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Predicting high-growth firms has attracted increasing interest from the technological forecasting and machine learning communities. Most existing studies primarily utilize financial data for these predictions. However, research suggests that a firm's research and development activities and its network position within technological ecosystems may also serve as valuable predictors. To unpack the relative importance of diverse features, this paper analyzes financial and patent data from 5,071 firms, extracting three categories of features: financial features, technological features of granted patents, and network-based features derived from firms' connections to their primary technologies. By utilizing ensemble learning algorithms, we demonstrate that incorporating financial features with either technological, network-based features, or both, leads to more accurate high-growth firm predictions compared to using financial features alone. To delve deeper into the matter, we evaluate the predictive power of each individual feature within their respective categories using explainable artificial intelligence methods. Among non-financial features, the maximum economic value of a firm's granted patents and the number of patents related to a firms' primary technologies stand out for their importance. Furthermore, firm size is positively associated with high-growth probability up to a certain threshold size, after which the association plateaus. Conversely, the maximum economic value of a firm's granted patents is positively linked to high-growth probability only after a threshold value is exceeded. These findings elucidate the complex predictive role of various features in forecasting high-growth firms and could inform technological resource allocation as well as investment decisions., Comment: 26 pages, 9 figures

Defining and finalizing Mergers and Acquisitions (M&A) requires complex human skills, which makes it very hard to automatically find the best partner or predict which firms will make a deal. In this work, we propose the MASS algorithm, a specifically designed measure of similarity between companies and we apply it to patenting activity data to forecast M&A deals. MASS is based on an extreme simplification of tree-based machine learning algorithms and naturally incorporates intuitive criteria for deals; as such, it is fully interpretable and explainable. By applying MASS to the Zephyr and Crunchbase datasets, we show that it outperforms LightGCN, a "black box" graph convolutional network algorithm. When similar companies have disjoint patenting activities, on the contrary, LightGCN turns out to be the most effective algorithm. This study provides a simple and powerful tool to model and predict M&A deals, offering valuable insights to managers and practitioners for informed decision-making.

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

We use algorithmic and network-based tools to build and analyze the bipartite network connecting jobs with the skills they require. We quantify and represent the relatedness between jobs and skills by using statistically validated networks. Using the fitness and complexity algorithm, we compute a skill-based complexity of jobs. This quantity is positively correlated with the average salary, abstraction, and non-routinarity level of jobs. Furthermore, coherent jobs - defined as the ones requiring closely related skills - have, on average, lower wages. We find that salaries may not always reflect the intrinsic value of a job, but rather other wage-setting dynamics that may not be directly related to its skill composition. Our results provide valuable information for policymakers, employers, and individuals to better understand the dynamics of the labor market and make informed decisions about their careers.

Tree-based machine learning algorithms provide the most precise assessment of the feasibility for a country to export a target product given its export basket. However, the high number of parameters involved prevents a straightforward interpretation of the results and, in turn, the explainability of policy indications. In this paper, we propose a procedure to statistically validate the importance of the products used in the feasibility assessment. In this way, we are able to identify which products, called explainers, significantly increase the probability to export a target product in the near future. The explainers naturally identify a low dimensional representation, the Feature Importance Product Space, that enhances the interpretability of the recommendations and provides out-of-sample forecasts of the export baskets of countries. Interestingly, we detect a positive correlation between the complexity of a product and the complexity of its explainers.

Mergers and Acquisitions represent important forms of business deals, both because of the volumes involved in the transactions and because of the role of the innovation activity of companies. Nevertheless, Economic Complexity methods have not been applied to the study of this field. By considering the patent activity of about one thousand companies, we develop a method to predict future acquisitions by assuming that companies deal more frequently with technologically related ones. We address both the problem of predicting a pair of companies for a future deal and that of finding a target company given an acquirer. We compare different forecasting methodologies, including machine learning and network-based algorithms, showing that a simple angular distance with the addition of the industry sector information outperforms the other approaches. Finally, we present the Continuous Company Space, a two-dimensional representation of firms to visualize their technological proximity and possible deals. Companies and policymakers can use this approach to identify companies most likely to pursue deals or to explore possible innovation strategies.

