An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control. Here, I discuss recent advances on mathematical and computational approaches to control high-dimensional nonlinear network dynamics under general constraints on the admissible interventions. I also discuss the potential of network control to address pressing scientific problems in various disciplines.
The identification of nodes occupying important positions in a network structure is crucial for the understanding of the associated real-world system. Usually, betweenness centrality is used to evaluate a node capacity to connect different graph regions. However, we argue here that this measure is not adapted for that task, as it gives equal weight to "local" centers (i.e. nodes of high degree central to a single region) and to "global" bridges, which connect different communities. This distinction is important as the roles of such nodes are different in terms of the local and global organisation of the network structure. In this paper we propose a decomposition of betweenness centrality into two terms, one highlighting the local contributions and the other the global ones. We call the latter bridgeness centrality and show that it is capable to specifically spot out global bridges. In addition, we introduce an effective algorithmic implementation of this measure and demonstrate its capability to identify global bridges in air transportation and scientific collaboration networks.
Detecting global bridges in networks Pablo Jensen, Matteo Morini, Marton Karsai, Tommaso Venturini, Alessandro Vespignani, Mathieu Jacomy, Jean-Philippe Cointet, Pierre Merckle, Eric Fleury
We study the role of geography in R&D networks by means of a quantitative, micro-geographic approach. Using a large database that covers international R&D collaborations from 1984 to 2009, we localize each actor precisely in space through its latitude and longitude. This allows us to analyze the R&D network at all geographic scales simultaneously. Our empirical results show that despite the high importance of the city level, transnational R&D collaborations at large distances are much more frequent than expected from similar networks. This provides evidence for the ambiguity of distance in economic cooperation which is also suggested by the existing literature. In addition we test whether the hypothesis of local buzz and global pipelines applies to the observed R&D network by calculating well-defined metrics from network theory.
The spatial component of R&D networks Tobias Scholl, Antonios Garas, Frank Schweitzer
The Anthropocene is a proposed time subdivision of the earth's history correlated to the strong human perturbation of the ecosystem. Much debate is ongoing about what date should be considered as the start of the Anthropocene, but much less on how it can evolve in the future and what are its ultimate limits. It is argued here that the phenomena currently defining the Anthropocene will rapidly decline and disappear in times of the order of one century as a result of the irreversible dispersal of the thermodynamic potentials associated to fossil carbon. However, it is possible that, in the future, the human economic system may catalyze the dissipation of solar energy in forms other than photosynthesis, e.g. using solid state photovoltaic devices. In this case, a strong human influence on the ecosystem may persists for much longer times, but in forms much different than the present ones.
What future for the Anthropocene? A biophysical perspective Ugo Bardi
Nature’s special issue probes how scientists and social scientists are coming together to solve the grand challenges of energy, food, water, climate and health. This special scrutinizes the data on interdisciplinary work and looks at its history, meaning and funding. A case study and a reappraisal of the Victorian explorer Richard Francis Burton explore the rewards of breaking down boundaries. Meanwhile, a sustainability institute shares its principles for researchers who work across disciplines. Thus inspired, we invite readers to test their polymathy in our lighthearted quiz.
The idea of a hierarchical spatial organization of society lies at the core of seminal theories in human geography that have strongly influenced our understanding of social organization. In the same line, the recent availability of large-scale human mobility and communication data has offered novel quantitative insights hinting at a strong geographical confinement of human interactions within neighboring regions, extending to local levels within countries. However, models of human interaction largely ignore this effect. Here, we analyze several country-wide networks of telephone calls and uncover a systematic decrease of communication induced by borders which we identify as the missing variable in state-of-the-art models. Using this empirical evidence, we propose an alternative modeling framework that naturally stylize the damping effect of borders. We show that this new notion substantially improves the predictive power of widely used interaction models, thus increasing our ability to predict social activities and to plan the development of infrastructures across multiple scales.
