Discrete Dynamic Model Research Articles

Analysis of COVID-19 epidemic traced data and stochastic discrete transmission dynamic model

The epidemic of novel coronavirus pneumonia has spread throughout the country. The early epidemic cases in many provinces, including Shaanxi, are mainly imported cases. The latest epidemic situation has been decreasing under restrict prevention and control strategies. Accessing the efficacy of control measures, analyzing the impact of population flow on the epidemic situation are of great significance for the study of the epidemic situation in Shaanxi (or other areas with imported cases as the main cases) and the future response to emergent infectious diseases. According to the detailed data published by Shaanxi, we can obtain the transmission chains (infection tree), and the median durations from the illness onset to the first medical visit, to the admission, and then to the final confirmation. We can obtain the daily number of latent, infectious and hospitalized individuals and the spatial distribution of their state evolution. The control reproduction number of COVID-19 epidemic was determined (1.48–1.69). We develop the statistical inference method to calculate the effective regeneration number under the strict control measures in Shaanxi province. Furthermore, a novel stochastic discrete transmission model for COVID-19 was proposed, which integrates possible interventions and import cases. The parameterization of the formulated model was realized through multiple source data. Our main conclusion shows that intermittent population flow, close attention and effective isolation of the floating populationcan effectively reduce the risk of secondary outbreak, which consequently provides decision support for the orderly organization of returning to work/school.

Identification of Intertemporal Preferences in History-Dependent Dynamic Discrete Choice Models

We study the identification of intertemporal preferences in a stationary dynamic discrete decision model. We propose a new approach which focuses on problems which are intrinsically dynamic: either there is endogenous variation in the choice set, or preferences depend directly on the history. History dependence links the choices of the decision-maker across periods in a more fundamental sense standard dynamic discrete choice models typically assume. We consider both exponential discounting as well as the quasi-hyperbolic discounting models of time preferences. We show that if the utility function or the choice set depends on the current states as well as the past choices and/or states, then time preferences are non-parametrically point-identified separately from the utility function under mild conditions on the data and we may also recover the instantaneous utility function without imposing any normalization on the utility across states.

Vacancy diffusion coupled discrete dislocation dynamic modeling of compression creep of micro-pillars at elevated temperature

A two-dimensional discrete-continuous scheme (DCS), which couples the motions of dislocations and diffusion of vacancies, is developed. There are three modules in this scheme. The glide and climb of dislocations are performed by the discrete dislocation dynamics (DDD) module, by which the evolution of dislocations is captured and the plastic strain due to dislocation motions is obtained. The diffusion of vacancies is performed by the finite difference method (FDM) module, by which the vacancy concentration field and the inelastic strain due to vacancy diffusion are obtained. The plastic strain by the DDD and the inelastic strain by the FDM, as the eigen-strains, are transferred to the finite element method (FEM) module, by which the stress field is obtained and then transferred back to the DDD module and FDM module to drive dislocation motions and vacancy diffusion. By this vacancy diffusion coupled discrete dislocation dynamics scheme, the compression creep of single crystalline and bi-crystalline aluminum micro-pillars at elevated temperature is modeled. Some interesting creep behaviors are computationally captured. The compression creep of single crystalline and bi-crystalline micro-pillars is size dependent: the creep strain of micro-pillars at higher compressive stress increases with increasing micro-pillar diameter, which is in good agreement with experimental results reported in the literature. This is believed to result from higher dislocation density in those micro-pillars with larger diameter.

Generalized Euler Equation Errors for Discrete Time Dynamic Portfolio Choice Models

The solution to dynamic portfolio choice models can be formulated in terms of a value function by the Bellman principle of optimality, which reduces the multi-period optimal policy choice problem to a sequence of one-period maximization problems. For two adjacent periods, economists compute the error of numerically obtained policies by measuring how much these policies violate the intertemporal first order conditions for the optimal policy choice problem---so-called Euler equation errors. In this paper, we derive generalized Euler equation errors for the solution to a broad class of discrete time dynamic portfolio choice models where the policies are continuous choice variables. Our key precondition is that the gradient of the value function with respect to the state variables can be approximated. This is, for example, the case when a global polynomial basis or B-spline basis functions are used for the approximation of the value function within the discrete time dynamic programming approach. We apply our theoretical results to exemplary, representative dynamic portfolio choice models.

Online estimation for catalyst activity of acetylene hydrogenation reactor

AbstractIn the ethylene industry, the high purity of the ethylene product depends on hydrogenation in acetylene hydrogenation reactor. Because the catalyst deactivation leads to the moving of the operating point, the operation scheme must be adjusted continually according to the catalyst activity. It is necessary to estimate the catalyst activity online. Based on the discrete dynamic model of the acetylene hydrogenation reactor, the extended Kalman filter (EKF) is used to build the soft sensor for catalyst activity. Considering that EKF involves the large computation costs, we propose a method that estimates the parameters of the time‐varying deactivation kinetics model for the tradeoff of accuracy and complexity. The method is effective to reduce computation complexity of estimation, and simultaneously, the accuracy satisfies the process requirement.

