Equitable access to essential urban services is a pillar of modern planning, yet most accessibility models rely strictly on static residential locations, ignoring how demand shifts throughout the daily loop. This study introduces a population-based, temporally differentiated framework to examine the resulting "moving target" of urban equity, focusing on medical facilities and green spaces in Hefei, China. Utilising large-scale mobile phone GPS data, we construct dynamic residential and workplace population exposure surfaces to capture shifting hourly demand. We then evaluate accessibility via network-based travel times paired with a novel per-capita provision metric that accounts for real-time demand competition. We define \textit{double disadvantage} as the co-occurrence of poor spatial accessibility and insufficient per-capita service availability. Counterintuitively, the results reveal that double-disadvantaged areas cluster primarily along the inner suburban belt rather than the remote periphery, where per-capita service provision remains relatively sufficient. Furthermore, temporal shifts drastically alter equity landscapes: daytime workplace concentrations intensely exacerbate demand competition in urban job centres. These findings demonstrate that urban inequality depends heavily on spatiotemporal population flows rather than just the fixed location of services. Ultimately, achieving true urban equity requires dynamic planning interventions that address time-varying demand rather than focusing solely on static, home-based metrics.

We estimate that data centers caused average retail electricity rates to fall modestly in the United States from 2015 to 2024 using an instrumental variables approach. Despite prevailing sentiment, the finding is consistent with economic reasoning: existing large power system fixed costs, economies of scale in transmission and distribution, and declining unit costs for generation imply that durable demand growth lowers average prices. We find patterns of economies of scale for transmission, distribution, and generation costs as well as within and across retail customer classes. We caution that future supply constraints could reverse the effect.

The expansion of the FIFA World Cup to 48 teams in 2026 introduces structural challenges in tournament design. To populate a 32-team knockout bracket from 12 groups of four, the current FIFA rules select the eight best third-placed teams using a global ranking across all groups. This global coupling creates several major problems: a combinatorial explosion of 495 possible bracket configurations; a fundamentally biased and unequal selection of third-placed qualifiers; lack of a clear path for group winners; vulnerability to collusion and ranking manipulation; and no guarantee of same-group separation beyond the first knockout round. We propose a simple unified solution called the four-section bracket (FSB) rule: split the 12 groups into four sections of three groups. All group winners, runners-up, and the two best third-placed teams in each section advance. Group winners remain in their home sections as local anchors, while lower-ranked qualifiers are transferred to other sections according to a fixed, symmetric rule. This structure guarantees same-group separation until the semifinal, protects the top eight group winners with a predictable knockout path, and reduces bracket complexity from 495 configurations to just one invariant topology per section, recovering the symmetry of the traditional 32-team format. We show substantial improvements in competitive fairness and scheduling predictability.

Modeling the circadian impact of seasonal clock changing requires precise synchronization between solar and social time. This report critiques a recent study that associated disease prevalence in the United States with seasonal clock exposure. We identify a fundamental computational error in which a sign reversal of the longitudinal offset effectively inverted the US East-West axis, cross-correlating local health data with the circadian burden of hypothetical locations on the opposite side of a time zone. We outline the methodology for a correct modelization of the circadian process in the context of US geography.

Tropes are recurring narrative devices in television and film. We carry out a computational analysis of tropes in the sitcom Friends, using human-curated trope annotations from TVTropes, episode transcripts, and IMDb ratings. Because automatic trope detection remains challenging, we treat existing trope annotations as a curated analytical layer and focus on their downstream narrative and semantic functions. We first examine the relationship between episode-level trope frequency and audience reception. We find a statistically significant positive association between trope count and weighted IMDb ratings, although the modest explanatory power suggests that more than trope density alone explains audience evaluation. We then connect trope annotations to dialogue transcripts and represent trope-related dialogue using TF-IDF-based semantic features. Using PCA and k-means clustering, we group 1,954 distinct tropes into 15 semantically interpretable clusters. Chi-square analyses show that the six main characters are unevenly distributed across these clusters, with character-specific trope profiles that are broadly consistent with their established narrative identities. Finally, we project trope clusters into the ousiometric power-danger space to examine their semantic organization. The results show that "Physical and Sexual Comedy" occupies a region associated with relatively high danger, while "Revelation, Surprise, and Reaction" occupies a region associated with relatively high power. Overall, our work demonstrates a way to operationalize trope measurement and shows that identifiable trope clusters can provide holistic "distant reading" descriptions of characters and stories.

