arXiv subjects

Gerardo Iñiguez

Publications and source records attributed to Gerardo Iñiguez.

At least 19 recordsLinked to original sources

arXiv2026

How large should academic departments be?

Academic departments are the primary unit of scholarship and education at universities, and they vary vastly in their sizes. However, the consequences and natural dynamics of department size are poorly understood. Small departments face disproportionate teaching and administrative overhead per faculty member, while large ones face coordination costs and thematic incoherence. Here, we characterize and model the dynamics of academic department sizes using $14,000$ U.S.-based departments in eight academic domains. Across all domains, similar broad-tailed distributions reveal a common size range from 4 to 23 faculty members, widening across domains at its upper border. Annual size-dependent closure risks and growth rates indicate that stability is greatest in this size range: below it, small departments either close or grow quickly; within it, closure risk is low and sizes stabilize; above it, large departments can persist, with marginal attrition and minimal closure risk. An analytically tractable model of size-dependent coagulation and fragmentation, informed only by the aggregated size distribution, reproduces department dynamics across the full size range. Rescaling each domain by its most stable size reveals a common regression toward the stable range across most domains. Our results establish academic departments as organizations with natural size dynamics defined by a grow-or-close pattern for the smallest departments, and a weak pressure against unlimited growth for the largest.

physics.soc-ph↗

arXiv2026

Statistical inference of dynamical processes on networks

Mechanisms of interaction in spreading models are central to our quantitative understanding of networked contagion processes, from disease transmission to opinion dynamics. Yet, while empirical data can reveal who interacts with whom, they rarely provide direct information about how interactions drive spreading, leaving the underlying mechanism to be inferred from observed dynamics, and selected among competing hypotheses. We propose a general framework for model selection in binary-state spreading processes on networks and show that asymptotic approximations in the thermodynamic limit can accurately predict inference outcomes in finite systems. By systematically exploring a broad parameter space, we characterize the detectability of six archetypal spreading mechanisms commonly used in the literature and find that accuracy generally increases in sparse networks, which are prevalent in real-world systems, and near phase transitions, such as the epidemic threshold of simple contagion processes. We further assess the prevalence of these mechanisms across a diverse set of empirical datasets, highlighting the impact of data preprocessing on model recovery. Our results show that statistical model selection can fail under common conditions and suggest new directions for overcoming these limitations.

physics.soc-ph↗

arXiv2026

Preferentiality and bandwidth drive tie activity in online and offline ego networks

Ego networks capture the variety of structural patterns in the social interactions of individuals. Recently it has been shown that ego networks in online settings display universal patterns of tie strength distributions, but it is unclear how constraints such as spatial proximity and bounded social bandwidth affect such generic behaviour in offline settings. Here, we analyse the time evolution of interaction activity in ego networks constructed from offline face-to-face and colocation data, compare them to online communication networks, and explore simple cumulative advantage models that capture the varying preferentiality of individuals for specific social ties. We find that patterns of preferentiality at the population level are similar for online and face-to-face networks, but not for colocation data, suggesting that the latter is a poor proxy of social network structure. We also provide evidence that empirical ego networks exhibit a bandwidth in the way communication events are allocated across connections. A model implementing this notion uncovers evidence of universal scaling between the tie preferentiality and bandwidth of individuals, common to all online and offline systems explored. Our findings strengthen our understanding of the fundamental mechanisms governing human communication and help disentangle the internal and external factors shaping tie evolution across social contexts.

