Set Of Initial Values Research Articles

BAYESIAN ESTIMATION OF FOUR PARAMETERS ADDITIVE CHEN-WEIBULL DISTRIBUTION

Models with bathtub-shaped failure rate function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this study, the additive Chen-Weibull (ACW) distribution with increasing and bathtub-shaped failure rates function is studied using Bayesian and non-Bayesian approach using two real data set. The Bayes estimator were obtained by assuming non-informative prior (Half-Cauchy) under square error loss function (SELF), the Laplace Approximation and Monte Carlo Markov Chain (MCMC) techniques conducted in R were used to approximate the posterior distribution of ACW model. In addition, the maximum product of spacing method (MPS) of estimation is also considered using mpsedist function in BMT package in R with good set of initial values of parameters. We compared the performance of the two difference estimation methods by using Kolmogorov-Smirnov test. And the result showed that MPSEs method outperformed Bayesian approach

Adaptive Pre-Aim Control of Driverless Vehicle Path Tracking Based on a SSA-BP Neural Network

Aiming at the problem that the tracking accuracy of unmanned vehicle path tracking preview control is greatly affected by the preview time, a BP neural network adaptive preview control method is proposed. Considering that the prediction effect of the BP neural network is limited to the initial value setting, a preview time adjuster based on the SSA-BP neural network was established; by establishing the relationship between the front wheel steering angle and the preview time, a new direction control driver model was formed. The driver model and the preview time adjuster together constitute an adaptive steering controller. In order to solve the influence of the longitudinal speed change on the vehicle stability, a PID variable-speed controller was designed to realize the horizontal and vertical coordinated control of the path tracking of the unmanned vehicle. Compared with the fixed preview time and the BP preview time control method, the results show that the proposed method has strong tracking ability when driving at various speeds on three consecutive curves and Alt 3 test roads, and can be used when driving at a variable speed.

Addendum: Painlevé transcendents and -symmetric Hamiltonians (2015 J. Phys. A: Math. Theor. 48 475202)

This paper is an Addendum to reference Bender and Komijani (2015 J. Phys. A: Math. Theor. 48 475202) (which stems from an earlier paper Bender et al (2014 J. Phys. A: Math. Theor. 47 235204)), where it was demonstrated that unstable separatrix solutions to the Painlevé equations I and II are determined by -symmetric Hamiltonians. Here, unstable separatrix solutions of the fourth Painlevé transcendent are studied numerically and analytically. It is shown that for a fixed initial value such as y(0) = 1 a discrete set of initial slopes y′(0) = b n give rise to separatrix solutions. Similarly, for a fixed initial slope such as y′(0) = 0 a discrete set of initial values y(0) = c n give rise to separatrix solutions. For Painlevé IV the large-n asymptotic behavior of b n is b n ∼ B IV n 3/4 and that of c n is c n ∼ C IV n 1/2. The constants B IV and C IV are determined both numerically and analytically. The analytical values of these constants are found by reducing the nonlinear Painlevé IV equation to the linear eigenvalue equation for the sextic -symmetric Hamiltonian .

Trajectory dimensionality reduction and hyperparameter settings of DBSCAN for trajectory clustering

The density-based spatial clustering of application with noise (DBSCAN) algorithm has good robustness and is widely employed to cluster vehicle trajectories for vehicle movement pattern recognition. However, the distance or similarity between two trajectories varies from tens to hundreds of thousands, and there is no effective method for determining the values of the hyperparameters eps and MinPts of DBSCAN. In addition, with increasing sizes of trajectory datasets, some trajectory clustering methods that directly analyse points and line segments incur large computational costs and time overhead. To solve these two dilemmas, the authors propose an effective trajectory dimensionality reduction method and a DBSCAN hyperparameter initial value setting method. The trajectory dimensionality reduction algorithm processes trajectories with different lengths into the same dimensionality (the same number of feature points). The reserved points preserve the spatial and temporal information of these trajectories as much as possible. The DBSCAN hyperparameter initial value setting algorithm obtains the effective initial values of eps and MinPts for facilitating subsequent adjustments. Finally, we validate these proposed methods on two trajectory datasets collected from two real-world scenes, and the experimental results are promising and effective.

A nonlinear version of Halanay's inequality for the uniform convergence to the origin

<p style='text-indent:20px;'>A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.</p>

対話型デザインにおける任意オノマトペを用いたデザインパラメータの初期値設定に対する主観評価

対話型デザインにおける任意オノマトペを用いたデザインパラメータの初期値設定に対する主観評価

Modeling and analysis on the transmission of covid-19 Pandemic in Ethiopia

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R0=1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally.