Identifying the structural discontinuities of human interactions Sebastian Grauwin, Michael Szell, Stanislav Sobolevsky, Philipp Hövel, Filippo Simini, Maarten Vanhoof, Zbigniew Smoreda, Albert-Laszlo Barabasi, Carlo Ratti
In this paper we put forward a theory of large systems change (LSC), where large systems are defined as having breadth (i.e. engaging large numbers of people, institutions, and geographies) and depth (i.e. changing the complex relationships among elements of power and structural relationships simultaneously). We focus primarily on transformational LSC, recognizing that such systems are complex adaptive systems in which change is continuous and emergent, but directions can be supported. A typology of change actions with two core dimensions of confrontation and collaboration on the horizontal axis and generative and ungenerative change on the vertical suggests that change strategies can be classified into four broad archetypes: forcing change, supporting change, paternalistic change, or co-creating change. LSC theory development focuses on three core questions: what is the foundation of LSC concepts and methods, what needs to change, and how does LSC occur? We conclude by reviewing how papers in the Special Issue fit into these questions.
Large Systems Change: An Emerging Field of Transformation and Transitions
Waddell, Steve; Waddock, Sandra; Cornell, Sarah; Dentoni, Domenico; McLachlan, Milla; Meszoely, Greta Journal of Corporate Citizenship, Volume 2015, Number 58, June 2015, pp. 5-30(26)
Our latest research demonstrates that among learners who complete courses, MOOCs do have a real impact: 72% of survey respondents reported career benefits and 61% reported educational benefits. Furthermore, our findings suggest that people from developing countries more frequently report benefits from taking MOOCs and, also in developing countries, people with lower socioeconomic status and with less education are more likely to report benefits. It appears that MOOCs are tangibly helping people who take the time and effort to complete courses.
Who’s Benefiting from MOOCs, and Why Chen Zhenghao, Brandon Alcorn, Gayle Christensen, Nicholas Eriksson, Daphne Koller, Ezekiel J. Emanuel
Inspired by Adam Smith and Friedrich Hayek, many economists have postulated the existence of invisible forces that drive economic markets. These market forces interact in complex ways making it difficult to visualize or understand the interactions in every detail. Here I show how these forces can transcend a zero-sum game and become a win-win business interaction, thanks to emergent social synergies triggered by division of labor. Computer simulations with the model Sociodynamica show here the detailed dynamics underlying this phenomenon in a simple virtual economy. In these simulations, independent agents act in an economy exploiting and trading two different goods in a heterogeneous environment. All and each of the various forces and individuals were tracked continuously, allowing to unveil a synergistic effect on economic output produced by the division of labor between agents. Running simulations in a homogeneous environment, for example, eliminated all benefits of division of labor. The simulations showed that the synergies unleashed by division of labor arise if: Economies work in a heterogeneous environment; agents engage in complementary activities whose optimization processes diverge; agents have means to synchronize their activities. This insight, although trivial if viewed a posteriori, improve our understanding of the source and nature of synergies in real economic markets and might render economic and natural sciences more consilient.
Agent based simulations visualize Adam Smith's invisible hand by solving Friedrich Hayek's Economic Calculus Klaus Jaffe
The availability of big data on human activity is currently changing the way we look at our surroundings. With the high penetration of mobile phones, nearly everyone is already carrying a high-precision sensor providing an opportunity to monitor and analyze the dynamics of human movement on unprecedented scales. In this article, we present a technique and visualization tool which uses aggregated activity measures of mobile networks to gain information about human activity shaping the structure of the cities. Based on ten months of mobile network data, activity patterns can be compared through time and space to unravel the "city's pulse" as seen through the specific signatures of different locations. Furthermore, the tool allows classifying the neighborhoods into functional clusters based on the timeline of human activity, providing valuable insights on the actual land use patterns within the city. This way, the approach and the tool provide new ways of looking at the city structure from historical perspective and potentially also in real-time based on dynamic up-to-date records of human behavior. The online tool presents results for four global cities: New York, London, Hong Kong and Los Angeles.
Visualizing signatures of human activity in cities across the globe Dániel Kondor, Pierrick Thebault, Sebastian Grauwin, István Gódor, Simon Moritz, Stanislav Sobolevsky, Carlo Ratti
Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. This framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.
