Accelerating growth and size-dependent distribution of human online activities

Company scaling and its deviations: New indicators for enterprise evaluation and bankruptcy prediction

Many studies have shown that scaling laws widely exist in various complex systems, such as living organisms, cities, and online communities. In this research, we found that scaling laws also hold for companies. The macroscopic variables of companies, such as incomes, expenses, or total liability, all have power-law relationships with respect to the sizes of companies, which can be measured by sales, total assets, or the total number of employees. What is more, we also found the power law exponents always deviate from 1. That means large companies naturally have certain advantages, but the widely used financial indicators based on total volume or ratio may not reflect the company's status well because they are also size-dependent. To tackle this problem, this paper proposes a new set of evaluation indices based on the deviations of the macroscopic variables from the scaling law to eliminate the size-dependent effect. We found that the indicators based on deviations can give more reasonable evaluations for companies and can outperform other conventional indicators to predict the financial distress of companies.

Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes

Rank-ordered distributions have been a matter of intense study. Often Zipf type invariant scaling is invoked; however, in the last decade the ubiquity of a Discrete Generalized Beta Distribution, DGBD, with two scaling exponents has been established. This distribution incorporates deviations from the power law at the extremes. A proper understanding of the meaning of these exponents is still lacking. Here, using two families of unimodal maps on the [0,1] interval, we construct binary sequences via standard symbolic dynamics. In both cases, the tent map, which is at the convex-concave border of the mapping families, separates intermittent regimes from chaotic dynamics. We show that the frequencies of n-tuples of the generated symbolic sequences are remarkably well fitted by the DGBD. We argue that in the underlying dynamics an order-disorder competition takes place and that one of the exponents is related to multiple range correlations, while the other is sensitive to disorder. In our study, we implement thermodynamic formalisms with which we can readily calculate n-tuple frequencies, in some particular cases, analytically. We show that for the convex mappings there is a first-order thermodynamic phase transition, while concave mappings have smooth free energy densities. Within our DGBD study, the transition between these two regimes coincides with a zero value for both exponents; in this sense, they may even be considered as indicators of the transition. An analysis of the difference between the exponents reinforces the interpretation we have assigned to them. Furthermore, the two regimes can be identified by the sign of such a difference. We also show that divergences in the invariant densities are responsible for the first order phase transitions observed in a range of the rank-frequency distributions. Our findings give further support to previous studies based on expansion-modification algorithms, birth-death processes, and random variable subtraction dynamics.

The Atlas of Chinese World Wide Web Ecosystem Shaped by the Collective Attention Flows

The web can be regarded as an ecosystem of digital resources connected and shaped by collective successive behaviors of users. Knowing how people allocate limited attention on different resources is of great importance. To answer this, we embed the most popular Chinese web sites into a high dimensional Euclidean space based on the open flow network model of a large number of Chinese users' collective attention flows, which both considers the connection topology of hyperlinks between the sites and the collective behaviors of the users. With these tools, we rank the web sites and compare their centralities based on flow distances with other metrics. We also study the patterns of attention flow allocation, and find that a large number of web sites concentrate on the central area of the embedding space, and only a small fraction of web sites disperse in the periphery. The entire embedding space can be separated into 3 regions(core, interim, and periphery). The sites in the core (1%) occupy a majority of the attention flows (40%), and the sites (34%) in the interim attract 40%, whereas other sites (65%) only take 20% flows. What's more, we clustered the web sites into 4 groups according to their positions in the space, and found that similar web sites in contents and topics are grouped together. In short, by incorporating the open flow network model, we can clearly see how collective attention allocates and flows on different web sites, and how web sites connected each other.

The Collective Direction of Attention Diffusion

We find that the flow of attention on the Web forms a directed, tree-like structure implying the time-sensitive browsing behavior of users. Using the data of a news sharing website, we construct clickstream networks in which nodes are news stories and edges represent the consecutive clicks between two stories. To identify the flow direction of clickstreams, we define the "flow distance" of nodes (Li), which measures the average number of steps a random walker takes to reach the ith node. It is observed that Li is related with the clicks (Ci) to news stories and the age (Ti) of stories. Putting these three variables together help us understand the rise and decay of news stories from a network perspective. We also find that the studied clickstream networks preserve a stable structure over time, leading to the scaling between users and clicks. The universal scaling behavior is confirmed by the 1,000 Web forums. We suggest that the tree-like, stable structure of clickstream networks reveals the time-sensitive preference of users in online browsing. To test our assumption, we discuss three models on individual browsing behavior, and compare the simulation results with empirical data.

The Role of Diverse Strategies in Sustainable Knowledge Production

Online communities are becoming increasingly important as platforms for large-scale human cooperation. These communities allow users seeking and sharing professional skills to solve problems collaboratively. To investigate how users cooperate to complete a large number of knowledge-producing tasks, we analyze Stack Exchange, one of the largest question and answer systems in the world. We construct attention networks to model the growth of 110 communities in the Stack Exchange system and quantify individual answering strategies using the linking dynamics on attention networks. We identify two answering strategies. Strategy A aims at performing maintenance by doing simple tasks, whereas strategy B aims at investing time in doing challenging tasks. Both strategies are important: empirical evidence shows that strategy A decreases the median waiting time for answers and strategy B increases the acceptance rate of answers. In investigating the strategic persistence of users, we find that users tends to stick on the same strategy over time in a community, but switch from one strategy to the other across communities. This finding reveals the different sets of knowledge and skills between users. A balance between the population of users taking A and B strategies that approximates 2:1, is found to be optimal to the sustainable growth of communities.

Scaling behaviours in the growth of networked systems and their geometric origins

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. We implement some realistic extensions to the basic model to offer more accurate predictions for cities of various scaling behaviours and the Zipf distribution reported in the literature and observed in our empirical studies. All of the empirical results can be precisely recovered by our model with analytical predictions of all major properties. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems.

The metabolism and growth of web forums

We view web forums as virtual living organisms feeding on user's clicks and investigate how they grow at the expense of clickstreams. We find that (the number of page views in a given time period) and (the number of unique visitors in the time period) of the studied forums satisfy the law of the allometric growth, i.e., . We construct clickstream networks and explain the observed temporal dynamics of networks by the interactions between nodes. We describe the transportation of clickstreams using the function , in which is the total amount of clickstreams passing through node and is the amount of the clickstreams dissipated from to the environment. It turns out that , an indicator for the efficiency of network dissipation, not only negatively correlates with , but also sets the bounds for . In particular, when and when . Our findings have practical consequences. For example, can be used as a measure of the “stickiness” of forums, which quantifies the stable ability of forums to remain users “lock-in” on the forum. Meanwhile, the correlation between and provides a method to predict the long-term “stickiness” of forums from the clickstream data in a short time period. Finally, we discuss a random walk model that replicates both of the allometric growth and the dissipation function .

Superlinear and sublinear urban scaling in geographical networks modeling cities

Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y(N) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y(N)∝N(β) with β>1, if Y(N) represents a creative productivity and the indicator scales sublinearly (β<1) if Y(N) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.