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Nowadays human interactions largely take place on social networks, with online users' behavior often falling into a few general typologies or "social roles". Among these, opinion leaders are of crucial importance as they have the ability to spread an idea or opinion on a large scale across the network, with possible tangible consequences in the real world. In this work we extract and characterize the different social roles of users within the Reddit WallStreetBets community, around the time of the GameStop short squeeze of January 2021 -- when a handful of committed users led the whole community to engage in a large and risky financial operation. We identify the profiles of both average users and of relevant outliers, including opinion leaders, using an iterative, semi-supervised classification algorithm, which allows us to discern the characteristics needed to play a particular social role. The key features of opinion leaders are large risky investments and constant updates on a single stock, which allowed them to attract a large following and, in the case of GameStop, ignite the interest of the community. Finally, we observe a substantial change in the behavior and attitude of users after the short squeeze event: no new opinion leaders are found and the community becomes less focused on investments. Overall, this work sheds light on the users' roles and dynamics that led to the GameStop short squeeze, while also suggesting why WallStreetBets no longer wielded such large influence on financial markets, in the aftermath of this event., Comment: main text: 15 pages, 4 figures. supplementary materials: 15 pages, 12 figures

We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between elements and compounds is distributed exponentially for materials, and with a fat tail for chemicals. Compounds networks show similar distribution of degrees, and feature a highly-connected club due to oxygen. Chemical compounds networks appear more modular than material ones, while the communities detected reveal different dominant elements specific to the topology. We successfully reproduce the connectivity of the empirical chemicals and materials networks by using a family of fitness models, where the fitness values are derived from the abundances of the elements in the aggregate compound data. Our results pave the way towards a relational network-based understanding of the inherent complexity of the vast chemical knowledge atlas, and our methodology can be applied to other systems with the ingredient-composite structure., Comment: main manuscript with 3 Figures, and supplementary information with 8 figures

In early 2021, the stock prices of GameStop, AMC, Nokia, and BlackBerry experienced dramatic increases, triggered by short squeeze operations that have been largely attributed to Reddit's retail investors. These events showcased, for the first time, the potential of online social networks to catalyze financial collective action. How, when and to what extent Reddit users played a causal role in driving up these prices, however, remains unclear. To address these questions, we employ causal inference techniques, leveraging data capturing activity on Reddit and Twitter, and trading volume with a high temporal resolution. We find that Reddit discussions foreshadowed trading volume before the GameStop short squeeze, with their predictive power being particularly strong on hourly time scales. This effect emerged abruptly and became prominent a few weeks before the event, but waned once the community of investors gained widespread visibility through Twitter. As the causal link unfolded, the collective investment of the Reddit community, quantified through each user's financial position on GameStop, closely mirrored the market capitalization of the stock. The evidence from our study suggests that Reddit users fueled the GameStop short squeeze, and thereby Reddit served as a coordination hub for a shared financial strategy. Towards the end of January, users talking about GameStop contributed to raise the popularity of BlackBerry, AMC and Nokia, which emerged as the most popular stocks as the community gained global recognition. Overall, our results shed light on the dynamics behind the first large-scale financial collective action driven by social media users.

The cognitive process of opinion formation is often characterized by stubbornness or resistance of agents to changes of opinion. To capture such a feature we introduce a constant latency time in the standard voter model of opinion dynamics: after switching opinion, an agent must keep it for a while. This seemingly simple modification drastically changes the stochastic diffusive behavior of the original model, leading to deterministic dynamical oscillations in the average opinion of the agents. We explain the origin of the oscillations and develop a mathematical formulation of the dynamics that is confirmed by extensive numerical simulations. We further characterize the rich phase space of the model and its asymptotic behavior. Our work offers insights into understanding and modeling opinion swings in diverse social contexts.