Scientists are frequently faced with the important decision to start or terminate a creative partnership. This process can be influenced by strategic motivations, as early career researchers are pursuers, whereas senior researchers are typically attractors, of new collaborative opportunities. Focusing on the longitudinal aspects of scientific collaboration, we analyzed 473 collaboration profiles using an ego-centric perspective which accounts for researcher-specific characteristics and provides insight into a range of topics, from career achievement and sustainability to team dynamics and efficiency. From more than 166,000 collaboration records, we quantify the frequency distributions of collaboration duration and tie-strength, showing that collaboration networks are dominated by weak ties characterized by high turnover rates. We use analytic extreme-value thresholds to identify a new class of indispensable `super ties', the strongest of which commonly exhibit >50% publication overlap with the central scientist. The prevalence of super ties suggests that they arise from career strategies based upon cost, risk, and reward sharing and complementary skill matching. We then use a combination of descriptive and panel regression methods to compare the subset of publications coauthored with a super tie to the subset without one, controlling for pertinent features such as career age, prestige, team size, and prior group experience. We find that super ties contribute to above-average productivity and a 17% citation increase per publication, thus identifying these partnerships - the analog of life partners - as a major factor in science career development.
Quantifying the impact of weak, strong, and super ties in scientific careers Alexander Michael Petersen
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been confronted to a representatively large number of texts. So, we can summarize the current support of Zipf's law in texts as anecdotic. We try to solve these issues by studying three different versions of Zipf's law and fitting them to all available English texts in the Project Gutenberg database (consisting of more than 30000 texts). To do so we use state-of-the art tools in fitting and goodness-of-fit tests, carefully tailored to the peculiarities of text statistics. Remarkably, one of the three versions of Zipf's law, consisting of a pure power-law form in the complementary cumulative distribution function of word frequencies, is able to fit more than 40% of the texts in the database (at the 0.05 significance level), for the whole domain of frequencies (from 1 to the maximum value) and with only one free parameter (the exponent).
Large-scale analysis of Zipf's law in English texts Isabel Moreno-Sánchez, Francesc Font-Clos, Álvaro Corral
Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using new harmonized definitions for functional urban areas, we examine to what extent these ideas apply to European cities. We show that while most large urban systems in Western Europe (France, Germany, Italy, Spain, UK) approximately agree with theoretical expectations, the small number of cities in each nation and their natural variability preclude drawing strong conclusions. We demonstrate how this problem can be overcome so that cities from different urban systems can be pooled together to construct larger datasets. This leads to a simple statistical procedure to identify urban scaling relations, which then clearly emerge as a property of European cities. We compare the predictions of urban scaling to Zipf's law for the size distribution of cities and show that while the former holds well the latter is a poor descriptor of European cities. We conclude with scenarios for the size and properties of future pan-European megacities and their implications for the economic productivity, technological sophistication and regional inequalities of an integrated European urban system.
Urban Scaling in Europe Luis M. A. Bettencourt, Jose Lobo
Search in an environment with an uncertain distribution of resources involves a trade-off between local exploitation and distant exploration. This extends to the problem of information foraging, where a knowledge-seeker shifts between reading in depth and studying new domains. To study this, we examine the reading choices made by one of the most celebrated scientists of the modern era: Charles Darwin. Darwin built his theory of natural selection in part by synthesizing disparate parts of Victorian science. When we analyze his extensively self-documented reading we find shifts, on multiple timescales, between choosing to remain with familiar topics and seeking cognitive surprise in novel fields. On the longest timescales, these shifts correlate with major intellectual epochs of his career, as detected by Bayesian epoch estimation. When we compare Darwin's reading path with publication order of the same texts, we find Darwin more adventurous than the culture as a whole.
Exploration and Exploitation of Victorian Science in Darwin's Reading Notebooks Jaimie Murdock, Colin Allen, Simon DeDeo
We examine community structure in time-dependent legislation cosponsorship networks in the Peruvian Congress, which we compare briefly to such networks in the United States Congress. To study these legislatures, we employ a multilayer representation of temporal networks, in which each layer connects legislators based on the similarity of their patterns for cosponsoring bills. We then use multilayer modularity maximization to detect communities. From our computations, we are able to capture power shifts in the Peruvian Congress during 2006−2011. For example, we observe the emergence of "opportunists", who switch from one community to another, as well as cohesive legislative communities whose initial component legislators never switch. Interestingly, many of the opportunists belonged to the group that won the majority in Congress.
