The centre aims at scientific breakthroughs as well as novel solutions for societally relevant issues by approaching existing problems from the perspective of complex systems science. Researchers now apply the insights of complexity theory to the behaviour of systems as diverse as fresh-water lakes, mammalian immune … What is the impact of complex system research? (d) The same as (c) but for impact broadness. In practical terms, this implies that behaviour change is … Other fields like philosophy or art are less likely to have connections with complex system study (Figure 2(a)). 3. Finally, one might argue that different scientific fields often show different citation patterns. Laboratory for Research in Complex Systems (LRC) develops powerful research-based solutions that drive scientific, commercial and social breakthroughs. Application of Coupled Map Lattice as an Alternative to Classical Finite Difference Method for Solving the Convection-Diffusion Boundary Value Problem, Sreeya Ghosh Particularly with the emergence of network science at the dawn of the twenty-first century, complex system study generates a substantial amount of original research [9]. Indeed, recent empirical work regarding knowledge flow and scientist mobility among academic fields have attracted much attention, including the field of artificial intelligence [18], subfields of physics [19–21], and science in general [22, 23], together with the diffusion model [24]. From air traffic control to constellations of satellites, these complex multi-systems are very interdependent. For example, chemistry lies between physics and biology, while engineering stands in the intersection of physics, mathematics, and computer science. Specifically, we focus on the z-score between the two fields as follows:where and represent the average number and the standard deviation of connections between fields A and B generated from multiple randomizations, respectively (Figures 2(c) and 2(e)). Throughout the past 60 years, major technological changes and paradigm shifts such as the development of chaos theory and computer science result in a substantial knowledge production in the field of complex systems, including network science, data science, and computational social science [3, 9, 27]. Environmental Protection. Then, the th element of the paper is given bywhere is the delta function with 1 when and 0 otherwise, k is the number of MAG level-1 fields a reference/citation belongs to, n is the number of references for a given paper, and and are the index looping from the paper’s reference list and field information of each reference, respectively. First, complex system research also affects mathematics and physics significantly before 2000, while computer science substantially cites complex system research after 2000 with steady growth pattern (Figures 2(d) and 2(e)). Causal Paths in Temporal Networks of Face-to-Face Human Interactions, Lukasz Korus The origin of graph theory dates back to Euler’s solution to the puzzle of Konigsberg’s bridges in 1736. Volume 30, Issue 1, R. Vilela Mendes and Carlos Aguirre Dean, “Efficient estimation of word representations in vector space,” 2013. To eliminate noise and insignificant links, we applied a backbone extraction method to the whole field citation network [29]. The knowledge production and citation networks. Our results thus show a multidisciplinary nature of complex system research, suggesting that complex systems research may offer a language in which many academic fields can interact with each other without border. Specifically, the percentage of complex system paper grows from less than 0.01% to 0.06% from 1970 to the end of 2010 with a sudden burst between 2000 and 2010, representing the golden age of complex systems (Figure 1(b)). As demonstrated by several articles in this collection, this interdisciplinary work provides a large toolkit from which psychiatry can draw in the effort to understand complex systems in mental health research. In the network, each node represents an academic field, and links between different fields are referencing or citation behaviors. The applied values and substantial implications of complex system study raise very interesting and important questions: where does complex system research come from? Indeed, we are surrounded by systems that are unprecedentedly complex, containing many individual components together with interactions among them, possibly nonlinear ones [1]. Everything: A postdisciplinary team of faculty and students working at the University of Vermont's College of Engineering and Mathematical Sciences on real-world, meaningful complex systems problems of all kinds. Different colors represent ancestor fields of these level-2 fields. Song et al., “An overview of microsoft academic service (MAS) and applications,” in, K. Wang, Z. Shen, C. Huang et al., “A review of Microsoft academic services for science of science studies,”, S. Fortunato, C. T. Bergstrom, K. Börner et al., “Science of science,”, M. A. Serrano, M. Boguná, and A. Vespignani, “Extracting the multiscale backbone of complex weighted networks,”, M. Ahmadpoor and B. F. Jones, “The dual frontier: patented inventions and prior scientific advance,”, D. Lazer, A. Pentland, L. Adamic et al., “Social science: computational social science,”, A. J. Gates, Q. Ke, O. Varol, and A.