physics.soc-ph↗

arXiv2026

Opinion dynamics: Statistical physics and beyond

Opinion dynamics, the study of how individual beliefs and collective public opinion evolve, is a fertile domain for applying statistical physics to complex social phenomena. Like physical systems, societies exhibit macroscopic regularities from localized interactions, leading to outcomes such as consensus or fragmentation. This field has grown significantly, attracting interdisciplinary methods and driven by a surge in large-scale behavioral data. This review covers its rapid progress, bridging the literature dispersion. We begin with essential concepts and definitions, encompassing the nature of opinions, microscopic and macroscopic dynamics. This foundation leads to an overview of empirical research, from lab experiments to large-scale data analysis, which informs and validates models of opinion dynamics. We then present individual-based models, categorized by their macroscopic phenomena (e.g., consensus, polarization, echo chambers) and microscopic mechanisms (e.g., homophily, assimilation). Furthermore, the review covers common analytical and computational tools, including stochastic processes, treatments, simulations, and optimization. Finally, we explore emerging frontiers, such as connecting empirical data to models and using AI agents as testbeds for novel social phenomena. By systematizing terminology and emphasizing analogies with traditional physics, this review aims to consolidate knowledge, provide a robust theoretical foundation, and shape future research in opinion dynamics.

physics.soc-ph↗

arXiv2026

To trace or not to trace: analytical insights from network-based contact-tracing models

Contact tracing is one of the most important control measures deployed during epidemics. Relying on the identification of contacts of known infected individuals, it necessitates a network perspective. Although pairwise models have been used extensively to study contact tracing, their analysis typically depends on a decoupling assumption-most commonly that contact tracing operates on a much faster timescale than disease transmission. Furthermore, contact tracing models often assume that all infected individuals become contact tracing-triggering, which is unrealistic given partial compliance to treatment. We relax both of these restrictive assumptions and provide a full analytical characterisation of the epidemic threshold in the pairwise mean-field model. Our analysis uses a fast-variables approach that captures the rapid early stabilisation of key network quantities. Inspired by mechanisms from social adoption dynamics, we introduce triplewise contact tracing in which an infected individual can be traced not only through direct contact with a single tracing-triggering neighbor (pairwise tracing), but also indirectly when connected to two tracing-triggering nodes simultaneously. For pure pairwise and pure triplewise contact tracing, we derive analytical expressions for critical contact tracing levels and demonstrate that when many infected individuals bypass treatment, the epidemic can become uncontrollable. When both contact tracing mechanisms operate together, we map out their combined contribution and relative impact on epidemic control. This unified framework yields rigorous and tractable threshold conditions for contact tracing dynamics on networks, extending the applicability of pairwise models beyond the fast-tracing regime and providing new insight into the interplay between disease progression, partial treatment compliance, and higher-order tracing processes.

physics.soc-ph↗

arXiv2025

Ranking dynamics in movies and music

Ranking systems are widely used to simplify and interpret complex data across diverse domains, from economic indicators and sports scores to online content popularity. While previous studies including the Zipf's law have focused on the static, aggregated properties of ranks, in recent years researchers have begun to uncover generic features in their temporal dynamics. In this work, we introduce and study a series of system-level indices that quantify the compositional changes in ranking lists over time, and also characterize the temporal ranking trajectories of individual items' ranking dynamics. We apply our method to analyze ranking dynamics of movies from the over-the-top services, including Netflix, as well as that of music items in Spotify charts. We find that newly released movies or music items influence most the system-level compositional changes of ranking lists; the highest ranks of items are strongly correlated with their lifetimes in the lists more than their first and last ranks. Our findings offer a novel lens to understand collective ranking dynamics and provide a basis for comparing fluctuation patterns across various ordered systems.

physics.soc-ph↗

arXiv2024

Cumulative Advantage of Brokerage in Academia

Science is a collaborative endeavor in which "who collaborates with whom" profoundly influences scientists' career trajectories and success. Despite its relevance, little is known about how scholars facilitate new collaborations among their peers. In this study, we quantify brokerage in academia and study its effect on the careers of physicists worldwide. We find that early-career participation in brokerage increases later-stage involvement for all researchers, with increasing participation rates and greater career impact among more successful scientists. This cumulative advantage process suggests that brokerage contributes to the unequal distribution of success in academia. Surprisingly, this affects both women and men equally, despite women being more junior in all brokerage roles and lagging behind men's participation due to their late and slow arrival to physics. Because of its cumulative nature, promoting brokerage opportunities to early career scientists might help reduce the inequalities in academic success.