Production networks arise from supply and customer relations among firms. These systems are gaining growing attention as a consequence of disruptions due to natural or man-made disasters that happened in the last years, such as the Covid-19 pandemic or the Russia-Ukraine war. However, data constraints force the few, available studies to consider only country-specific production networks. In order to fully capture the cross-country structure of modern supply chains, here we focus on the global automotive industry as represented by the MarkLines Automotive dataset. After representing this data as a network of manufacturers, suppliers, and products, we perform a pattern-detection exercise using a statistically grounded validation technique based on the maximum entropy principle. We reveal the presence of a significantly large number of V-shaped and square-shaped motifs, indicating that manufacturing firms compete and are seldom engaged in a buyer-supplier relationship, while they typically have many suppliers in common. Interestingly, generalist and specialist suppliers coexist in the network. Additionally, we unveil the presence of geographical patterns, with manufacturers clustering around groups of suppliers; for instance, Chinese firms constitute a disconnected community, likely an effect of the protectionist policies promoted by the Chinese government. We also show the tendency of suppliers to organize their production by targeting specific functional modules of a vehicle. Besides shedding light on the self-organising principles shaping production networks, our findings open up the possibility of designing realistic generative models of supply chains, to be used for testing the resilience of the interconnected global economy., Comment: 27 pages, 12 figures

People nowadays express their opinions in online spaces, using different forms of interactions such as posting, sharing and discussing with one another. These digital traces allow to capture how people dynamically react to the myriad of events occurring in the world. By unfolding the structure of Reddit conversations, we describe how highly engaging events happening in the society affect user interactions and behaviour with respect to unperturbed discussion patterns. Conversations, defined as a post and the comments underneath, are analysed along their temporal and semantic dimensions. We disclose that changes in the pace and language used in conversations exhibit notable similarities across diverse events. Conversations tend to become repetitive with a more limited vocabulary, display different semantic structures and feature heightened emotions. As the event approaches, the shifts occurring in conversations are reflected in the users' dynamics. Users become more active and they exchange information with a growing audience, despite using a less rich vocabulary and repetitive messages. The peers of each user fill up more semantic space, shifting the dialogue and widening the exchange of information. The recurring patterns we discovered are persistent across several contexts, thus represent a fingerprint of human behavior, which could impact the modeling of online social networks interactions.

Modelling systems with networks has been a powerful approach to tame the complexity of several phenomena. Unfortunately, such an approach is often made difficult by the large number of variables to take into consideration. Methods of dimensional reduction are useful tools to rescale a complex dynamical network down to a low-dimensional effective system and thus to capture the global features of the dynamics. Here we study the application of the degree-weighted and spectral reduction methods to an important class of dynamical processes on networks: the propagation of credit shocks within an interbank network, modelled according to the DebtRank algorithm. In particular we introduce an effective version of the dynamics, characterised by functions with continuous derivatives that can be handled by the dimensional reduction. We test the reduction methods against the full dynamical system in different interbank market settings: homogeneous and heterogeneous networks generated from state-of-the-art reconstruction methods as well as networks derived from empirical e-MID data. Our results indicate that, for proper choices of the bank default probability, reduction methods are able to provide reliable estimates of systemic risk in the market, with the spectral reduction better handling heterogeneous networks. Finally we provide new physical insights on the nature and working principles of dimensional reduction methods.

The evolution of economic and innovation systems at the national scale is shaped by a complex dynamics, the footprint of which is the nested structure of the activities in which different countries are competitive. Nestedness is a persistent feature across multiple kinds (layers) of activities related to the production of knowledge and goods: scientific research, technological innovation, industrial production and trade. We observe that in the layers of innovation and trade the competitiveness of countries correlates unambiguously with their diversification, while the science layer displays some peculiar feature. The evolution of scientific domains leads to an increasingly modular structure, in which the most developed nations become less competitive in the less advanced scientific domains, where they are replaced by the emerging countries. This observation is in line with a capability-based view of the evolution of economic systems, but with a slight twist. Indeed, while the accumulation of specific know-how and skills is a fundamental step towards development, resource constraints force countries to acquire competitiveness in the more complex research fields at the price of losing ground in more basic, albeit less visible (or more crowded), fields. This tendency towards a relatively specialized basket of capabilities leads to a trade-off between the need to diversify in order to evolve and the need to allocate resources efficiently. Collaborative patterns among developed nations reduce the necessity to be competitive in the less sophisticated fields, freeing resources for the more complex domains.