State feedback H ∞ control for a class of affine nonlinear singular systems: Input restricting approach

Here, a new method for solving the H∞ control problem for a class of affine nonlinear singular systems is presented. The main idea is to restrict the control inputs and initial states to the sets of admissible inputs and consistent initial values, respectively. Consequently, the impulse-freeness of the system response is guaranteed. In this regard, a novel concept of “distance from the admissible inputs set” is introduced. Based on this concept, a set of sufficient conditions for the H∞ control problem's solvability and the corresponding H∞ controller is provided. The adopted approach can also be employed to solve the H∞ control problem for indefinite nonlinear singular systems as well as non-singular nonlinear systems with a restricted inputs set. Sufficient conditions for the solvability of and corresponding solution to these problems are also presented. Finally, the practicality of this method is illustrated using a numerical example.

Comparing Three Different Estimators of Fuzzy Reliability of Modified Weibull

This paper deals with obtaining two parameters (p,θ), modified weibull, using entropy transformation, and also the cumulative distribution function, and also reliability function are obtained, and the rth moment formula about origin is derived. The two parameters (p,θ) estimated by Maximum Likelihood (MLE) and Moments Estimator and Proposed method and, then fuzzy reliability is compared by simulation methods.Taking four size of sample (n= 20, 40, 60, and 80), and different sets of initial values of parameters (p,θ) as well as fuzzy parameter(ki), and all the results are explained in tables.

Assessing the role of initial conditions in the local structural identifiability of large dynamic models

Structural identifiability is a binary property that determines whether or not unique parameter values can, in principle, be estimated from error-free input–output data. The many papers that have been written on this topic collectively stress the importance of this a priori analysis in the model development process. The story however, often ends with a structurally unidentifiable model. This may leave a model developer with no plan of action on how to address this potential issue. We continue this model exploration journey by identifying one of the possible sources of a model’s unidentifiability: problematic initial conditions. It is well-known that certain initial values may result in the loss of local structural identifiability. Nevertheless, literature on this topic has been limited to the analysis of small toy models. Here, we present a systematic approach to detect problematic initial conditions of real-world systems biology models, that are usually not small. A model’s identifiability can often be reinstated by changing the value of such problematic initial conditions. This provides modellers an option to resolve the “unidentifiable model” problem. Additionally, a good understanding of which initial values should rather be avoided can be very useful during experimental design. We show how our approach works in practice by applying it to five models. First, two small benchmark models are studied to get the reader acquainted with the method. The first one shows the effect of a zero-valued problematic initial condition. The second one illustrates that the approach also yields correct results in the presence of input signals and that problematic initial conditions need not be zero-values. For the remaining three examples, we set out to identify key initial values which may result in the structural unidentifiability. The third and fourth examples involve a systems biology Epo receptor model and a JAK/STAT model, respectively. In the final Pharmacokinetics model, of which its global structural identifiability has only recently been confirmed, we indicate that there are still sets of initial values for which this property does not hold.

Environment humidity and temperature prediction in agriculture using Mamdani inference systems

<span>This paper presents the results of a humidity and temperature prediction model in the environment for agriculture, using diffuse sets and optimizing their parameters by heuristic methods, such as genetic algorithms, and exact methods such as Quasi-Newton. It has been identified that non-specialized users could have difficulties in understanding the system dynamics and the behavior of variables over time. The aim of this research is obtain models with a high level of interpretability and accuracy that allows predicting the temperature and humidity values for the environment. The use of fuzzy logic to present a solution has great advantages as this system is highly rated for interpretability. Furthermore, by relating the obtained values for environment humidity and temperature to qualitative categories as high, medium or low, it allows non-specialized users to have a better understanding of the system dynamics. Two optimization techniques are applied to two different diffuse sets that allow the prediction of the humidity and temperature. It is found that the best implementation involves a Mamdani fuzzy inference system optimized with Quasi-Newton algorithm that uses a set of initial values attained through a previous optimization process with a genetic algorithm.</span>