physics.soc-ph↗

arXiv2024

Disentangling degree and tie strength heterogeneity in egocentric social networks

The structure of personal networks reflects how we organise and maintain social relationships. The distribution of tie strengths in personal networks is heterogeneous, with a few close, emotionally intense relationships and a larger number of weaker ties. Recent results indicate this feature is universal across communication channels. Within this general pattern, there is a substantial and persistent inter-individual variation that is also similarly distributed among channels. The reason for the observed universality is yet unclear -- one possibility is that people's traits determine their personal network features on any channel. To address this hypothesis, we need to compare an individual's personal networks across channels, which is a non-trivial task: while we are interested in measuring the differences in tie strength heterogeneity, personal network size is also expected to vary a lot across channels. Therefore, for any measure that compares personal networks, one needs to understand the sensitivity with respect to network size. Here, we study different measures of personal network similarity and show that a recently introduced alter-preferentiality parameter and the Gini coefficient are equally suitable measures for tie strength heterogeneity, as they are fairly insensitive to differences in network size. With these measures, we show that the earlier observed individual-level persistence of personal network structure cannot be attributed to network size stability alone, but that the tie strength heterogeneity is persistent too. We also demonstrate the effectiveness of the two measures on multichannel data, where tie strength heterogeneity in personal networks is seen to moderately correlate for the same users across two communication channels (calls and text messages).

physics.soc-ph↗

arXiv2024

Assortative and preferential attachment lead to core-periphery networks

Core-periphery is a key feature of large-scale networks underlying a wide range of social, biological, and transportation phenomena. Despite its prevalence in empirical data, it is unclear whether this property is a consequence of more fundamental network evolution processes. While preferential attachment can create degree heterogeneity indistinguishable from core-periphery, it doesn't explain why specific groups of nodes gain dominance and become cores. We show that even small amounts of assortative attachment, e.g. homophily in social networks, can break this symmetry, and that the interplay of the two mechanisms leads to one of the groups emerging as a prominent core. A systematic analysis of the phase space of the proposed model reveals the levels of assortative and preferential attachment necessary for a group to become either core or periphery, depending on initial conditions. We find that relative group size is significant, with minority groups typically having a disadvantage on becoming the core for similar assortative attachment levels among groups. We also find that growing networks are less prone to develop core-periphery than dynamically evolving networks, and that these two network evolution mechanisms lead to different types of core-periphery structures. Analyzing five empirical networks, our findings suggest that core nodes are highly assortative, illustrating the potential of our model as a tool for designing and analyzing interventions on evolving networks.

physics.soc-ph↗

arXiv2024

Multidimensional political polarization in online social networks

Political polarization in online social platforms is a rapidly growing phenomenon worldwide. Despite their relevance to modern-day politics, the structure and dynamics of polarized states in digital spaces are still poorly understood. We analyze the community structure of a two-layer, interconnected network of French Twitter users, where one layer contains members of Parliament and the other one regular users. We obtain an optimal representation of the network in a four-dimensional political opinion space by combining network embedding methods and political survey data. We find structurally cohesive groups sharing common political attitudes and relate them to the political party landscape in France. The distribution of opinions of professional politicians is narrower than that of regular users, indicating the presence of more extreme attitudes in the general population. We find that politically extreme communities interact less with other groups as compared to more centrist groups. We apply an empirically tested social influence model to the two-layer network to pinpoint interaction mechanisms that can describe the political polarization seen in data, particularly for centrist groups. Our results shed light on the social behaviors that drive digital platforms towards polarization, and uncover an informative multidimensional space to assess political attitudes online.

physics.soc-ph↗

arXiv2023

Coordination-free Decentralised Federated Learning on Complex Networks: Overcoming Heterogeneity