The patterns of human mobility play a key role in the spreading of infectious diseases and thus represent a key ingredient of epidemic modeling and forecasting. Unfortunately, as the Covid-19 pandemic has dramatically highlighted, for the vast majority of countries there is no availability of granular mobility data. This hinders the possibility of developing computational frameworks to monitor the evolution of the disease and to adopt timely and adequate prevention policies. Here we show how this problem can be addressed in the case study of Italy. We build a multiplex mobility network based solely on open data, and implement a SIR metapopulation model that allows scenario analysis through data-driven stochastic simulations. The mobility flows that we estimate are in agreement with real-time proprietary data from smartphones. Our modeling approach can thus be useful in contexts where high-resolution mobility data is not available., Comment: 10 pages, 3 figures

Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they are nearest-neighbors. Cumulative Merging Percolation (CMP) is an new percolation process that assumes long-range interactions, such that nodes can merge into clusters even if they are topologically distant. Hence in CMP percolation clusters do not coincide with the topological connected components of the network. Previous work has shown that a specific formulation of CMP features peculiar mechanisms for the formation of the giant cluster, and allows to model different network dynamics such as recurrent epidemic processes. Here we develop a more general formulation of CMP in terms of the functional form of the cluster interaction range, showing an even richer phase transition scenario with competition of different mechanisms resulting in crossover phenomena. Our analytic predictions are confirmed by numerical simulations., Comment: 12 pages, 6 figures

The short squeeze of GameStop (GME) shares in mid-January 2021 has been primarily orchestrated by retail investors of the Reddit r/wallstreetbets community. As such, it represents a paramount example of collective coordination action on social media, resulting in large-scale consensus formation and significant market impact. In this work we characterise the structure and time evolution of Reddit conversation data, showing that the occurrence and sentiment of GME-related comments (representing how much users are engaged with GME) increased significantly much before the short squeeze actually took place. Taking inspiration from these early warnings as well as evidence from previous literature, we introduce a model of opinion dynamics where user engagement can trigger a self-reinforcing mechanism leading to the emergence of consensus, which in this particular case is associated to the success of the short squeeze operation. Analytical solutions and model simulations on interaction networks of Reddit users feature a phase transition from heterogeneous to homogeneous opinions as engagement grows, which we qualitatively compare to the sudden hike of GME stock price. Although the model cannot be validated with available data, it offers a possible and minimal interpretation for the increasingly important phenomenon of self-organized collective actions taking place on social networks.

Using ideas and tools of complexity science we design a holistic measure of \textit{Scientific Fitness}, encompassing the scientific knowledge, capabilities and competitiveness of a research system. We characterize the temporal dynamics of Scientific Fitness and R\&D expenditures at the geographical scale of nations, highlighting patterns of similar research systems, and showing how developing nations (China in particular) are quickly catching up the developed ones. Down-scaling the aggregation level of the analysis, we find that even developed nations show a considerable level of inequality in the Scientific Fitness of their internal regions. Further, we assess comparatively how the competitiveness of each geographic region is distributed over the spectrum of research sectors. Overall, the Scientific Fitness represents the first high quality estimation of the scientific strength of nations and regions, opening new policy-making applications for better allocating resources, filling inequality gaps and ultimately promoting innovation.