-L. Barabási, “Nature’s reach: narrow work has broad impact,”, F. Radicchi, S. Fortunato, and C. Castellano, “Universality of citation distributions: toward an objective measure of scientific impact,”, T. Jia, D. Wang, and B. K. Szymanski, “Quantifying patterns of research-interest evolution,”, A. Zeng, Z. Shen, J. Zhou et al., “Increasing trend of scientists to switch between topics,”, Y. Ma, S. Mukherjee, and B. Uzzi, “Mentorship and protégé success in STEM fields,”. To eliminate the effect of exponential growth of the paper production (Figure 1(a)), we calculate the share of references made from complex system study to other academic fields, as well as papers in other fields to complex system study. The authors declare that they have no conflicts of interest regarding the publication of this paper. Standard errors are clustered at the MAG level-0 field level. How does complex system research affect other fields? We find academic papers related to complex system research also showing a similar exponential growth pattern with a doubling time of 10.33 years (Figure 1(a)). Knowledge between complex system study and other academic fields. In this work, we present an anatomy of complex system research by leveraging a large-scale dataset that contains more than 100 million digitalized publications. The MAG dataset is from Microsoft Academic Services [25, 26], which contains more than 100 million papers from 1800 to 2018 together with their citation relationships. Our PhD in Complex Systems and Data Science (CSDS) enables students to build a deep portfolio of research on important, complicated, data-rich problems that matter. The citation relationships and paper field information, together with the sufficient time span, allow us to understand the evolution of scientific fields. Founded by Stephen Wolfram in 1987 »The original journal devoted to the science, mathematics and engineering of systems with simple components but complex overall behavior. The Center for the Study of Complex Systems (CSCS) is a broadly interdisciplinary program in the College of Literature, Science and the Arts (LSA) at the University of Michigan in Ann Arbor, Michigan. Specifically, we follow the definition of related papers to complex system research, and Figure 2(a) shows the distribution of their academic fields. Given that many important discoveries emerge from the intersections of various fields [16], the analysis of knowledge graph using large-scale dataset could help us uncover or predict emerging/promising research areas. After that, we define papers related to complex systems if its relationships (references or citations) to complex system field are significantly higher than expected by chance [19]. A. Evans, “Choosing experiments to accelerate collective discovery,”, A. M. Petersen, “Quantifying the impact of weak, strong, and super ties in scientific careers,”, B. Uzzi, S. Mukherjee, M. Stringer, and B. Jones, “Atypical combinations and scientific impact,”, D. Li, P. Azoulay, and B. N. Sampat, “The applied value of public investments in biomedical research,”, M. R. Frank, D. Wang, M. Cebrian, and I. Rahwan, “The evolution of citation graphs in artificial intelligence research,”, R. Sinatra, P. Deville, M. Szell, D. Wang, and A.-L. Barabási, “A century of physics,”, F. Battiston, F. Musciotto, D. Wang, A.-L. Barabási, M. Szell, and R. Sinatra, “Taking census of physics,”, Y. Computer science, however, shows comparable knowledge flow from and to complex system research (Figure 3(b)), suggesting an extensive convolution structure between these two fields. The above examples vividly illustrate that today’s complex system research has implications for our society, from human mobilities [4], to economics [5], world trades [6], and human interactions or collaborations [7, 8]. Hundreds of published papers, encompassing three decades of leading-edge complex systems research, are available for free and immediate download. Complex systems analyses range from detailed studies of specific systems, to studies of the mechanisms by which patterns of collective behaviors arise, to general studies of the principles of description and representation of complex systems. Our understanding of the story that complex system research tends to be inspired by a diverse set of academic areas is not without limitation. Answering challenging problems in fields that lie at the core of the information age, and have implications for social, medical and economic advances. Another example is science. To address this issue, we compare the citation patterns of all MAG papers to a null model in which each paper’s references are assigned randomly given their publication time, regardless of a paper’s journal or research field [16]. Complex systems research is becoming ever more important in both the natural and social sciences. Tools to Characterize the Correlated Nature of Collective Dynamics, Agostino Funel Finally, we average the entropy over all papers within the same academic field to get the field reference or impact broadness. To quantify the knowledge production, Figure 1(a) shows the yearly number of publications from 1960 to 2018. Moreover, citation behaviors change over time [11]. This emerging system-of-systems concept describes the large-scale integration of many independent, self-contained systems in order to satisfy a global need. Our mission is to encourage and facilitate research and education in the general area of nonlinear, dynamical and adaptive systems. Mechanical Engineering. Moving beyond a single year, we repeat the same analysis for all academic fields from 1970 to 2018, finding similar results (Figures 4(c) and 4(d)). In order to answer these questions, we quantify the broadness of disciplines reflected in the references and citations for every paper that belongs to the same academic field using the entropy measurement [34]. Several insightful patterns emerge. In this paper, we present an anatomy of complex system research spanning from 1960 to 2018 by leveraging a large-scale bibliometric dataset. Moreover, we find empirical evidence that complex system research tends to have multidisciplinary nature, as it is often inspired by or affects a diverse set of disciplines. Consider, for example, the survival of human society needs cooperation