From ancient Mesopotamia to modern cities, dense human settlements coincide with bursts of economic productivity, cultural innovation, and social change. But how does packing people more tightly together alter social organization in ways that reshape collective outcomes? Here, I use a minimal agent-based model to isolate the effect of population density, holding population size and individual behavior fixed while varying only how closely individuals are placed in space. In the model, individuals form social ties gradually, favoring those nearby and those already well-connected. Under these simple rules, varying population density alone is sufficient to reorganize social network structure: sparse populations develop locally clustered communities, while denser ones form globally integrated networks with shorter social distances and a tightly interconnected core of popular individuals. This structural transition occurs sharply over a narrow range of densities and is governed by whether physical proximity or social popularity dominates tie formation. Simulating contagions on these networks reveals that the consequences of this shift depend on what is spreading. Simple contagions (e.g., information or disease) reach a majority of individuals more quickly in denser populations. Complex contagions (e.g., social norms or collective behaviors) do not spread faster, but instead achieve broader and more reliable adoption as density increases. Together, these results show that population density can act as a structural force independent of the economic and behavioral mechanisms typically invoked to explain why cities are engines of change.

This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge.

This work follows the evolution of financial networks in Norway over a period of nine years at a monthly rate. The data consist of board directors and their affiliations to companies, which we model as simplicial complexes. In this framework, directors are represented as nodes and companies as faces of the complex. To characterize the latter, we focus on three topological measures: the Euler characteristic, computed through the Betti numbers, torsion computed through the reduced determinant of the higher-order Laplacians, and higher-order clustering coefficients. The first two fail to capture the effect of imposed law on representation, unlike our notion of curvature which is a geometrical measure computed from the coefficients of the series expansion of the heat kernel in powers of time, which is our major contribution in this work. In particular, the Euler characteristic integrates curvature, and thus local information is lost. Subsequently, not every topological measure can reliably capture shocks in networks. Further, the number of spanning trees may undergo significant changes at the lowest order, yet these changes need not be reflected in the torsion. Conversely, the change in the curvature revealed variation in the board interlock due to legislation, and serves as a sensitive measure for detecting shocks in networks. Inflection points in curvature are associated with external forcing, and minima with shock arrival times. Sharp transitions are also observed in the components of torsion, while smooth changes are observed in higher-order clustering.

Urban venues serve as arenas for social mixing. While residential and activity-space segregation have been extensively studied, less is known about how the spatial structure of cities, particularly public transit infrastructure, shapes the geography of social mixing at specific locations. This study examines how transit accessibility associates with visitor diversity -- the compositional heterogeneity of visitors sharing a venue, used here as an indicator of social mixing potential -- at points of interest (POIs) in nine cities in Sweden and three cities in the United States (New York, Washington DC, Atlanta). Using mobile phone GPS data in 2024, we compute visitor diversity indices based on the birth background composition of visitors' home neighborhoods. Transit catchment diversity positively predicts visitor diversity, but this association is robust only in the largest metropolitan areas; in smaller Swedish cities, the coefficient attenuates to insignificance once geographic catchment composition, centrality, and venue density are controlled. Transit-diversity hotspots concentrate not in already diverse venues, but in lower-diversity POIs with lower commercial density, greater distance from transit in US cities, and greater centrality in Sweden. These patterns are consistent with transit infrastructure playing a bridging role, linking diverse populations to venues where alternative pathways are limited.

The Swiss system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments if an odd number of rounds is played. To analyse this issue, our paper compares the number of points scored in the tournament between players who played one game more with the white pieces and players who played one game fewer with the white pieces. Using data from 28 highly prestigious competitions, we find that players with an extra white game score significantly more points. In particular, the advantage exceeds the value of a draw in the four Grand Swiss tournaments. A potential solution to this unfairness could be organising Swiss-system chess tournaments with an even number of rounds, and guaranteeing a balanced colour assignment for all players using a recently proposed pairing mechanism.

Graph symmetries identify structural regularities and reduce the computational complexity of network analysis. In weighted graphs, however, exact automorphisms are rare because real-valued weights seldom coincide. We introduce a general framework for detecting approximate symmetries by aggregating weights into discrete categories, generating a sequence of coarser graphs on which classical automorphism analysis applies. The approximation path is fully configurable, based on interaction magnitudes, and can be matched to the empirical weight distribution. Applied to 250 empirical food webs using logarithmic aggregation, the method reveals that automorphisms emerge even at low approximation levels and almost always form small orbits. Orbit sizes rarely exceed two or three vertices, reflecting the combinatorial fragility of larger symmetric sets. Even so, symmetric vertices occupy diverse structural positions in the network and high connectivity does not imply asymmetry. The observation of just local permutations confirms the conclusions of trophic species and niche analysis. A case study demonstrates that automorphisms can also recover latent ecological structure. The minimal aggregation level at which two vertices become substitutable provides a quantitative measure of role similarity. The framework offers a principled, automorphism-based approach for quantifying similarity and redundancy in weighted complex networks.