arXiv subjects

Alexander J. Gates

Publications and source records attributed to Alexander J. Gates.

10 recordsLinked to original sources

arXiv2026

Finite-Resolution Information from Collision Statistics

Collision statistics provide a finite-resolution view of information by measuring how often a fixed number of independent samples fall on the same state. These directly countable quantities form the basis of integer-order R\'enyi entropies. Here, we use low-order R\'enyi entropies to approximate Shannon entropy and mutual information, while characterizing what is necessarily lost when only finitely many collision moments are used. We derive interpolation-error bounds showing that approximation error is controlled by the shape of the R\'enyi entropy path near the Shannon point. We also separate this deterministic error from finite-sample estimation error: for fixed collision order, increasing sample size improves estimation of the finite-resolution target but does not eliminate its deterministic difference from Shannon entropy or mutual information. Finally, we show that finite collision moments do not generally identify Shannon entropy, and that increasing collision order shifts sensitivity toward high-probability events. Numerical experiments illustrate the approximation--estimation tradeoff and compare collision-based approximations with plug-in and Miller--Madow estimators. The framework links collision counts, R\'enyi entropy, Shannon limits, and mutual information through a finite-resolution view of information, clarifying when low-order coincidence structure is informative and when irreducible information is lost.

cs.IT↗

arXiv2025

Unifying Information-Theoretic and Pair-Counting Clustering Similarity

Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic, reflecting whether they quantify agreement through element pairs or aggregate information across full cluster contingency tables. Prior work has uncovered parallels between these families and applied empirical normalization or chance-correction schemes, but their deeper analytical connection remains only partially understood. Here, we develop an analytical framework that unifies these families through two complementary perspectives. First, both families are expressed as weighted expansions of observed versus expected co-occurrences, with pair-counting arising as a quadratic, low-order approximation and information-theoretic measures as higher-order, frequency-weighted extensions. Second, we generalize pair-counting to k-tuple agreement and show that information-theoretic measures can be viewed as systematically accumulating higher-order co-assignment structure beyond the pairwise level. We illustrate the approaches analytically for the Rand index and Mutual Information, and show how other indices in each family emerge as natural extensions. Together, these views clarify when and why the two regimes diverge, relating their sensitivities directly to weighting and approximation order, and provide a principled basis for selecting, interpreting, and extending clustering similarity measures across applications.

stat.ML↗

arXiv2025

Quantifying Institutional Gender Inequality in Contemporary Visual Art

From disparities in the number of exhibiting artists to auction opportunities, there is evidence of women's under-representation in visual art. Here we explore the exhibition history and auction sales of 65,768 contemporary artists in 20,389 institutions, revealing gender differences in the artist population, exhibitions and auctions. We distinguish between two criteria for gender equity: gender-neutrality, when artists have gender-independent access to exhibition opportunities, and gender-balanced, that strives for gender parity in representation, finding that 58\% of institutions are gender-neutral but only 24\% are gender-balanced, and that the fraction of man-overrepresented institutions increases with institutional prestige. We define artist's co-exhibition gender to capture the gender inequality of the institutions that an artist exhibits. Finally, we use logistic regression to predict an artist's access to the auction market, finding that co-exhibition gender has a stronger correlation with success than the artist's gender. These results help unveil and quantify the institutional forces that relate to the persistent gender imbalance in the art world.

cs.SI↗

arXiv2025

The increasing fragmentation of global science limits the diffusion of ideas

Global science is often portrayed as a unified system of shared knowledge and open exchange. Yet this vision contrasts with emerging evidence that scientific recognition is uneven and increasingly fragmented along regional and cultural lines. Traditional models emphasize Western dominance in knowledge production but overlook regional dynamics, reinforcing a core-periphery narrative that sustains disparities and marginalizes less prominent countries. In this study, we introduce a rank-based signed measure of national citation preferences, enabling the construction of a global recognition network that distinguishes over- and under-recognition between countries. Using a multinomial logistic link prediction model, we assess how economic, cultural, and scientific variables shape the presence and direction of national citation preferences. We uncover a global structure composed of multiple scientific communities, characterized by strong internal citation preferences and negative preferences between them-revealing growing fragmentation in the international scientific system. A separate weighted logistic regression framework suggests that this network significantly influences the international diffusion of scientific ideas, even after controlling for common covariates. Together, these findings highlight the structural barriers to equitable recognition and underscore the importance of scientific community membership in shaping influence, offering valuable insights for policymakers aiming to foster inclusive and impactful global science.