Time-dependent community structure in legislation cosponsorship networks in the Congress of the Republic of Peru Sang Hoon Lee, José Manuel Magallanes, Mason A. Porter
Quantifying the similarity between symbolic sequences is a traditional problem in Information The- ory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is char- acterized by heavy-tailed distributions (e.g., Zipf’s law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences, e.g., they hinder an accurate finite-size estimation of entropies. Here we show how the accuracy of estimations depend on the sample size N, not only for the Shannon entropy (α = 1) and its corresponding similarity measures (e.g., the Jensen-Shanon divergence) but also for measures based on the generalized entropy of order α. For small α’s, including α = 1, the bias and fluctuations in the estimations decay slower than the 1/N decay observed in short-tailed distributions. For α larger than a critical value α∗ ≤ 2, the 1/N-scaling is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete α-spectrum of measures. We find that frequent words change more slowly than less frequent words and that α = 2 provides the most robust measure to quantify language change.
On the similarity of symbol frequency distributions with heavy tails Martin Gerlach, Francesc Font-Clos, Eduardo G. Altmann
An extrapolation of the genetic complexity of organisms to earlier times suggests that life began before the Earth was formed. Life may have started from systems with single heritable elements that are functionally equivalent to a nucleotide. The genetic complexity, roughly measured by the number of non-redundant functional nucleotides, is expected to have grown exponentially due to several positive feedback factors: gene cooperation, duplication of genes with their subsequent specialization, and emergence of novel functional niches associated with existing genes. Linear regression of genetic complexity on a log scale extrapolated back to just one base pair suggests the time of the origin of life 9.7 billion years ago. This cosmic time scale for the evolution of life has important consequences: life took ca. 5 billion years to reach the complexity of bacteria; the environments in which life originated and evolved to the prokaryote stage may have been quite different from those envisaged on Earth; there was no intelligent life in our universe prior to the origin of Earth, thus Earth could not have been deliberately seeded with life by intelligent aliens; Earth was seeded by panspermia; experimental replication of the origin of life from scratch may have to emulate many cumulative rare events; and the Drake equation for guesstimating the number of civilizations in the universe is likely wrong, as intelligent life has just begun appearing in our universe. Evolution of advanced organisms has accelerated via development of additional information-processing systems: epigenetic memory, primitive mind, multicellular brain, language, books, computers, and Internet. As a result the doubling time of complexity has reached ca. 20 years. Finally, we discuss the issue of the predicted technological singularity and give a biosemiotics perspective on the increase of complexity.
Life Before Earth Alexei A. Sharov, Richard Gordon
Scientific collaboration networks are an important component of scientific output and contribute significantly to expanding our knowledge and to the economy and gross domestic product of nations. Here we examine a dataset from the Mendeley scientific collaboration network. We analyze this data using a combination of machine learning techniques and dynamical models. We find interesting clusters of countries with different characteristics of collaboration. Some of these clusters are dominated by developed countries that have higher number of self connections compared with connections to other countries. Another cluster is dominated by impoverished nations that have mostly connections and collaborations with other countries but fewer self connections. We also propose a complex systems dynamical model that explains these characteristics. Our model explains how the scientific collaboration networks of impoverished and developing nations change over time. We also find interesting patterns in the behaviour of countries that may reflect past foreign policies and contemporary geopolitics. Our model and analysis gives insights and guidelines into how scientific development of developing countries can be guided. This is intimately related to fostering economic development of impoverished nations and creating a richer and more prosperous society.
Analysis of a Planetary Scale Scientific Collaboration Dataset Reveals Novel Patterns Soumya Banerjee
Animal societies rely on interactions between group members to effectively communicate and coordinate their actions. To date, the transmission properties of interaction networks formed by direct physical contacts have been extensively studied for many animal societies and in all cases found to inhibit spreading. Such direct interactions do not, however, represent the only viable pathways. When spreading agents can persist in the environment, indirect transmission via ‘same-place, different-time’ spatial coincidences becomes possible. Previous studies have neglected these indirect pathways and their role in transmission. Here, we use rock ant colonies, a model social species whose flat nest geometry, coupled with individually tagged workers, allowed us to build temporally and spatially explicit interaction networks in which edges represent either direct physical contacts or indirect spatial coincidences. We show how the addition of indirect pathways allows the network to enhance or inhibit the spreading of different types of agent. This dual-functionality arises from an interplay between the interaction-strength distribution generated by the ants' movement and environmental decay characteristics of the spreading agent. These findings offer a general mechanism for understanding how interaction patterns might be tuned in animal societies to control the simultaneous transmission of harmful and beneficial agents.
