Elsa Andres, Romualdo Pastor-Satorras, Michele Starnini, and Márton Karsai

Phys. Rev. Research 7, 043088

Behavioral adoptions of individuals are influenced by their peers in different ways. While in some cases an individual may change behavior after a single incoming influence, in other cases multiple cumulated attempts of social influence are necessary for the same outcome. These two mechanisms, known as simple and complex contagion, often occur together in social contagion phenomena, yet their distinguishability based on the observable contagion dynamics is challenging. In this paper we define a social contagion model evolving on temporal networks where individuals can switch between contagion mechanisms. We explore three spreading scenarios: predominated by simple or complex contagion, or where the dominant mechanism changes during the unfolding process. We propose analytical and numerical methods relying on global spreading observables to identify which of these three scenarios characterizes a social spreading outbreak. This work offers insights into social contagion dynamics on temporal networks, without assuming prior knowledge about the contagion mechanism driving the adoptions of individuals.

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Fernando Diaz-Diaz, Elena Candellone, Miguel A. Gonzalez-Casado, Emma Fraxanet, Antoine Vendeville, Irene Ferri, Andreia Sofia Teixeira

Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This polarity reshapes how we think about structure and dynamics in complex systems: a negative tie is not simply a missing positive one but a constraint that generates tension, and possibly asymmetry. Across disciplines, from sociology to neuroscience and machine learning, signed networks provide a shared language to formalise duality, balance, and opposition as integral components of system behaviour. This review provides a comprehensive and foundational summary of signed network theory. It formalises the mathematical principles of signed graphs and surveys signed-network-specific measures, including signed degree distributions, clustering, centralities, motifs, and Laplacians. It revisits balance theory, tracing its cognitive and structural formulations and their connections to frustration. Structural aspects of signed networks are examined, analysing key topics such as null models, node embeddings, sign prediction, and community detection. Subsequent sections address dynamical processes on and of signed networks, such as opinion dynamics, contagion models, and data-driven approaches for studying evolving networks. Practical challenges in constructing, inferring and validating signed data from real-world systems are also highlighted, and we offer an overview of currently available datasets. We also address common pitfalls and challenges that arise when modelling or analysing signed data. Overall, this review integrates theoretical foundations, methodological approaches, and cross-domain examples, providing a structured entry point and a reference framework for researchers interested in the study of signed networks in complex systems.

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Paola Di Maio

Artificial Intelligence and Digital Forensics

The intersection of artificial intelligence (AI) and digital forensics (DF) is becoming increasingly complex, ubiquitous, and pervasive, with overlapping techniques and technologies being adopted in all types of scientific and technical inquiry. Despite incredible advances, forensic sciences are not exempt from errors and remain vulnerable to fallibility. To mitigate the limitations of errors in DF, the systemic complexity is identified and addressed with the adoption of human-readable artifacts and open standards. A DF AI model schema based on the state of the art is outlined.

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Luiz H. A. Monteiro

Complexities 2025, 1(1), 2

Defining a complex system and evaluating its complexity typically requires an interdisciplinary approach, integrating information theory, signal processing techniques, principles of dynamical systems, algorithm length analysis, and network science. This overview presents the main characteristics of complex systems and outlines several metrics commonly used to quantify their complexity. Simple examples are provided to illustrate the key concepts. Speculative ideas regarding these topics are also discussed here.

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