Stochastic Model Research Articles

Stochastic parabolic growth promotes coexistence and a relaxed error threshold in RNA-like replicator populations

The RNA world hypothesis proposes that during the early evolution of life, primordial genomes of the first self-propagating evolutionary units existed in the form of RNA-like polymers. Autonomous, non-enzymatic, and sustained replication of such information carriers presents a problem, because product formation and hybridization between template and copy strands reduces replication speed. Kinetics of growth is then parabolic with the benefit of entailing competitive coexistence, thereby maintaining diversity. Here, we test the information-maintaining ability of parabolic growth in stochastic multispecies population models under the constraints of constant total population size and chemostat conditions. We find that large population sizes and small differences in the replication rates favor the stable coexistence of the vast majority of replicator species (‘genes’), while the error threshold problem is alleviated relative to exponential amplification. In addition, sequence properties (GC content) and the strength of resource competition mediated by the rate of resource inflow determine the number of coexisting variants, suggesting that fluctuations in building block availability favored repeated cycles of exploration and exploitation. Stochastic parabolic growth could thus have played a pivotal role in preserving viable sequences generated by random abiotic synthesis and providing diverse genetic raw material to the early evolution of functional ribozymes.

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

ИССЛЕДОВАНИЕ ПОЖАРНОЙ ОПАСНОСТИ ЭЛЕКТРИЧЕСКОЙ СИСТЕМЫ АВТОТРАНСПОРТНОГО СРЕДСТВА

The article examines the change of the probability of an emergency mode (failure) of the vehicle's electrical wiring depending on the time of its operation. We revealed necessity of establishing the wear and operation time of electrical wiring in a vehicle. Emergency modes in the vehicle electrical network have been identified and analyzed. The behavior of some contact connections of a vehicle was studied for an increase in contact resistance. It is concluded that it is necessary to develop deterministic and stochastic mathematical models that describe the state of the vehicle’s electrical network in order to assess its fire hazard.

Fractional-Order PIλDμ Control to Enhance the Driving Smoothness of Active Vehicle Suspension in Electric Vehicles

The suspension system is a crucial part of an electric vehicle, which directly affects its handling performance, driving comfort, and driving safety. The dynamics of the 8-DoF full-vehicle suspension with seat active control are established based on rigid-body dynamics, and the time-domain stochastic excitation model of four tires is constructed by the filtered white noise method. The suspension dynamics model and road surface model are constructed on the Matlab/Simulink simulation software platform, and the simulation study of the dynamic characteristics of active suspension based on the fractional-order PIλDμ control strategy is carried out. The three performance indicators of acceleration, suspension dynamic deflection, and tire dynamic displacement are selected to construct the fitness function of the genetic algorithm, and the structural parameters of the fractional-order PIλDμ controller are optimized using the genetic algorithm. The control effect of the optimized fractional-order PIλDμ controller based on the genetic algorithm is analyzed by comparing the integer-order PID control suspension and passive suspension. The simulation results show that for optimized fractional-order PID control suspension, compared with passive suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions reaches over 25%, the average optimization of suspension dynamic deflection exceeds 30%, and the average optimization of tire dynamic displacement is 5%. However, compared to the integer-order PID control suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions decreased by 5%, the average optimization of suspension dynamic deflection increased by 3%, and the average optimization of tire dynamic displacement increased by 2%.

Stochastic parabolic growth promotes coexistence and a relaxed error threshold in RNA-like replicator populations.

The RNA world hypothesis proposes that during the early evolution of life, primordial genomes of the first self-propagating evolutionary units existed in the form of RNA-like polymers. Autonomous, non-enzymatic, and sustained replication of such information carriers presents a problem, because product formation and hybridization between template and copy strands reduces replication speed. Kinetics of growth is then parabolic with the benefit of entailing competitive coexistence, thereby maintaining diversity. Here, we test the information-maintaining ability of parabolic growth in stochastic multispecies population models under the constraints of constant total population size and chemostat conditions. We find that large population sizes and small differences in the replication rates favor the stable coexistence of the vast majority of replicator species ('genes'), while the error threshold problem is alleviated relative to exponential amplification. In addition, sequence properties (GC content) and the strength of resource competition mediated by the rate of resource inflow determine the number of coexisting variants, suggesting that fluctuations in building block availability favored repeated cycles of exploration and exploitation. Stochastic parabolic growth could thus have played a pivotal role in preserving viable sequences generated by random abiotic synthesis and providing diverse genetic raw material to the early evolution of functional ribozymes.