between billions of individuals or communication infrastructures that connect and integrate human efforts. First, Figures 4(a) and 4(b) show the distribution of field reference and impact broadness at 1995, documenting the narrow range of both referencing and impact broadness that are in contrast to the fat-tail citations distribution [35]. (a) The distribution of academic fields for papers that cite or are cited by complex system research at least once. A large z-score means fields A and B are more likely to be connected with respect to the null model. Interdisciplinary complex systems research targets a better understanding of phenomena. Complex Systems & Networks. Submissions for Complex Systems may be made by webform or email. Our faculty study diverse systems, from power grids to microbial communities and everything in between. The multidisciplinary nature of complex system research encourages us to explore the association between field’s reference broadness and its scientific impact, which has policy implications for funding agencies. Complex Systems Faculty See all WID Faculty Complexity underlies nearly all research at WID. Complex systems play important roles in science and economy and have become one of the major intellectual and scientific challenges of the twenty-first century. There are no publication charges. Interestingly, the references from complex system to chemistry and biology are largely driven by the dominance fraction of chemistry/biology papers with respect to the whole science. Managing the complexity of the unexpected. Looking across different periods, we find complex system research moved from mathematics in the 1980s to computer science in the 2000s (Figures 1(c)–1(e)), indicating a substantial paradigm shift towards computational research [30]. We repeat the above analysis by calculating the reference share and z-score from other fields to complex system research. To further eliminate the effect of the number of references, we did the same regression analysis for subsamples with similar number of references, finding consistent results. To test the robustness of this association, we repeat the analysis from 1970 to 2008, finding consistent and significant results (Figure 5(c)). (b) The fraction of yearly number of papers of complex system relative to the whole MAG, together with a linear fit. First, we find that complex system research shows a steady growth relative to the whole science in the last 60 years, with a sudden burst after 2000, which might be related to the development of computational technologies. The Centre for Complex Systems Studies (CCSS) brings together the complexity research of Utrecht University. This work was supported by the National Natural Science Foundation of China under Grant nos. By comparing z-score from complex system field to other fields (Figure 3, red bars) with the same quantity from other fields to complex system research (Figure 3, blue bars), we find the z-score from complex system to the field of mathematics is higher than the other way around, suggesting that complex system research consistently affects mathematics more from the year of 1980 (Figure 3(a)). (c) The correlation as a function of time. Following in his definition, we expand the field of complex systems to a broad perspective by including papers that cite or were cited by complex system papers. Complex system research also shows an exponential growth trend (Figure 1(a)). These studies enable us to understand and modify complex systems, design new ones for new capabilities or create contexts in which they self-organize … Sun and V. Latora, “The evolution of knowledge within and across fields in modern physics,”, E. Yan, “Disciplinary knowledge production and diffusion in science,”, Y. Dong, H. Ma, Z. Shen, and K. Wang, “A century of science: globalization of scientific collaborations, citations, and innovations,” in, C. Jin, C. Song, J. Bjelland, G. Canright, and D. Wang, “Emergence of scaling in complex substitutive systems,”, A. Sinha, Z. Shen, Y. Complex systems are systems that are difficult to model and predict. We find a significant positive correlation between field reference broadness and the scientific impact (Figures 5(a) and 5(b)), suggesting that fields with more diverse reference lists are more likely to have more scientific impact in the future. Comparing the knowledge production of complex systems and the whole science, we find that complex system research shows a steady growth relative to science. Complex Systems, Network Science and Computation. With the very nature of complex system research that may transfer to future scientific impact, our findings may have broad policy implications. The Complex Adaptive Engineered Systems Research (CAESR) Laboratory is focused on developing theories, methods and tools for the design and analysis of adaptive systems. “I think the next century will be the century of complexity” said Stephen Hawking, who is a famous theoretical physicist and cosmologist. The results also agree with the Stephen Hawking’s famous quote mentioned in the beginning of the paper. Comparing the reference or impact broadness of complex system research with the same quantities for nuclear physics, which is often considered as a deeply disciplinary field [19], we find that complex system research consistently shows higher value of reference or impact broadness (Figures 4(c) and 4(d)). Despite of that, we lack a systematic and empirical understanding on how complex system research affects or is affected by other academic fields. Therefore, we hope to understand the relevant knowledge flow. Our results also go beyond case studies, which only focus on referencing/citation behaviors within a specific field. T. Mikolov, K. Chen, G. Corrado, and J. Where does the knowledge created by complex system