We study the difference between the level of systemic risk that is empirically measured on an interbank network and the risk that can be deduced from the balance sheets composition of the participating banks. Using generalised DebtRank dynamics, we measure observed systemic risk on e-MID network data (augmented by BankFocus information) and compare it with the expected systemic risk of a null model network, obtained through an appropriate maximum-entropy approach constraining relevant balance sheet variables. We show that the aggregate levels of observed and expected systemic risks are usually compatible but differ significantly during turbulent times (in our case, after the default of Lehman Brothers and the VLTRO implementation by the ECB). At the individual level instead, banks are typically more or less risky than what their balance sheet prescribes due to their position in the network. Our results confirm on one hand that balance sheet information used within a proper maximum-entropy network model provides good aggregate estimates of systemic risk, and on the other hand the importance of knowing the empirical details of the network for conducting precise stress tests on individual banks, especially after systemic events.

Monopartite projections of bipartite networks are useful tools for modeling indirect interactions in complex systems. The standard approach to identify significant links is statistical validation using a suitable null network model, such as the popular configuration model (CM) that constrains node degrees and randomizes everything else. However different CM formulations exist, depending on how the constraints are imposed and for which sets of nodes. Here we systematically investigate the application of these formulations in validating the same network, showing that they lead to different results even when the same significance threshold is used. Instead a much better agreement is obtained for the same density of validated links. We thus propose a meta-validation approach that allows to identify model-specific significance thresholds for which the signal is strongest, and at the same time to obtain results independent of the way in which the null hypothesis is formulated. We illustrate this procedure using data on scientific production of world countries.

The field of Financial Networks is a paramount example of the novel applications of Statistical Physics that have made possible by the present data revolution. As the total value of the global financial market has vastly outgrown the value of the real economy, financial institutions on this planet have created a web of interactions whose size and topology calls for a quantitative analysis by means of Complex Networks. Financial Networks are not only a playground for the use of basic tools of statistical physics as ensemble representation and entropy maximization; rather, their particular dynamics and evolution triggered theoretical advancements as the definition of DebtRank to measure the impact and diffusion of shocks in the whole systems. In this review we present the state of the art in this field, starting from the different definitions of financial networks (based either on loans, on assets ownership, on contracts involving several parties -- such as credit default swaps, to multiplex representation when firms are introduced in the game and a link with real economy is drawn) and then discussing the various dynamics of financial contagion as well as applications in financial network inference and validation. We believe that this analysis is particularly timely since financial stability as well as recent innovations in climate finance, once properly analysed and understood in terms of complex network theory, can play a pivotal role in the transformation of our society towards a more sustainable world., Comment: version submitted to Nature Reviews Physics

Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant patterns in graphs, counting networked configurations with given properties. From a technical point of view, the ERGMs workflow is defined by two subsequent optimization steps: the first one concerns the maximization of Shannon entropy and leads to identify the functional form of the ensemble probability distribution that is maximally non-committal with respect to the missing information; the second one concerns the maximization of the likelihood function induced by this probability distribution and leads to its numerical determination. This second step translates into the resolution of a system of $O(N)$ non-linear, coupled equations (with $N$ being the total number of nodes of the network under analysis), a problem that is affected by three main issues, i.e. accuracy, speed and scalability. The present paper aims at addressing these problems by comparing the performance of three algorithms (i.e. Newton's method, a quasi-Newton method and a recently-proposed fixed-point recipe) in solving several ERGMs, defined by binary and weighted constraints in both a directed and an undirected fashion. While Newton's method performs best for relatively little networks, the fixed-point recipe is to be preferred when large configurations are considered, as it ensures convergence to the solution within seconds for networks with hundreds of thousands of nodes (e.g. the Internet, Bitcoin). We attach to the paper a Python code implementing the three aforementioned algorithms on all the ERGMs considered in the present work., Comment: Python code available at the following URL: https://pypi.org/project/NEMtropy/

We study the correlation between the codon usage bias of genetic sequences and the network features of protein-protein interaction (PPI) in bacterial species. We use PCA techniques in the space of codon bias indices to show that genes with similar patterns of codon usage have a significantly higher probability that their encoded proteins are functionally connected and interacting. Importantly, this signal emerges when multiple aspects of codon bias are taken into account at the same time. The present study extends our previous observations on E.Coli over a wide set of 34 bacteria. These findings could allow for future investigations on the possible effects of codon bias on the topology of the PPI network, with the aim of improving existing bioinformatics methods for predicting protein interactions.