Discrete Computational Neural Dynamics Models for Solving Time-Dependent Sylvester Equation With Applications to Robotics and MIMO Systems

In this article, a neural dynamics model is constructed and investigated for solving time-dependent Sylvester equation with matrix inversion involved in the solving process. Besides, to eliminate the matrix inversion in the model, the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno method is leveraged to construct a new model. Moreover, the global convergence performance and the effectiveness of the two discrete computational models are testified by providing theoretical analyses and numerical experiments with comparisons to the existing solutions, respectively. Two applications to robotics and the multiple-input multiple-output system are given to elucidate the feasibility of the proposed models for solving time-dependent Sylvester equation.

Market development of autonomous driving in Germany

Abstract This paper presents a model to predict the market penetration of autonomous cars for passenger transportation, focussing on autonomous taxis without a steering wheel. For this, a discrete system dynamics model was created and evaluated where the input parameters have been taken from the literature and a survey. In this survey, user demands were investigated among 873 participants. It showed that gender, age, job situation, city size and monthly income have an impact on the trust in the technology of autonomous driving as well as on the willingness to use autonomous taxis. In contrast, no evidence of an impact was found for the respondent’s education or the numbers of adults or children in the household. The results indicate that the majority of autonomous driving vehicles will be private and will have a steering wheel within the scope of this study, which covers the time frame until 2040. These are expected to reach 12.4 million units. At the same time, autonomous taxis will enter the market. These are expected to be mainly non-controllable (without a steering wheel), reaching a maximum of 2.4 million units by 2038. This maximum mainly depends on the trust in the technology as well as on people’s willingness to give up their own car due to cost or usage factors. As an autonomous taxi supports more people on average, the total number of vehicles is expected to drop from 45.1 million to around 41.7 million by 2040. Furthermore, the percentage of people travelling primarily by taxis and public transport is expected to increase from today’s 20.0% to about 32% in 2040. Then, about 19% will use autonomous taxis at least occasionally. Lastly, the vehicle miles travelled are expected to increase by 25% with people switching from public transport to autonomous taxis.

Research on Discrete Dynamic Forecasting Model of Government Human Resources

For the evolution of complex system, especially the unbalanced complex system, dynamic is its universal attribute. In this paper, by introducing the discrete dynamic system model in complex system research, a method of establishing the discrete dynamic system model of government human resources system is proposed from the vertical level. In this study, human resources were forecasted by the method of manpower/population ratio, linear regression and grey system, and the total number of health human resources in A city from 2018 to 2022 was forecasted by weighted average combination method. The results show that we should make great efforts to innovate the training mode of health personnel, improve the enthusiasm of staff, and reasonably control the expansion of hospitals.

A Dynamical Evolution Approach to High Placement Performance and Low Fault-Tolerant Cost for Bio-Inspired Self-Repairing Hardware

Bio-inspired self-repairing hardware is a reconfigurable system characterized by high fault-tolerant ability. To further increase the placement performance and reduce the fault-tolerant cost, a dynamical evolution approach to multi-objective dynamic placement is developed. A primary challenge for our study is computational complexity. Based on group theory, the computing task was divided on the dimensions of time and space to increase the utilization of online computing resources. By introducing the multi-step placement transformation, a discrete dynamical system model was built and the multi-objective dynamic placement was converted into a stability problem of constrained systems. In order to satisfy the dynamical requirements, an artificial particle system model was built and its evolution laws were verified by dynamic analysis. By simulating the evolution laws, a dynamical evolution algorithm was proposed, which could avoid large-scale iterative calculation used in the conventional optimization search algorithms. Experiments have shown that the dynamical evolution method could offer high placement performance with low fault-tolerant cost. Besides, it also has the advantage of high design flexibility since there is no initial placement constraint.

A New Formulation of Coupling and Sliding Motions of Grain Boundaries Based on Dislocation Structure

A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157--178] in which the long-range dislocation interaction is explicitly calculated.

Comparison of Planning Models for Dynamic Berth Allocation Problem Using A Sailfish-based Algorithm

Abstract Decide when and where allocate incoming ships at a container terminal is among the main problem confronted by port operators. This problem often called the Berth Allocation Problem (BAP).In this work, we realize an analytical study on the major planning models presented in the literature for the berth allocation problem, namely dynamic and discrete berth allocation problem model (DDBAP), dynamic and continuous berth allocation problem model (DCBAP) and dynamic and hybrid berth allocation problem model (DHBAP). The objective of this study is determine which model among the mentioned above can be used as a standard model for all type of terminal layouts and which of them ensure satisfactory outcome at level of minimization of ships turnaround time in the port. A commercial solver (CPLEX) as well as an efficient sailfish-based algorithm (SFA) are used to solve each model. Finally, computational experiences and comparison have been presented to demonstrate the most suited planning model.

