Changing demographics of scientific careers: The rise of the temporary workforce.

Contemporary science has been characterized by an exponential growth in publications and a rise of team science. At the same time, there has been an increase in the number of awarded PhD degrees, which has not been accompanied by a similar expansion in the number of academic positions. In such a competitive environment, an important measure of academic success is the ability to maintain a long active career in science. In this paper, we study workforce trends in three scientific disciplines over half a century. We find dramatic shortening of careers of scientists across all three disciplines. The time over which half of the cohort has left the field has shortened from 35 y in the 1960s to only 5 y in the 2010s. In addition, we find a rapid rise (from 25 to 60% since the 1960s) of a group of scientists who spend their entire career only as supporting authors without having led a publication. Altogether, the fraction of entering researchers who achieve full careers has diminished, while the class of temporary scientists has escalated. We provide an interpretation of our empirical results in terms of a survival model from which we infer potential factors of success in scientific career survivability. Cohort attrition can be successfully modeled by a relatively simple hazard probability function. Although we find statistically significant trends between survivability and an author's early productivity, neither productivity nor the citation impact of early work or the level of initial collaboration can serve as a reliable predictor of ultimate survivability.

Differences in Collaboration Patterns across Discipline, Career Stage, and Gender.

Collaboration plays an increasingly important role in promoting research productivity and impact. What remains unclear is whether female and male researchers in science, technology, engineering, and mathematical (STEM) disciplines differ in their collaboration propensity. Here, we report on an empirical analysis of the complete publication records of 3,980 faculty members in six STEM disciplines at select U.S. research universities. We find that female faculty have significantly fewer distinct co-authors over their careers than males, but that this difference can be fully accounted for by females' lower publication rate and shorter career lengths. Next, we find that female scientists have a lower probability of repeating previous co-authors than males, an intriguing result because prior research shows that teams involving new collaborations produce work with higher impact. Finally, we find evidence for gender segregation in some sub-disciplines in molecular biology, in particular in genomics where we find female faculty to be clearly under-represented.

Uncertainty Reduction for Stochastic Processes on Complex Networks.

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by a large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes. However, choosing these points of observation in an optimal way is a highly nontrivial task, depending on the nature of the stochastic process and on the structure of the underlying interaction pattern. In this paper, we introduce a computationally efficient algorithm to determine quasioptimal solutions to the problem. The method leverages network sparsity to reduce computational complexity from exponential to almost quadratic, thus allowing the straightforward application of the method to mid-to-large-size systems. Although the method is exact only for equilibrium stochastic processes defined on trees, it turns out to be effective also for out-of-equilibrium processes on sparse loopy networks.

Characterizing the Analogy Between Hyperbolic Embedding and Community Structure of Complex Networks.

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We take advantage of the analogy for reinterpreting results originally obtained through network hyperbolic embedding in terms of community structure only. First, we show that the robustness of a multiplex network can be controlled by tuning the correlation between the community structures across different layers. Second, we deploy an efficient greedy protocol for network navigability that makes use of routing tables based on community structure.

Defining and identifying Sleeping Beauties in science.

A Sleeping Beauty (SB) in science refers to a paper whose importance is not recognized for several years after publication. Its citation history exhibits a long hibernation period followed by a sudden spike of popularity. Previous studies suggest a relative scarcity of SBs. The reliability of this conclusion is, however, heavily dependent on identification methods based on arbitrary threshold parameters for sleeping time and number of citations, applied to small or monodisciplinary bibliographic datasets. Here we present a systematic, large-scale, and multidisciplinary analysis of the SB phenomenon in science. We introduce a parameter-free measure that quantifies the extent to which a specific paper can be considered an SB. We apply our method to 22 million scientific papers published in all disciplines of natural and social sciences over a time span longer than a century. Our results reveal that the SB phenomenon is not exceptional. There is a continuous spectrum of delayed recognition where both the hibernation period and the awakening intensity are taken into account. Although many cases of SBs can be identified by looking at monodisciplinary bibliographic data, the SB phenomenon becomes much more apparent with the analysis of multidisciplinary datasets, where we can observe many examples of papers achieving delayed yet exceptional importance in disciplines different from those where they were originally published. Our analysis emphasizes a complex feature of citation dynamics that so far has received little attention, and also provides empirical evidence against the use of short-term citation metrics in the quantification of scientific impact.

Reconstruction of multiplex networks via graph embeddings.

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations of a large variety of real systems whose elements interact in multiple fashions or flavors. However, multiplex networks are not always simple to observe in the real world; often, only partial information on the layer structure of the networks is available, whereas the remaining information is in the form of aggregated, single-layer networks. Recent works have proposed solutions to the problem of reconstructing the hidden multiplexity of single-layer networks using tools proper for network science. Here, we develop a machine-learning framework that takes advantage of graph embeddings, i.e., representations of networks in geometric space. We validate the framework in systematic experiments aimed at the reconstruction of synthetic and real-world multiplex networks, providing evidence that our proposed framework not only accomplishes its intended task, but often outperforms existing reconstruction techniques.

