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.

In this work, an analysis of the italian high-voltage power grid based on a mapping between power grid nodes and Kuramoto-like oscillators is proposed. The network is able to reach a global synchronous state, after which a perturbation is applied in order to study the dynamical robustness of the network to faults. Several dynamical parameters such as the minimum value of perturbation leading to desynchronization and the time to reach the complete loss of synchronism have been introduced. A non-trivial complex relationship between dynamical and topological parameters of the network emerges.

/pdf/analysis-of-the-italian-power-grid-based-on-kuramoto-like-9x7sjb5pnx.pdf

Analysis of the italian power grid based on kuramoto-like model

Complex Networks: from Biology to Information Technology

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads. Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions. We first discuss the methods to represent higher-order interactions and give a unified presentation of the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures, such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. We focus on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond pairwise interactions. We elucidate the relations between higher-order topology and dynamical properties, and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.

Networks beyond pairwise interactions: structure and dynamics

Epidemics-inspired techniques have received huge attention in recent years from the distributed systems and networking communities. These algorithms and protocols rely on probabilistic message replication and redundancy to ensure reliable communication. Moreover, they have been successfully exploited to support group communication in distributed systems, broadcasting, multicasting and information dissemination in fixed and mobile networks. However, in most of the existing work, the probability of infection is determined heuristically, without relying on any analytical model. This often leads to unnecessarily high transmission overheads. 
In this paper we show that models of epidemic spreading in complex networks can be applied to the problem of tuning and controlling the dissemination of information in wireless ad hoc networks composed of devices carried by individuals, i.e., human-based networks. The novelty of our idea resides in the evaluation and exploitation of the structure of the underlying human network for the automatic tuning of the dissemination process in order to improve the protocol performance. We evaluate the results using synthetic mobility models and real human contacts traces.

Vito Latora

Papers

Analysis of the italian power grid based on kuramoto-like model

Complex Networks: from Biology to Information Technology

Networks beyond pairwise interactions: structure and dynamics

Epcast: Controlled Dissemination in Human-based Wireless Networks by means of Epidemic Spreading Models

Dynamics of unstable matter