Initial Value Conditions Research Articles

Efficient probabilistic inference in biochemical networks

Biochemical networks are usually modeled by ordinary differential equations that describe the time evolution of the concentrations of the interacting (biochemical) species for specific initial concentrations and certain values of the interaction rates. They consist, in general, of many variables and parameters. Parameter estimation of such systems using standard optimization algorithms is computationally expensive since a large number of numerical simulations must be performed for numerous values of initial conditions and parameters, making these approaches either inefficient or inaccurate. In this paper, we explain how biochemical networks can be approximated by dynamic Bayesian networks, a class of discrete probabilistic models. This type of approximation enables the use of Bayesian inference for performing tasks such as parameter estimation. We explain how to make this type of approximations and the subsequent parameter estimation task as accurate and computationally efficient as possible. Our approach is applied on concrete examples such as the EGF-NGF cellular signaling pathway.

Preassigned Time Adaptive Neural Tracking Control for Stochastic Nonlinear Multiagent Systems With Deferred Constraints.

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

Kiphynet: an online network simulation tool connecting cellular kinetics and physiological transport.

Human metabolism is sustained by functional networks that operate at diverse scales. Capturing local and global dynamics in the human body by hierarchically bridging multi-scale functional networks is a major challenge in physiological modeling. To develop an interactive, user-friendly web application that facilitates the simulation and visualization of advection-dispersion transport in three-dimensional (3D) microvascular networks, biochemical exchange, and metabolic reactions in the tissue layer surrounding the vasculature. To help modelers combine and simulate biochemical processes occurring at multiple scales, KiPhyNet deploys our discrete graph-based modeling framework that bridges functional networks existing at diverse scales. KiPhyNet is implemented in Python based on Apache web server using MATLAB as the simulator engine. KiPhyNet provides the functionality to assimilate multi-omics data from clinical and experimental studies as well as vascular data from imaging studies to investigate the role of structural changes in vascular topology on the functional response of the tissue. With the network topology, its biophysical attributes, values of initial and boundary conditions, parameterized kinetic constants, biochemical species-specific transport properties such as diffusivity as inputs, a user can use our application to simulate and view the simulation results. The results of steady-state velocity and pressure fields and dynamic concentration fields can be interactively examined. KiPhyNet provides barrier-free access to perform time-course simulation experiments by building multi-scale models of microvascular networks in physiology, using a discrete modeling framework. KiPhyNet is freely accessible at http://pallab.cds.iisc.ac.in/kiphynet/ and the documentation is available at https://deepamahm.github.io/kiphynet_docs/ .

APPLICATION OF ROLE-PLAYING METHOD TO OVERCOME STUDENTS' LEARNING DIFFICULTIES IN LEARNING MATH STORY PROBLEMS IN SANGUWATANG 1 STATE ELEMENTARY SCHOOL KARANGJAMBU SUBDISTRICT

The background is the evaluation results of Class V students at SD Negeri 1 Sanguwatang where, from the composition of the questions tested, in general the students were not capable and still found it difficult to complete story questions. From the results of observations of students' answer sheets, it appears that there are several reasons why students have difficulty solving mathematics story problems, such as: the ability to interpret the language of the questions is still lacking, students cannot determine what is known and what is being asked and students' ability to determine the mathematical model to be used. in solving problems. Therefore, the role-playing method is applied in the learning process. This research aims to determine the effectiveness of applying the role-playing method in improving student learning outcomes, especially in mathematics story problems. With role-playing, it is hoped that students will be able to realistically describe abstract things in the story. The research procedure was carried out in three cycles: planning, implementation, observation and reflection stages. Data collection techniques use qualitative (attitudes) and quantitative (values) data. Data analysis was carried out using comparative descriptive analysis, namely comparing the values ​​of students' initial conditions, first cycle, second cycle and third cycle. Based on the actions taken, it can be concluded that the role-playing method can improve mathematics learning outcomes in story problems at SD Negeri 1 Sanguwatang. The results of observations on student activities turned out to have good relevance to support improved learning outcomes. The average test results for learning mathematics story problems through role - playing were 60.16 in the initial condition, 64.36 in the first cycle, 68.6 in the second cycle and 79.56 in the third cycle. For the level of learning completeness with a completeness limit of 65, the initial condition is 40%, the first cycle is 56%, the second cycle is 76%, and the third cycle is 92%.