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, we shall focus on the inference methods rooted in statistical physics and information theory. The discussion will be organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections., Comment: 107 pages, 25 figures

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees by contrasting real data. Specifically, we analyze by finite-size scaling analysis the datasets of real networks to check whether purported departures from the power law behavior are due to the finiteness of the sample size. In this case, power laws would be recovered in the case of progressively larger cutoffs induced by the size of the sample. We find that a large number of the networks studied follow a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially infrastructure and transportation but also social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite-size effects due to the nature of the sample data.

We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The specific implementation of the quality function and the resulting optimal community structure thus become dependent both on the type of Markov process and on the specific Markov times considered. For instance, if we use a natural Markov chain dynamics and discount its stationary distribution -- that is, we take as reference process the dynamics at infinite time -- we obtain the standard formulation of the Markov stability. Notably, the possibility to use finite-time transition probabilities to define the reference process naturally allows detecting communities at different resolutions, without the need to consider a continuous-time Markov chain in the small time limit. The main advantage of our general formulation of Markov stability based on dynamical flows is that we work with lumped Markov chains on network partitions, having the same stationary distribution of the original process. In this way the form of the quality function becomes invariant under partitioning, leading to a self-consistent definition of community structures at different aggregation scales.

We study whether specific combinations of technological advancements can signal the presence of local capabilities allowing for a given industrial production. To this end, we generate a multi-layer network using country-level patent and trade data, and perform a motif-based analysis on this network using a statistical validation approach derived from maximum entropy arguments. We show that in many cases the signal far exceeds the noise, providing robust evidence of synergies between different technologies that can lead to a competitive advantage in specific markets. Our results can be highly useful for policy makers to inform industrial and innovation policies.

Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however cause a deviation between the empirical percolation threshold $p_c$ and its model-predicted value $\pi_c$. Here we show the existence of an empirical linear relation between $p_c$ and $\pi_c$ across a large number of real and model networks. Such a putatively universal relation can then be used to correct the estimated value of $\pi_c$. We further show how to obtain a more precise relation using the concept of the complement graph, by investigating on the connection between the percolation threshold of a network, $p_c$, and that of its complement, $\bar{p}_c$.

The cornerstone of statistical mechanics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here we formulate a mapping between weighted networks and lattice gasses, making the conceptual step forward of interpreting weighted links as particles with a generalised coordinate. This leads to the definition of the grand canonical ensemble of weighted complex networks. We derive exact expressions for the partition function and thermodynamic quantities, both in the cases of global and local (i.e., node-specific) constraints on density and mean energy of particles. We further show that, when modelling real cases of networks, the binary and weighted statistics of the ensemble can be disentangled, leading to a simplified framework for a range of practical applications.

In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models for networks reproducing some features of real-world systems, but otherwise as random as possible. We review here the statistical physics approach and the various null models for complex networks, focusing in particular on the analytic frameworks reproducing the local network features. We then show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics models that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, as well as the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes., Comment: accepted version (after revision)

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transition are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer, and has a well defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers, and is characterised by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous trend in the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon and to estimate the critical threshold for which the abrupt transition is more likely to occur. Remarkably, finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

When studying social, economic and biological systems, one has often access to only limited information about the structure of the underlying networks. An example of paramount importance is provided by financial systems: information on the interconnections between financial institutions is privacy-protected, dramatically reducing the possibility of correctly estimating crucial systemic properties such as the resilience to the propagation of shocks. The need to compensate for the scarcity of data, while optimally employing the available information, has led to the birth of a research field known as network reconstruction. Since the latter has benefited from the contribution of researchers working in disciplines as different as mathematics, physics and economics, the results achieved so far are still scattered across heterogeneous publications. Most importantly, a systematic comparison of the network reconstruction methods proposed up to now is currently missing. This review aims at providing a unifying framework to present all these studies, mainly focusing on their application to economic and financial networks., Comment: 79 pages, 6 figures, 3 tables