Symmetry breaking in optimal transport networks.

Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers. Here, we show that optimal networks undergo sharp transitions from symmetric to asymmetric shapes, indicating that it is sometimes better to avoid serving a whole area to save on switching costs. Also, we analyze the real transportation networks of the cities of Atlanta, Boston, and Toronto using our theoretical framework and find that they are farther away from their optimal shapes as traffic congestion increases.

Dynamical methods for target control of biological networks.

Estimating the influence that individual nodes have on one another in a Boolean network is essential to predict and control the system's dynamical behaviour, for example, detecting key therapeutic targets to control pathways in models of biological signalling and regulation. Exact estimation is generally not possible due to the fact that the number of configurations that must be considered grows exponentially with the system size. However, approximate, scalable methods exist in the literature. These methods can be divided into two main classes: (i) graph-theoretic methods that rely on representations of Boolean dynamics into static graphs and (ii) mean-field approaches that describe average trajectories of the system but neglect dynamical correlations. Here, we compare systematically the performance of these state-of-the-art methods on a large collection of real-world gene regulatory networks. We find comparable performance across methods. All methods underestimate the ground truth, with mean-field approaches having a better recall but a worse precision than graph-theoretic methods. Computationally speaking, graph-theoretic methods are faster than mean-field ones in sparse networks, but are slower in dense networks. The preference of which method to use, therefore, depends on a network's connectivity and the relative importance of recall versus precision for the specific application at hand.

Influence maximization: Divide and conquer.

The problem of influence maximization, i.e., finding the set of nodes having maximal influence on a network, is of great importance for several applications. In the past two decades, many heuristic metrics to spot influencers have been proposed. Here, we introduce a framework to boost the performance of such metrics. The framework consists in dividing the network into sectors of influence, and then selecting the most influential nodes within these sectors. We explore three different methodologies to find sectors in a network: graph partitioning, graph hyperbolic embedding, and community structure. The framework is validated with a systematic analysis of real and synthetic networks. We show that the gain in performance generated by dividing a network into sectors before selecting the influential spreaders increases as the modularity and heterogeneity of the network increase. Also, we show that the division of the network into sectors can be efficiently performed in a time that scales linearly with the network size, thus making the framework applicable to large-scale influence maximization problems.

Multiplex reconstruction with partial information.

A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation of many real-world systems. However, due to a variety of potential factors, such as limited budget and equipment, or physical impossibility, multiplex data can be difficult to observe directly. Often, only partial information on the layer structure of the system is available, whereas the remaining information is in the form of a single-layer network. In this work we face the problem of reconstructing the hidden multiplex structure of an aggregated network from partial information. We propose an algorithm that leverages the layerwise community structure that can be learned from partial observations to reconstruct the ground-truth topology of the unobserved part of the multiplex. The algorithm is characterized by a computational time that grows linearly with the network size. We perform a systematic study of reconstruction problems for both synthetic and real-world multiplex networks. We show that the ability of the proposed method to solve the reconstruction problem is affected by the heterogeneity of the individual layers and the similarity among the layers. On real-world networks, we observe that the accuracy of the reconstruction saturates quickly as the amount of available information increases. In genetic interaction and scientific collaboration multiplexes, for example, we find that 10% of ground-truth information yields 70% accuracy, while 30% information allows for more than 90% accuracy.

Critical avalanches of susceptible-infected-susceptible dynamics in finite networks.

We investigate the avalanche temporal statistics of the susceptible-infected-susceptible (SIS) model when the dynamics is critical and takes place on finite random networks. By considering numerical simulations on annealed topologies we show that the survival probability always exhibits three distinct dynamical regimes. Size-dependent crossover timescales separating them scale differently for homogeneous and for heterogeneous networks. The phenomenology can be qualitatively understood based on known features of the SIS dynamics on networks. A fully quantitative approach based on Langevin theory is shown to perfectly reproduce the results for homogeneous networks, while failing in the heterogeneous case. The analysis is extended to quenched random networks, which behave in agreement with the annealed case for strongly homogeneous and strongly heterogeneous networks.

The dynamic nature of percolation on networks with triadic interactions.

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

Heterogeneous message passing for heterogeneous networks.