Identification and characterization of chitinase producing marine microorganism: Unleashing the potential of chitooligosaccharides for bioethanol synthesis

The dwindling supply of the petroleum product and its carbon footprint has initiated search for a sustainable fuel and alternate feed-stocks. One such underexplored feedstock is chitin, a waste derived from sea food processing. The limitation of insolubility and crystallinity inherent in chitin is addressed with the chitin hydrolysates. In the present study, a chitinases producing marine isolate was isolated from the sediments of Arabian Sea from a depth of 20 m. In order to increase the expression of the chitinases, sequential optimisation using one factor at a time and Taguchi experimental designs were employed which resulted in a yield of 13.46 U/mL which was 2.62 fold higher than the initial bioprocess condition values. In a two-step refinery protocol, Candida albicans was evolved towards chitooligosaccharides using chemically synthesized hydrolysates. In a fed –batch fermentation design the Candida yielded a 12.8 % conversion of these commercial chitin oligosaccharides into bioethanol in a run time of 48 h. This is the first report demonstrating the potential of Candida to utilise chitin oligosaccharides for the production of bioethanol.

Optimized energy management for plug-in hybrid vehicles with predicted driving cycles1

The traditional rule-based energy management strategy for plug-in hybrid vehicles has issues, such as difficulty in online correction and limited online optimization capabilities. In addition, the global optimization energy management strategy cannot be applied online or in real-time. Considering the above difficulties, this study proposes a real-time optimization energy management strategy based on the Markov chain for driving condition prediction and online optimization with the minimum principle. To verify the proposed control strategy, the plug-in hybrid vehicle dynamics model, driving condition prediction model, and online optimization control model were first established. The initial value of the battery state of charge was set to 0.4 under the UDDS (Urban Dynamometer Driving Schedule) standard cycle. The simulation results showed that the comprehensive fuel consumption cost was 1.66 yuan, which was 8.28% better than the energy economy of the traditional rule-based energy management strategy. At the same time, a complete vehicle test was also conducted based on a sample vehicle test platform. The experimental results indicated that the energy management strategy proposed herein exhibits better fuel economy compared to that exhibited by the traditional rule-based energy management strategy. Simulations and experiments have verified the effectiveness of the proposed control strategy in this study.

Model order reduction based on Laguerre orthogonal polynomials for parabolic equation constrained optimal control problems

In this paper, two model order reduction methods based on Laguerre orthogonal polynomials for parabolic equation constrained optimal control problems are studied. The spatial discrete scheme of the cost function subject to a parabolic equation is obtained by Galerkin approximation, and then the coupled ordinary differential equations of the optimal original state and adjoint state with initial value and final value conditions are obtained by Pontryagin's minimum principle. For this original system, we propose two kinds of model order reduction methods based on the differential recurrence formula and integral recurrence formula of Laguerre orthogonal polynomials, respectively, and they are totally different from these existing researches on model order reduction only for initial value problems. Furthermore, we prove the coefficient-matching properties of the outputs between the reduced system and the original system. Finally, two numerical examples are given to verify the feasibility of the proposed methods.

Comprehensive evaluation of intrinsic safety of railway facilities and equipment based on improved cloud model-fuzzy Petri net

In order to achieve the goal of transforming China into a modernized railway powerhouse, a comprehensive evaluation model of intrinsic safety is constructed in this paper by focussing on the intrinsic safety of railway facilities and equipment. Firstly, the index system for evaluating the intrinsic safety of railway facilities and equipment is divided. Secondly, the fuzzy Petri net (FPN) model for intrinsic safety evaluation is constructed according to the fuzzy generative rules, and the similarity calculation method of the cloud model based on shape and distance is applied to derive the initial state value of the FPN model and carry out the calculation of fuzzy reasoning of the intrinsic safety. Finally, the comprehensive evaluation of intrinsic safety is carried out using the example of railroad facilities and equipment at one China Railway Group bureau’s station section. The results indicate that the intrinsic safety level of the station section falls into Class IV intrinsic safety, exhibiting a few vulnerabilities. However, the risk level is low, aligning with the findings of the actual research. Moreover, the evaluation results based on the FPN, the cloud model’s similarity calculation method and the suggested method are compared and analysed with the findings of the actual research. The comparative results demonstrate the accuracy and scientificity of the proposed method, providing a reference for enhancing the intrinsic safety of railway facilities and equipment.