Will advancement in technologies bring fear and damage human employment? Evidence from China's manufacturing industry.

Advancement in technologies such as robotic industries and artificial intelligence bring fear among human being that jobs will be substituted by robots. Base on the panel data of 28 China's manufacturing industries, this research analyzed the impact of technical progress bias on employment. First, we calculate the technical progress bias index of 28 industries base on the stochastic frontier model with transcendental logarithm function found 16 industries were toward the skilled labor while the remaining 12 industries were toward the unskilled labor. Second, the empirical results show that technical progress bias has a positive impact on the total manufacturing employment and significant positive effect on the unskilled labor, while no significant impact on skilled labor employment. Third, the threshold effect test proves that if taking industry value-added per capita or R&D capital stock as threshold variable, the threshold about the impact exist, making the impact on skilled labor was insignificant.

Jump Clustering, Information Flows, and Stock Price Efficiency

Abstract We study the clustering behavior of stock return jumps modeled by a self/cross-exciting process embedded in a stochastic volatility model. Based on the model estimates, we propose a novel measurement of stock price efficiency characterized by the extent of jump clustering that stock returns exhibit. This measurement demonstrates the capability of capturing the speed at which stock prices assimilate new information, especially at the firm-specific level. Furthermore, we assess the predictability of self-exciting (clustered) jumps in stock returns. We employ a particle filter to sample latent states in the out-of-sample period and perform one-step-ahead probabilistic forecasting on upcoming jumps. We introduce a new statistic derived from predicted probabilities of positive and negative jumps, which has been shown to be effective in return predictions.

Power generation–network–load–energy storage co-planning under uncertainty

With the aggregation of renewable energy in the power system, the uncertainty caused by the renewable energy affects the planning and operation of power systems. Meanwhile, the existing planning models fail to consider renewable energy uncertainty methods, specifically concerning renewable energy confidence and future possible scenarios; thus, a confidence-based scenario cluster method is presented. A novel generator, network, load, and energy storage (GNLS) co-planning model is proposed in the paper. First, a confidence-based scenario cluster is built, which can reflect uncertainties by clustering and analyzing wind, solar, and load. Second, the proposed model focuses on load and energy storage co-planning, and in addition, relevant flexible indices are used to assess the model. Finally, the GNLS co-planning model is built as a bi-level stochastic model on continuous time scales. The model is solved using the Benders decomposition algorithm. The method in this paper is validated using an IEEE RTS 24-bus and a real test system in China to demonstrate the reduction in renewable energy curtailment and optimization of economic factors in power system planning.

Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process

In this paper, we explore and analyze a stochastic epidemiological model with vaccination and two mean-reverting Ornstein-Uhlenbeck processes to describe the dynamics of HBV transmission. Our study begins by deriving a sufficient condition for the extinction of hepatitis B. Additionally, we determine the presence of a stationary distribution using the Markov process stability theory. Next, we utilize algebraic equation theory and the associated Fokker-Planck equation to derive an explicit expression for the unique probability density function. To validate our theoretical findings, we conduct several numerical simulations using hepatitis B data provided by the World Health Organization (WHO). The results of these simulations support and complement our analytical approach.

Synchronization of two non-identical Chialvo neurons

We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the synchronization of the neurons is studied as a function of this mismatch, the noise introduced in the stochastic model, and the coupling strength between the neurons. We propose the simplest neural network for study, as its analysis is more straightforward and does not compromise generality. Within this network, two non-identical neurons are electrically coupled. In order to understand whether specific behaviors affect the global behavior of the system, we consider different cases related to the behavior of the neurons (chaotic or periodic). Furthermore, we study how variations in model parameters affect the firing frequency in each case. Additionally, we consider that the two neurons have both excitatory and inhibitory couplings. Consequently, we identify critical values of noise and mismatch for achieving satisfactory synchronization between the neurons in each case. Finally, we propose that the results have general applicability across various neuron models.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási–Albert (BA), Erdös–Rényi (ER), and Watts–Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

How Does the Proportion of Never Treatment Influence the Success of Mass Drug Administration Programs for the Elimination of Lymphatic Filariasis?

