Optimizing epidemic control: Nash game approach to stochastic modeling with Brownian motion

Thermally induced thermophoresis and Brownian motion in bio-convection with motile organisms over a progressively curved surface

Averaging principle for stochastic fractional differential equations driven by Tempered Fractional Brownian Motion with two-time-scale Markov switching

Quasi-stationarity of the Dyson Brownian motion with collisions

ABSTRACT Efforts like the EU Emissions Trading System (EU ETS), have long faced criticism for encouraging overseas production and carbon leakage. In response, the EU has introduced the Carbon Border Adjustment Mechanism (CBAM), which took effect from January 2026. Under EU Regulation No. 956/2023, CBAM requires firms to purchase certificates for unpaid emissions when importing carbon-intensive products. The pricing mechanism offers a one-week price predictability window which simplifies compliance for importers while ensuring administrative convenience. This paper identifies the existence of a predictability benefit, where we demonstrate that solely by the one-week window, CBAM compliers are capable of navigating local price minima and strategically allocate certificate purchases. We also estimate the magnitude of the predictability benefit using geometric Brownian motion to simulate EUA prices and performing 20,000 iterations for each Monte Carlo simulation. The analysis assumes an efficient EUA market, among other practical simplifications. Our findings reveal an average 4.36% predictability benefit under typical market conditions, which intensifies as EUA prices decline. This highlights potential shortfalls in the CBAM framework, prone to times of downward price trends. Further research is needed to explore the tail risks and long-term impacts of this price disparity.

Ancestral state reconstruction is a fundamental challenge in evolutionary biology, requiring methods that can capture complex morphological changes while accounting for phylogenetic relationships. Current approaches are based on linear assumptions that often oversimplify the spatial relationships between anatomical features and fail to incorporate landmark correlations within shapes directly in the modeling. Here, we introduce a novel method that combines the ability of Large Deformation Diffeomorphic Metric Mapping (LDDMM) to model smooth, invertible transformations between shapes while preserving the relationships between landmarks with Felsenstein's Independent Contrasts (IC) to iteratively reconstruct ancestral shapes along the branches of a phylogenetic tree. We call this method Diffeomorphic Independent Contrasts for Ancestral Reconstruction of Shapes (DICAROS). We validate DICAROS against three existing methods: (1) linear predictors using Ordinary Least Squares (2) ancestral character estimation using maximum likelihood under Brownian Motion and (3) ridge archetypal penalized likelihood. We apply DICAROS to a dataset of swallowtail butterfly species (Family Papilionidae, Order Lepidoptera) to reconstruct the ancestral shape and visualize evolutionary trajectories in a phylomorphospace from the contrasts. We conclude that DICAROS outperforms the existing methods in terms of accuracy and provides a more accurate reconstruction of the ancestral shape for non-symmetric phylogenetic trees. With DICAROS we show a transition between untailed and tailed Papilionidae species while also illustrating how images of modern species would look under the DICAROS ancestral reconstruction.

Abstract Peristaltic transport phenomena play a crucial role in microscale thermal and biological fluid systems; however, efficient regulation of heat transfer, entropy generation, and microorganism dynamics under combined electromagnetic and radiative effects remains inadequately understood. In this study, peristaltic transport of a conducting fluid in a wavy microchannel is analyzed by incorporating the dynamics of motile microorganisms, quadratic thermal radiation, and Lorentz forces. A nonlinear mathematical framework is formulated to capture the coupled behavior of velocity, temperature, microorganism concentration, and entropy generation, and the resulting system is solved numerically under long-wavelength and low-Reynolds-number assumptions relevant to microfluidic applications. Mathematical models are formulated via incorporating electro-kinetic effects, thermophoresis and Brownian motion, and rheological performance of hyperbolic tangent fluid. The governing nonlinear equations are formulated and solved numerically using a finite element method. The results reveal that the Lorentz force significantly suppresses the axial velocity and enhances flow resistance, leading to a notable reduction in pumping efficiency, while simultaneously increasing entropy generation due to intensified electromagnetic dissipation. Quadratic thermal radiation is found to markedly elevate the temperature field, which in turn amplifies thermal irreversibility and alters the spatial distribution of motile microorganisms. An increase in microorganism concentration strengthens bioconvective effects, stabilizing the flow structure but contributing to higher entropy production through enhanced mass transfer irreversibility.