SUBSTANTIATION OF THE RESULTS OF THE LASER LOCATION OF THE TRAJECTORY OF THE MOON MOVING AWAY FROM THE EARTH

Progress in astronomical measurements of the trajectories of the movement of celestial bodies reveals new effects that require justification. In particular, it refers to the slight drift of the Moon from the Earth. A solution to this problem is possible only based on an adequate mathematical model. To perform this, it was adapted Newton's law of universal gravitation to the case of moving masses in flat space and physical time. At the same time, the final speed of propagation of the gravitational field can be considered. The differential equations of motion of the three-mass Sun-Earth-Moon cosmic system are obtained. In the heliocentric coordinate system, transient processes of the movement of the named celestial bodies are simulated, which testify to the presence of the Moon moving away from the Earth and the influence of the effects of movement on its course. The significant dependence of the final result on numerical methods of integration, computer calculation tools, and the values of space-velocity initial conditions is shown. The results of the simulation of transient processes are attached.

The infinite-dimensional Pontryagin maximum principle for optimal control problems of fractional evolution equations with endpoint state constraints

<abstract><p>In this paper, we study the infinite-dimensional endpoint state-constrained optimal control problem for fractional evolution equations. The state equation is modeled by the $ \mathsf{X} $-valued left Caputo fractional evolution equation with the analytic semigroup, where $ \mathsf{X} $ is a Banach space. The objective functional is formulated by the Bolza form, expressed in terms of the left Riemann-Liouville (RL) fractional integral running and initial/terminal costs. The endpoint state constraint is described by initial and terminal state values within convex subsets of $ \mathsf{X} $. Under this setting, we prove the Pontryagin maximum principle. Unlike the existing literature, we do not assume the strict convexity of $ \mathsf{X}^* $, the dual space of $ \mathsf{X} $. This assumption is particularly important, as it guarantees the differentiability of the distance function of the endpoint state constraint. In the proof, we relax this assumption via a separation argument and constructing a family of spike variations for the Ekeland variational principle. Subsequently, we prove the maximum principle, including nontriviality, adjoint equation, transversality, and Hamiltonian maximization conditions, by establishing variational and duality analysis under the finite codimensionality of initial- and end-point variational sets. Our variational and duality analysis requires new representation results on left Caputo and right RL linear fractional evolution equations in terms of (left and right RL) fractional state transition operators. Indeed, due to the inherent complex nature of the problem of this paper, our maximum principle and its proof technique are new in the optimal control context. As an illustrative example, we consider the state-constrained fractional diffusion PDE control problem, for which the optimality condition is derived by the maximum principle of this paper.</p></abstract>

Research on rapid extraction of internal resistance of lithium battery based on short-time transient response

Unlike laboratory measurements and online parameter observations based on long-term continuous operation data, offline fast measurement of battery parameters is widely used for convenient and accurate acquisition of battery parameters in battery production and maintenance processes. However, too short allowable measurement time in engineering results in a small amount of dynamic information that the algorithm can obtain and unclear initial state values, making it difficult to improve the accuracy of the algorithm. This paper employs a local coordinate system established in the vicinity of the measurement moment to extract the transient behavior of battery terminal voltage response under excitation current, and investigates the characterization capability of these transients on ohmic and polarization internal resistance of batteries at different time points. Moreover, based on an equivalent circuit model, it evaluates how initial values of transient voltage affect accuracy in calculating internal resistance. Through customized working condition verification, the selection principles for rapid identification of time points and the basic requirements for excitation conditions have been determined. Comparative verification of online parameter identification results based on continuous time series demonstrates that the fast identification algorithm can accurately identify Ohmic internal resistance and effectively characterize the variation law of battery polarization.

