arXiv subjects

Aurelio Patelli

Publications and source records attributed to Aurelio Patelli.

At least 19 recordsLinked to original sources

arXiv2026

An exact and fast solution of the inverse Regularized Optimal Transport problem

Optimal transport describes the most efficient way to move mass between two distributions, given a cost matrix for moving mass between each pair of locations. Entropic optimal transport, solved via the Sinkhorn algorithm, is a widely used regularized version of this problem. Its inverse problem asks the opposite question: given an observed transport plan, what cost matrix produced it? This is difficult because the cost is identifiable only up to an additive gauge freedom. Here we show that this freedom can be fixed exactly by a single double-centering operation applied to the observed plan, yielding the true cost matrix in closed form, with no iterative optimization required. When a modest number of true cost entries are known, the same approach lets us jointly estimate the temperature parameter controlling the entropic regularization, together with a diagnostic for the reliability of this estimate. We further show that the method is not specific to the entropic optimal transport, but extends to a broader class of transport models defined by an invertible relation between cost and plan.

cond-mat.stat-mech↗

arXiv2026

Information-theoretic formulation of the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) asks for the shortest route to visit a set of cities exactly once. It combines a simple local rule - each city must be visited once - with a hard, global constraint- all cities must be traversed within a single cycle. We cast the problem within a probabilistic, information-theoretic framework. The coexistence of local and global constraints is precisely what makes the problem difficult to address in this framework: the local rule can be enforced through vertex-level constraints, whereas the global constraint cannot be captured by independent edge probabilities. We show that this obstacle can be overcome by defining a maximum-entropy probability distribution over graphs, in which edge costs and degree constraints generate an assignment-like ensemble, and a global term, describing the hard constraint, tilts this ensemble toward Hamiltonian cycles. To make the construction tractable, we derive a mean-field approximation in terms of edge occupancies and implement a differentiable cycle penalty that suppresses sub-tours. This leads to a self-consistent numerical procedure whose output is not only a candidate tour but also a probability matrix encoding competing edges and degenerate solutions. We test the method on synthetic ensembles and on TSPLIB instances. The algorithm converges to connected tours in polynomial time, matching the best-known solution in the majority of instances and remaining within a small relative gap otherwise. Beyond its competitive performance, the proposed framework offers a general approach for handling hard constraints while reducing hard combinatorial optimization problems to simpler ones.

cond-mat.stat-mech↗

arXiv2026

Structural Change, Employment, and Inequality in Europe: an Economic Complexity Approach

Structural change consists of industrial diversification towards more productive, knowledge intensive activities. However, changes in the productive structure bear inherent links with job creation and income distribution. In this paper, we investigate the consequences of structural change, defined in terms of labour shifts towards more complex industries, on employment growth, wage inequality, and functional distribution of income. The analysis is conducted for European countries using data on disaggregated industrial employment shares over the period 2010-2018. First, we identify patterns of industrial specialisation by validating a country-industry industrial employment matrix using a bipartite weighted configuration model (BiWCM). Secondly, we introduce a country-level measure of labour-weighted Fitness, which can be decomposed in such a way as to isolate a component that identifies the movement of labour towards more complex industries, which we define as structural change. Thirdly, we link structural change to i) employment growth, ii) wage inequality, and iii) labour share of the economy. The results indicate that our structural change measure is associated negatively with employment growth. However, it is also associated with lower income inequality. As countries move to more complex industries, they drop the least complex ones, so the (low-paid) jobs in the least complex sectors disappear. Finally, structural change predicts a higher labour ratio of the economy; however, this is likely to be due to the increase in salaries rather than by job creation.

econ.GN↗

arXiv2026

Statistical Mechanics of the Sub-Optimal Transport

Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit, where systems collapse onto optimal configurations, a.k.a. the ground states. Real-world systems often occupy intermediate regimes where entropy and cost minimization genuinely compete, producing configurations that are structured yet sub-optimal. The Sub-Optimal Transport (SOT) model captures this competition through an ensemble of weighted bipartite graphs: a coupling parameter interpolates between entropy-dominated dense configurations and cost-dominated sparse structures. This crossover has been observed numerically but lacked analytical understanding. Here we develop a mean-field theory that characterizes this transition. We show that local fluctuations in Lagrange multipliers become sub-extensive in the thermodynamic limit, reducing the full model with strength constraints to an effective single-constraint problem admitting an exact solution in some intermediate regime. The resulting free energy is analytic in the coupling parameter, confirming a smooth crossover rather than a phase transition. We derive closed-form expressions for thermodynamic observables and weight distributions, validated against numerical simulations. These results establish the first analytical description of the SOT model, extending statistical mechanics methods beyond the zero-temperature regime.