Inversion of Initial Field Based on a Temperature Transport Adjoint

The setting of initial values is one of the key problems in ocean numerical prediction, with the accuracy of sea water temperature (SWT) simulation and prediction greatly affected by the initial field quality. In this paper, we describe the development of an adjoint assimilation model of temperature transport used to invert the initial temperature field by assimilating the observed data of sea surface temperature (SST) and vertical temperature. Two ideal experiments were conducted to verify the feasibility and validity of this method. By assimilating the “observed data”, the mean absolute error (MAE) between the simulated temperature data and the “observed data” decreased from 1.74 °C and 1.87 °C to 0.13 °C and 0.14 °C, respectively. The spatial distribution of SST difference and the comparison of vertical data also indicate that the regional error of vertical data assimilation is smaller. In the practical experiment, the monthly average temperature field provided by World Ocean Atlas 2018 was selected as background filed and optimized by assimilating the SST data and Argo vertical temperature observation data, to invert the temperature field at 0 a.m. on 1 December 2014 in the South China Sea. Through data assimilation, MAE was reduced from 1.29 °C to 0.65 °C. In terms of vertical observations data comparison and SST spatial distribution, the temperature field obtained by inversion is in good agreement with SST and Argo observations.

A super-fast optimal attitude matrix in attitude determination

The fast optimal attitude matrix (FOAM) for minimizing Wahba’s loss function solves the optimal attitude matrix directly and efficiently. This method is more intuitive compared with the method of calculating attitude quaternion. A method named super-FOAM (SFOAM) is proposed with a more precise initial iteration value and a faster iterative algorithm. A condition number estimation method of third-order matrices is presented for cases without exact singular value. When the matrix condition number is not particularly large, the root-seeking formula for the quartic equation is directly used to obtain the maximum characteristic root. Otherwise, under large condition numbers, a high-accuracy estimation algorithm for the maximum eigenvalue is given to achieve a high-accuracy initial value set, which is beneficial to iteration reduction and convergence speed improvement. Finally, some comparative simulations show that the SFOAM method has the same accuracy as the singular value decomposition (Matlab) method even in the case of a very large matrix condition number, while the SFOAM’s computation is only 50%–60% of the traditional FOAM algorithm. This algorithm has good generalization and application values.

Bayesian multivariate latent class profile analysis: Exploring the developmental progression of youth depression and substance use

Multivariate latent class profile analysis (MLCPA) is a useful tool for exploring the stage-sequential process of multiple latent class variables, but the inference can be challenging due to the high-dimensional latent structure of the model. In this paper, a Bayesian approach via Markov chain Monte Carlo (MCMC) is proposed for MLCPA as an alternative to the maximum-likelihood (ML) method. Compared to the ML solution, Bayesian estimates are less sensitive to the set of initial values as well as easier to obtain standard errors. We also address issues in MCMC such as label-switching problem with a dynamic data-dependent prior and computational complexity with a recursive formula. Simulation studies revealed the validity and efficiency of the proposed algorithm. An empirical analysis of MLCPA using the National Longitudinal Survey of Youth 97 (NLSY97) identified a small number of representative developmental progressions of adolescent depression and substance use.

Image Compression Using Fractal Functions

The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

The impact of social media marketing strategies on promoting sustainability of tourism with fuzzy cognitive mapping: a case of Kalanggaman Island (Philippines)

The current literature has espoused the role of social media platforms in promoting tourism destinations. Despite such advances, limited works are reported on how social media foster the sustainability of tourist destinations. This work builds upon the argument that sustainable tourism (ST) agenda and initiatives can be integrated alongside the traditional competitive mission of social media marketing as a communications strategy of tourism stakeholders. With such an argument and the scarce literature on the topic, this paper analyzes the impact of social media strategies on marketing indicators contextualized within ST. In addressing this objective, a fuzzy cognitive mapping technique is adopted to examine the changes in marketing performance indicators given an initial set of activation values of social media marketing strategies. A case study in Kalanggaman Island (Philippines), an emerging tourist destination, is carried out to demonstrate the evaluation process. Three policy scenarios with interrelated social media marketing strategies are examined: minimal effort, moving visuals, and collaborative strategies. The minimal effort scenario increases counting metrics, comments, and Web traffic, while the moving visuals scenario yields increases in reach, counting metrics, comments, and Web traffic. Finally, the collaborative strategies scenario enhances indicators on awareness, the share of voice, counting metrics, comments, and lead. The findings generated from the proposed framework provide policy- and decision-makers a platform for analyzing possible social media policies in disseminating the ST agenda.

