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A person’s decisions vary even when options stay the same, like when a gambler changes bets despite constant odds of winning. Internal bias (e.g., emotion) contributes to this variability and is shaped by past outcomes, yet its neurobiology during decision-making is not well understood. To map neural circuits encoding bias, we administered a gambling task to 10 participants implanted with intracerebral depth electrodes in cortical and subcortical structures. We predicted the variability in betting behavior within and across patients by individual bias, which is estimated through a dynamical model of choice. Our analysis further revealed that high-frequency activity increased in the right hemisphere when participants were biased toward risky bets, while it increased in the left hemisphere when participants were biased away from risky bets. Our findings provide electrophysiological evidence that risk-taking bias is a lateralized push–pull neural system governing counterintuitive and highly variable decision-making in humans.

• Recent observations suggest that repeated fires could drive Mediterranean forests to shrublands, hosting flammable vegetation that regrows quickly after fire. This feedback supposedly favours shrubland persistence and may be strengthened in the future by predicted increased aridity. An assessment was made of how fires and aridity in combination modulated the dynamics of Mediterranean ecosystems and whether the feedback could be strong enough to maintain shrubland as an alternative stable state to forest. • A model was developed for vegetation dynamics, including stochastic fires and different plant fire-responses. Parameters were calibrated using observational data from a period up to 100 yr ago, from 77 sites with and without fires in Southeast Spain and Southern France. • The forest state was resilient to the separate impact of fires and increased aridity. However, water stress could convert forests into open shrublands by hampering post-fire recovery, with a possible tipping point at intermediate aridity. • Projected increases in aridity may reduce the resilience of Mediterranean forests against fires and drive post-fire ecosystem dynamics toward open shrubland. The main effect of increased aridity is the limitation of post-fire recovery. Including plant fire-responses is thus fundamental when modelling the fate of Mediterranean-type vegetation under climate-change scenarios.

1. Migration is a widespread phenomenon in the animal kingdom, including many taxonomic groups and modes of locomotion. Developing an understanding of the proximate and ultimate causes for this behaviour not only addresses fundamental ecological questions but has relevance to many other fields, for example in relation to the spread of emerging zoonotic diseases, the proliferation of invasive species, aeronautical safety as well as the conservation of migrants. 2. Theoretical methods can make important contributions to our understanding of migration, by allowing us to integrate findings on this complex behaviour, identify caveats in our understanding and to guide future empirical research efforts. Various mechanistic models exist to date, but their applications seem to be scattered and far from evenly distributed across taxonomic units. 3. Therefore, we provide an overview of the major mechanistic modelling approaches used in the study of migration behaviour and characterize their fundamental features, assumptions and limitations and discuss their typical data requirements both for model parameterization and for scrutinizing model predictions. 4. Furthermore, we review 155 studies that have used mechanistic models to study animal migration and analyse them with regard to the approaches used and the focal species, and also explore their contribution to advancing current knowledge within six broad migration ecology research themes. 5. This identifies important gaps in our present knowledge, which should be tackled in future research using existing and to-be developed theoretical approaches.

This study investigates the complex dynamic behavior of three-tailed helical microrobots operating in confined spaces. A stochastic dynamic model has been developed to analyze the effects of input angular velocity, current, fluid viscosity, and channel width on their motion trajectories, velocity, mean squared displacement (MSD), and wobbling rate. The results indicate that Gaussian white noise exerts a dispersive driving effect on the motion characteristics of the microrobots, leading to a 49% reduction in their velocity compared to deterministic conditions. Additionally, the time required for microrobots to traverse from the initial position to the bifurcation point decreases by 65% when the current is increased and by 39% when the fluid viscosity is reduced. These findings underscore the importance of optimizing control parameters to effectively mitigate noise impacts, enhancing the practical performance of the microrobots in real-world applications. This research offers solid theoretical support and guidance for the deployment of microrobots in complex environments.

With the increase in the proportion of multiple renewable energy sources, power electronics equipment and new loads, power systems are gradually evolving towards the integration of multi-energy, multi-network and multi-subject affected by more stochastic excitation with greater intensity. There is a problem of establishing an effective stochastic dynamic model and algorithm under different stochastic excitation intensities. A Milstein-Euler predictor-corrector method for a nonlinear and linearized stochastic dynamic model of a power system is constructed to numerically discretize the models. The optimal threshold model of stochastic excitation intensity for linearizing the nonlinear stochastic dynamic model is proposed to obtain the corresponding linearization threshold condition. The simulation results of one-machine infinite-bus (OMIB) systems show the correctness and rationality of the predictor-corrector method and the linearization threshold condition for the power system stochastic dynamic model. This study provides a reference for stochastic modelling and efficient simulation of power systems with multiple stochastic excitations and has important application value for stability judgment and security evaluation.