This paper mainly investigates the stability of fractional-order time-delayed neural networks (FOTDNNs) driven by fractional Brownian motion. In particular, it examines the mean-square uniform stability of FOTDNNs with the Hurst parameters 12<H<1. By applying the Cauchy-Schwarz inequality and analytical techniques, we establish sufficient conditions that guarantee mean-square uniform stability and further derive the stability criteria for systems with H=12. The validity of the theoretical results is confirmed through two numerical examples. Finally, we analyze the influence of the Hurst parameter (12⩽H⩽1) and key parameters of the sufficient conditions on FOTDNNs.

The enquiry inspects the movement of bioconvection through a nanoliquid near the stagnant flow subject to a stretchable surface. The effects of convective flow condition, radiative flow with rate of heat generation/absorption and chemical reaction are considered in energy and concentration equations. A well-known Buongiorno’s the nanofluid model is applied to examine the effects of Brownian movement and thermophoresis characteristics. Irreversible analysis of the proposed system is also carried out. The modelled formulations having partial differential equations (PDEs) are transmuted through suitable transformations. Further, the set of transmuted ordinary differential equations (ODEs) can be employed by the analytical method recognised as the homotopic technique. The significance of numerous important variables in represented equations has been visually illustrated along with pertinent physical outcomes. The outcomes indicates that the rate of flow reduces due the rising values of Casson fluid variable (𝛾) while the Bejan profile is increasing with a bigger estimation of (𝛾). The augmentation in the thermal radiation (Rd) and Biot number (Bi) improved in the temperature field. However, reduction in motile density due to the larger magnitude of Bioconvection Lewis number (Lb). Comparison has been endeavored in the results of past publishing result.

Abstract In this paper, we explore square-mean asymptotically $$\varkappa$$ -periodic mild solutions from square mean $$\varkappa$$ -periodic limit for a stochastic integro-differential equations driven by Brownian motion, utilizing Grimmer’s resolvent and a version of Darbo’s fixed point theorem based on the degree of nondensifiability. Additionally, an example is given to illustrate our results.

People need to sustain focused attention to achieve goals. Yet, attention often lapses, as minds wander towards task-unrelated thoughts. The conventional way to study such shifts in attention is through thought probes that explicitly ask if thoughts are task-related. However, probes are rare and interrupt behavior. Other methods to measure mind wandering assume a 50/50 split in time spent on-task vs off-task. We address these issues with a framework to infer mind wandering (MW) using computational modeling. We use a random dot motion task with varying evidence, but with a strong bias inducing a repetitive response requirement. Occasional thought probes were used for validation. When participants (N = 93) reported being off-task, accuracy was higher and reaction time (RT) was lower, suggesting less stimulus processing and more reliance on bias. To classify internal states for individual trials from performance, we fit a Hidden Markov Model with Generalized Linear Models (GLM-HMM) for each state to responses. A two-state GLM-HMM predicted lower RTs on off-task trials, revealed an increase in mind wandering across the task, and aligned with self-reported focus. This shows that temporal variation in attentional states can be measured on a trial-to-trial basis without thought probes, paving the way for future MW research.