Inclusive Fitness Theory (IFT) was proposed half a century ago by W.D. Hamilton to explain the emergence and maintenance of cooperation between individuals that allows the existence of society. Contemporary evolutionary ecology identified several factors that increase inclusive fitness, in addition to kin-selection, such as assortation or homophily, and social synergies triggered by cooperation. Here we propose an Extend Inclusive Fitness Theory (EIFT) that includes in the fitness calculation all direct and indirect benefits an agent obtains by its own actions, and through interactions with kin and with genetically unrelated individuals. This formulation focuses on the sustainable cost/benefit threshold ratio of cooperation and on the probability of agents sharing mutually compatible memes or genes. This broader description of the nature of social dynamics allows to compare the evolution of cooperation among kin and non-kin, intra- and inter-specific cooperation, co-evolution, the emergence of symbioses, of social synergies, and the emergence of division of labor. EIFT promotes interdisciplinary cross fertilization of ideas by allowing to describe the role for division of labor in the emergence of social synergies, providing an integrated framework for the study of both, biological evolution of social behavior and economic market dynamics.
Extended Inclusive Fitness Theory bridges Economics and Biology through a common understanding of Social Synergy Klaus Jaffe
Many agrarian communities in developing countries suffer from insufficient productivity and use farming practices that deteriorate the environment both locally and globally. Research suggests that social networks play a role in environmental management, different studies emphasize different aspects of network structures, and the implications of the scales at which networks operate are not explicitly discussed. Here, I ask what types of social structures in farmer networks are conducive to environmental protection and agricultural productivity enhancement, and I show that the answer depends on the scale of the investigation.
The results highlight the need for environmental management policies to be based on research at multiple scales and demonstrate that, counter-intuitively, increasing global economic interconnectivity may, in some cases, stimulate the adoption of conservation practices via local social networks.
We propose a method to decompose a multivariate dynamical system into weakly-coupled modules based on the idea that module boundaries constrain the spread of perturbations. Using a novel quality function called 'perturbation modularity', we find system coarse-grainings that optimally separate the dynamics of perturbation spreading into fast intra-modular and slow inter-modular components. Our method is defined directly in terms of system dynamics, unlike approaches that find communities in networks (whether in structural networks or 'functional networks' of statistical dependencies) or that impose arbitrary dynamics onto graphs. Due to this, we are able to capture the variation of modular organization across states, timescales, and in response to different perturbations, aspects of modularity which are all relevant to real-world dynamical systems. However, in certain cases, mappings exist between perturbation modularity and community detection methods of `Markov stability' and Newman's modularity. Our approach is demonstrated on several examples of coupled logistic maps. It uncovers hierarchical modular organization present in a system's coupling matrix. It also identifies the onset of a self-organized modular regime in coupled map lattices, where it is used to explore dependence of modularity on system state, parameters, and perturbations.
Modularity and the Spread of Perturbations in Complex Dynamical Systems Artemy Kolchinsky, Alexander J. Gates, Luis M. Rocha
In this paper we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion, and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and in this sense they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviour of humans and predict the changes that could arise due to a varying tolerance for lies in society.
Dynamics of deceptive interactions in social networks Rafael A. Barrio, Tzipe Govezensky, Robin Dunbar, Gerardo Iñiguez, Kimmo Kaski
Neighborhoods populated by amenities, such as restaurants, cafes, and libraries, are considered to be a key property of desirable cities. Yet, despite the global enthusiasm for amenity-rich neighborhoods, little is known about the empirical laws governing the colocation of amenities at the neighborhood scale. Here, we contribute to our understanding of the naturally occurring neighborhood-scale agglomerations of amenities observed in cities by using a dataset summarizing the precise location of millions of amenities. We use this dataset to build the network of co-location of amenities, or Amenity Space, by first introducing a clustering algorithm to identify neighborhoods, and then using the identified neighborhoods to map the probability that two amenities will be co-located in one of them. Finally, we use the Amenity Space to build a recommender system that identifies the amenities that are missing in a neighborhood given its current pattern of specialization. This opens the door for the construction of amenity recommendation algorithms that can be used to evaluate neighborhoods and inform their improvement and development.
Do we need another coffee house? The amenity space and the evolution of neighborhoods César A. Hidalgo, Elisa E. Castañer
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