arXiv · 0705.0891
No abstract given. Contents: I. Definition and Introduction II. Schelling Model III. Opinion Dynamics IV. Languages, Hierarchies and Football V. Future Directions
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D. Stauffer. 2007-05-07. Opinion Dynamics and Sociophysics. https://arxiv.org/abs/0705.0891
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The potential expansion of the National Basketball Association (NBA) to 32 teams raises the question of how to restructure its conferences and divisions while balancing travel efficiency, fairness in team travel burdens, and commercial exposure. This study provides a quantitative framework for expansion planning. We develop two optimization models: one minimizing total travel distance and another following the Kalai-Smorodinsky (KS) proportional-improvement principle. The KS model maximizes the smallest normalized travel improvement between a team's fixed reference and individual ideal. Both models incorporate an opponent-exposure constraint to account for commercial considerations, and take into account road trips when measuring travel distance. Using data from all 30 current franchises and six candidate cities (Seattle, Las Vegas, Montreal, Vancouver, Tampa, and Mexico City), we evaluate 15 pairwise expansion scenarios under alternative season lengths and divisional formats. In the 30-team comparison, KS strikes a good balance between overall travel efficiency and fairness across teams, giving greater attention to individual travel burdens while keeping total travel close to the distance-minimizing solution. The expansion results show that travel requirements depend jointly on the candidate city pair and the competition format, highlighting the need to assess expansion and realignment together. Our study offers a flexible decision support framework for league executives, policymakers, and sports economists. It makes the trade-offs between total travel, individual gains, and opponent exposure explicit, providing evidence-based guidance for strategic league design.
In this article, we connect statistical inference for spatial point processes with the analysis of waiting pedestrian crowds through two interconnected contributions. First, on the methodological side we develop an inference procedure for semiparametric spatial point process models leveraging replicated spatial patterns, i.e., multiple approximately independent realizations from the same process. Second, we show that spatial point processes provide a suitable modeling framework for waiting pedestrians, capturing two key aspects: spatial inhomogeneity driven by location attractiveness and repulsive interactions between pedestrians. These two components are central to the inference problem itself, since spatial point process modeling hinges on disentangling background intensity from interaction. Although replicated spatial patterns are rare in point process literature, they are available here through a unique real-life pedestrian dataset, thereby directly linking the methodological development to the physical application. We use the proposed methods to fit and evaluate determinantal and Gibbs point processes in a simulation study and a real-world case study. Despite persistent challenges in decoupling the influences of inhomogeneity from interaction, these models are able to reproduce key empirical features of waiting pedestrians.
Synchronization of coupled oscillators on complex networks underlies critical functions in natural and engineered systems, including power-grid operation. While synchronization stability on fixed network topologies has been studied extensively, less is known about how an added transmission link affects stability depending on where it is placed relative to generation and consumption. We address this question using simplified ring-network power-grid models in which producer and consumer nodes are spatially organized into clusters. Long-range transmission links, which we refer to as shortcuts, are added between non-adjacent nodes, and synchronization stability is quantified by basin stability in second-order coupled-oscillator dynamics. We compare shortcut placements across four scenarios varying network size, power allocation, power-injection heterogeneity, and producer--consumer arrangement. When producers and consumers form two spatially separated clusters, center-to-center shortcuts do not reduce the mean basin stability in the configurations examined and increase it by up to 75\% relative to the shortcut-less baseline. Peripheral shortcuts instead reduce mean basin stability by up to 28\% in some configurations despite the added connection, producing Braess-like degradation. In alternating multi-block networks, however, no single shortcut placement provides the same substantial enhancement, indicating that the center-to-center advantage does not directly generalize to more complex spatial arrangements. Representative time-domain simulations further show faster decay of frequency deviations for center-to-center than for peripheral shortcuts. These results demonstrate that the effect of added connectivity depends critically on where the new link is placed relative to the spatial organization of generation and consumption.