Analysis of Linear LIF Neuron Model under Particular Initial Value Conditions and Solution Method

Leaky Integrate and Fire (LIF) modeli, nöronların matematiksel olarak modellenmesi ve çalışma prensiplerinin anlaşılması için yaygın olarak kullanılmaktadır. Birçok metot ve yöntem sayesinde modelin simülasyonu ve analizi yapılsa da mühendislik çalışmalarına uygun çözümlerin azlığından söz etmek mümkündür. Birinci dereceden adi diferansiyel denklemler içeren LIF modelinin çözümüne ideal başlangıç koşulları altında kolayca ulaşılırken, karmaşık şartlar sunulduğunda sonucu bulmak zorlaşmaktadır. Bu çalışmada nöronun, birim adım akımı, darbe akımı ve rastgele seçilen akım girişleri için çözümleri yapılmıştır. Böylece literatürde yer alan metotların özel durumlar ortaya çıktığında nasıl uygulanması gerektiği gösterilmiştir.

Reinforcement learning-based optimal adaptive fuzzy control for nonlinear multi-agent systems with prescribed performance

In this paper, the problem of optimal adaptive consensus tracking control for nonlinear multi-agent systems with prescribed performance is investigated. To address the issue of satisfying the initial value conditions in existing results, an improved performance function is employed as the prescribed performance boundary, effectively resolving this problem. Then, by employing the error transformation function, the constrained system is converted into an unconstrained one. Furthermore, fuzzy logic systems are employed to identify unknown system parts. By applying the dynamic surface technique, the problem of "differential explosion", which often occurs in backstepping, is solved. Moreover, a distributed optimal adaptive fuzzy control protocol based on the reinforcement learning actor-critic algorithm is proposed. Under the proposed control scheme, it is proved that all the signals within the closed-loop system are bounded, and the consensus tracking errors have remained within the predefined bounds. Finally, the numerical simulation results demonstrate the effectiveness of the proposed scheme.

Reform and Innovation of Civic and Political Education Based on Deep Enhanced Learning Methods

Abstract The use of an initial state value function and an optimal strategy are used in this paper to solve educational problems based on deep reinforcement learning. Deep reinforcement learning’s approximate function is defined, and the matrix model is created by training tuning using learning methods like gradient descent. To analyze the modeling process of reinforcement learning, reward values are added to the Markov decision transfer matrix and the expected value of cumulative returns is calculated. The weights are trained using the Bellman equation to enhance the algorithm’s stability. In evaluating the effect of reform and innovation in Civic Education, the teacher education concept is rated as 10 points. The reform and innovation of civic education, combined with deep reinforcement learning, can promote the reform of education and teaching modes, improving the efficiency and quality of education.

On Local Unique Solvability for a Class of Nonlinear Identification Problems

Nonlinear identification problems for evolution differential equations, solved with respect to the highest-order Dzhrbashyan–Nersesyan fractional derivative, are studied. An equation of the considered class contains a linear unbounded operator, which generates analytic resolving families for the corresponding linear homogeneous equation, and a continuous nonlinear operator, which depends on lower-order Dzhrbashyan–Nersesyan derivatives and a depending on time unknown element. The identification problem consists of the equation, Dzhrbashyan–Nersesyan initial value conditions and an abstract overdetermination condition, which is defined by a linear continuous operator. Using the contraction mappings theorem, we prove the unique local solvability of the identification problem. The cases of mild and classical solutions are studied. The obtained abstract results are applied to an investigation of a nonlinear identification problem to a linearized phase field system with time dependent unknown coefficients at Dzhrbashyan–Nersesyan time-derivatives of lower orders.

Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator

Differential equations containing fractional derivatives, for both time and spatial variables, have now begun to attract the attention of mathematicians and physicists; they are used in connection with these equations as mathematical models of various processes. The fractional derivative equation tool plays a crucial role in describing plenty of natural processes concerning physics, biology, geology, and so on. In this paper, we studied a loaded equation in relation to a spatial variable for a linear pseudoparabolic equation, with an initial and second boundary value condition (the Neumann condition), and a fractional Caputo derivative. A distinctive feature of the considered problem is that the load at the point is in the higher partial derivatives of the solution. The problem is reduced to a loaded equation with a nonlocal boundary value condition. A way to solve the considered problem is by using the method of energy inequalities, so that a priori estimates of solutions for non-local boundary value problems are obtained. To prove that this nonlocal problem is solvable, we used the method of continuation with parameters. The existence and uniqueness theorems for regular solutions are proven.