cond-mat.stat-mech↗

arXiv2025

Maximum entropy modeling of Optimal Transport: the sub-optimality regime and the transition from dense to sparse networks

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply or receive, while an external cost field favors a minimal set of links, driving the system toward a sparse, tree-like structure. By tuning the control parameter, one transitions from uniformly distributed weights to an optimal transport regime in which weights condense onto cost-favorable edges. We quantify this dense-to-sparse transition, showing with numerical analyses that the process does not hinge on specific assumptions about the node-strength or cost distributions. Finite-size analysis confirms that the results persist in the thermodynamic limit. Because the model offers explicit control over the degree of sub-optimality, this approach lends to practical applications in link prediction, network reconstruction, and statistical validation, particularly in systems where partial optimization coexists with other noise-like factors.

cond-mat.stat-mech↗

arXiv2025

Vulnerabilities and capabilities in the EU Automotive industry: Leveraging Input-Output Analysis and Economic Complexity

This paper investigates the structural vulnerabilities and competitive dynamics of the EU27 automotive sector, with a focus on the complexity and the fragmentation of production processes across global value chains. Employing a mixed-methods approach, our analysis integrates input-output tables to quantify the sector's reliance on non-EU economic branches, alongside an economic complexity framework to assess the underlying productive capabilities of European countries in automotive-related industries. The findings indicate an increasing dependency on extra-EU suppliers, particularly China, for critical components such as lithium-ion batteries, which heightens supply chain risks. Currently, Eastern European countries-most notably Poland, Czechia, and Hungary-have enhanced their competitiveness in the production of automotive components, surpassing traditional leaders such as Germany. The paper advances the literature by providing a novel, granular list of 6-digit products within the automotive supply chain and offers new insights into the challenges posed by the ongoing electric mobility transition in the European Union, particularly in relation to electric accumulators.

econ.GN↗

arXiv2024

Follow the money: a startup-based measure of AI exposure across occupations, industries and regions

The integration of artificial intelligence (AI) into the workplace is advancing rapidly, necessitating robust metrics to evaluate its tangible impact on the labour market. Existing measures of AI occupational exposure largely focus on AI's theoretical potential to substitute or complement human labour on the basis of technical feasibility, providing limited insight into actual adoption and offering inadequate guidance for policymakers. To address this gap, we introduce the AI Startup Exposure (AISE) index-a novel metric based on occupational descriptions from O*NET and AI applications developed by startups funded by the Y Combinator accelerator. Our findings indicate that while high-skilled professions are theoretically highly exposed according to conventional metrics, they are heterogeneously targeted by startups. Roles involving routine organizational tasks-such as data analysis and office management-display significant exposure, while occupations involving tasks that are less amenable to AI automation due to ethical or high-stakes, more than feasibility, considerations -- such as judges or surgeons -- present lower AISE scores. By focusing on venture-backed AI applications, our approach offers a nuanced perspective on how AI is reshaping the labour market. It challenges the conventional assumption that high-skilled jobs uniformly face high AI risks, highlighting instead the role of today's AI players' societal desirability-driven and market-oriented choices as critical determinants of AI exposure. Contrary to fears of widespread job displacement, our findings suggest that AI adoption will be gradual and shaped by social factors as much as by the technical feasibility of AI applications. This framework provides a dynamic, forward-looking tool for policymakers and stakeholders to monitor AI's evolving impact and navigate the changing labour landscape.

econ.GN↗

arXiv2024

Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms

We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn-Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both converge to the same fixed-point solution up to normalization. The discovered connection allows us to derive a rigorous interpretation of the Fitness and the Complexity metrics as the potentials of a suitable energy function. Under this interpretation, high-energy products are unfeasible for low-fitness countries, which explains why the algorithm is effective at displaying nested patterns in bipartite networks. We also show that the proposed interpretation reveals the scale invariance of the Fitness-Complexity algorithm, which has practical implications for the algorithm's implementation in different datasets. Further, analysis of empirical trade data under the new perspective reveals three categories of countries that might benefit from different development strategies.

econ.GN↗

arXiv2024

Economic complexity and the sustainability transition: A review of data, methods, and literature

Economic Complexity (EC) methods have gained increasing popularity across fields and disciplines. In particular, the EC toolbox has proved particularly promising in the study of complex and interrelated phenomena, such as the transition towards a greener economy. Using the EC approach, scholars have been investigating the relationship between EC and sustainability, proposing to identify the distinguishing characteristics of green products and to assess the readiness of productive and technological structures for the sustainability transition. This article proposes to review and summarize the data, methods, and empirical literature that are relevant to the study of the sustainability transition from an EC perspective. We review three distinct but connected blocks of literature on EC and environmental sustainability. First, we survey the evidence linking measures of EC to indicators related to environmental sustainability. Second, we review articles that strive to assess the green competitiveness of productive systems. Third, we examine evidence on green technological development and its connection to non-green knowledge bases. Finally, we summarize the findings for each block and identify avenues for further research in this recent and growing body of empirical literature.