Federated Learning (FL) is a well-known framework for successfully performing a learning task in an edge computing scenario where the devices involved have limited resources and incomplete data representation. The basic assumption of FL is that the devices communicate directly or indirectly with a parameter server that centrally coordinates the whole process, overcoming several challenges associated with it. However, in highly pervasive edge scenarios, the presence of a central controller that oversees the process cannot always be guaranteed, and the interactions (i.e., the connectivity graph) between devices might not be predetermined, resulting in a complex network structure. Moreover, the heterogeneity of data and devices further complicates the learning process. This poses new challenges from a learning standpoint that we address by proposing a communication-efficient Decentralised Federated Learning (DFL) algorithm able to cope with them. Our solution allows devices communicating only with their direct neighbours to train an accurate model, overcoming the heterogeneity induced by data and different training histories. Our results show that the resulting local models generalise better than those trained with competing approaches, and do so in a more communication-efficient way.

cs.LG↗

arXiv2023

Universal patterns in egocentric communication networks

Tie strengths in social networks are heterogeneous, with strong and weak ties playing different roles at both the network and the individual level. Egocentric networks, networks of relationships around a focal individual, exhibit a small number of strong ties and a larger number of weaker ties, a pattern that is evident in electronic communication records, such as mobile phone calls. Mobile phone data has also revealed persistent individual differences within this pattern. However, the generality and the driving mechanisms of this tie strength heterogeneity remain unclear. Here, we study tie strengths in egocentric networks across multiple datasets containing records of interactions between millions of people over time periods ranging from months to years. Our findings reveal a remarkable universality in the distribution of tie strengths and their individual-level variation across different modes of communication, even in channels that may not reflect offline social relationships. With the help of an analytically tractable model of egocentric network evolution, we show that the observed universality can be attributed to the competition between cumulative advantage and random choice, two general mechanisms of tie reinforcement whose balance determines the amount of heterogeneity in tie strengths. Our results provide new insights into the driving mechanisms of tie strength heterogeneity in social networks and have implications for the understanding of social network structure and individual behavior.

physics.soc-ph↗

arXiv2022

Opinion dynamics in social networks: From models to data

Opinions are an integral part of how we perceive the world and each other. They shape collective action, playing a role in democratic processes, the evolution of norms, and cultural change. For decades, researchers in the social and natural sciences have tried to describe how shifting individual perspectives and social exchange lead to archetypal states of public opinion like consensus and polarization. Here we review some of the many contributions to the field, focusing both on idealized models of opinion dynamics, and attempts at validating them with observational data and controlled sociological experiments. By further closing the gap between models and data, these efforts may help us understand how to face current challenges that require the agreement of large groups of people in complex scenarios, such as economic inequality, climate change, and the ongoing fracture of the sociopolitical landscape.

physics.soc-ph↗

arXiv2022

The effect of algorithmic bias and network structure on coexistence, consensus, and polarization of opinions

Individuals of modern societies share ideas and participate in collective processes within a pervasive, variable, and mostly hidden ecosystem of content filtering technologies that determine what information we see online. Despite the impact of these algorithms on daily life and society, little is known about their effect on information transfer and opinion formation. It is thus unclear to what extent algorithmic bias has a harmful influence on collective decision-making, such as a tendency to polarize debate. Here we introduce a general theoretical framework to systematically link models of opinion dynamics, social network structure, and content filtering. We showcase the flexibility of our framework by exploring a family of binary-state opinion dynamics models where information exchange lies in a spectrum from pairwise to group interactions. All models show an opinion polarization regime driven by algorithmic bias and modular network structure. The role of content filtering is, however, surprisingly nuanced; for pairwise interactions it leads to polarization, while for group interactions it promotes coexistence of opinions. This allows us to pinpoint which social interactions are robust against algorithmic bias, and which ones are susceptible to bias-enhanced opinion polarization. Our framework gives theoretical ground for the development of heuristics to tackle harmful effects of online bias, such as information bottlenecks, echo chambers, and opinion radicalization.

