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.

Identifying and discriminating seismic patterns leading flank eruptions at Mt. Etna Volcano during 1981–1996

Urban network resilience analysis in case of earthquakes

A novel scaling for the distributions of total number of fragments (i.e., multiplicity) is found in the shattering phase of nonequilibrium, sequential-fragmentation process and in the percolation process. It is the counterpart of the Koba-Nielsen-Olesen scaling when multiplicity fluctuations are small. The relations between n-fragment cumulants and two-fragment cumulants provide easy tests to check this scaling experimentally. [S0031-9007(97)03383-8]

http://www.maths.qmul.ac.uk/%7Elatora/marek.pdf

Novel Scaling of Multiplicity Distributions in Sequential-Fragmentation and Percolation Processes

The interconnectedness of financial institutions affects instability and credit crises. To quantify systemic risk we introduce here the PD model, a dynamic model that combines credit risk techniques with a contagion mechanism on the network of exposures among banks. A potential loss distribution is obtained through a multi-period Monte Carlo simulation that considers the probability of default (PD) of the banks and their tendency of defaulting in the same time interval. A contagion process increases the PD of banks exposed toward distressed counterparties. The systemic risk is measured by statistics of the loss distribution, while the contribution of each node is quantified by the new measures PDRank and PDImpact. We illustrate how the model works on the network of the European Global Systemically Important Banks. For a certain range of the banks' capital and of their assets volatility, our results reveal the emergence of a strong contagion regime where lower default correlation between banks corresponds to higher losses. This is the opposite of the diversification benefits postulated by standard credit risk models used by banks and regulators who could therefore underestimate the capital needed to overcome a period of crisis, thereby contributing to the financial system instability.

/pdf/a-dynamic-approach-merging-network-theory-and-credit-risk-4gy3rb135g.pdf

A dynamic approach merging network theory and credit risk techniques to assess systemic risk in financial networks

The Hamiltonian Mean Field (HMF) model describes a system of N fully coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a “water bag” initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and Levy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N . In particular when the N →∞ limit is taken before the t →∞ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by Tsallis [C. Tsallis, in: S.R.A. Salinas, C. Tsallis (Eds.), Nonextensive statistical mechanics and thermodynamics, Braz. J. Phys. 29 (1999) 1 cond-mat/9903356 and contribution to this conference.

Vito Latora

Papers

Identifying and discriminating seismic patterns leading flank eruptions at Mt. Etna Volcano during 1981–1996

Urban network resilience analysis in case of earthquakes

Novel Scaling of Multiplicity Distributions in Sequential-Fragmentation and Percolation Processes

A dynamic approach merging network theory and credit risk techniques to assess systemic risk in financial networks

Dynamical quasi-stationary states in a system with long-range forces