Mass drug administration (MDA) is the cornerstone for the elimination of lymphatic filariasis (LF). The proportion of the population that is never treated (NT) is a crucial determinant of whether this goal is achieved within reasonable time frames. Using 2 individual-based stochastic LF transmission models, we assess the maximum permissible level of NT for which the 1% microfilaremia (mf) prevalence threshold can be achieved (with 90% probability) within 10 years under different scenarios of annual MDA coverage, drug combination and transmission setting. For Anopheles-transmission settings, we find that treating 80% of the eligible population annually with ivermectin + albendazole (IA) can achieve the 1% mf prevalence threshold within 10 years of annual treatment when baseline mf prevalence is 10%, as long as NT <10%. Higher proportions of NT are acceptable when more efficacious treatment regimens are used. For Culex-transmission settings with a low (5%) baseline mf prevalence and diethylcarbamazine + albendazole (DA) or ivermectin + diethylcarbamazine + albendazole (IDA) treatment, elimination can be reached if treatment coverage among eligibles is 80% or higher. For 10% baseline mf prevalence, the target can be achieved when the annual coverage is 80% and NT ≤15%. Higher infection prevalence or levels of NT would make achieving the target more difficult. The proportion of people never treated in MDA programmes for LF can strongly influence the achievement of elimination and the impact of NT is greater in high transmission areas. This study provides a starting point for further development of criteria for the evaluation of NT.

Combining Crop and Water Decisions to Manage Groundwater Overdraft over Decadal and Longer Timescales

Coordinating management of groundwater, surface water, and irrigated crops is fundamental economically for many arid and semi-arid regions. This paper examines conjunctive water management for agriculture using hydro-economic optimization modeling. The analysis is integrated across two timescales: a two-stage stochastic decadal model for managing annual and perennial crops spanning dry and wet years and a far-horizon dynamic program embedding the decadal model into a longer groundwater policy setting. The modeling loosely represents California’s San Joaquin Valley and has insights for many irrigated arid and semi-arid regions relying on groundwater with variable annual hydrology. Results show how conjunctive water management can stabilize crop decisions and improve agricultural profitability across different water years by pumping more in dry years and increasing recharging groundwater in wetter years. Using groundwater as a buffer for droughts allows growing more higher-value perennial crops, which maximizes profit even with water-scarce conditions. Nevertheless, ending overdraft in basins with declining groundwater for profit-maximizing farming reduces annual crops to maintain more profitable perennial crops through droughts. Results are affected by economic discount rates and future climates. Operating and opportunity costs from forgone annual crops can reduce aquifer recharge early in regulatory periods.

Morphology of nanoporous glass: Stochastic 3D modeling, stereology and the influence of pore width

Morphology of nanoporous glass: Stochastic 3D modeling, stereology and the influence of pore width

An Updated Economic Assessment of Moxidectin Treatment Strategies for Onchocerciasis Elimination.

Concerns that annual mass administration of ivermectin, the predominant strategy for onchocerciasis control and elimination, may not lead to elimination of parasite transmission (EoT) in all endemic areas have increased interest in alternative treatment strategies. One such strategy is moxidectin. We performed an updated economic assessment of moxidectin- relative to ivermectin-based strategies. We investigated annual and biannual community-directed treatment with ivermectin (aCDTI, bCDTI) and moxidectin (aCDTM, bCDTM) with minimal or enhanced coverage (65% or 80% of total population taking the drug, respectively) in intervention-naive areas with 30%, 50%, or 70% microfilarial baseline prevalence (representative of hypo-, meso-, and hyperendemic areas). We compared programmatic delivery costs for the number of treatments achieving 90% probability of EoT (EoT90), calculated with the individual-based stochastic transmission model EPIONCHO-IBM. We used the costs for 40 years of program delivery when EoT90 was not reached earlier. The delivery costs do not include drug costs. aCDTM and bCDTM achieved EoT90 with lower programmatic delivery costs than aCDTI with 1 exception: aCDTM with minimal coverage did not achieve EoT90 in hyperendemic areas within 40 years. With minimal coverage, bCDTI delivery costs as much or more than aCDTM and bCDTM. With enhanced coverage, programmatic delivery costs for aCDTM and bCDTM were lower than for aCDTI and bCDTI. Moxidectin-based strategies could accelerate progress toward EoT and reduce programmatic delivery costs compared with ivermectin-based strategies. The costs of moxidectin to national programs are needed to quantify whether delivery cost reductions will translate into overall program cost reduction.

