My latest research problems are updated here (Chinese)!
Collective Attention Flows in Digital Space
Nowadays, as information overload, attention becomes a kind of scarce resource. How attention allocate on various digital resources becomes very important. Different with conventional analysis on collective attention attention flows focus on not only the competition of attention on different digital resources but also how the resources connect and interrelate to become an ecosystem.
The main technique that we incorporate on attention flows is the flow network analysis approach. The sequential actions which include browsing, tagging, answering questions, etc. of users form streams on different resources. By integrate all these streams together, a flow network is constructed in which nodes are digital resources, and weighted directed links are the number of users jumping from one resource to another. Then we can use flow analysis and network approaches to study the overall structure of these networks
Several large sets of data enable us to analyse the flow structure of online communities, websites, and WWW. Most works on this topic are collabrated with Dr. Lingfei Wu in Arisona State University.
- Metrics of flow structure
Stickness is an important metric for digital systems, we propose an innovative measure of stickness borrowed from allometric scaling laws of animals for online forums. It is interesting to treat a website or an online forum as a virtual organism. And in parallel with real organisms, all these virtual living systems consume users' attention to survive.
- Wu L, Zhang J, Zhao M (2014) The Metabolism and Growth of Web Forums. PLoS ONE 9(8): e102646. In this paper, we analyse ten thousands online forums of Baidu Tieba. We find a generalized Kleiber law, that is the scaling between UV(unique visitors of a forum) and PV(page views). And the exponent can be treated as the quantification of "stickness" of a forum. Furthermore, our study points out the "stickness" of a forum is related with the dissipation mode of the clickstream network.
Inspired by the studies of food webs, we found that the allometric scaling exponent of a flow network can characterize the hiearchicality of a network. This may give us the insights on how the attention flows among web sites
Currently, more than 70% population lives in cities, and this ratio will be increasing continuously in recent years. Thus, the quantitative understandings of cities in distribution and dynamics of various variables are of great important. By integrating big data in different sources like road network, nighttime lights, and human mobility, we attempt to find some basic and simple mechanisms accounting for the growth and the distributions of various variables in a city.
- Jiang Zhang,Xintong Li,Xinran Wang, Wen-xu Wang, Lingfei Wu: Scaling behaviours in the growth of networked systems and their geometric origins; SCIENTIFIC REPORTS 2015, 5: 9767In this work, a simple model based on geometric matching is proposed to model the growth of networked systems. The super-linear scaling of interactions and the sub-linear of diversity which are observed occasionally in various socioeconomic systems including cities and online communities are explained by this model. By introducing new parameters, this simple model can reproduce the patterns of natural cities
- Xintong Li,Xinran Wang,Jiang Zhang, Lingfei Wu: Allometric scaling, size distribution and pattern formation of natural cities; Palgrave Communications, 1, 15017 (2015) In this paper, we treated connected clusters of nighttime light as natural cities. We then study the allometric scaling laws, Zipf laws, and fractals on these natural cities. A concise model based on geometric matching mechanism is built to reproduce all the observed patterns.
- Ruiqi Li, Lei Dong, Jiang Zhang, Wen-xu Wang, Spatial scaling of cities: a unified model of population, road network, and socioeconomic interactions, In preparation
Flows in Complex Systems
Energy flows in ecosystems, money flows in economic systems, traffic flows in urban systems. There are many kinds of flows in various complex systems. Are there universal patterns or laws governing these flows? In many cases, flows can be regarded as a special kind of complex networks, i.e., weighted directed network. However, flows should contain more information about dynamics, evolution and time than static topological structure.
Some of my current researches are focusing on flow structures in various systems.
- General metrics and properties of flow networks
- Xintong Li,Xinran Wang,Jiang Zhang, Lingfei Wu: Allometric scaling, size distribution and pattern formation of natural cities; Palgrave Communications, 1, 15017 (2015)In this paper, we define a set of new metrics of distances on flow networks. These metrics incorporate network structure and flow dynamics on the network. These measures can be used to cluster nodes, calculate centrality, and so forth.
- Trade Flows on the Wolrd Wide Trade Network
As a flow system, trade flows on the world wide trade network is particular since each trade flow on an edge from one country to another has several different kinds of commodities. Interestingly, the allometric scaling exponent of a trade flow network can be used to characterize the complexity of this product.
Another topic that I'm interested in is diversity in complex systems. One of the example is the export product diversity in international trade. We can simply study the empirical relationship between export diversity and economic size, an "S" curve is found. The ceilling effect of the export diversity is due to the substitutability of capabilities.
- Hongmei Lei,Ying Chen,Ruiqi Li, Deli He, Jiang Zhang: Maximum Entropy for the International Division of Labor; PLoS ONE 2015, 10(7): e0129955. This paper proposes that the distributions of trade flows on different products can be understood by the maximum entropy principle. Each country need to balance between diversification of their products and the profit from the export, therefore they try to maximize entropy under the complexity constraint. The results show that most countries' distributions are in good agreement with maximum entropy
- Hongmei Lei,Jiang Zhang: Capabilities' substitutability and the “S” curve of export diversity; EPL 105 (2014) 68003, This paper explains the "S" curve relationship according to a tri-partite network model, in which the middle layer stands for abilities. Therefore, the ceiling effect of export diversity is explained as the substitutability of capabilities.