cs.SI↗

arXiv2022

Mapping Philanthropic Support of Science

While philanthropic support for science has increased in the past decade, there is limited quantitative knowledge about the patterns that characterize it and the mechanisms that drive its distribution. Here, we map philanthropic funding to universities and research institutions based on IRS tax forms from 685,397 non-profit organizations. We identify nearly one million grants supporting institutions involved in science and higher education, finding that in volume and scope, philanthropic funding has grown to become comparable to federal research funding. Yet, distinct from government support, philanthropic funders tend to focus locally, indicating that criteria beyond research excellence play an important role in funding decisions. We also show evidence of persistence, i.e., once a grant-giving relationship begins, it tends to continue in time. Finally, we leverage the bipartite network of supporters and recipients to help us demonstrate the predictive power of the underlying network in foreseeing future funder-recipient relationships. The developed toolset could offer funding recommendations to organizations and help funders diversify their portfolio. We discuss the policy implications of our findings for philanthropic funders, individual researchers, and quantitative understanding of philanthropy.

physics.soc-ph↗

arXiv2019

Historical comparison of gender inequality in scientific careers across countries and disciplines

There is extensive, yet fragmented, evidence of gender differences in academia suggesting that women are under-represented in most scientific disciplines, publish fewer articles throughout a career, and their work acquires fewer citations. Here, we offer a comprehensive picture of longitudinal gender discrepancies in performance through a bibliometric analysis of academic careers by reconstructing the complete publication history of over 1.5 million gender-identified authors whose publishing career ended between 1955 and 2010, covering 83 countries and 13 disciplines. We find that, paradoxically, the increase of participation of women in science over the past 60 years was accompanied by an increase of gender differences in both productivity and impact. Most surprisingly though, we uncover two gender invariants, finding that men and women publish at a comparable annual rate and have equivalent career-wise impact for the same size body of work. Finally, we demonstrate that differences in dropout rates and career length explain a large portion of the reported career-wise differences in productivity and impact. This comprehensive picture of gender inequality in academia can help rephrase the conversation around the sustainability of women's careers in academia, with important consequences for institutions and policy makers.

cs.DL↗

arXiv2019

Element-centric clustering comparison unifies overlaps and hierarchy

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science.

stat.ML↗

arXiv2018

CANA: A python package for quantifying control and canalization in Boolean Networks

Logical models offer a simple but powerful means to understand the complex dynamics of biochemical regulation, without the need to estimate kinetic parameters. However, even simple automata components can lead to collective dynamics that are computationally intractable when aggregated into networks. In previous work we demonstrated that automata network models of biochemical regulation are highly canalizing, whereby many variable states and their groupings are redundant (Marques-Pita and Rocha, 2013). The precise charting and measurement of such canalization simplifies these models, making even very large networks amenable to analysis. Moreover, canalization plays an important role in the control, robustness, modularity and criticality of Boolean network dynamics, especially those used to model biochemical regulation (Gates and Rocha, 2016; Gates et al., 2016; Manicka, 2017). Here we describe a new publicly-available Python package that provides the necessary tools to extract, measure, and visualize canalizing redundancy present in Boolean network models. It extracts the pathways most effective in controlling dynamics in these models, including their effective graph and dynamics canalizing map, as well as other tools to uncover minimum sets of control variables.

cs.OH↗

arXiv2015

Modularity and the spread of perturbations in complex dynamical systems

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the 'Markov stability' method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., 'relevance networks' or 'functional networks'). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously-coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.

physics.soc-ph↗

arXiv2015

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.

q-bio.MN↗