physics.soc-ph↗

arXiv2022

Temporal patterns of reciprocity in communication networks

Human communication, the essence of collective social phenomena ranging from small-scale organizations to worldwide online platforms, features intense reciprocal interactions between members in order to achieve stability, cohesion, and cooperation in social networks. While high levels of reciprocity are well known in aggregated communication data, temporal patterns of reciprocal information exchange have received far less attention. Here we propose measures of reciprocity based on the time ordering of interactions and explore them in data from multiple communication channels, including calls, messaging and social media. By separating each channel into reciprocal and non-reciprocal temporal networks, we find persistent trends that point to the distinct roles of one-on-one exchange versus information broadcast. We implement several null models of communication activity, which identify memory, a higher tendency to repeat interactions with past contacts, as a key source of reciprocity. When adding memory to a model of activity-driven, time-varying networks, we reproduce the levels of reciprocity seen in empirical data. Our work adds to the theoretical understanding of the emergence of reciprocity in human communication systems, hinting at the mechanisms behind the formation of norms in social exchange and large-scale cooperation.

physics.soc-ph↗

arXiv2022

Heterogeneity extends criticality

Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are considered homogeneous, criticality is restricted to phase transitions, leading either to robust (ordered) or adaptive (chaotic) phases in most of the parameter space. Many real-world complex systems, however, are not homogeneous. Some elements change in time faster than others, with slower elements (usually the most relevant) providing robustness, and faster ones being adaptive. Structural patterns of connectivity are also typically heterogeneous, characterized by few elements with many interactions and most elements with only a few. Here we take a few traditionally homogeneous dynamical models and explore their heterogeneous versions, finding evidence that heterogeneity extends criticality. Thus, parameter fine-tuning is not necessary to reach a phase transition and obtain the benefits of (homogeneous) criticality. Simply adding heterogeneity can extend criticality, making the search/evolution of complex systems faster and more reliable. Our results add theoretical support for the ubiquitous presence of heterogeneity in physical, social, and technological systems, as natural selection can exploit heterogeneity to evolve complexity "for free". In artificial systems and biological design, heterogeneity may also be used to extend the parameter range that allows for criticality.

cond-mat.stat-mech↗

arXiv2022

Dynamics of ranking

Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from socioeconomic policy to knowledge extraction. A century of research has found regularities when temporal rank data is aggregated. Far less is known, however, about how rankings change in time. Here we explore the dynamics of 30 rankings in natural, social, economic, and infrastructural systems, comprising millions of elements and timescales from minutes to centuries. We find that the flux of new elements determines the stability of a ranking: for high flux only the top of the list is stable, otherwise top and bottom are equally stable. We show that two basic mechanisms - displacement and replacement of elements - capture empirical ranking dynamics. The model uncovers two regimes of behavior; fast and large rank changes, or slow diffusion. Our results indicate that the balance between robustness and adaptability in ranked systems might be governed by simple random processes irrespective of system details.

physics.soc-ph↗

arXiv2021

Socioeconomic biases in urban mixing patterns of US metropolitan areas

Urban areas serve as melting pots of people with diverse socioeconomic backgrounds, who may not only be segregated but have characteristic mobility patterns in the city. While mobility is driven by individual needs and preferences, the specific choice of venues to visit is usually constrained by the socioeconomic status of people. The complex interplay between people and places they visit, given their personal attributes and homophily leaning, is a key mechanism behind the emergence of socioeconomic stratification patterns ultimately leading to urban segregation at large. Here we investigate mixing patterns of mobility in the twenty largest cities of the United States by coupling individual check-in data from the social location platform Foursquare with census information from the American Community Survey. We find strong signs of stratification indicating that people mostly visit places in their own socioeconomic class, occasionally visiting locations from higher classes. The intensity of this `upwards bias' increases with socioeconomic status and correlates with standard measures of racial residential segregation. Our results indicate an even stronger socioeconomic segregation in individual mobility than one would expect from system-level distributions, shedding further light on uneven mobility mixing patterns in cities.

physics.soc-ph↗