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This paper develops a regression framework for histogram-valued data using unbalanced optimal transport. By generalizing classical optimal transport theory to account for mass imbalances, the proposed methodology operates within the space of non-negative measures, offering a more flexible and robust framework for regression analysis in distributional settings. The framework aims to determine the optimal barycentric coordinates to construct unbalanced Wasserstein barycenters that establish an optimal mapping between input and target histograms while preserving the underlying distributional structures. The effectiveness of the approach is demonstrated through simulation studies and an empirical application to football analytics, utilizing performance metrics from the 2023–2024 Italian Serie A season. By regressing player-level statistics onto team-level histograms, we quantify the extent to which individual player contributions align with team-level collective dynamics. By analyzing the deviation of individual contributions across different match outcomes, wins, losses, and draws, we uncover patterns that distinguish successful team strategies from less effective ones.

Mobility restrictions have been identified as key non-pharmaceutical interventions to limit the spread of the SARS-COV-2 epidemics. However, these interventions present significant drawbacks to the social fabric and negative outcomes for the real economy. In this paper we propose a real-time monitoring framework for tracking the economic consequences of various forms of mobility reductions involving European countries. We adopt a granular representation of mobility patterns during both the first and second waves of SARS-COV-2 in Italy, Germany, France and Spain to provide an analytical characterization of the rate of losses of industrial production by means of a nowcasting methodology. Our approach exploits the information encoded in massive datasets of human mobility provided by Facebook and Google, which are published at higher frequencies than the target economic variables, in order to obtain an early estimate before the official data becomes available. Our results show, in first place, the ability of mobility-related policies to induce a contraction of mobility patterns across jurisdictions. Besides this contraction, we observe a substitution effect which increases mobility within jurisdictions. Secondly, we show how industrial production strictly follows the dynamics of population commuting patterns and of human mobility trends, which thus provide information on the day-by-day variations in countries’ economic activities. Our work, besides shedding light on how policy interventions targeted to induce a mobility contraction impact the real economy, constitutes a practical toolbox for helping governments to design appropriate and balanced policy actions aimed at containing the SARS-COV-2 spread, while mitigating the detrimental effect on the economy. Our study reveals how complex mobility patterns can have unequal consequences to economic losses across countries and call for a more tailored implementation of restrictions to balance the containment of contagion with the need to sustain economic activities.

The European Union Emissions Trading System (EU ETS) is designed to promote cost-effective carbon emission reductions through allowance trading. However, observed trade patterns suggest potential inefficiencies. This study conducts a province-level analysis of the EU ETS trade network of allowances, demonstrating that trades predominantly occur between entities within the same country and sector, even in recent phases of the system. To systematically examine the mesoscale structure of the trade network while accounting for geographical and sectoral homophily, we introduce a community detection framework based on the gravity model and optimal transport theory. By disentangling home and sectoral biases, we identify trade communities that align with cultural dimensions. Our findings reveal a complex interplay between geographical, economic, and cultural factors that shape carbon allowances trade patterns. These findings contribute to a deeper understanding of structural constraints within the EU ETS trade network and inform strategies for improving its cost-effectiveness.

We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that, while an early lockdown shifts the contagion in time, beyond a critical value of lockdown strength the epidemic tends to restart after lifting the restrictions. We characterize the relative importance of different lockdown lifting schemes by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian Regions as separate administrative entities, in which social interactions between age classes occur. We show that, due to the sparsity of the inter-Regional mobility matrix, once started, the epidemic spreading tends to develop independently across areas, justifying the adoption of mobility restrictions targeted to individual Regions or clusters of Regions. Second, we show that social contacts between members of different age classes play a fundamental role and that interventions which target local behaviours and take into account the age structure of the population can provide a significant contribution to mitigate the epidemic spreading. Our model aims to provide a general framework, and it highlights the relevance of some key parameters on non-pharmaceutical interventions to contain the contagion.

