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1. Dynamic response thresholds: heterogeneous ranges allow specialization while mitigating convergence to sink states

   Wu, Annie S.; Mathias, H. David (January 2020, Proceedings of the 12th International Conference on Swarm Intelligence)

   null (Ed.)

   We argue that heterogeneous threshold ranges allow agents in a decentralized swarm to effectively adapt thresholds in response to dynamic task demands while avoiding the pitfalls of positive feedback sinks. Dynamic response thresholds allow agents to dynamically evolve specializations which can improve the responsiveness and stability of a swarm. Dynamic thresholds that adapt in response to previous experience, however, are vulnerable to getting stuck in sink states due to the positive feedback nature of such systems. We show that heterogeneous threshold ranges result in comparable task allocation and improved stability as compared to homogeneous threshold ranges, and that simple static random thresholds should be considered in situations where agent resources are plentiful. 

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2. Bifurcations and global dynamics of a predator–prey mite model of Leslie type

   https://doi.org/10.1111/sapm.12675  

   Yang, Yue; Xu, Yancong; Rong, Libin; Ruan, Shigui (May 2024, Studies in Applied Mathematics)

   Abstract In this paper, we study a predator–prey mite model of Leslie type with generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focus‐type and cusp‐type degenerate Bogdanov–Takens bifurcations of codimension 3, originating from a nilpotent focus or cusp of codimension 3 that acts as the organizing center for the bifurcation set. Coexistence of multiple steady states, multiple limit cycles, and homoclinic cycles is also found. Interestingly, the coexistence of two limit cycles is guaranteed by investigating generalized Hopf bifurcation and degenerate homoclinic bifurcation, and we also find that two generalized Hopf bifurcation points are connected by a saddle‐node bifurcation curve of limit cycles, which indicates the existence of global regime for two limit cycles. Our work extends some results in the literature. 

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3. Threshold Mechanisms for Dynamic Procurement with Abandonment

   https://doi.org/10.1007/978-3-031-43254-5_22  

   Khodabakhsh, Ali; Nikolova, Evdokia; Pountourakis, Emmanouil; Horn Jimmy (September 2023, Lecture notes in computer science)

   Deligkas, Argyrios; Filos-Ratsikas, Aris (Ed.)

   We study a dynamic model of procurement auctions in which the agents (sellers) will abandon the auction if their utility does not satisfy their private target, in any given round. We call this “abandonment” and analyze its consequences on the overall cost to the mechanism designer (buyer), as it reduces competition in future rounds of the auction and drives up the price. We show that in order to maintain competition and minimize the overall cost, the mechanism designer has to adopt an inefficient (per-round) allocation, namely to assign the demand to multiple agents in a single round. We focus on threshold mechanisms as a simple way to achieve ex-post incentive compatibility, akin to reserves in revenue-maximizing forward auctions. We then consider the optimization problem of finding the optimal thresholds. We show that even though our objective function does not have the optimal substructure property in general, if the underlying distributions satisfy some regularity properties, the global optimal solution lies within a region where the optimal thresholds are monotone and can be calculated with a greedy approach, or even more simply in a parallel fashion. 

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4. An extremeness threshold determines the regional response of floods to changes in rainfall extremes

   https://doi.org/10.1038/s43247-021-00248-x  

   Brunner, Manuela I.; Swain, Daniel L.; Wood, Raul R.; Willkofer, Florian; Done, James M.; Gilleland, Eric; Ludwig, Ralf (December 2021, Communications Earth & Environment)

   Abstract Precipitation extremes will increase in a warming climate, but the response of flood magnitudes to heavier precipitation events is less clear. Historically, there is little evidence for systematic increases in flood magnitude despite observed increases in precipitation extremes. Here we investigate how flood magnitudes change in response to warming, using a large initial-condition ensemble of simulations with a single climate model, coupled to a hydrological model. The model chain was applied to historical (1961–2000) and warmer future (2060–2099) climate conditions for 78 watersheds in hydrological Bavaria, a region comprising the headwater catchments of the Inn, Danube and Main River, thus representing an area of expressed hydrological heterogeneity. For the majority of the catchments, we identify a ‘return interval threshold’ in the relationship between precipitation and flood increases: at return intervals above this threshold, further increases in extreme precipitation frequency and magnitude clearly yield increased flood magnitudes; below the threshold, flood magnitude is modulated by land surface processes. We suggest that this threshold behaviour can reconcile climatological and hydrological perspectives on changing flood risk in a warming climate. 

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5. A Heterogeneous Schelling Model for Wealth Disparity and its Effect on Segregation

   https://doi.org/10.1145/3551624.3555293  

   Zhao, Zhanzhan; Randall, Dana (October 2022, EAAMO '22: Equity and Access in Algorithms, Mechanisms, and Optimization)

   The Schelling model of segregation was introduced in economics to show how micro-motives can influence macro-behavior. Agents on a lattice have two colors and try to move to a different location if the number of their neighbors with a different color exceeds some threshold. Simulations reveal that even such mild local color preferences, or homophily, are sufficient to cause segregation. In this work, we propose a stochastic generalization of the Schelling model, based on both race and wealth, to understand how carefully architected placement of incentives, such as urban infrastructure, might affect segregation. In our model, each agent is assigned one of two colors along with a label, rich or poor. Further, we designate certain vertices on the lattice as “urban sites,” providing civic infrastructure that most benefits the poorer population, thus incentivizing the occupation of such vertices by poor agents of either color. We look at the stationary distribution of a Markov process reflecting these preferences to understand the long-term effects. We prove that when incentives are large enough, we will have ”urbanization of poverty,” an observed effect whereby poor people tend to congregate on urban sites. Moreover, even when homophily preferences are very small, if the incentives are large and there is income inequality in the two-color classes, we can get racial segregation on urban sites but integration on non-urban sites. In contrast, we find an overall mitigation of segregation when the urban sites are distributed throughout the lattice and the incentives for urban sites exceed the homophily biases. We prove that in this case, no matter how strong homophily preferences are, it will be exponentially unlikely that a configuration chosen from stationarity will have large, homogeneous clusters of agents of either color, suggesting we will have racial integration with high probability. 

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