econ.GN↗

arXiv2023

Ranking species in complex ecosystems through nestedness maximization

Identifying the rank of species in a social or ecological network is a difficult task, since the rank of each species is invariably determined by complex interactions stipulated with other species. Simply put, the rank of a species is a function of the ranks of all other species through the adjacency matrix of the network. A common system of ranking is to order species in such a way that their neighbours form maximally nested sets, a problem called nested maximization problem (NMP). Here we show that the NMP can be formulated as an instance of the Quadratic Assignment Problem, one of the most important combinatorial optimization problem widely studied in computer science, economics, and operations research. We tackle the problem by Statistical Physics techniques: we derive a set of self-consistent nonlinear equations whose fixed point represents the optimal rankings of species in an arbitrary bipartite mutualistic network, which generalize the Fitness-Complexity equations widely used in the field of economic complexity. Furthermore, we present an efficient algorithm to solve the NMP that outperforms state-of-the-art network-based metrics and genetic algorithms. Eventually, our theoretical framework may be easily generalized to study the relationship between ranking and network structure beyond pairwise interactions, e.g. in higher-order networks.

cond-mat.stat-mech↗

arXiv2023

Inferring comparative advantage via entropy maximization

We revise the procedure proposed by Balassa to infer comparative advantage, which is a standard tool, in Economics, to analyze specialization (of countries, regions, etc.). Balassa's approach compares the export of a product for each country with what would be expected from a benchmark based on the total volumes of countries and products flows. Based on results in the literature, we show that the implementation of Balassa's idea generates a bias: the prescription of the maximum likelihood used to calculate the parameters of the benchmark model conflicts with the model's definition. Moreover, Balassa's approach does not implement any statistical validation. Hence, we propose an alternative procedure to overcome such a limitation, based upon the framework of entropy maximisation and implementing a proper test of hypothesis: the `key products' of a country are, now, the ones whose production is significantly larger than expected, under a null-model constraining the same amount of information employed by Balassa's approach. What we found is that countries diversification is always observed, regardless of the strictness of the validation procedure. Besides, the ranking of countries' fitness is only partially affected by the details of the validation scheme employed for the analysis while large differences are found to affect the rankings of products Complexities. The routine for implementing the entropy-based filtering procedures employed here is freely available through the official Python Package Index PyPI.

cs.SI↗

arXiv2022

The Evolution of Competitiveness across Economic, Innovation and Knowledge production activities

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.

econ.GN↗

arXiv2021

Geography of Science: Competitiveness and Inequality

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.

cs.DL↗

arXiv2021

Universal Database for Economic Complexity

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.

econ.GN↗

arXiv2021

Landau kinetic equation for dry aligning active models

The Landau equation is a kinetic equation based on the weak coupling approximation of the interaction between the particles. In the framework of dry active matter this new kinetic equation relies on the weak coupling approximation of both the alignment strength and the magnitude of the angular noise, instead of the hypothesis of diluteness. Therefore, it is a kinetic equation bridging between the Boltzmann [3], and the Smoluchowski [2] approximations, and allowing analytical descriptions at moderate densities. The form of the equation presents non-linear and density dependent diffusions and advections fully derived by the microscopic equations of motions. Finally, implementing the BGL procedure [25], the parameters of the Toner-Tu equations are derived showing the appearance of linearly stable homogeneous ordered solutions and mimicking the results obtained from the Boltzmann approach.

cond-mat.soft↗

arXiv2020

Generalized Markov stability of network communities

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.

physics.soc-ph↗

arXiv2019

Understanding dense active nematics from microscopic models

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to ``arch'' solutions forming a globally polar, smectic arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.

cond-mat.soft↗

arXiv2018

Deriving hydrodynamic equations from dry active matter models in three dimensions

We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a Boltzmann equation expressed in terms of an expansion in spherical harmonics. All their transport coefficients are given with explicit dependences on particle-level parameters. The linear stability analysis of their spatially-homogeneous solutions is presented. While the equations derived for the polar case (original Vicsek model with ferromagnetic alignment) and their solutions do not differ much from their 2D counterparts, the active nematics case exhibits remarkable differences: we find a true discontinuous transition to order with a bistability region, and cholesteric solutions whose stability we discuss.

cond-mat.soft↗