The spread of SARS-COV-2 has affected many economic and social systems. This paper aims at estimating the impact on regional productive systems in Italy of the interplay between the epidemic and the mobility restriction measures put in place to contain the contagion. We focus then on the economic consequences of alternative lockdown lifting schemes. We leverage a massive dataset of human mobility which describes daily movements of over four million individuals in Italy and we model the epidemic spreading through a metapopulation SIR model, which provides the fraction of infected individuals in each Italian district. To quantify economic backslashes this information is combined with socio-economic data. We then carry out a scenario analysis to model the transition to a post-lockdown phase and analyze the economic outcomes derived from the interplay between (a) the timing and intensity of the release of mobility restrictions and (b) the corresponding scenarios on the severity of virus transmission rates. Using a simple model for the spreading disease and parsimonious assumptions on the relationship between the infection and the associated economic backlashes, we show how different policy schemes tend to induce heterogeneous distributions of losses at the regional level depending on mobility restrictions. Our work shed lights on how recovery policies need to balance the interplay between mobility flows of disposable workers and the diffusion of contagion.

We introduce an indicator that aims to detect the emergence of market instabilities by quantifying the intensity of self-organizing processes arising from stock returns’ co-movements. In financial markets, phenomena like imitation, herding and positive feedbacks characterize the emergence of endogenous instabilities, which can modify the qualitative and quantitative behavior of the underlying system. The impossibility to formalize ex-ante the dynamic laws that rule the evolution of financial systems motivates the use of a parsimonious synthetic indicator to detect the disruption of an existing equilibrium configuration. Here we show that the emergence of an interconnected sub-graph of stock returns co-movements from a broader market index is a signal of an out-of-equilibrium transition of the underlying system. To test the validity of our approach, we propose a model-free application that builds on the identification of up and down market phases. Phenomena like imitation, herding and positive feedbacks in the complex financial markets characterize the emergence of endogenous instabilities, which however is still understudied. Here the authors show that the graph-based approach is helpful to timely recognize phases of increasing instability that can drive the system to a new market configuration.

Understanding the complexity of pharmaceutical expenditures across U.S. states is critical for designing efficient healthcare policies and ensuring equitable drug access. This study applies network-based economic complexity methods to analyze state-level Medicaid drug spending, leveraging Medicaid State Drug Utilization Data (SDUD) from 2018 to 2024. Using Revealed Comparative Advantage (RCA) and the Method of Reflections, we quantify the sophistication of pharmaceutical consumption and identify structural inefficiencies in drug reimbursement policies. Our findings reveal substantial heterogeneity in pharmaceutical complexity across states, with highly diversified markets in states like California and Texas, while others, such as Wyoming and West Virginia, exhibit lower complexity due to restrictive formulary policies and healthcare infrastructure limitations. A 15% decline in network density over the study period suggests consolidation in reimbursement practices, influenced by regulatory interventions and cost-containment strategies. Additionally, Medicaid expansion states show a 20% increase in prescription utilization, particularly for antiviral and mental health medications. Null model comparisons highlight systematic deviations from expected expenditure patterns, with states like Arkansas and Nebraska showing lower-than-expected pharmaceutical embeddedness, whereas Massachusetts and California appear more integrated than network models predict. These findings suggest that state-specific policies, provider behavior, and market dynamics significantly shape pharmaceutical expenditures beyond structural network constraints, as well as they offer significant implications for policymakers and healthcare providers seeking to balance cost efficiency with equitable medication distribution.

By exploiting a bipartite network representation of the relationships between mutual funds and portfolio holdings, we propose an indicator that we derive from the analysis of the network, labelled the Average Commonality Coefficient (ACC), which measures how frequently the assets in the fund portfolio are present in the portfolios of the other funds of the market. This indicator reflects the investment behavior of funds’ managers as a function of the popularity of the assets they held. We show that ACC provides useful information to discriminate between funds investing in niche markets and those investing in more popular assets. More importantly, we find that ACC is able to provide indication on the performance of the funds. In particular, we find that funds investing in less popular assets generally outperform those investing in more popular financial instruments, even when correcting for standard factors. Moreover, funds with a low ACC have been less affected by the 2007–2008 global financial crisis, likely because less exposed to fire sales spillovers.

This paper proposes a new methodology based on non-negative matrix factorization to detect communities and to identify central nodes in a network as well as within communities. The method is specifically designed for directed weighted networks and, consequently, it has been applied to the interbank network derived from the e-MID interbank market. In an interbank network indeed links are directed, representing flows of funds between lenders and borrowers. Besides distinguishing between Systemically Important Borrowers and Lenders, the technique complements the detection of systemically important banks, revealing the community structure of the network, that proxies the most plausible areas of contagion of institutions' distress.

[This corrects the article DOI: 10.1371/journal.pone.0167781.].