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally treelike networks but require corrections to maintain their accuracy level in networks rich with short cycles. However, MP may already be computationally challenging on very large networks and additional costs incurred by correcting for cycles could be prohibitive. We show how the issue can be addressed. By allowing each node in the network to have its own level of approximation, one can focus on improving the accuracy of MP approaches in a targeted manner. We perform a systematic analysis of 109 real-world networks and show that our node-based MP approximation is able to increase both the accuracy and speed of traditional MP approaches. We find that, compared to conventional MP, a heterogeneous approach based on a simple heuristic is more accurate in 81% of tested networks, faster in 64% of cases, and both more accurate and faster in 49% of cases.

Influence maximization in Boolean networks.

The optimization problem aiming at the identification of minimal sets of nodes able to drive the dynamics of Boolean networks toward desired long-term behaviors is central for some applications, as for example the detection of key therapeutic targets to control pathways in models of biological signaling and regulatory networks. Here, we develop a method to solve such an optimization problem taking inspiration from the well-studied problem of influence maximization for spreading processes in social networks. We validate the method on small gene regulatory networks whose dynamical landscapes are known by means of brute-force analysis. We then systematically study a large collection of gene regulatory networks. We find that for about 65% of the analyzed networks, the minimal driver sets contain less than 20% of their nodes.

Effective submodularity of influence maximization on temporal networks.

We study influence maximization on temporal networks. This is a special setting where the influence function is not submodular, and there is no optimality guarantee for solutions achieved via greedy optimization. We perform an exhaustive analysis on both real and synthetic networks. We show that the influence function of randomly sampled sets of seeds often violates the necessary conditions for submodularity. However, when sets of seeds are selected according to the greedy optimization strategy, the influence function behaves effectively as a submodular function. Specifically, violations of the necessary conditions for submodularity are never observed in real networks, and only rarely in synthetic ones. The direct comparison with exact solutions obtained via brute-force search indicates that the greedy strategy provides approximate solutions that are well within the optimality gap guaranteed for strictly submodular functions. Greedy optimization appears, therefore, to be an effective strategy for the maximization of influence on temporal networks.

Universality, criticality and complexity of information propagation in social media.

Statistical laws of information avalanches in social media appear, at least according to existing empirical studies, not robust across systems. As a consequence, radically different processes may represent plausible driving mechanisms for information propagation. Here, we analyze almost one billion time-stamped events collected from several online platforms - including Telegram, Twitter and Weibo - over observation windows longer than ten years, and show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns across platforms, irrespective of the details of the specific system at hand. Critical behavior is deduced from the power-law distributions, and corresponding hyperscaling relations, characterizing size and duration of avalanches of information. Statistical testing on our data indicates that a mixture of simple and complex contagion characterizes the propagation of information in social media. Data suggest that the complexity of the process is correlated with the semantic content of the information that is propagated.

Universality of citation distributions: toward an objective measure of scientific impact.

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited c times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator c(f) = c/c(0) is considered, where c(0) is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of c(f) as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h index suitable for comparing scientists working in different fields.

Systematic comparison of graph embedding methods in practical tasks.

Network embedding techniques aim to represent structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph embedding methods available on the market is large, and practitioners face the nontrivial choice of selecting the proper approach for a given application. The present work attempts to close this gap of knowledge through a systematic comparison of 11 different methods for graph embedding. We consider methods for embedding networks in the hyperbolic and Euclidean metric spaces, as well as nonmetric community-based embedding methods. We apply these methods to embed more than 100 real-world and synthetic networks. Three common downstream tasks - mapping accuracy, greedy routing, and link prediction - are considered to evaluate the quality of the various embedding methods. Our results show that some Euclidean embedding methods excel in greedy routing. As for link prediction, community-based and hyperbolic embedding methods yield an overall performance that is superior to that of Euclidean-space-based approaches. We compare the running time for different methods and further analyze the impact of different network characteristics such as degree distribution, modularity, and clustering coefficients on the quality of the embedding results. We release our evaluation framework to provide a standardized benchmark for arbitrary embedding methods.

Model-free hidden geometry of complex networks.

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular methods employed in network embedding either rely on implicit approximations of the principle of proximity preservation or implement it by enforcing the geometry of the embedding space, thus hindering geometric properties that networks may spontaneously exhibit. Here we take advantage of a model-free embedding method explicitly devised for preserving pairwise proximity and characterize the geometry emerging from the mapping of several networks, both real and synthetic. We show that the learned embedding has simple and intuitive interpretations: the distance of a node from the geometric center is representative for its closeness centrality, and the relative positions of nodes reflect the community structure of the network. Proximity can be preserved in relatively low-dimensional embedding spaces, and the hidden geometry displays optimal performance in guiding greedy navigation regardless of the specific network topology. We finally show that the mapping provides a natural description of contagion processes on networks, with complex spatiotemporal patterns represented by waves propagating from the geometric center to the periphery. The findings deepen our understanding of the model-free hidden geometry of complex networks.