Scientific attention is unevenly distributed, creating inequities in recognition and distorting access to opportunities. Using citations as a proxy, we quantify disparities in attention by gender and institutional prestige. We find that women receive systematically fewer citations than men, and that attention is increasingly concentrated among authors from elite institutions -- patterns not fully explained by underrepresentation alone. To explain these dynamics, we introduce a model of citation network growth that incorporates homophily (tendency to cite similar authors), preferential attachment (favoring highly cited authors) and group size (underrepresentation). The model shows that disparities arise not only from group size imbalances but also from cumulative advantage amplifying biased citation preferences. Importantly, increasing representation alone is often insufficient to reduce disparities. Effective strategies should also include reducing homophily, amplifying the visibility of underrepresented groups, and supporting equitable integration of newcomers. Our findings highlight the challenges of mitigating inequities in asymmetric networks like citations, where recognition flows in one direction. By making visible the mechanisms through which attention is distributed, we contribute to efforts toward a more responsible web of science that is fairer, more transparent, and more inclusive, and that better sustains innovation and knowledge production.

Humans and large language models (LLMs) now co-produce and co-consume the web's shared knowledge archives. Such human-AI collective knowledge ecosystems contain feedback loops with both benefits (e.g., faster growth, easier learning) and systemic risks (e.g., quality dilution, skill reduction, model collapse). To understand such phenomena, we propose a minimal, interpretable dynamical model of the co-evolution of archive size, archive quality, model (LLM) skill, aggregate human skill, and query volume. The model captures two content inflows (human, LLM) controlled by a gate on LLM-content admissions, two learning pathways for humans (archive study vs. LLM assistance), and two LLM-training modalities (corpus-driven scaling vs. learning from human feedback). Through numerical experiments, we identify different growth regimes (e.g., healthy growth, inverted flow, inverted learning, oscillations), and show how platform and policy levers (gate strictness, LLM training, human learning pathways) shift the system across regime boundaries. Two domain configurations (PubMed, GitHub and Copilot) illustrate contrasting steady states under different growth rates and moderation norms. We also fit the model to Wikipedia's knowledge flow during pre-ChatGPT and post-ChatGPT eras separately. We find a rise in LLM additions with a concurrent decline in human inflow, consistent with a regime identified by the model. Our model and analysis yield actionable insights for sustainable growth of human-AI collective knowledge on the Web.

Affective polarization, the emotional divide between ideological groups marked by in-group love and out-group hate, has intensified in the United States, driving contentious issues like masking and lockdowns during the COVID-19 pandemic. Despite its societal impact, existing models of opinion change fail to account for emotional dynamics nor offer methods to quantify affective polarization robustly and in real-time. In this paper, we introduce a discrete choice model that captures decision-making within affectively polarized social networks and propose a statistical inference method estimate key parameters---in-group love and out-group hate---from social media data. Through empirical validation from online discussions about the COVID-19 pandemic, we demonstrate that our approach accurately captures real-world polarization dynamics and explains the rapid emergence of a partisan gap in attitudes towards masking and lockdowns. This framework allows for tracking affective polarization across contentious issues has broad implications for fostering constructive online dialogues in digital spaces.

This article introduces a novel mutual information-based measure to assess the glass ceiling effect in preferential attachment networks, which advances the analysis of inequalities in attributed networks. Using Shannon entropy and generalizing to Rényi entropy, our measure evaluates the conditional probability distributions of node attributes given the node degrees of adjacent nodes, which offers a more nuanced understanding of inequality compared to traditional methods that emphasize node degree distributions and degree assortativity alone. To evaluate the efficacy of the proposed measure, we evaluate it using an analytical structural inequality model as well as historical publication data. Results show that our mutual information measure aligns well with both the theoretical model and empirical data, underscoring its reliability as a robust approach for capturing inequalities in attributed networks. Moreover, we introduce a novel stochastic optimization algorithm that utilizes a parameterized conditional logit model for edge addition. Our algorithm is shown to outperform the baseline uniform distribution based approach in mitigating the glass ceiling effect. By strategically recommending links based on this algorithm, we can effectively hinder the glass ceiling effect within networks.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti’s Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

This article deals with the modeling and estimation of the sociological phenomena called echo chambers and segregation in social networks. Specifically, we present a novel community-based graph model that represents the emergence of segregated echo chambers as a Markov bridge (MB) process. An MB is a 1-D Markov random field that facilitates modeling the formation and disassociation of communities at deterministic times, which is important in social networks with known timed events. We justify the proposed model with real-world examples and examine its performance on a recent Twitter dataset. We provide a model parameter estimation algorithm based on maximum likelihood and a Bayesian filtering algorithm for recursively estimating the level of segregation using noisy samples obtained from the network. Numerical results indicate that the proposed filtering algorithm outperforms the conventional hidden Markov modeling in terms of the mean-squared error. The proposed filtering method is useful in computational social science where data-driven estimation of the level of segregation from noisy data is required.

This paper deals with the modeling and estimation of the sociological phenomena called segregation in social networks. Specifically, we present a novel community-based graph model that represent segregation as a Markov bridge process. A Markov bridge is a one-dimensional Markov random field that facilitates modeling the formation and disassociation of communities at deterministic times which is important in social networks with known timed events. Based on the proposed model, we provide Bayesian filtering algorithms for recursively estimating the level of segregation using noisy samples obtained from the graph. Numerical results indicate that the proposed filtering algorithm outperforms the conventional hidden Markov modeling in terms of the mean-squared error. The proposed filtering method is useful in computational social science where data-driven estimation of the level of segregation from noisy data is required.

This article considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g., linear regression on double-logarithmic axes and maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution. As a solution, we present a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution. We analytically show that the proposed method results in a smaller bias, variance and a Cramèr–Rao lower bound compared to the vanilla maximum likelihood estimate obtained with uniformly sampled nodes (which is the most commonly used method in literature). Detailed numerical and empirical results are presented to illustrate the performance of the proposed method under different conditions and how it compares with alternative methods. We also show that the proposed method and its desirable properties (i.e., smaller bias, variance, and Cramèr–Rao lower bound compared to vanilla method based on uniform samples) extend to parametric degree distributions other than the power-law such as exponential degree distributions as well. All the numerical and empirical results are reproducible and the code is publicly available on Github.

This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose two NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph, and (ii) the social network graph is unknown but, uniformly sampled nodes from the network are available. For both cases, algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.