A growing body of studies on systemic risk in financial markets has emphasized the key importance of taking into consideration the complex interconnections among financial institutions. Much effort has been put in modeling the contagion dynamics of financial shocks, and to assess the resilience of specific financial markets - either using real network data, reconstruction techniques or simple toy networks. Here we address the more general problem of how shock propagation dynamics depends on the topological details of the underlying network. To this end we consider different realistic network topologies, all consistent with balance sheets information obtained from real data on financial institutions. In particular, we consider networks of varying density and with different block structures, and diversify as well in the details of the shock propagation dynamics. We confirm that the systemic risk properties of a financial network are extremely sensitive to its network features. Our results can aid in the design of regulatory policies to improve the robustness of financial markets.

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked system, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems.

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank markets seem better characterised by a bipartite structure with more core-periphery connections than inside the core. Using a novel core-periphery detection method on the eMID interbank market, we enrich this picture by showing that the network is actually characterised by multiple core-periphery pairs. Moreover, a transition from core-periphery to bipartite structures occurs by shortening the temporal scale of data aggregation. We further show how the global financial crisis transformed the market, in terms of composition, multiplicity and internal organisation of core-periphery pairs. By unveiling such a fine-grained organisation and transformation of the interbank market, our method can find important applications in the understanding of how distress can propagate over financial networks., Comment: 17 pages, 9 figures, 1 table

Statistical physics of complex systems exploits network theory not only to model, but also to effectively extract information from many dynamical real-world systems. A pivotal case of study is given by financial systems: market prediction represents an unsolved scientific challenge yet with crucial implications for society, as financial crises have devastating effects on real economies. Thus, nowadays the quest for a robust estimator of market efficiency is both a scientific and institutional priority. In this work we study the visibility graphs built from the time series of several trade market indices. We propose a validation procedure for each link of these graphs against a null hypothesis derived from ARCH-type modeling of such series. Building on this framework, we devise a market indicator that turns out to be highly correlated and even predictive of financial instability periods.

Protein-protein interaction (PPI) networks are the backbone of all processes in living cells. In this work we relate conservation, essentiality and functional repertoire of a gene to the connectivity $k$ (i.e., the number of interaction links) of the corresponding protein in the PPI network. On a set of 42 bacterial genomes of different sizes, and with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivities changes between PPI subnetworks of essential and nonessential genes; ii) how gene conservation, measured both by the evolutionary retention index (ERI) and by evolutionary pressures, is related to the the connectivity of the corresponding protein; iii) how PPI connectivities are modulated by evolutionary and functional relationships, as represented by the Clusters of Orthologous Genes (COGs). We show that conservation, essentiality and functional specialisation of genes constrain the connectivity of the corresponding proteins in bacterial PPI networks. In particular, we isolate a core of highly connected proteins (with connectivities $k\ge40$), which is ubiquitous among the species considered here -- though mostly visible in the degree distributions of bacteria with small genomes (less than 1000 genes). The genes that belong to this highly connected core are conserved, essential and, in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.

We show that the space in which scientific, technological and economic developments interplay with each other can be mathematically shaped using pioneering multilayer network and complexity techniques. We build the tri-layered network of human activities (scientific production, patenting, and industrial production) and study the interactions among them, also taking into account the possible time delays. Within this construction we can identify which capabilities and prerequisites are needed to be competitive in a given activity, and even measure how much time is needed to transform, for instance, the technological know-how into economic wealth and scientific innovation, being able to make predictions with a very long time horizon. Quite unexpectedly, we find empirical evidence that the naive knowledge flow from science, to patents, to products is not supported by data, being instead technology the best predictor for industrial and scientific production for the next decades.

