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.

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the ecosystemic complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators.

Reconstructing higher-order interactions in coupled dynamical systems

Gabriele Di Bona, Iacopo Iacopini, Enrico Ubaldi, Vito Latora, and Vittorio Loreto School of Mathematical Science, Queen Mary University of London, London E1 4NS, United Kingdom Department of Network and Data Science, Central European University, 1100 Vienna, Austria SONY Computer Science Laboratories, Paris, 6, rue Amyot, 75005, Paris, France Dipartimento di Fisica ed Astronomia, Università di Catania and INFN, I-95123 Catania, Italy Complexity Science Hub, Josefst äadter Strasse 39, A 1080 Vienna, Austria Sapienza Univ. of Rome, Physics Dept., Piazzale Aldo Moro 2, 00185 Rome, Italy

Socially-enhanced discovery processes

We propose a dynamical model of price formation on a spatial market where sellers and buyers are placed on the nodes of a graph, and the distribution of the buyers depends on the positions and prices of the sellers. We ﬁnd that, depending on the positions of the sellers and on the level of information available, the price dynamics of our model can either converge to ﬁxed prices, or produce cycles of diﬀerent amplitudes and periods. We show how to measure the strength of competition in a spatial network by extracting the exponent of the scaling of the prices with the size of the system. As an application, we characterize the diﬀerent level of competition in street networks of real cities across the globe. Finally, using the model dynamics we can deﬁne a novel measure of node centrality, which quantiﬁes the relevance of a node in a competitive market.

Model of spatial competition on discrete markets

We describe the bailout of banks by governments as a Markov Decision Process (MDP) where the actions are equity investments The underlying dynamics is derived from the network of financial institutions linked by mutual exposures, and the negative rewards are associated to the banks' default Each node represents a bank and is associated to a probability of default per unit time (PD) that depends on its capital and is increased by the default of neighbouring nodes Governments can control the systemic risk of the network by providing additional capital to the banks, lowering their PD at the expense of an increased exposure in case of their failure Considering the network of European global systemically important institutions, we find the optimal investment policy that solves the MDP, providing direct indications to governments and regulators on the best way of action to limit the effects of financial crises

Artificial intelligence applied to bailout decisions in financial systemic risk management.

We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents, by solving numerically a rate equation. The opinions are here represented by bidimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the final opinion configuration, when more clusters survive, is determined by the shape of the opinion space. If the latter is a square, which is the case we consider, the clusters in general occupy the sites of a square lattice, although we sometimes observe interesting deviations from this general pattern, especially near the center of the opinion space.

https://arxiv.org/pdf/physics/0504017.pdf

Vito Latora

Papers

Reconstructing higher-order interactions in coupled dynamical systems

Socially-enhanced discovery processes

Model of spatial competition on discrete markets

Artificial intelligence applied to bailout decisions in financial systemic risk management.

Vector Opinion Dynamics in a Bounded Confidence Consensus Model