Bipartite networks are currently regarded as providing a major insight into the organization of many real-world systems, unveiling the mechanisms driving the interactions occurring between distinct groups of nodes. One of the most important issues encountered when modeling bipartite networks is devising a way to obtain a (monopartite) projection on the layer of interest, which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated projections of bipartite networks, according to which any two nodes sharing a statistically-significant number of neighbors are linked. Since assessing the statistical significance of nodes similarity requires a proper statistical benchmark, here we consider a set of four null models, defined within the Exponential Random Graph framework. Our algorithm outputs a matrix of link-specific p-values, from which a validated projection is straightforwardly obtainable, upon running a multiple hypothesis testing procedure. Finally, we test our method on an economic network (i.e. the countries-products World Trade Web representation) and a social network (i.e. MovieLens, collecting the users' ratings of a list of movies). In both cases non-trivial communities are detected: while projecting the World Trade Web on the countries layer reveals modules of similarly-industrialized nations, projecting it on the products layer allows communities characterized by an increasing level of complexity to be detected; in the second case, projecting MovieLens on the films layer allows clusters of movies whose affinity cannot be fully accounted for by genre similarity to be individuated.

Devising strategies for economic development in a globally competitive landscape requires a solid and unbiased understanding of countries' technological advancements and similarities among export products. Both can be addressed through the bipartite representation of the International Trade Network. In this paper, we apply the recently proposed grand canonical projection algorithm to uncover country and product communities. Contrary to past endeavors, our methodology, based on information theory, creates monopartite projections in an unbiased and analytically tractable way. Single links between countries or products represent statistically significant signals, which are not accounted for by null models such as the bipartite configuration model. We find stable country communities reflecting the socioeconomic distinction in developed, newly industrialized, and developing countries. Furthermore, we observe product clusters based on the aforementioned country groups. Our analysis reveals the existence of a complicated structure in the bipartite International Trade Network: apart from the diversification of export baskets from the most basic to the most exclusive products, we observe a statistically significant signal of an export specialization mechanism towards more sophisticated products.

We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models-that admit three conservation laws-by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.

Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analysis of their topological structures has revealed the ubiquitous presence of properties which seem to characterize many -apparently different -systems. Nestedness, for example, has been observed in plants-pollinator as well as in country-product trade networks. This has raised questions about the significance of these patterns, which are often believed to constitute a genuine signature of self-organization. Here, we review several methods that have been developed for the analysis of such evidence. Due to the interdisciplinary character of complex networks, tools developed in one field, for example ecology, can greatly enrich other areas of research, such as economy and finance, and vice versa. With this in mind, we briefly review several entropy-based bipartite null models that have been recently proposed and discuss their application to several real-world systems. The focus on these models is motivated by the fact that they show three very desirable features: analytical character, general applicability and versatility. In this respect, entropy-based methods have been proven to perform satisfactorily both in providing benchmarks for testing evidence-based null hypotheses and in reconstructing unknown network configurations from partial information. On top of that, entropy-based models have been successfully employed to analyze ecological as well as economic systems, thus representing an ideal, interdisciplinary tool to approach the study of bipartite complex systems. As an example, the application of an appropriately defined null model has revealed early-warning signals, both in economic and financial systems, of the 2007-2008 world crisis; another interesting application of the entropy formalism is provided by the detection of statistically-significant export specializations of countries in international trade, a result that seems to reconcile Ricardo's hypothesis in classical economics with the recent findings about the (empirical) diversification of the national productions.Keywords complex networks · mutualistic networks · bipartite networks · ecology · trade · financial networks · systemic risk · nestedness · bipartite motifs · checkerboards · null models · exponential random graphs · network projection · network validation · network filtering 1 Introduction "Data is the New Oil" has become the unofficial slogan for the enthusiasts of technological progress in the recent decade [93]. New data sources have created new economic and political possibilities. Catalyzed by the need for new analytical and numerical tools, the theory of complex networks has gained much

Given the rise of computational power since the beginning of the millennium, agent-based modelling is now a viable option for models capable of capturing the complex nature of an economy. However, the coding implementation can be tedious. Because of this we introduce ABCE, the Agent-Based Computational Economics library. ABCE is an agent-based modeling library for Python that is specifically tailored for economic phenomena. ABCE's core idea is that the modeler specifies the decision logic of the agents, the order of actions, the goods and their physical transformation (the production and the consumption functions). Then, ABCE automatically handles the actions, such as production and consumption, trade and agent interaction. The result is a program where the source code consists of only economically meaningful commands (e.g. decisions, buy, sell, produce, consume, contract, etc.). ABCE scales on multi-core computers, without the intervention of the modeler. The model can be packaged into a nice web application or run in a Jupyter notebook.