- Lunchao Hu,Jiang Zhang: The "S" curve relationship between export diversity and economic size; Physica A 391 (2012) 731-739, [ download ] This paper discover an "S" curve between export diversity and log(GDP) for different countries. The particular relationship may indicate that the neutral random process found in ecology may be applied to multi-goods trade flow
- Energy Flows on Food Webs
I started to study the energy flows of ecological networks from my post doctoral works. I was shocked when realizing that the empirical weighted food webs do have some regularities once they are regarded as flow networks. Following papers are related with empirical facts about energy flows on food webs:
- Jiang Zhang, Lingfei Wu: Allometry and Dissipation of Ecological Flow Networks, PLoS ONE 8(9): e72525. doi:10.1371/journal.pone.0072525, 2013 , The latest results: we find a negative relationship between the dissipation law exponent and allometric law exponent, and we re-interpret the meaning of the allometric exponent as the degree of centralization of the whole flow network.
- Jiang Zhang,Liangpeng Guo: Scaling Behaviors of Weighted Food Webs as Energy Transportation Networks; Journal of Theoretical Biology 264 (2010) 760-770 ， I further developped the approach mentioned in the following paper and also discussed the distributions of energy flows on food webs. This approach is based on Markovian chains derived from the flux matrix. And one of the astonishing result is that the allometric scaling exponents of all the empirical weighted food webs are approaching 1.
- Jiang Zhang: Allometric Scaling of Weighted Food Webs; Complex Sciences, ed. Jie Zhou, First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, 1441-1450. In this paper, I found a method to generate the allometric scaling law to the weighted food webs.
- Jiang Zhang: Energy Flows in Complex Ecological Systems: A Review; Journal of Systems Science and Complexity 2009 22 (3): 345-359 This paper gives a short review on the allometric scaling patterns in ecology and transportation networks and modeling method on food webs.
Beyond these empirical facts, I also studied how to model the energy flow dynamics on the food web.
- Jiang Zhang: Modeling Multi-species Interacting Ecosystem by a Simple Equation; CSO, vol. 1, pp.1003-1007, 2009 International Joint Conference on Computational Sciences and Optimization, 2009, [ download ] Some simulation results in following paper are published in a proceeding.
- Jiang Zhang: Energy Flows and Maximum Power on an Evolutionary Ecological Community Model; Post Doc Report,2008 [ download ] This paper follows the similar way as the following one, however the equation simulating population dynamics on the evolutionary food webs is much simpler. And also, I have given a rigourous mathematical proof of maximum power principle in my mathematical framework although the final result is never been published.
- Jiang Zhang: Energy Flows and Maximum Power on an Evolutionary Ecological Network Model; : Energy Flows and Maximum Power on an Evolutionary Ecological Network Model, Advances in Artificial Life: 9th European Conference, ECAL 2007, Lisbon, Portugal, 113~123, [ download ] In this paper, I used a population dynamics model on an evolutionary network topology to discuss the Lotka's Maximum Power Principle. Although this paper is short and only published in a proceeding, I like it because I have built a way to study Lotka's maximum power principle in a simulation model.
I also have done some works on this direction which is left for the future introduction.
Allometric Scaling in Various Complex Systems
Allometric scaling laws, found by biologists, indicate that lots of biological variables (such as metabolism, heart beat rate, life span) have a power law relationship as body size which deviates the isometric scaling predictions for various species. More discussions about allometric scaling laws in biology or ecology can be refered to West and Brown et al's papers. However, I mainly focus on the allometric scaling relationships in social systems both in the empirical facts and the generative mechanisms
- Ling-Fei Wu,Jiang Zhang: Accelerating growth and size-dependent distribution of human online activities; Physical Review E 84, 026113, 2011 [ download ] Similar with the following paper below, this paper studied the super-linear relationship between active users (corresponding population in countries) and the total activities generated by these users (GDP in countries). And by using the so called DGBD curves, we build a connection of this relationship with the size dependency of the activity distribution curve.
- Jiang Zhang,You Gui Wang: Size-Dependency of Income Distributions and Its Implications; Chinese Physics Letters, 2011,28(2):038901, [ download ] This paper focus on the super-linear relationship between population and GDP in countries, and build a connection with income distribution patterns.
- Jiang Zhang,Tongkui Yu: Allometric Scaling of Countries; Physica A Vol.389(2): 4887-4896(2010), [ download ] This paper extends allometric scaling relationships to countries. We found that there are several interesting differences of allometric exponents between countries and cities. For example, the population and GDP relation has a nearly linear relationship in countries but super linear relationship in cities.
However, all of these current studies only limitted in the empirical facts, I have tried buid a model to understand the origin of the super-linear relationships in social systems.
I used to be obsessed on building computer simulation models of artificial life during my Ph.D. study. Although my current studies are not focus on that, I'd like to list some my earlier works.
- Jiang Zhang,Xuewei Li: The Environment and Control of Complex System; International Journal of Information and System Sciences, Vol 1(3~4): 372~381, 2005, [ download ] Autolife is a simple and interesting aritificial life model introduced in this paper. And also I have given a framework about how to control the multi-agent system by adjusting the evironment of the system but not the system itself.
- Li Jianhui, Zhang Jiang: Digital Genisis- New science of artificial life , Science publishing house, 2006(In Chinese)
李建会,张江： 数字创世纪——人工生命的新科学 ，科学出版社，2006. This is a book collabrated with Prof. Li introducing the ideas and methodology of artificial life.
- Jiang Zhang: Complexity and Universality of Iterated Finite Automata; Journal of Complex Systems, 2008,18(1): 145-158, [ download ] This work is done during the participand of Wolfram's NKS summer school in 2007. I have proved that the so called iterated finite state automata is computational equivalant with cellular automata.