The latent cognitive structures of social networks

Abstract When people are asked to recall their social networks, theoretical and empirical work tells us that they rely on shortcuts, or heuristics. Cognitive social structures (CSSs) are multilayer social networks where each layer corresponds to an individual’s perception of the network. With multiple perceptions of the same network, CSSs contain rich information about how these heuristics manifest, motivating the question, Can we identify people who share the same heuristics? In this work, we propose a method for identifying cognitive structure across multiple network perceptions, analogous to how community detection aims to identify social structure in a network. To simultaneously model the joint latent social and cognitive structure, we study CSSs as three-dimensional tensors, employing low-rank nonnegative Tucker decompositions (NNTuck) to approximate the CSS—a procedure closely related to estimating a multilayer stochastic block model (SBM) from such data. We propose the resulting latent cognitive space as an operationalization of the sociological theory of social cognition by identifying individuals who share relational schema. In addition to modeling cognitively independent, dependent, and redundant networks, we propose a specific model instance and related statistical test for testing when there is social-cognitive agreement in a network: when the social and cognitive structures are equivalent. We use our approach to analyze four different CSSs and give insights into the latent cognitive structures of those networks.

Dynamics and probability density function of a stochastic COVID-19 epidemic model with nonlinear incidence

Dynamics and probability density function of a stochastic COVID-19 epidemic model with nonlinear incidence

A New Model Making the Transition From Oil to Solar Energy

Today, the use of renewable energy sources such as sun, wind and hot water to generate electricity is increasingly becoming a global priority. In this paper, we propose a deterministic dynamical system reporting the transition from oil to solar energy, in which we then add the randomness of this phenomenon. First, we study the positivity of the deterministic oil-solar model and show that there is a maximum solution of the deterministic model and that the system is controllable at any time T &gt; 0 from an initial point. We also prove the existence of an equilibrium state, study its nature and prove that there is no limit cycle between the quantity of oil available and the solar production capacity installed. Secondly, we formulate the stochastic solar energy model from the deterministic model, for which we proved the existence of a unique solution. Finally, using a model extracted from the model performed and examining the transition from the amount of available oil to the installed solar generation capacity, we associate a linear optimal control problem, from which we prove that the optimal control components are of bang-bang type, and we characterize them.

Scenarios of future mpox outbreaks among men who have sex with men: a modelling study based on cross-sectional seroprevalence data from the Netherlands, 2022.

BackgroundFollowing the 2022-2023 mpox outbreak, crucial knowledge gaps exist regarding orthopoxvirus-specific immunity in risk groups and its impact on future outbreaks.AimWe combined cross-sectional seroprevalence studies in two cities in the Netherlands with mathematical modelling to evaluate scenarios of future mpox outbreaks among men who have sex with men (MSM).MethodsSerum samples were obtained from 1,065 MSM attending Centres for Sexual Health (CSH) in Rotterdam or Amsterdam following the peak of the Dutch mpox outbreak and the introduction of vaccination. For MSM visiting the Rotterdam CSH, sera were linked to epidemiological and vaccination data. An in-house developed ELISA was used to detect vaccinia virus (VACV)-specific IgG. These observations were combined with published data on serial interval and vaccine effectiveness to inform a stochastic transmission model that estimates the risk of future mpox outbreaks.ResultsThe seroprevalence of VACV-specific antibodies was 45.4% and 47.1% in Rotterdam and Amsterdam, respectively. Transmission modelling showed that the impact of risk group vaccination on the original outbreak was likely small. However, assuming different scenarios, the number of mpox cases in a future outbreak would be markedly reduced because of vaccination. Simultaneously, the current level of immunity alone may not prevent future outbreaks. Maintaining a short time-to-diagnosis is a key component of any strategy to prevent new outbreaks.ConclusionOur findings indicate a reduced likelihood of large future mpox outbreaks among MSM in the Netherlands under current conditions, but emphasise the importance of maintaining population immunity, diagnostic capacities and disease awareness.

Cost-based distributionally robust tourist attraction recommendation with demand uncertainty

Tourist attraction recommendation (TAR) problem has gained attention due to its potential to enhance tourist services. Existing studies focus on meeting tourists’ individual needs, but overlook the tour operator’s interests as the TAR service provider. The TAR problem is more challenging due to the high variability of customer demand, which is difficult to predict accurately beforehand. This paper examines TAR in response to random changes in tourist demand, aiming to minimize transportation costs, cooperation expenses between tour operators and attractions, ticket booking fees, and promotion costs, where ambiguity set is defined by means, mean absolute deviations, and the support set. Firstly a distributionally robust model is proposed to identify suitable attractions for cooperation, along with determining the associated costs of ticket booking, promotion, and tourist transportation, while considering chance constraint on the service level. Subsequently, the model is reformulated into a tractable mixed integer linear programming model using duality theory. Numerical experiments illustrate that the proposed model outperforms both the stochastic programming model and the deterministic model in terms of risk level by out-of-sample test. In particularly, considering uncertainty and distributional ambiguity can make the model more accurate and credible.