the outer boundary of the cells as well as with the disks. They do not interact with each other but can transfer energy from one to another through collisions with the disks. The state of the system is defined by the positions and velocities of the particles and by the angular positions and angular velocities of the disks. We show that each model in this class is controllable with respect to the baths, i.e. we prove that the action of the baths can drive the system from any state to any other state in a finite time. As a consequence, one obtains the existence of at most one regular invariant measure characterizing its states (out of equilibrium).

Controllability for chains of dynamical scatterers

Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the equation $\partial_t^2 u(x,t) = \alpha (\partial_x u(x,t))^2 +\beta \partial_x^2 u(x,t)$ in $1+1$ dimensions. It has been known for quite some time that solutions to this equation diverge in finite time, when $\alpha>0$. We study the nature of this divergence as a function of the parameters $\alpha>0 $ and $\beta\ge0$. The divergence does not disappear even when $\beta $ is very large contrary to what one might believe (note that since we consider fixed initial data, $\alpha$ and $\beta$ cannot be scaled away). But it will take longer to appear as $\beta$ increases when $\alpha$ is fixed. We note that there are two types of divergence and we discuss the transition between these two as a function of parameter choices. The blowup is unavoidable unless the corresponding equations are modified. Our results extend to $3+1$ dimensions.

Instabilities Appearing in Cosmological Effective Field theories: When and How?

This paper is an adaptation of the introduction to a book project by the late Mitchell J. Feigenbaum (1944-2019). While Feigenbaum is certainly mostly known for his theory of period doubling cascades, he had a lifelong interest in optics. His book project is an extremely original discussion of the apparently very simple study of anamorphs, that is, the reflections of images on a cylindrical mirror. He observed that there are \emph{two images} to be seen in the tube, and discovered that the brain preferentially chooses one of them. I edited and wrote an introduction to this planned book. As the book is still not published, I have now adapted my introduction as a standalone version, so that some of Feigenbaum's remarkable work will be accessible to a larger audience.

An Introduction to the Unpublished Book"Reflections on a Tube"by Mitchell J. Feigenbaum

Proteins need to selectively interact with specific targets among a multitude of similar molecules in the cell. But despite a firm physical understanding of binding interactions, we lack a general theory of how proteins evolve high specificity. Here, we present such a model that combines chemistry, mechanics and genetics, and explains how their interplay governs the evolution of specific protein-ligand interactions. The model shows that there are many routes to achieving molecular discrimination – by varying degrees of flexibility and shape/chemistry complementarity – but the key ingredient is precision. Harder discrimination tasks require more collective and precise coaction of structure, forces and movements. Proteins can achieve this through correlated mutations extending far from a binding site, which fine-tune the localized interaction with the ligand. Thus, the solution of more complicated tasks is enabled by increasing the protein size, and proteins become more evolvable and robust when they are larger than the bare minimum required for discrimination. The model makes testable, specific predictions about the role of flexibility and shape mismatch in discrimination, and how evolution can independently tune affinity and specificity. Thus, the proposed theory of specific binding addresses the natural question of “why are proteins so big?”. A possible answer is that molecular discrimination is often a hard task best performed by adding more layers to the protein.

/pdf/general-theory-of-specific-binding-insights-from-a-genetic-2rcq69l5.pdf

General Theory of Specific Binding: Insights from a Genetic-Mechano-Chemical Protein Model

We study metastable behavior in a discrete nonlinear Schrodinger equation from the viewpoint of Hamiltonian systems theory. When there are 
$$n<\infty $$

 sites in this equation, we consider initial conditions in which almost all the energy is concentrated in one end of the system. We are interested in understanding how energy flows through the system, so we add a dissipation of size 
$$\gamma $$

 at the opposite end of the chain, and we show that the energy decreases extremely slowly. Furthermore, the motion is localized in the phase space near a family of breather solutions for the undamped system. We give rigorous, asymptotic estimates for the rate of evolution along the family of breathers and the width of the neighborhood within which the trajectory is confined.

/pdf/decay-of-hamiltonian-breathers-under-dissipation-2wh9k5vjio.pdf

Jean-Pierre Eckmann

Papers

Controllability for chains of dynamical scatterers

Instabilities Appearing in Cosmological Effective Field theories: When and How?

An Introduction to the Unpublished Book"Reflections on a Tube"by Mitchell J. Feigenbaum

General Theory of Specific Binding: Insights from a Genetic-Mechano-Chemical Protein Model

Decay of Hamiltonian Breathers under Dissipation