research go? The program is hosted by faculty at the associated Center for Complex Networks and Systems Research (CNetS) who are investigating complex systems in action, from determining how a YouTube video goes viral, mining Instagram data for public-health monitoring, developing models to predict the spread of online misinformation, studying innovation and conflict in parliamentary documents, to understanding … Join the leading edge of complex systems research today! Research — New England Complex Systems Institute. To answer this question, we calculate, for each field, its reference broadness and its impact, which is measured by the average paper citations within 8 years of publication for a specific field (C8). Followed by the whole procedure, we end up with more than 1.2 million papers that are related to complex systems, showing consistent results with Figure 1(a). The above analysis allows us to uncover the relationships between complex system study and other academic fields, prompting us to aggregate multiple years in order to investigate whether complex system study affects other fields more or vice versa. In order to foster and nurture multidisciplinary science that is key to many real-world problems, funding agencies and government may support fields with multidisciplinary nature. What is the nature of complex system study? Answering challenging problems in fields that lie at the core of the information age, and have implications for social, medical and economic advances. 2020, Article ID 5208356, 11 pages, 2020. https://doi.org/10.1155/2020/5208356, 1School of Public Policy and Administration, Xi’an Jiaotong University, Xi’an 710049, China, 2School of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, China. The results can be interpreted as follows: one standard deviation (SD) increase of reference broadness for a scientific field is associated with on average 13.9% increase of future scientific impact. From the perspective of individual scientist [20], our results provide actionable strategies of choosing future research areas [14, 36, 37] and mentors [38]. To visualize the knowledge graph, we extracted citation relationships among different fields to construct a field citation network (here, we use the MAG level-2 fields since complex system research belongs to this level). To help people and their communties flourish at all scales through research and education about complex systems. Scales of Learning. The amount of information required to fully document a complex system at a point in time is prohibitively large such that they can't be fully modeled by any known methods. One may argue that papers that cite or were cited by complex system papers may not belong to its related fields, since such citation relationships might come from noise or random connections in the whole citation network. COSREC achieves its goals in. Stevens is a global leader in systems design and integration techniques that enable a more informed, more intelligent and more responsive world. The steady growth of complex systems and its related fields raises an interesting question: Where does complex system research locate in the scientific knowledge space? Research in our lab seeks to address specific scientific questions such as: How to characterize, quantify, and implement the emergent system property of adaptability Field citation networks in the (c) 1980s, (d) 1990s, and (e) 2000s, with nodes being MAG level-2 fields and links of the citation/reference relationships between two fields. Finally, with the intense connections between science and technology, future work is to investigate the association between fields’ multidisciplinarity and their roles in advancing technologies. Occupational Safety. The reference share measurement controls the number of references made by field A, thus controlling for its knowledge production (Figures 2(b) and 2(d)). It goes beyond the traditional, reductionist approach of focusing on the parts of a system, to integrating the network of … The empirical results are in line with many anecdotal evidences from textbooks or review articles [3, 9]. The Santa Fe Institute, New Mexico, is an independent research and education centre where complex systems research is undertaken and the science of complex adaptive systems was defined. Scroll. Before 2000, complex system research frequently cites papers from mathematics and physics (Figure 2(b)); we find similar results after controlling for the paper production in referenced field (Figure 2(c)), suggesting early complex system study was shaped by mathematics and physics. Overview. Hence, the field’s exponential growth is not only driven by social needs, but also by paradigm changes, such as the development of computer science and artificial intelligence. Many of us involve with reviewers for funding agencies or publishers may confront with questions like: Can a particular work belong to the framework of complex system research? Submissions for Complex Systems may be made by … Sam Edwards remarked the definition of physics as “what physicists do” [28]. Complex Systems. The knowledge production by the field of complex system, together with its position in the whole knowledge graph, prompts us to ask the following: Which specific field is closely related to complex systems and how to quantify the relationships between various fields rather than inspections? Field referencing and citation broadness. Finally, we find significant positive correlations between fields’ reference broadness and future scientific impacts. In fact, complex system research is less likely to cite biology and chemistry compared to the null model (Figure 2(c)). Science of science offers us unprecedented opportunities to explore and uncover the citation dynamics [11–13], knowledge space [14], collaboration