Optimization of Dynamic Dispatch for Multiarea Integrated Energy System Based on Hierarchical Learning Method

The integrated energy system (IES) with various energy demands and distributed energy resources has been a significant approach to improve the efficiency of energy utilization. Considering the uncertainties of renewable energy sources and loads, the energy dispatch optimization for multiarea IESs is studied in this paper. Different from the most current studies, not only the electrical power and heat distribution in each area is optimized, but also the coordination power dispatch between areas. A hierarchical learning method is proposed inhere to improve the operation performance of the multiarea IESs. The proposed method with data-driven way is a model-free method which has no requirement for the accurate mathematical model. With the hierarchical structure, the electrical power dispatched between areas is optimized in upper layer, together with the dispatching optimization in each area at lower layer, to decrease the operation cost for the system and power demand from the power grid. Finite horizon discrete dynamic process model is adopted to simulate the data for learning. The simulation results show the effectiveness of the optimization policy can achieve an economic and stable operation for the multiarea IES.

Influence of rafted microstructures on creep in Ni-base single crystal superalloys: a 3D discrete dislocation dynamics study

Ni-base single-crystal superalloys exhibit a dynamic evolution of their microstructure during operation at elevated temperatures. The rafting of γ′ precipitates changes the mechanical behavior in a way that was understood insufficiently. In this work, we combine a phase-field method with a discrete dislocation dynamics model to clarify the influence of different rafted microstructures with the same initial dislocation density and configuration on creep behavior. The unrafted and rafted microstructures of Ni-base single crystal superalloys are simulated by a phase-field crystal plasticity method. By introducing these microstructures into a 3D discrete dislocation dynamics (DDD) model, the creep behavior under uniaxial loads of 350 and 250 MPa along [100] direction at 950 °C is studied. Due to the negative lattice mismatch of Ni-base superalloys, the N-type rafting with the formation of plate-like γ′ precipitates occurs under uniaxial tensile loads along {100} direction at high temperatures, while the P-type rafting with the formation of rod-like γ′ precipitates occurs under compressive loads. Taking the cuboidal, N-type rafted and P-type rafted microstructures as the initial and fixed microstructures for the same loading conditions, it is found from DDD simulations that the rafted microstructures result in smaller creep deformation than the cuboidal microstructure. The reason for this is that the coalescence of γ′ precipitates during the rafting diminishes the width of some γ channels, so as to increase the local Orowan stresses which retard the dislocation glide. For tensile loads, the N-type rafted microstructure has the best creep resistance. For a low compressive load, the P-type rafting shows a better creep resistance than N-type rafting.

One dimensional map-based neuron model: A phase space interpretation

Abstract Computational models play an essential role in studying and predicting the behavior of a bio-system. Discrete dynamical models, usually known as maps, are important, especially when it comes to the mathematical study of the behavior of the neurons and neural network. Map-based neural models are simple, yet powerful and computationally efficient tools to study complex dynamical systems. In this paper, a one-dimensional map-based neuron model is proposed for which various dynamical behaviors are investigated using phase-space interpretation. In order to reproduce the behaviors observed in the real neurons such as action potential (AP), spike, burst, chaotic burst and, myocardial AP, different multi-criteria functions are formulated. In our proposed model, all the mentioned dynamical behaviors can be obtained only by changing the respective parameter. Therefore, though being simple, in terms of both analytical solutions and numerical calculations, our model is perfectly capable of demonstrating complex behaviors. In this study, the response of the model to various stimuli (excitation current) is explored. The time series analysis, phase-space and cobweb plot are provided as well for each multi-criteria function. Also, the bifurcation analysis with respect to different parameters of the model is carried out.

Multifunctional Forestry and Interaction with Site Quality

Several studies have shown the economic value of various ecosystem services provided by the forest. However, the economic value of how site-specific ecological conditions interact with other functions provided by the forest, such as timber value and carbon sequestration, has been less studied. As a result, this paper constructs a numerical discrete dynamic optimization model to estimate the economic value of site quality, taking into account its interaction with timber value and carbon sequestration, in Swedish forests. Analytical results show that the inclusion of the interaction of site quality with forest growth affects the optimal volume of harvest per year, compared to the case without consideration of site quality. The empirical results show that net present value, when considering timber values plus carbon sequestration and site quality interaction, is higher than the case where only timber and carbon sequestration were considered. However, the calculated net present value is sensitive to, in particular, the price of carbon sequestration and discount rate.

