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

Hypercontractivity for anharmonic oscillators

We give upper and lower bounds on the number of graphs of fixed degree which have a positive density of triangles. In particular, we show that there are very few such graphs, when compared to the number of graphs without this restriction. We also show that in this case the triangles seem to cluster even at low density.

https://arxiv.org/pdf/math-ph/0203009.pdf

The Number of Large Graphs with a Positive Density of Triangles

We define a frustrated spin-glass model for which the Migdal-Kadanoff renormalization group is exact. Our model has random couplings, and the renormalization group acts on these. We study the high and low temperature phases of the model, exhibit a critical fixed point (in high dimension), and show that the Edwards-Anderson parameter takes a non-zero value in the low-temperature phase.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1103941128

A spin-glass model with random couplings

We discuss various questions which arise when one considers the central projection of three-dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small. Further characteristics of the projected set—in particular scaling—depend sensitively on how the apparent sizes of galaxies are taken into account. Finally, we discuss the influence of the opacity of galaxies. Combining these ideas, seemingly contradictory statements about lacunarity and apparent projections can be reconciled.

/pdf/angular-projections-of-fractal-sets-znjcec2ezo.pdf

Jean-Pierre Eckmann

Papers

Hypercontractivity for anharmonic oscillators

The Number of Large Graphs with a Positive Density of Triangles

The Number of Large Graphs with a Positive Density of Triangles

A spin-glass model with random couplings

Angular projections of fractal sets