Many bipartite networks describe systems where an edge represents a relation between a user and an item. Measuring the similarity between either users or items is the basis of memory-based collaborative filtering, a widely used method to build a recommender system with the purpose of proposing items to users. When the edges of the network are unweighted, the popular common neighbors-based approaches, allowing only positive similarity values, neglect the possibility and the effect of two users (or two items) being very dissimilar. Moreover, they underperform with respect to model-based (machine learning) approaches, although providing higher interpretability. Inspired by the functioning of Decision Trees, we propose a method to compute similarity that allows also negative values, the Sapling Similarity. The key idea is to look at how the information that a user is connected to an item influences our prior estimation of the probability that another user is connected to the same item: if it is reduced, then the similarity between the two users will be negative, otherwise, it will be positive. We show that, when used to build memory-based collaborative filtering, Sapling Similarity provides better recommendations than existing similarity metrics. Then we compare the Sapling Similarity Collaborative Filtering (SSCF, a hybrid of the item-based and the user-based) with state-of-the-art models using standard datasets. Even if SSCF depends on only one straightforward hyperparameter, it has comparable or higher recommending accuracy, and outperforms all other models on the Amazon-Book dataset, while retaining the high explainability of memory-based approaches., Comment: 27 pages, 11 figures

We study the empirical relationship between green technologies and industrial production at very fine-grained levels by employing Economic Complexity techniques. Firstly, we use patent data on green technology domains as a proxy for competitive green innovation and data on exported products as a proxy for competitive industrial production. Secondly, with the aim of observing how green technological development trickles down into industrial production, we build a bipartite directed network linking single green technologies at time $t_1$ to single products at time $t_2 \ge t_1$ on the basis of their time-lagged co-occurrences in the technological and industrial specialization profiles of countries. Thirdly we filter the links in the network by employing a maximum entropy null-model. In particular, we find that the industrial sectors most connected to green technologies are related to the processing of raw materials, which we know to be crucial for the development of clean energy innovations. Furthermore, by looking at the evolution of the network over time, we observe that more complex green technological know-how requires more time to be transmitted to industrial production, and is also linked to more complex products.

Translation Quality Assessment (TQA) is a process conducted by human translators and is widely used, both for estimating the performance of (increasingly used) Machine Translation, and for finding an agreement between translation providers and their customers. While translation scholars are aware of the importance of having a reliable way to conduct the TQA process, it seems that there is limited literature that tackles the issue of reliability with a quantitative approach. In this work, we consider the TQA as a complex process from the point of view of physics of complex systems and approach the reliability issue from the Bayesian paradigm. Using a dataset of translation quality evaluations (in the form of error annotations), produced entirely by the Professional Translation Service Provider Translated SRL, we compare two Bayesian models that parameterise the following features involved in the TQA process: the translation difficulty, the characteristics of the translators involved in producing the translation, and of those assessing its quality - the reviewers. We validate the models in an unsupervised setting and show that it is possible to get meaningful insights into translators even with just one review per translation; subsequently, we extract information like translators' skills and reviewers' strictness, as well as their consistency in their respective roles. Using this, we show that the reliability of reviewers cannot be taken for granted even in the case of expert translators: a translator's expertise can induce a cognitive bias when reviewing a translation produced by another translator. The most expert translators, however, are characterised by the highest level of consistency, both in translating and in assessing the translation quality., Comment: 21 pages, 14 figures

A key element to understand complex systems is the relationship between the spatial scale of investigation and the structure of the interrelation among its elements. When it comes to economic systems, it is now well-known that the country-product bipartite network exhibits a nested structure, which is the foundation of different algorithms that have been used to scientifically investigate countries' development and forecast national economic growth. Changing the subject from countries to companies, a significantly different scenario emerges. Through the analysis of a unique dataset of Italian firms' exports and a worldwide dataset comprising countries' exports, here we find that, while a globally nested structure is observed at the country level, a local, in-block nested structure emerges at the level of firms. Remarkably, this in-block nestedness is statistically significant with respect to suitable null models and the algorithmic partitions of products into blocks have a high correspondence with exogenous product classifications. These findings lay a solid foundation for developing a scientific approach based on the physics of complex systems to the analysis of companies, which has been lacking until now.