New stochastic convergence theorems: Overcoming the limitations of LaSalle theorems

LaSalle theorems, sometimes called as invariance-like theorems, have witnessed abundant applications as powerful tools of analysing system convergence. However, these theorems have twofold limitations: On the one hand, the uniformity of convergence with respect to initial state values cannot be offered, which indicates that the possibility of excessively slow convergence could not be ruled out for a given bounded set of initial state values. On the other hand, unbounded time-variations are not allowed in the systems, and meanwhile, the boundedness of all the states are required even if one merely concerns the convergence of partial states, precluding many scenarios with the unboundedness (e.g., induced by stochastic noise) for some states defined on the whole time horizon. Towards the limitations of LaSalle theorems, this paper seeks to further develop convergence theorems in the stochastic framework. First, a Lyapunov-like function based theorem on the convergence owning the uniformity with respect to initial state values is presented for Itô-type stochastic systems, with the infinitesimal of Lyapunov-like functions exploited more delicately than those in stochastic LaSalle theorems. Based on this, a framework of adaptive stabilization with the uniformity of convergence is established for uncertain stochastic nonlinear systems. In particular, the performance specifications involved are impossible to achieve by applying LaSalle theorems as in the related results. Second, an enlarged convergence theorem is established with Lyapunov-like conditions moderately relaxed, which allows the unboundedness for partial states defined on the whole time horizon and has potential applications in the presence of unbounded time-variations. What is notable, the enlarged convergence theorem is nontrivial to verify, which compels us to propose an extended Barbălat lemma with the conventional requirement of uniform continuity relaxed in the stochastic framework.

Relationship between fluorescence characteristics of coal macerals and excitation time

The fluorescence characteristics of coal macerals can be used as one of the indexes to evaluate the properties of coking coal. In this work, a single-wavelength laser with a wavelength of 360 nm was used as the excitation source to excite the surface of particulate block under a polarizing microscope. Effect of excitation time on fluorescence characteristics of the macerals was studied. The relationship between spontaneous fluorescence intensity and the excitation time of each maceral of six kinds of coking coals show that the fluorescence characteristics of coal macerals are related to the type and metamorphism of coal. The excitation time has a certain effect on the fluorescence parameters of the macerals. By comparing the relative fluorescence intensity values under different excitation times, it is found that the mean relative fluorescence intensity within 15 s can be used as an optical parameter to characterize the structure and metamorphic grade of different macerals. The essence of this method is to express movement of electrons in outer layer of nucleus by macroscopic fluorescence spectrum and relative fluorescence intensity of the initial state value and simplify microscopic complexity into macroscopic and numerical form generally accepted.

Optical undular bores in Riemann problem of photon fluid with quintic nonlinearity.

This work develops the Whitham theory to study the Riemann problem of the Gerdjikov-Ivanov equationthat describes the photon fluid with quintic nonlinearity. The one-phase periodic solution of the Gerdjikov-Ivanov equationand the corresponding Whitham equationare derived by the finite gap integration method. Subsequently, the main basic wave structures arising from the discontinuous initial-value conditions are found by distinguishing the distributions of the Riemann invariants. Some exotic optical undular bores are observed by classifying the solutions of the Riemann problem of the Gerdjikov-Ivanov equation. It is observed that the analytical results from Whitham theory are in excellent agreement with the numerical solutions.

Quantification of forest carbon flux and stock uncertainties under climate change and their use in regionally explicit decision making: Case study in Finland

Uncertainties are essential, yet often neglected, information for evaluating the reliability in forest carbon balance projections used in national and regional policy planning. We analysed uncertainties in the forest net biome exchange (NBE) and carbon stocks under multiple management and climate scenarios with a process-based ecosystem model. Sampled forest initial state values, model parameters, harvest levels and global climate models (GCMs) served as inputs in Monte Carlo simulations, which covered forests of the 18 regions of mainland Finland over the period 2015–2050. Under individual scenarios, the results revealed time- and region-dependent variability in the magnitude of uncertainty and mean values of the NBE projections. The main sources of uncertainty varied with time, by region and by the amount of harvested wood. Combinations of uncertainties in the representative concentration pathways scenarios, GCMs, forest initial values and model parameters were the main sources of uncertainty at the beginning, while the harvest scenarios dominated by the end of the simulation period, combined with GCMs and climate scenarios especially in the north. Our regionally explicit uncertainty analysis was found a useful approach to reveal the variability in the regional potentials to reach a policy related, future target level of NBE, which is important information when planning realistic and regionally fair national policy actions.