Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

https://arxiv.org/pdf/cond-mat/9910332.pdf

Emergence of Scaling in Random Networks

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

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

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

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

/pdf/community-structure-in-social-and-biological-networks-1jamu4rcfv.pdf

Community structure in social and biological networks

In this essay we make four interrelated points. First, we reiterate previous arguments (Kleinberg et al 2015) that forecasting problems are more common in social science than is often appreciated. From this observation it follows that social scientists should care about predictive accuracy in addition to unbiased or consistent estimation of causal relationships. Second, we argue that social scientists should be interested in prediction even if they have no interest in forecasting per se. Whether they do so explicitly or not, that is, causal claims necessarily make predictions; thus it is both fair and arguably useful to hold them accountable for the accuracy of the predictions they make. Third, we argue that prediction, used in either of the above two senses, is a useful metric for quantifying progress. Important differences between social science explanations and machine learning algorithms notwithstanding, social scientists can still learn from approaches like the Common Task Framework (CTF) which have successfully driven progress in certain fields of AI over the past 30 years (Donoho, 2015). Finally, we anticipate that as the predictive performance of forecasting models and explanations alike receives more attention, it will become clear that it is subject to some upper limit which lies well below deterministic accuracy for many applications of interest (Martin et al 2016). Characterizing the properties of complex social systems that lead to higher or lower predictive limits therefore poses an interesting challenge for computational social science.

Explanation, prediction, and causality: Three sides of the same coin?

/pdf/le-sens-commun-et-les-explications-sociologiques-ehg3wxp6fe.pdf

Le sens commun et les explications sociologiques

I am grateful to Catherine Turco and Ezra Zuckerman for writing such a thoughtful critique of my article, “Common Sense and Sociological Explanations” (AJS 120 [2014]: 313–51). There ismuch of value in their discussion— including, not the least, pointers to some interesting sociological research— and I encourage everyone to read it. As I will explain, however, I think there is less daylight between my own position and theirs than they contend. I suspect, in fact, that much (although not all) of their objection to my argument rests on a misunderstanding of my claim that the interpretability of sociological explanations sits in tension with their scientific (i.e., causal) validity. That said, it is a misunderstanding that, on reflection, is easily made, so I welcome the opportunity to clarify my initial claim. The misunderstanding appears to derive from a sentence (p. 315) in which I argue that “if sociologists want their explanations to be causal, they must place less emphasis on understandability (i.e., sense making) and more on their ability tomake predictions.”From this sentence, Turco and Zuckerman infer that “the strong implication is that the pursuit of verstehen is a diversion—a waste of sociological time and energy” (2017, p. 1273). Actually, I didn’t intend to imply any such thing. Quite to contrary, I later argue that neither social life nor sociology would be possible without the ability of humans to put themselves in the place of others via some process of mental simulation (pp. 326–27). I am certainly not advocating, as Turco and Zuckerman seem to infer, for some form of verstehen-free sociology—in fact, I can’t even imagine what that would look like. On reflection, what that sentence should have said is “if sociologists want their explanations to be causal, then when evaluating them they must place less emphasis on understandability.” This phrase is just four extra words, but with it I would have more clearly articulated my actual point, which is somewhat different than the one that Turco and Zuckerman spend much of their commentary rebutting. As far as I’mconcerned, sociological explanations can be generated in many ways: from data mining, from mathematical models, from the historical record, from ethnographic observations, from survey results, from everyday anecdotal experience, or simply from sitting and thinking about why people do what they do. All these modes of inquiry are useful in their own way and verstehen plays a role in all of them, as Turco

Response to Turco and Zuckerman’s “Verstehen for Sociology”

Unobserved or unknown confounders complicate even the simplest attempts to estimate the effect of one variable on another using observational data. When cause and effect are both affected by unobserved confounders, methods based on identifying natural experiments have been proposed to eliminate confounds. However, their validity is hard to verify because they depend on assumptions about the independence of variables, that by definition, cannot be measured. In this paper we investigate a particular scenario in time series data that permits causal identification in the presence of unobserved confounders and present an algorithm to automatically find such scenarios. Specifically, we examine what we call the split-door setting, when the effect variable can be split up into two parts: one that is potentially affected by the cause, and another that is independent of it. We show that when both of these variables are caused by the same (unobserved) confounders, the problem of identification reduces to that of testing for independence among observed variables. We discuss various situations in which split-door variables are commonly recorded in both online and offline settings, and demonstrate the method by estimating the causal impact of Amazon’s recommender system, obtaining more than 23,000 natural experiments that provide similar—but more precise—estimates than past studies.

Split-door criterion for causal identification: Automatic search for natural experiments.

Methods, system and computer readable medium for discovering social groups include extracting activity related data associated with a user's social interactions from a source. The activity related data identifies information related to social contacts used during the social interactions at the source. The activity related data of the user is analyzed to identify co-occurrences of the social contacts. The co-occurrences determine a set of related contacts. The set of related contacts identified from the activity related data are clustered into distinct social groups. The social groups are used by a user to facilitate subsequent interactions.

Duncan J. Watts

Papers

Explanation, prediction, and causality: Three sides of the same coin?

Le sens commun et les explications sociologiques

Response to Turco and Zuckerman’s “Verstehen for Sociology”

Split-door criterion for causal identification: Automatic search for natural experiments.

System and method to enable communication group identification