The relatedness between a country or a firm and a product is a measure of the feasibility of that economic activity. As such, it is a driver for investments at a private and institutional level. Traditionally, relatedness is measured using networks derived by country-level co-occurrences of product pairs, that is counting how many countries export both. In this work, we compare networks and machine learning algorithms trained not only on country-level data, but also on firms, that is something not much studied due to the low availability of firm-level data. We quantitatively compare the different measures of relatedness, by using them to forecast the exports at the country and firm-level, assuming that more related products have a higher likelihood to be exported in the future. Our results show that relatedness is scale-dependent: the best assessments are obtained by using machine learning on the same typology of data one wants to predict. Moreover, we found that while relatedness measures based on country data are not suitable for firms, firm-level data are very informative also for the development of countries. In this sense, models built on firm data provide a better assessment of relatedness. We also discuss the effect of using parameter optimization and community detection algorithms to identify clusters of related companies and products, finding that a partition into a higher number of blocks decreases the computational time while maintaining a prediction performance well above the network-based benchmarks., Comment: 14 pages, 4 figures

Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such events are sometimes referred to as Black Swans, but a quantitative definition of a Black Swan is still lacking. Here, by leveraging on the properties of Zipf-Mandelbrot law, we investigate the relations between such extreme events and the dynamics of the upper cutoff of the inherent distribution. This approach permits a quantification of extreme events and allows to classify them as White, Grey, or Black Swans. Our criterion is in accordance with some previous findings, but also allows us to spot new examples of Black Swans, such as Lionel Messi and the Turkish Airline Flight 981 disaster. The systematic and quantitative methodology we developed allows a scientific and immediate categorization of rare events, providing also new insight into the generative mechanism behind Black Swans.

We reconstruct the innovation dynamics of about two hundred thousand companies by following their patenting activity for about ten years. We define the technological portfolios of these companies as the set of the technological sectors present in the patents they submit. By assuming that companies move more frequently towards related sectors, we leverage on their past activity to build network-based and machine learning algorithms to forecast the future submission of patents in new sectors. We compare different evaluation metrics and prediction methodologies, showing that tree-based machine learning algorithms overperform the standard methods based on networks of co-occurrences. This methodology can be applied by firms and policymakers to disentangle, given the present innovation activity, the feasible technological sectors from those that are out of reach, given their present innovation activity.

We present an integrated database suitable for the investigations of the Economic development of countries by using the Economic Fitness and Complexity framework. Firstly, we implement machine learning techniques to reconstruct the database of Trade of Services and we integrate it with the database of the Trade of the physical Goods, generating a complete view of the International Trade and denoted the Universal database. Using this data, we derive a statistically significant network of interaction of the Economic activities, where preferred paths of development and clusters of High-Tech industries naturally emerge. Finally, we compute the Economic Fitness, an algorithmic assessment of the competitiveness of countries, removing the unexpected misbehaviour of Economies under-represented by the sole consideration of the Trade of the physical Goods.

Scientific and technological progress is largely driven by firms in many domains, including artificial intelligence and vaccine development. However, we do not know yet whether the success of firms' research activities exhibits dynamic regularities and some degree of predictability. By inspecting the research lifecycles of 7,440 firms, we find that the economic value of a firm's early patents is an accurate predictor of various dimensions of a firm's future research success. At the same time, a smaller set of future top-performers do not generate early patents of high economic value, but they are detectable via the technological value of their early patents. Importantly, the observed predictability cannot be explained by a cumulative advantage mechanism, and the observed heterogeneity of the firms' temporal success patterns markedly differs from patterns previously observed for individuals' research careers. Our results uncover the dynamical regularities of the research success of firms, and they could inform managerial strategies as well as policies to promote entrepreneurship and accelerate human progress., Comment: 15 pages,7 figures