Transport and mixing of tracers in the ocean is thought to be preferentially along neutral planes defined by the potential temperature and salinity fields. This gives rise to a conceptual model of ocean transport in which water parcel trajectories are everywhere neutral, that is, tangent to the neutral planes. Because the distribution of neutral planes is not integrable, neutral transport, while locally two-dimensional, is globally three-dimensional. We describe this form of transport, building on its connection with contact and sub-Riemannian geometry.We discuss a Lie-bracket interpretation of local dianeutral transport, the quantitative meaning of helicity, and the implications of the accessibility theorem. We compute sub-Riemannian geodesics for climatological neutral planes and put forward the use of the associated Carnot–Carathéodory distance as a diagnostic of the strong anisotropy of neutral transport.We propose a stochastic toy model of neutral transport which represents motion along neutral planes by a Brownian motion. The corresponding diffusion process is degenerate and not (strongly) elliptic. The non-integrability of the neutral planes however ensures that the diffusion is hypoelliptic. As a result, trajectories are not confined to surfaces but visit the entire three-dimensional ocean. The short-time behaviour is qualitatively different from that obtained with a non-degenerate highly anisotropic diffusion. We examine both short- and long-time behaviours using Monte Carlo simulations. The simulations provide an estimate for the time scale of ocean vertical transport implied by the constraint of neutrality.

Challenges in predicting and tuning nanoscale crystal growth stem from the fact that there are plenty of individual elementary steps occurring in the liquid-solid two phase zone involving phase transitions and that these steps are highly dynamic in nature. Direct visualization with high spatiotemporal resolution is indispensable to unveiling the important intermediate states underlying those alloying processes. Here, our in situ observations reveal that additional unexpected phase transformation between the crystalline and amorphous states also occurs periodically, even after the typical transition from the liquid to the precipitated solid nanoparticles (NPs) in the two-phase zone. The NPs demonstrate interesting oscillatory rotation in the liquid, followed by the anomalous Brownian motion type due to the nanoscale confinement. Such rotation further enhances the intermediate crystalline ↔ amorphous phase transition. The NPs finally become crystalline with a fixed orientation once the liquid region is nearly depleted. The underlying mechanism is discussed. The findings offer a fundamental understanding of the phase behaviors with dynamic intermediate structures in the complex liquid-solid zone under the input of nanoscale confinement and pave the way for optimizing the nanoalloy nucleation and growth with the desired properties.

Abstract We show that, under certain conditions, a strongly continuous semigroup admits an almost surely frequently hypercyclic random vector defined as a stochastic integral in Fréchet spaces with respect to the Brownian motion. Two criteria are given. We will apply the second criterion to three examples: translation semigroups on spaces of integrable functions, the exponential of weighted shifts, and the translation operators on the space of entire functions. This last example, with a stochastic approach, seems to be new in the literature. Some other examples are given.

Humans often co-perceive stimuli with others, yet the neurocognitive effects of such shared perceptual contexts are underexplored. We tested whether awareness that a visual stimulus is simultaneously available to another person, without interaction, modulates behavioral performance and neurophysiological signatures of perceptual decision-making. Thirty-three participants completed 640 trials of a Random Dot Kinematogram motion discrimination task while EEG and pupillometry data were recorded. A confederate was present, with a divider ensuring that, on each trial, the stimulus was either jointly visible to both or privately visible to the participant. Participants received no feedback and engaged in no interaction, isolating the effect of joint visibility. Behavioral performance was unaffected by social context, but EEG analysis revealed context-specific neural patterns emerging after cue onset and before stimulus presentation, suggesting proactive encoding of the social context. Additionally, pupil size was significantly greater during public visibility trials, indicating heightened arousal associated with social vigilance. These findings suggest that co-perception induces covert social vigilance-anticipatory arousal and neural readiness in response to co-visibility, even without interaction. Such covert markers could serve as biomarkers for altered social salience processing in clinical populations, such as those with social anxiety disorder or autism.

ABSTRACT This article presents a novel extension of the GARCH model incorporating weighted liquidity, modeled by fractional Brownian motion. The existence of a stationary solution is proven, and the higher‐order moments are calculated to illustrate the statistical properties of the model. Analysis of the auto‐correlation function of the squared process confirms the long‐term memory characteristic of the model. Numerical simulations are employed to validate the theoretical findings, demonstrating the significance of the model in the financial market.