Dynamic identification of boundary conditions for convection-diffusion transport model subject to noisy measurements

The paper addresses the problem of dynamic identification of boundary conditions for one-dimensional convection-diffusion transport model based on noisy measurements of the function of interest. Using finite difference method the original model with the partial differential equation is replaced with the discrete linear dynamic system model with noisy multisensor measurements in which boundary conditions are included as the unknown input vector. To solve the problem, the algorithm of simultaneous the state and input vector estimation is used. The results of numerical experiments are presented which confirm the practical applicability of the proposed approach.

Model-driven discovery of calcium-related protein-phosphatase inhibition in plant guard cell signaling.

The plant hormone abscisic acid (ABA) promotes stomatal closure via multifarious cellular signaling cascades. Our previous comprehensive reconstruction of the stomatal closure network resulted in an 81-node network with 153 edges. Discrete dynamic modeling utilizing this network reproduced over 75% of experimental observations but a few experimentally supported results were not recapitulated. Here we identify predictions that improve the agreement between model and experiment. We performed dynamics-preserving network reduction, resulting in a condensed 49 node and 113 edge stomatal closure network that preserved all dynamics-determining network motifs and reproduced the predictions of the original model. We then utilized the reduced network to explore cases in which experimental activation of internal nodes in the absence of ABA elicited stomatal closure in wet bench experiments, but not in our in silico model. Our simulations revealed that addition of a single edge, which allows indirect inhibition of any one of three PP2C protein phosphatases (ABI2, PP2CA, HAB1) by cytosolic Ca2+ elevation, resolves the majority of the discrepancies. Consistent with this hypothesis, we experimentally show that Ca2+ application to cellular lysates at physiological concentrations inhibits PP2C activity. The model augmented with this new edge provides new insights into the role of cytosolic Ca2+ oscillations in stomatal closure, revealing a mutual reinforcement between repeated increases in cytosolic Ca2+ concentration and a self-sustaining feedback circuit inside the signaling network. These results illustrate how iteration between model and experiment can improve predictions of highly complex cellular dynamics.

Modeling Wolbachia infection in mosquito population via discrete dynamical models

ABSTRACTWe formulate discrete dynamical models to study Wolbachia infection persistence by releasing Wolbachia-infected mosquitoes, which display rich dynamics including bistable, semi-stable and globally asymptotically stable equilibria. Our analysis shows a maximal maternal leakage rate threshold, denoted by , such that infected mosquitoes can only persist if it is not exceeded by . When , we find the Wolbachia infection frequency threshold, denoted by , such that the infected mosquitoes can persist provided that the initial infection frequency . For the case when , we find the release rate threshold, denoted by , for , the Wolbachia infection frequency threshold is reduced, and for , the threshold infection frequency is further lowered to 0 which implies that Wolbachia persistence is always successful for any initial infection frequency above 0.

Televacuna: ¿a qué estás esperando?

Discrete dislocation dynamics models dislocation-mediated plastic deformation and microstructural evolution in solids whilst discretely representing and tracking all line defects present in the medium. Hybrid methodologies for evaluating mechanical fields using continuum approaches while retaining the discrete formalism for evaluating dislocation kinematics and interactions have greatly improved the numerical efficiency of the method. In the present work, we propose a spectrally-based continuum solution of the mechanical fields based on the field dislocation mechanics framework which produces highly accurate elastic fields near dislocation cores in both isotropic and anisotropic media. Application of the model to a few elementary cases (i.e. dislocation junction formation, dislocation migration) show that the model proposed predicts accurate elastic fields both on the short and long range.

Development of Hybrid Simulation Model of Air Traffic Management in the Terminal Control Area

The air traffic density at the Terminal Control Area can lead to several problems related to the safety and efficiency of flight operation if not adequately managed. These problems include the increased risk of crashes between aircraft, airborne and ground delays, waste of fuel and environmental problems caused by gas emission and noise. One of the analysis tools to solve these problems is the hybrid simulation model. The socio technic characteristics of the system can be observed more intact using a hybrid simulation model so that the results of the analysis more precise and comprehensive. This article describes the research framework and progress on the development of the hybrid simulation model of an ATM system in the Terminal Control Area. The final model will integrate of agent-based simulation, discrete event simulation, and system dynamics models. An agent-based simulation model that defines the movement of aircraft in the Terminal Control Area has been developed in this early research phase. The initial model can describe the rules for minimum separation between aircraft that are applied to ensure the safety of flight operations. The following aircraft will reduce its speed so that an adequate separation distance is obtained with the aircraft in front of it. The model then will be improved by integrating a discrete event simulation and system dynamics models on the initial model to obtain a complete hybrid simulation model.