Although the effect of biodiversity on ecosystem functioning has become a major focus in ecology, its significance in a fluctuating environment is still poorly understood. According to the insurance hypothesis, biodiversity insures ecosystems against declines in their functioning because many species provide greater guarantees that some will maintain functioning even if others fail. Here we examine this hypothesis theoretically. We develop a general stochastic dynamic model to assess the effects of species richness on the expected temporal mean and variance of ecosystem processes such as productivity, based on individual species' productivity responses to environmental fluctuations. Our model shows two major insurance effects of species richness on ecosystem productivity: (i) a buffering effect, i.e., a reduction in the temporal variance of productivity, and (ii) a performance-enhancing effect, i.e., an increase in the temporal mean of productivity. The strength of these insurance effects is determined by three factors: (i) the way ecosystem productivity is determined by individual species responses to environmental fluctuations, (ii) the degree of asynchronicity of these responses, and (iii) the detailed form of these responses. In particular, the greater the variance of the species responses, the lower the species richness at which the temporal mean of the ecosystem process saturates and the ecosystem becomes redundant. These results provide a strong theoretical foundation for the insurance hypothesis, which proves to be a fundamental principle for understanding the long-term effects of biodiversity on ecosystem processes.

In this article, we develop a two-factor model of commodity prices that allows meanreversion in short-term prices and uncertainty in the equilibrium level to which prices revert. Although these two factors are not directly observable, they may be estimated from spot and futures prices. Intuitively, movements in prices for long-maturity futures contracts provide information about the equilibrium price level, and differences between the prices for the short- and long-term contracts provide information about short-term variations in prices. We show that, although this model does not explicitly consider changes in convenience yields over time, this short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990). We estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil-linked assets to demonstrate its use and some of its advantages over the Gibson-Schwartz model.

This study develops a stochastic dynamic model to optimize site value from timber and non-timber benefits for a landowner in the southeast United States who integrates wildfire risk and fuel accumulation into forest management and fire prevention decisions. The derived model determines optimal fuel treatment frequencies, timing, and level simultaneously and as a function of fire risk and fuel biomass dynamics under a range of economic and biophysical conditions. The landowner’s optimal prevention decisions are highly dependent on the type of fuel biomass growth and the association between fire arrival rate and fuel accumulation, which can vary across a broad forest landscape. Results indicate that policymakers should develop their management strategies based on their long-run objectives and fuel accumulation patterns, and these strategies should vary in timing and effort level within each rotation.

Wildfires have caused significant ecological and social losses in terms of forest benefits, private dwellings, and suppression costs. Although great efforts have been made in wildfire policies and wildfire-mitigating strategies on private and public lands, devastating wildfires continue to occur. This implies there is a need for effective incentive-driven policies to encourage forest owners to undertake an increasing level of wildfire-mitigating actions. This study evaluates the effectiveness of alternative incentive-driven policies for the problem of two adjacent forest owners under various scenarios of misinformation about wildfire occurrence and spread using a stochastic dynamic model. The study also investigates how the implementation of these policies encourages wildfire-mitigating actions, yields larger reductions in social losses, and alleviates free-riding behavior. The outcomes of the analysis confirm that the effectiveness of incentive programs in reducing social losses and increasing forest value is influenced by the level of misinformation held by a forest owner when making wildfire prevention decisions. The results also revealed that fuel stock regulation is more effective at mitigating wildfire damages and associated costs than cost-share programs under all misinformation scenarios. It was also found that fuel stock regulation could correct free-riding behavior due to the restrictive nature of this policy. The findings provide additional motivation for educational programs that seek to improve forest owners’ knowledge about the private benefits of fuel removal and collaboration efforts between neighboring forest owners. Collaborative efforts could yield substantial savings for the government through eliminating cost-share programs and reducing suppression costs.

Although a large body of work is devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolution in a dynamic social network. The proposed model captures the evolution of communities by explicitly modeling the transition of community memberships for individual nodes in the network. Unlike many existing approaches for modeling social networks that estimate parameters by their most likely values (i.e., point estimation), in this study, we employ a Bayesian treatment for parameter estimation that computes the posterior distributions for all the unknown parameters. This Bayesian treatment allows us to capture the uncertainty in parameter values and therefore is more robust to data noise than point estimation. In addition, an efficient algorithm is developed for Bayesian inference to handle large sparse social networks. Extensive experimental studies based on both synthetic data and real-life data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several state-of-the-art algorithms.