There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

/pdf/finding-and-evaluating-community-structure-in-networks-1o9f6y8pyr.pdf

Finding and evaluating community structure in networks.

Chaos and statistical mechanics in the Hamiltonian mean field model

Cooperation among unrelated individuals is frequently observed in social groups when their members combine efforts and resources to obtain a shared benefit that is unachievable by an individual alone However, understanding why cooperation arises despite the natural tendency of individuals toward selfish behavior is still an open problem and represents one of the most fascinating challenges in evolutionary dynamics Recently, the structural characterization of the networks in which social interactions take place has shed some light on the mechanisms by which cooperative behavior emerges and eventually overcomes the natural temptation to defect In particular, it has been found that the heterogeneity in the number of social ties and the presence of tightly knit communities lead to a significant increase in cooperation as compared with the unstructured and homogeneous connection patterns considered in classical evolutionary dynamics Here, we investigate the role of social-ties dynamics for the emergence of cooperation in a family of social dilemmas Social interactions are in fact intrinsically dynamic, fluctuating, and intermittent over time, and they can be represented by time-varying networks By considering two experimental data sets of human interactions with detailed time information, we show that the temporal dynamics of social ties has a dramatic impact on the evolution of cooperation: the dynamics of pairwise interactions favors selfish behavior

/pdf/evolutionary-dynamics-of-time-resolved-social-interactions-5ag7hpuibn.pdf

Evolutionary dynamics of time-resolved social interactions.

In this work, we investigate the possibility of occurrence of a critical behavior related to a liquid-gas phase transition in a finite classical system. The equation of state of such a classical system resembles that of nuclear matter. Through a study of mass distributions, scaled factorial moments, anomalous fractal dimensions, and moments of cluster mass distributions, we find evidence for the presence of a critical behavior of our finite system. Such a critical behavior is connected, by the use of Fisher's droplet model and Campi analysis, to a liquid-gas phase transition.

Critical evolution of a finite system.

In this paper we discuss opinion dynamics in the opinion changing rate ( OCR ) model, recently proposed in Pluchino et al. [Int. J. Mod. Phys. C 16(4) (2005) 515–531]. The OCR model allows to study whether and how a group of social agents, with a different intrinsic tendency ( rate ) to change opinion, finds agreement. In particular, we implement the OCR model on a small graph describing the topology of a real social system. The nodes of the graph are scientists participating in the Tepoztlan conference, celebrating Alberto Robledo's 60th birthday, and the links are based on coauthorship in scientific papers. We study how opinions evolve in time according to the frequency rates of the nodes, to the coupling term, and also to the presence of group structures.

https://arxiv.org/pdf/physics/0607210.pdf

Opinion dynamics and synchronization in a network of scientific collaborations

We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node subgraph, we propose an analytic method to measure the stability of the synchronous state (SSS) the subgraph displays. We show that, for undirected graphs, the SSS is correlated with the relative abundance, while in directed graphs the correlation exists only for some specific motifs.

https://iopscience.iop.org/article/10.1209/0295-5075/78/28001/pdf

Vito Latora

Papers

Chaos and statistical mechanics in the Hamiltonian mean field model

Evolutionary dynamics of time-resolved social interactions.

Critical evolution of a finite system.

Opinion dynamics and synchronization in a network of scientific collaborations

Synchronization properties of network motifs