Economic complexity methods, and in particular relatedness measures, lack a systematic evaluation and comparison framework. We argue that out-of-sample forecast exercises should play this role, and we compare various machine learning models to set the prediction benchmark. We find that the key object to forecast is the activation of new products, and that tree-based algorithms clearly overperform both the quite strong auto-correlation benchmark and the other supervised algorithms. Interestingly, we find that the best results are obtained in a cross-validation setting, when data about the predicted country was excluded from the training set. Our approach has direct policy implications, providing a quantitative and scientifically tested measure of the feasibility of introducing a new product in a given country., Comment: 17 pages, 9 figures

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 growth in AI is rapidly transforming the structure of economic production. However, very little is known about how within-AI specialization may relate to broad-based economic diversification. This paper provides a data-driven framework to integrate the interconnection between AI-based specialization with goods and services export specialization to help design future comparative advantage based on the inherent capabilities of nations. Using detailed data on private investment in AI and export specialization for more than 80 countries, we propose a systematic framework to help identify the connection from AI to goods and service sector specialization. The results are instructive for nations that aim to harness AI specialization to help guide sources of future competitive advantage. The operational framework could help inform the public and private sector to uncover connections with nearby areas of specialization., Comment: 27 pages, 20 figures, 3 tables

Relatedness is a quantification of how much two human activities are similar in terms of the inputs and contexts needed for their development. Under the idea that it is easier to move between related activities than towards unrelated ones, empirical approaches to quantify relatedness are currently used as predictive tools to inform policies and development strategies in governments, international organizations, and firms. Here we focus on countries' industries and we show that the standard, widespread approach of estimating Relatedness through the co-location of activities (e.g. Product Space) generates a measure of relatedness that performs worse than trivial auto-correlation prediction strategies. We argue that this is a consequence of the poor signal-to-noise ratio present in international trade data. In this paper we show two main findings. First, we find that a shift from two-products correlations (network-density based) to many-products correlations (decision trees) can dramatically improve the quality of forecasts with a corresponding reduction of the risk of wrong policy choices. Then, we propose a new methodology to empirically estimate Relatedness that we call Continuous Projection Space (CPS). CPS, which can be seen as a general network embedding technique, vastly outperforms all the co-location, network-based approaches, while retaining a similar interpretability in terms of pairwise distances.

The flourishing of fake news is favored by recommendation algorithms of online social networks which, based on previous users activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and how consensus is reached. Remarkably, polarization can be avoided only for weak interaction with the personalized information and if the number of agents is below a threshold. We analytically compute this critical size, which depends on the interaction probability in a strongly non linear way., Comment: 15 pages, 9 figures

A recent paper by Hausmann and collaborators (1) reaches the important conclusion that Complexity-weighted diversification is the essential element to predict country growth. We like this result because Complexity-weighted diversification is precisely the first equation of the Fitness algorithm that we introduced in 2012 (2,3). However, contrary to what is claimed in (1), it is incorrect to say that diversification is contained also in the ECI algorithm (4). We discuss the origin of this misunderstanding and show that the ECI algorithm contains exactly zero diversification. This is actually one of the reasons for the poor performances of ECI which leads to completely unrealistic results, as for instance, the derivation that Qatar or Saudi Arabia are industrially more competitive than China (5,6). Another important element of our new approach is the representation of the economic dynamics of countries as trajectories in the GDPpc-Fitness space (7-10). In some way also this has been rediscovered by Hausmann and collaborators and renamed as "Stream plots", but, given their weaker metrics and methods, they propose it to use it only for a qualitative insight, while ours led to quantitative and successful forecasting. The Fitness approach has paved the way to a robust and testable framework for Economic Complexity resulting in a highly competitive scheme for growth forecasting (7-10). According to a recent report by Bloomberg (9): The new Fitness method, "systematically outperforms standard methods, despite requiring much less data".

The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others presents Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut example of such coherence is natural language. Our framework allows us to derive some quantitative results that go well beyond the usual Zipf's law: i) earthquakes can evolve only incoherently and thus show Zipf's law spuriously; this allows an assessment of the largest possible magnitude of an earthquake occurring in a geographical region. ii) We prove that Zipfian dynamics are not additive, explaining analytically why US cities evolve coherently, while world cities do not. iii) Our concept of coherence can be used for model selection, for example, the Yule-Simon process can describe the dynamics of world countries' GDP. iv) World cities present spurious Zipf's law and we use this property for estimating the maximal population of an urban agglomeration.