networks [7, 8, 15], and their association with societal impact [16, 17]. Consistent with prior studies [19, 23], we find that science grows at an exponential rate, doubling every 12.3 years (Figure 1(a)). Do computer science and engineering apply methodologies developed by the field of complex systems? The next question is as follows: How to detect fields that are related to complex systems? Complex systems science bridges the natural and social sciences, enriching both, and reduces the gap between science, engineering, and policy. For example, biology and chemistry often have, on average, more citations than mathematics and engineering [35]. Also, it is related to many revolutionary technologies of the twenty-first century, including Google, Facebook, and Twitter [10]. It is commonly implied that there is such a thing as a complex system, different examples of which are studied across many disciplines. In order to eliminate this concern, we use a simple linear regression by focusing on the effect of reference broadness on field impact, while controlling for time, ancestor field categories, the number of publications within each field, and the average number of references. Anecdotal evidence indicates that complex system study may be rooted in chaos theory, and it is also believed to be tightly connected to self-organization, agent-based modeling, and artificial intelligence. The distribution of field reference (a) and impact broadness (b) at 1995, with the dashed line representing complex system research. Moreover, due to the rapid development of the computational technologies and the availability of large-scale datasets, complex system study has become largely connected with computer science afterwards. Additionally, we consider the number of citations/references between two fields as the link weight in the citation network. The original journal devoted to the science, mathematics and engineering of systems with simple components but complex overall behavior. To investigate, we study the association between complex system research and various scientific fields through the relationship of references and citations. Complex systems. 2. Following previous research [18, 19], the reference share from field A to field B is defined as. Specifically, given a paper with a reference or citation list, we embed each reference/citation to a vector of academic fields based on the MAG level-1 fields. We also annotate the field of complex system in the citation network. Additionally, in order to control the paper production in field B that is the referenced field, we also compare the real number of references between fields A and B with the same quantity in the randomized citation network as defined in the previous section. The association between field’s reference broadness and its scientific impact. Complex systems—whether integrated circuits, information relays, transportation routing, social systems, or biochemical reactions in a living cell—all behave in ways that cannot be fully explained by understanding their component parts. Overall, our findings are consistent with several characteristics of complex system research, i.e., its multidisciplinary, quantitative, and computational nature, and may have broad policy implications for supporting and nurturing multidisciplinary research. Copyright © 2020 Yang Wang and Xinyue Wang. Interestingly, engineering is more affected by complex system research since 2000, indicating the applied value of complex system research (Figure 3(e)). The “linear model” of science demonstrates the importance of basic science to the development of applied research and technological development [31]. Thanks to the availability of large-scale bibliometric datasets and the development of science of science research, the above-mentioned questions can be empirically answered for now. We then calculate the normalized entropy for each paper aswhere is the total number of level-1 fields in the MAG dataset. © Complex Systems Publications, Inc. Complex Systems is a journal devoted to the science, mathematics and engineering of systems with simple components but complex overall behavior. A CAS describes a collection of heterogeneous agents interacting within a particular context, adapting to each other's actions. Students will receive a wide and rich training in empirical, computational, and theoretical methods for describing and understanding complex systems. Complex Systems. Classification of Chaotic Behaviors in Jerky Dynamical Systems. Specifically, in the randomized MAG citation network, we switch all citation links between papers but preserve the total number of references of each paper and the year of referencing and referenced papers [16]. of complex systems in: Information and Communication Systems. Research and Development. The goal of the Center for Complex Systems & Enterprises (CCSE) is to enable rapid conceptualization, development and validation of multi-level computational models, with associated interactive visualizations, for exploration of the types of issues outlined above. Hundreds of published papers, encompassing three decades of leading-edge complex systems research, are available for free and immediate download. (a) The yearly number of publications as a function of time from 1960 to 2018, for the whole Microsoft Academic Graph (green) and the field of complex systems (red) and its related fields (blue). The Science and Technology Directorate should ensure that the research agendas of these institutions advance DHS's understanding and application of complex systems analysis. Telecommunications. School of Public Policy and Administration, Xi’an Jiaotong University, Xi’an 710049, China, School of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, China, Y. 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