This work examines the influence of Cattaneo–Christov heat flux on magneto hydrodynamic (MHD) flow of non-Newtonian fluids; Jeffrey, Maxwell and Oldroyd-Bover a stretching sheet, integrating activation energy and velocity slip effects. The governing partial differential equations are converted into similarity-based nonlinear ordinary differential equations and solved numerically utilizing MATLAB’s BVP5C solver. Results reveal that higher relaxation-to-retardation ratios, larger Deborah numbers and increased slip significantly reduce fluid velocity with Oldroyd-B fluid and Maxwell fluid exhibits the greatest decrease, while Jeffrey fluid is minimally affected. Thermal Deborah number enhances heat flux relaxation, leading to elevated temperature profiles and a thicker thermal boundary layer. Increased activation energy slows chemical reactions but raises nanoparticle concentration with Jeffrey fluid. Validation against previous studies confirms the accuracy and reliability of the solutions. Furthermore, skin friction decreases with magnetic parameters, relaxation ratio and slip, whereas the Nusselt number increases with heat flux relaxation and radiation but diminishes due to Brownian motion, thermophoresis and non-uniform heat. Sherwood number rises with Lewis number, reaction rate, Brownian motion and reaction strength but decreases with thermophoresis and activation energy. Maxwell fluid consistently exhibits the most favourable transport rates, Jeffrey fluid the least, with Oldroyd-B liquid intermediate due to rheological differences.

Abstract The ternary hybrid nanofluids are in high demand in the context of engineering systems such as compact heat exchangers, rotating chemical reactors, and high-performance cooling of electronics engineering devices, which are seeking far more advanced thermal management solutions. This research provides an extensive computational model of a ternary hybrid nanofluid flow (molybdenum disulfide (MoS 2 ), graphene oxide (GO) and copper (Cu) in acetic acid–water base) between two turns comprising of concentric cylinders. The model has a unique combination of the influence of chemical reaction, thermal radiation, and the shape fracture of nanoparticles (spherical, cylindrical, platelet) to fill a considerable gap in the literature. The main aim is to create a strong mathematical model of this complicated system, define the heat generated in the system, and determine the effect of shape fracture on the thermal conductivity and fluid dynamics. The resulting governing nonlinear partial differential equations are then reduced to ordinary differential equations and solved through the use of the Adomian Decomposition Method (ADM) with the validation of the results by the Homotopy Analysis Method (HAM)-package, which reveals very good agreement (e.g., velocity profiles within 3% of benchmark studies). The most important quantitative results are that the flow velocity is increased with an increase in the Grashof number by half, and the radiation parameter may drop the temperature of the fluid by 20%. Moreover, nanoparticles in the form of plates produce approximately 8% more entropy than the spheres. These outcome proves that the forces of buoyancy, Brownian motion, and thermo-phoresis severely affect the flow and heat transfer. The findings present the critical information toward the optimisation of the thermal efficiency and design of advanced energy systems, which have a great contribution to the thermal engineering and sustainable energy technology.

Asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion

Abstract The planar Skorokhod embedding problem was first proposed and solved by Gross [‘A conformal Skorokhod embedding’, Electron. Commun. Probab. 24 (2019), 11 pages; doi:10.1214/19-ECP272]. Gross worked with probability distributions having finite second moment. Boudabra and Markowsky [‘Remarks on Gross’ technique for obtaining a conformal Skorokhod embedding of planar Brownian motion’, Electron. Commun. Probab. 25 (2020), 13 pages; doi:10.1214/20-ECP300] extended the solution to all distributions with a finite p th moment for $p>1$ . The case $p=1$ has remained uncovered since then. In this note, we show that the planar Skorokhod embedding problem is solvable for $p=1$ when the Hilbert transform of its quantile function is integrable, effectively closing this line of investigation.