We propose an original approach to describe the scientific progress in a quantitative way. Using innovative Machine Learning techniques we create a vector representation for the PACS codes and we use them to represent the relative movements of the various domains of Physics in a multi-dimensional space. This methodology unveils about 25 years of scientific trends, enables us to predict innovative couplings of fields, and illustrates how Nobel Prize papers and APS milestones drive the future convergence of previously unrelated fields.

Development and growth are complex and tumultuous processes. Modern economic growth theories identify some key determinants of economic growth. However, the relative importance of the determinants remains unknown, and additional variables may help clarify the directions and dimensions of the interactions. The novel stream of literature on economic complexity goes beyond aggregate measures of productive inputs, and considers instead a more granular and structural view of the productive possibilities of countries, i.e. their capabilities. Different endowments of capabilities are crucial ingredients in explaining differences in economic performances. In this paper we employ economic fitness, a measure of productive capabilities obtained through complex network techniques. Focusing on the combined roles of fitness and some more traditional drivers of growth, we build a bridge between economic growth theories and the economic complexity literature. Our findings, in agreement with other recent empirical studies, show that fitness plays a crucial role in fostering economic growth and, when it is included in the analysis, can be either complementary to traditional drivers of growth or can completely overshadow them.

Users online tend to acquire information adhering to their system of beliefs and to ignore dissenting information. Such dynamics might affect page popularity. In this paper we introduce an algorithm, that we call PopRank, to assess both the Impact of Facebook pages as well as users' Engagement on the basis of their mutual interactions. The ideas behind the PopRank are that i) high impact pages attract many users with a low engagement, which means that they receive comments from users that rarely comment, and ii) high engagement users interact with high impact pages, that is they mostly comment pages with a high popularity. The resulting ranking of pages can predict the number of comments a page will receive and the number of its posts. Pages impact turns out to be slightly dependent on pages' informative content (e.g., science vs conspiracy) but independent of users' polarization., Comment: 10 pages, 5 figures

This note is a contribution to the debate about the optimal algorithm for Economic Complexity that recently appeared on ArXiv [1, 2] . The authors of [2] eventually agree that the ECI+ algorithm [1] consists just in a renaming of the Fitness algorithm we introduced in 2012, as we explicitly showed in [3]. However, they omit any comment on the fact that their extensive numerical tests claimed to demonstrate that the same algorithm works well if they name it ECI+, but not if its name is Fitness. They should realize that this eliminates any credibility to their numerical methods and therefore also to their new analysis, in which they consider many algorithms [2]. Since by their own admission the best algorithm is the Fitness one, their new claim became that the search for the best algorithm is pointless and all algorithms are alike. This is exactly the opposite of what they claimed a few days ago and it does not deserve much comments. After these clarifications we also present a constructive analysis of the status of Economic Complexity, its algorithms, its successes and its perspectives. For us the discussion closes here, we will not reply to further comments.

Recently a measure for Economic Complexity named ECI+ has been proposed by Albeaik et al. We like the ECI+ algorithm because it is mathematically identical to the Fitness algorithm, the measure for Economic Complexity we introduced in 2012. We demonstrate that the mathematical structure of ECI+ is strictly equivalent to that of Fitness (up to normalization and rescaling). We then show how the claims of Albeaik et al. about the ability of Fitness to describe the Economic Complexity of a country are incorrect. Finally, we hypothesize how the wrong results reported by these authors could have been obtained by not iterating the algorithm.

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.

We study the relationship between firms' performance and their technological portfolios using tools borrowed from the complexity science. In particular, we ask whether the accumulation of knowledge and capabilities related to a coherent set of technologies leads firms to experience advantages in terms of productive efficiency. To this end, we analyzed both the balance sheets and the patenting activity of about 70 thousand firms that have filed at least one patent over the period 2004-2013. From this database it is possible to define a measure of the firms' coherent diversification, based on the network of technological fields, and relate it to the firms' perfomance in terms of labor productivity. Such a measure favors companies with a diversification structure comprising blocks of closely related fields over firms with the same breadth of scope, but a more scattered diversification structure. We find that the coherent diversification of firms is quantitatively related to their economic performance and captures relevant information about their productive structure. In particular, we prove on a statistical basis that a naive definition of technological diversification can explain labor productivity only as a proxy of size and coherent diversification. This approach can be used to investigate possible synergies within firms and to recommend viable partners for merging and acquisitions.