Essential genes constitute the core of genes which cannot be mutated too much nor lost along the evolutionary history of a species. Natural selection is expected to be stricter on essential genes and on conserved (highly shared) genes, than on genes that are either nonessential or peculiar to a single or a few species. In order to further assess this expectation, we study here how essentiality of a gene is connected with its degree of conservation among several unrelated bacterial species, each one characterised by its own codon usage bias. Confirming previous results on E. coli, we show the existence of a universal exponential relation between gene essentiality and conservation in bacteria. Moreover we show that, within each bacterial genome, there are at least two groups of functionally distinct genes, characterised by different levels of conservation and codon bias: i) a core of essential genes, mainly related to cellular information processing; ii) a set of less conserved nonessential genes with prevalent functions related to metabolism. In particular, the genes in the first group are more retained among species, are subject to a stronger purifying conservative selection and display a more limited repertoire of synonymous codons. The core of essential genes is close to the minimal bacterial genome, which is in the focus of recent studies in synthetic biology, though we confirm that orthologs of genes that are essential in one species are not necessarily essential in other species. We also list a set of highly shared genes which, reasonably, could constitute a reservoir of targets for new anti-microbial drugs.

Determining how scientific achievements influence the subsequent process of knowledge creation is a fundamental step in order to build a unified ecosystem for studying the dynamics of innovation and competitiveness. Relying separately on data about scientific production on one side, through bibliometric indicators, and about technological advancements on the other side, through patents statistics, gives only a limited insight on the key interplay between science and technology which, as a matter of fact, move forward together within the innovation space. In this paper, using citation data of both research papers and patents, we quantify the direct influence of the scientific outputs of nations on further advancements in science and on the introduction of new technologies. Our analysis highlights the presence of geo-cultural clusters of nations with similar innovation system features, and unveils the heterogeneous coupled dynamics of scientific and technological advancements. This study represents a step forward in the buildup of an inclusive framework for knowledge creation and innovation.

Assessing the stability of economic systems is a fundamental research focus in economics, that has become increasingly interdisciplinary in the currently troubled economic situation. In particular, much attention has been devoted to the interbank lending market as an important diffusion channel for financial distress during the recent crisis. In this work we study the stability of the interbank market to exogenous shocks using an agent-based network framework. Our model encompasses several ingredients that have been recognized in the literature as pro-cyclical triggers of financial distress in the banking system: credit and liquidity shocks through bilateral exposures, liquidity hoarding due to counterparty creditworthiness deterioration, target leveraging policies and fire-sales spillovers. But we exclude the possibility of central authorities intervention. We implement this framework on a dataset of 183 European banks that were publicly traded between 2004 and 2013. We document the extreme fragility of the interbank lending market up to 2008, when a systemic crisis leads to total depletion of market equity with an increasing speed of market collapse. After the crisis instead the system is more resilient to systemic events in terms of residual market equity. However, the speed at which the crisis breaks out reaches a new maximum in 2011, and never goes back to values observed before 2007. Our analysis points to the key role of the crisis outbreak speed, which sets the maximum delay for central authorities intervention to be effective.

In the last years, increasing efforts have been put into the development of effective stress tests to quantify the resilience of financial institutions. Here we propose a stress test methodology for central counterparties based on a network characterization of clearing members, whose links correspond to direct credits and debits. This network constitutes the ground for the propagation of financial distress: equity losses caused by an initial shock with both exogenous and endogenous components reverberate within the network and are amplified through credit and liquidity contagion channels. At the end of the dynamics, we determine the vulnerability of each clearing member, which represents its potential equity loss. We apply the proposed framework to the Fixed Income asset class of CC&G, the central counterparty operating in Italy whose main cleared securities are Italian Government Bonds. We consider two different scenarios: a distributed, plausible initial shock, as well as a shock corresponding to the cover 2 regulatory requirement (the simultaneous default of the two most exposed clearing members). Although the two situations lead to similar results after an unlimited reverberation of shocks on the network, the distress propagation is much more hasty in the latter case, with a large number of additional defaults triggered at early stages of the dynamics. Our results thus show that setting a default fund to cover insolvencies only on a cover 2 basis may not be adequate for taming systemic events, and only very conservative default funds, such as CC&G's one, can face total losses due to the shock propagation. Overall, our network-based stress test represents a refined tool for calibrating default fund amounts.

Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to reliably replicate the empirical degree sequence, which is however unknown in many realistic situations. More recently, it has been found that the knowledge of the degree sequence can be replaced by the knowledge of the strength sequence, which is typically accessible, complemented by that of the total number of links, thus considerably relaxing the observational requirements. Here we further relax these requirements and devise a procedure valid when even the the total number of links is unavailable. We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density. We show that the best way of sampling nodes is the random selection scheme, any other procedure being biased towards unrealistically large, or small, link densities. We then introduce our core technique for reconstructing both the topology and the link weights of the unknown network in detail. When tested on real economic and financial data sets, our method achieves a remarkable accuracy and is very robust with respect to the sampled subsets, thus representing a reliable practical tool whenever the available topological information is restricted to small portions of nodes., Comment: 8 pages, 1 figure, 4 tables

Financial contagion from liquidity shocks has being recently ascribed as a prominent driver of systemic risk in interbank lending markets. Building on standard compartment models used in epidemics, in this work we develop an EDB (Exposed-Distressed-Bankrupted) model for the dynamics of liquidity shocks reverberation between banks, and validate it on electronic market for interbank deposits data. We show that the interbank network was highly susceptible to liquidity contagion at the beginning of the 2007/2008 global financial crisis, and that the subsequent micro-prudential and liquidity hoarding policies adopted by banks increased the network resilience to systemic risk---yet with the undesired side effect of drying out liquidity from the market. We finally show that the individual riskiness of a bank is better captured by its network centrality than by its participation to the market, along with the currently debated concept of "too interconnected to fail".

Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets is strongly affected by the interconnections among financial institutions. Yet, while the aggregate balance sheets of institutions are publicly disclosed, information on single positions is mostly confidential and, as such, unavailable. Standard approaches to reconstruct the network of financial interconnection produce unrealistically dense topologies, leading to a biased estimation of systemic risk. Moreover, reconstruction techniques are generally designed for monopartite networks of bilateral exposures between financial institutions, thus failing in reproducing bipartite networks of security holdings (\eg, investment portfolios). Here we propose a reconstruction method based on constrained entropy maximization, tailored for bipartite financial networks. Such a procedure enhances the traditional {\em capital-asset pricing model} (CAPM) and allows to reproduce the correct topology of the network. We test this ECAPM method on a dataset, collected by the European Central Bank, of detailed security holdings of European institutional sectors over a period of six years (2009-2015). Our approach outperforms the traditional CAPM and the recently proposed MECAPM both in reproducing the network topology and in estimating systemic risk due to fire-sales spillovers. In general, ECAPM can be applied to the whole class of weighted bipartite networks described by the fitness model.

Using bibliometric data artificially generated through a model of citation dynamics calibrated on empirical data, we compare several indicators for the scientific impact of individual researchers. The use of such a controlled setup has the advantage of avoiding the biases present in real databases, and allows us to assess which aspects of the model dynamics and which traits of individual researchers a particular indicator actually reflects. We find that the simple citation average performs well in capturing the intrinsic scientific ability of researchers, whatever the length of their career. On the other hand, when productivity complements ability in the evaluation process, the notorious $h$ and $g$ indices reveal their potential, yet their normalized variants do not always yield a fair comparison between researchers at different career stages. Notably, the use of logarithmic units for citation counts allows us to build simple indicators with performance equal to that of $h$ and $g$. Our analysis may provide useful hints for a proper use of bibliometric indicators. Additionally, our framework can be extended by including other aspects of the scientific production process and citation dynamics, with the potential to become a standard tool for the assessment of impact metrics., Comment: 12 pages, 8 figures