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

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

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Numerical Initial Value Problems in Ordinary Differential Equations

What is Twitter

We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin by proposing a model to estimate opinions in which a minority of influential individuals propagate their opinions through a social network. The result of the model is an opinion probability density function. Next, we propose an index to quantify the extent to which the resulting distribution is polarized. Finally, we apply the proposed methodology to a Twitter conversation about the late Venezuelan president, Hugo Chavez, finding a good agreement between our results and offline data. Hence, we show that our methodology can detect different degrees of polarization, depending on the structure of the network.

Measuring Political Polarization: Twitter shows the two sides of Venezuela

Transmitting messages in the most efficient way as possible has always been one of politicians main concerns during electoral processes. Due to the rapidly growing number of users, online social networks have become ideal platforms for politicians to interact with their potential voters. Exploiting the available potential of these tools to maximize their influence over voters is one of politicians actual challenges. To step in this direction, we have analyzed the user activity in the online social network Twitter, during the 2011 Spanish Presidential electoral process, and found that such activity is correlated with the election results. We introduce a new measure to study political support in Twitter, which we call the Relative Support. We have also characterized user behavior by analyzing the structural and dynamical patterns of the complex networks emergent from the mention and retweet networks. Our results suggest that the collective attention is driven by a very small fraction of users. Furthermore we have analyzed the interactions taking place among politicians, observing a lack of debate. Finally we develop a network growth model to reproduce the interactions taking place among politicians.

Characterizing and modeling an electoral campaign in the context of Twitter: 2011 Spanish Presidential Election as a case study

Transmitting messages in the most efficient way as possible has always been one of politicians’ main concerns during electoral processes. Due to the rapidly growing number of users, online social networks have become ideal platforms for politicians to interact with their potential voters. Exploiting the available potential of these tools to maximize their influence over voters is one of politicians’ actual challenges. To step in this direction, we have analyzed the user activity in the online social network Twitter, during the 2011 Spanish Presidential electoral process, and found that such activity is correlated with the election results. We introduce a new measure to study political sentiment in Twitter, which we call the relative support. We have also characterized user behavior by analyzing the structural and dynamical patterns of the complex networks emergent from the mention and retweet networks. Our results suggest that the collective attention is driven by a very small fraction of users. Furthermore, we have analyzed the interactions taking place among politicians, observing a lack of debate. Finally, we develop a network growth model to reproduce the interactions taking place among politicians.

Characterizing and modeling an electoral campaign in the context of Twitter: 2011 Spanish Presidential election as a case study.

Efficiency of human activity on information spreading on Twitter

Over the past years, new technologies and specially online social networks have penetrated into the world’s population at an accelerated pace. In this paper we analyze collected data from the web application Twitter, in order to describe the structure and dynamics of the emergent social networks, based on complexity science. We focused on a Venezuelan protest that took place exclusively by Twitter during December, 2010. We found a community structure with highly connected hubs and three different kinds of user behavior that determine the information flow dynamics. We noticed that even though online social networks appear to be a pure social environment, traditional media still holds loads of influence inside the network.

Juan Carlos Losada

Papers

Measuring Political Polarization: Twitter shows the two sides of Venezuela

Characterizing and modeling an electoral campaign in the context of Twitter: 2011 Spanish Presidential Election as a case study

Characterizing and modeling an electoral campaign in the context of Twitter: 2011 Spanish Presidential election as a case study.

Efficiency of human activity on information spreading on Twitter

Users structure and behavior on an online social network during a political protest