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.

We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products' aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition., Comment: 20 pages, 5 figures, supporting information. This paper was published on PLOS One on May 17, 2017

We analyze the decisive role played by the complexity of economic systems at the onset of the industrialization process of countries over the past 50 years. Our analysis of the input growth dynamics, based on a recently introduced measure of economic complexity, reveals that more differentiated and more complex economies face a lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. Moreover, adding the complexity dimension to the industrialization process description helps to reconcile current theories with empirical findings., Comment: 12 pages, 5 figures

We discuss, at the macro-level of nations, the contribution of research funding and rate of international collaboration to research performance, with important implications for the science of science policy. In particular, we cross-correlate suitable measures of these quantities with a scientometric-based assessment of scientific success, studying both the average performance of nations and their temporal dynamics in the space defined by these variables during the last decade. We find significant differences among nations in terms of efficiency in turning (financial) input into bibliometrically measurable output, and we confirm that growth of international collaboration positively correlate with scientific success, with significant benefits brought by EU integration policies. Various geo-cultural clusters of nations naturally emerge from our analysis. We critically discuss the possible factors that potentially determine the observed patterns.

We have considered the statistical distributions of the volumes of the different products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries' economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. The ranking curves of the exported volumes from each country seldom cross each other, showing a clear hierarchy of export volumes. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramer-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy., Comment: 10 pages, 5 figures, submitted to IWcee15 conference

We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 minutes) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of market and limit orders: in other words, the missed revelation of the latent order book breaks the dynamical equilibrium between the flows, triggering the large price jumps. On smaller time scales (30 seconds), instead, the static depletion of the limit order book is an indicator of an intrinsic fragility of the system, which is related to a strongly non linear enhancement of the response. In order to quantify this phenomenon we introduce a measure of the liquidity imbalance present in the book and we show that it is correlated to both the sign and the magnitude of the next price movement. These findings provide a quantitative definition of the effective liquidity, which results to be strongly dependent on the considered time scales., Comment: 23 pages, 10 figures

We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied., Comment: 13 pages, 8 figures

We introduce an algorithm able to reconstruct the relevant network structure on which the time evolution of country-product bipartite networks takes place. The significant links are obtained by selecting the largest values of the projected matrix. We first perform a number of tests of this filtering procedure on synthetic cases and a toy model. Then we analyze the bipartite network constituted by countries and exported products, using two databases for a total of almost 50 years. It is then possible to build a hierarchically directed network, in which the taxonomy of products emerges in a natural way. We study the influence of the structure of this taxonomy network on countries' development; in particular, guided by an example taken from the industrialization of South Korea, we link the structure of the taxonomy network to the empirical temporal connections between product activations, finding that the most relevant edges for countries' development are the ones suggested by our network. These results suggest paths in the product space which are easier to achieve, and so can drive countries' policies in the industrialization process., Comment: 16 pages, 8 figures

Technical trading represents a class of investment strategies for Financial Markets based on the analysis of trends and recurrent patterns of price time series. According standard economical theories these strategies should not be used because they cannot be profitable. On the contrary it is well-known that technical traders exist and operate on different time scales. In this paper we investigate if technical trading produces detectable signals in price time series and if some kind of memory effect is introduced in the price dynamics. In particular we focus on a specific figure called supports and resistances. We first develop a criterion to detect the potential values of supports and resistances. As a second step, we show that memory effects in the price dynamics are associated to these selected values. In fact we show that prices more likely re-bounce than cross these values. Such an effect is a quantitative evidence of the so-called self-fulfilling prophecy that is the self-reinforcement of agents' belief and sentiment about future stock prices' behavior., Comment: 21 pages, 8 figures, 2 tables