We study the growth spectrum of groups acting on hyperbolic spaces, i.e. the set of exponential growth rates achieved by subgroups. For a finitely generated free group or a surface group acting convex-cocompactly on a proper geodesic hyperbolic metric space, we prove that the growth spectrum is the full interval [0, ω_G]. For any hyperbolic group, we prove that the growth spectrum contains a large interval [0, ω_ℱ] where ω_ℱ≥ ω_G / 2, with strict inequality when the action is divergent. In the case of the Cayley graph of a free group, we also present an approach via the non-backtracking matrix of the configuration model, connecting the density of growth rates to a spectral concentration result for random graphs.
Traditional measures of urban accessibility often rely on static models or survey data. However, location information from mobile networks enables large-scale, dynamic analyses of how people navigate cities. In this study, we employ eXtended Detail Records (XDRs) from mobile phone activity to analyze commuting patterns and accessibility inequalities in Santiago, Chile. We identify residential and work locations and model commuting routes by public transport and walking using the R5 multimodal routing engine. Spatial patterns are examined using bivariate local indicators of spatial association (LISA) alongside regression techniques to identify distinct commuting behaviors and their alignment with vulnerable population groups. Our results show that while average public transport commuting times do not differ significantly across socioeconomic groups, marked inequalities emerge when accessibility is considered. High-income neighborhoods consistently exhibit high accessibility, whereas low-income areas show substantially lower levels. Importantly, these disparities do not translate into longer commuting times for lower-income groups, indicating a weak relationship between proximity to opportunities and observed travel times. The analysis also reveals significant disparities across sociodemographic groups, particularly in relation to Indigenous populations and gender. The proposed approach is readily scalable and can support evaluations of changes in commuting patterns and the impacts of urban interventions.
In this article, we study two important properties of ${\rm{sym}}^3$ transfers of the automorphic representation $\pi$ associated to a modular form. First we compute the conductor of ${\rm{sym}}^3(\pi)$. Then we detect the types of local automorphic representations at bad primes by the variation of the epsilon factors of symmetric cube transfer of the representation $\pi$ attached to a cusp form $f$. Here we twist the modular forms by a specific quadratic character. From this variation number, for each prime $p$, we classify all possible types of symmetric cube transfers of the local representations $\pi_p$. For ${\rm{sym}}^3$ transfer, the most difficult prime is $p=3$.
We initiate the study of matching roommates and rooms wherein the preferences of agents over other agents and rooms are complementary and represented by Leontief utilities. In this setting, 2n agents must be paired up and assigned to n rooms. Each agent has cardinal valuations over the rooms as well as compatibility values over all other agents. Under Leontief preferences, an agents utility for a matching is the minimum of the two values. We focus on the tradeoff between maximizing utilitarian social welfare and strategyproofness. Our main result shows that, in a stark contrast to the additive case, under binary Leontief utilities, there exist strategyproof mechanisms that maximize the social welfare. We further devise a strategyproof mechanism that implements such a welfare maximizing algorithm and is parameterized by the number of agents. Along the way, we highlight several possibility and impossibility results, and give upper bounds and lower bounds for welfare with or without strategyproofness.
Background: Advances in artificial intelligence have enabled the simulation of human-like behaviors, raising the possibility of using large language models (LLMs) to generate synthetic population samples for research purposes, which may be particularly useful in health and social sciences. Methods: This paper explores the potential of LLMs to simulate population samples mirroring real ones, as well as the feasibility of using personality questionnaires to assess the personality of LLMs. To advance in that direction, 2 experiments were conducted with GPT-4o using the Eysenck Personality Questionnaire Revised-Abbreviated (EPQR-A) in 6 languages: Spanish, English, Slovak, Hebrew, Portuguese, and Turkish. Results: We find that GPT-4o exhibits distinct personality traits, which vary based on parameter settings and the language of the questionnaire. While the model shows promising trends in reflecting certain personality traits and differences across gender and academic fields, discrepancies between the synthetic populations’ responses and those from real populations remain. Conclusions: These inconsistencies suggest that creating fully reliable synthetic population samples for questionnaire testing is still an open challenge. Further research is required to better align synthetic and real population behaviors.
