Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an element. However, novelties can also be generated by combining what is already known. We hence define higher-order novelties as the first time two or more elements appear together, and we introduce higher-order Heaps’ exponents as a way to characterize their pace of discovery. Through extensive analysis of real-world data, we find that processes with the same pace of discovery, as measured by the standard Heaps’ exponent, can instead differ at higher orders. We then propose to model an exploration process as a random walk on a network in which the possible connections between elements evolve in time. The model reproduces the empirical properties of higher-order novelties, revealing how the network we explore changes over time along with the exploration process.

A central role in shaping the experience of users online is played by recommendation algorithms. On the one hand they help retrieving content that best suits users taste, but on the other hand they may give rise to the so-called “filter bubble” effect, favoring the rise of polarization. In the present paper we study how a user-user collaborative-filtering algorithm affects the behavior of a group of agents repeatedly exposed to it. By means of analytical and numerical techniques we show how the system stationary state depends on the strength of the similarity and popularity biases, quantifying respectively the weight given to the most similar users and to the best rated items. In particular, we derive a phase diagram of the model, where we observe three distinct phases: disorder, consensus, and polarization. In the last users spontaneously split into different groups, each focused on a single item. We identify, at the boundary between the disorder and polarization phases, a region where recommendations are nontrivially personalized without leading to filter bubbles. Finally, we show that our model well reproduces the behavior of users on the online music platform last.fm. This analysis paves the way to a systematic analysis of recommendation algorithms by means of statistical physics methods and opens the possibility of devising less polarizing recommendation algorithms.

As often happens in science, tools, and methods originally developed in one field can unexpectedly become useful in others. This paper explores the formalism of Economic Fitness Complexity (EFC), initially designed to predict and explain the economic trajectories of countries, cities, and regions, which has also proven applicable in diverse contexts such as ecology and chess openings. The success of EFC is attributed to its ability to indirectly assess hidden capabilities within a system. However, existing EFC algorithms are constrained to bipartite graphs, becoming inapplicable even with minor deviations in the bipartite structure. This paper introduces an extension of EFC and its cousin Economic Complexity Index that applies to any graph, thereby overcoming the bipartite constraint. This extension introduces fitness centrality, a novel centrality measure that can be used for assessing node vulnerability. By broadening the scope of economic complexity analysis to diverse network structures, this work expands the applicability and robustness of EFC in complexity science.

Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The urn model with triggering (UMT) has been instrumental in modeling these innovation dynamics. Yet a generalization is needed to capture the richer empirical phenomenology. Here we introduce a time-dependent urn model with triggering (TUMT), a generalization of the UMT that crucially integrates time-dependent parameters for reinforcement and triggering to offer a broader framework for modeling innovation in nonstationary systems. Through analytical computation and numerical simulations, we show that the TUMT reconciles various behaviors observed in a broad spectrum of systems from patenting activity to the analysis of gene mutations. We highlight how the TUMT features a “critical” region where both Heaps' and Zipf's laws coexist, for which we compute the exponents. Published by the American Physical Society 2025

Economic complexity algorithms aim to uncover the hidden capabilities that drive economic systems. Here we present a fundamental reinterpretation of two of these algorithms, the economic complexity index (ECI) and the economic fitness and complexity (EFC), by reformulating them as optimization problems that minimize specific cost functions. We show that ECI computation is equivalent to finding eigenvectors of the network's transition matrix by minimizing the quadratic form associated with the network's Laplacian. For EFC, we derive a novel cost function that exploits the algorithm's intrinsic logarithmic structure and clarifies the role of the regularization parameter in its nonhomogeneous version. Additionally, we establish the existence and uniqueness of its solution, providing theoretical foundations for its application. This optimization-based reformulation bridges economic complexity and established frameworks in spectral theory, network science, and optimization. The theoretical insights translate into practical computational advantages: We introduce a conservative, gradient-based update rule that substantially accelerates algorithmic convergence, with potential implications for a broader class of algorithms, including the Sinkhorn-Knopp method. Finally, we apply the energetic framework to a real-world trade network, demonstrating how linkwise energy provides a direct way to identify structurally relevant and vulnerable regions of the export matrix, thus complementing and enriching standard economic complexity analyses. Beyond advancing our theoretical understanding of economic complexity indicators, this work opens new pathways for algorithmic improvements and extends applicability to general network structures beyond traditional bipartite economic networks.

As AI agents increasingly operate in multi-agent settings, alongside other models and humans, understanding how they respond to the opinions they find in their prompt becomes critical for predicting the outcome of these interactions. This study examines conformity-like behavior, the tendency to align with group opinions, in large multimodal language models functioning as AI agents. By adapting classic visual experiments from social psychology, we investigate how these agents respond to social signals in the prompt. Our experiments reveal that AI agents exhibit a systematic conformity bias consistent with Social Impact Theory. Their responses vary with majority size, group unanimity, task difficulty, and source characteristics, including perceived authority and shared group membership. Critically, AI agents achieving near-perfect performance in isolation become highly susceptible to manipulation through social influence. This vulnerability persists across model scales: while larger models show reduced conformity bias on simple tasks, they remain vulnerable when the task is difficult. These findings reveal security vulnerabilities in AI agent decision-making that could enable malicious manipulation, misinformation campaigns, and bias propagation in interactions with other models and with humans, highlighting the urgent need for safeguards in AI deployments.