Reducing Criteria in Multicriteria Group Decision-Making Methods Using Hierarchical Clustering Methods and Fuzzy Ontologies

Multicriteria group decision-making environments that have a high number of criterion values can be difficult for the experts to handle. This is due to the fact that the experts have to take too much information into account. Thus, they get lost among all the possibilities and have difficulties making the right decision. In order to solve this problem, we present a novel multicriteria group decision-making method that reduces the initial set of criterion values in an organized way. Hierarchical clustering methods are used in order to generate a new reduced criteria set that can be handled by the experts. Fuzzy ontologies are used as an aid system that stores how much each alternative fulfills each criterion. The presented method makes it possible for the experts to carry out the group decision-making process by focusing on ranking the reduced set of criterion values. As a result, a comfortable decision environment is generated, in which the experts can make decisions by managing a fair amount of information. The aid provided by fuzzy ontologies allows the experts to focus on establishing the importance of the criterion values, leaving the rest to the computational system.

Attribute‐Based Worker Selection Scheme by Using Blockchain in Decentralized Crowdsourcing Scenario

Traditional crowdsourcing based on centralized management platform is vulnerable to Distributed denial of service (DDoS) attack and single point of failure. Combining blockchain technology with crowdsourcing can well solve the above problems, enabling users to realize peer-to-peer transactions and collaboration based on decentralized trust in distributed systems where nodes do not need to trust each other. Although the current methods have solved the above problems, task publishers select workers based on their reputation values, which has two disadvantages: subjectivity and difficulty in initial value setting. Due to the complexity of crowdsourcing network, there will be malicious users in the network. The requirement for anonymity protects both legitimate and malicious users. In order to solve these problems, we propose an attribute-based worker selection scheme using the private set intersection technology. Our scheme also realizes the malicious user identity disclosure function. A concrete example of our scheme is given.

Determination of the Initial Value Ranges of Nonlinear Solutions for a Log Ratio Bathymetric Inversion Model and Bathymetry Retrieval

The log-ratio model (LRM) with three model parameters ( ${\boldsymbol{n}}$ , ${{\boldsymbol{m}}_1},$ and ${{\boldsymbol{m}}_0}$ ) has been widely used in shallow water bathymetry of multispectral images. At present, obtaining LRM model parameters by optimization algorithms depends on the setting of initial values [ ${\boldsymbol{n}}(0)$ , ${{\boldsymbol{m}}_1}(0),$ and ${{\boldsymbol{m}}_0}(0)$ ] or initial value ranges. However, how to set the initial value can obtain model parameters more effectively and credibly, and the significance of each initial value in the optimization process is very important for LRM bathymetric retrieval method. In this article, remote sensing images and bathymetric data were used to determine the initial value ranges of credible model parameters, and then the sensitivity of each parameter was analyzed in the algorithm optimization process from the partial differential perspective, and the bathymetry was retrieved in the sea area near Ganquan Island. The results show that according to the partial differential analysis of model parameters, ${\boldsymbol{n}}$ , with the smallest change rate in three LRM parameters and the rate of ${{\boldsymbol{m}}_1}$ and ${{\boldsymbol{m}}_0}$ is at least five times of it. So ${\boldsymbol{n}}(0)$ needs more iterations to achieve the optimal. Therefore, the initial value ${\boldsymbol{n}}(0)$ determines whether the optimization method can obtain credible LRM model parameters and the algorithm convergence speed. And when ${\boldsymbol{n}}(0) \in ({1/{{\boldsymbol{R}}_{{{\bf min}}}}, 1000} ]$ ( ${{\boldsymbol{R}}_{{{\bf min}}}}$ is the minimum reflectance in blue and green bands), there must be a credible model parameter solution. The bathymetric retrieval results of the sea area with coral and sand substrates show the applicability of our initial value ranges in different substrate area.

Research on Gold Demand Prediciton Based on GM-GPR Model

The prediction system of gold demands in China is faced with issues such as uncertain factors, limited historical data, and nonlinearity. In order to have a more accurate prediction of gold demands, a prediction method based on the integration of grey prediction and Gaussian process regression is proposed. Specifically, equal weights are assigned to each model and a grey prediction is adopted to reflect the uncertain and changing relationship of gold demands, with Gaussian process regression indicating the nonlinear impacts of factors on gold demands. Moreover, modified particle swarm optimization plays a role in optimizing the hyper-parameters of Gaussian process regression, which solves the issue that conjugate gradient algorithms depend on initial value setting and are susceptible to be confined by locally optimal solutions. According to the study, the proposal of the paper is superior to a separate Gaussian process regression or grey prediction in terms of better predicting gold demands.