Quenched Decay of Correlations for One-dimensional Random Lorenz Maps

We study rates of mixing for small random perturbations of one-dimensional Lorenz maps. Using a random tower construction, we prove that, for Hölder observables, the random system admits exponential rates of quenched correlation decay.

Service management concepts and the role of banks’ creative economic in Indonesia during the COVID-19 pandemic era

The COVID-19 pandemic has disturbed people all over the world. The economy is limited, even services in various institutions are also limited. Thus, the purpose of this paper is to describe the concept of service management and the role of developing the creative economy of Banks in Indonesia in the COVID-19 Pandemic Era. This research is descriptive qualitative research. The types of research data are statements and patterns of service behavior of the tire management team in Indonesia. Data were collected through observation and interviews. The interview subjects were the public as bank consumers (respondents) and bank employees. The respondent selection system was used with a random system in accordance with research needs. The results prove the role of customer service in providing information to customers very well. Because the media used customer service in providing the information is very good and customers feel very satisfied for the services provided customer service.

Perceptions of Indonesian Students on the Role of Teachers in Offline and Online Learning During the Covid-19 Pandemic Period

This study aimed to analyze student perceptions regarding the role of teachers in classroom learning compared to online learning during the Covid-19 pandemic by applying a quantitative approach with a survey method. Population in this study was students throughout Indonesia who were actively learning during the Covid-19 pandemic. The research used Cluster Sampling technique by distributing online forms to students studying at home in all provinces in Indonesia, from Aceh to Papua; while sampling was conducted by random system. Chi square data analysis was carried out to analyze the close relationship between two variables that had nominal data. The results showed that almost all respondents (683 students or 93.8% of them) preferred face-to-face learning with teachers, while a small portion of 45 respondents (6.2%) liked face-to-screen learning (online). Out of 728 respondents, 647 students (88.9%) thought that the teacher's role could not be replaced by technology, and 81 students (11.1%) thought that the teacher's role could be replaced by technology. Thus, it can be concluded that most students in Indonesia still preferred face-to-face learning in class. Inequality in the distribution of learning resources such as internet network and teacher competence became a major problem in online learning, especially for students who lived in rural and disadvantaged areas.

Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations.

Wong–Zakai approximations and limiting dynamics of stochastic Ginzburg–Landau equations

This paper deals with the Wong–Zakai approximations and random attractors for stochastic Ginzburg–Landau equations with a white noise. We first prove the existence of a pullback random attractor for the approximate equation under much weaker conditions than the original stochastic equation. In addition, when the stochastic Ginzburg–Landau equation is driven by an additive white noise, we establish the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation tends to zero.

Bayesian Maximal Information Coefficient (BMIC) to Reason Novel Trends in Large Datasets

Bayesian network (BN) is a probability inference model to describe the explicit relationship of cause and effect, which may examine the complex system of rice price with data uncertainty. However, discovering the optimized structure from a super-exponential number of graphs in the search space is an NP-hard problem. In this paper, Bayesian maximal information coefficient (BMIC) is proposed to uncover the causal correlations from a large dataset in a random system by integrating probabilistic graphical model (PGM) and maximal information coefficient (MIC) with Bayesian linear regression (BLR). First, MIC is to capture the strong dependence between predictor variables and a target variable to reduce the number of variables for the BN structural learning of PGM. Second BLR is to assign orientation in a graph resulting by a posterior probability distribution. It conforms to what BN needs to acquire a conditional probability distribution when given the parents for each node by the Bayes' Theorem. Third, Bayesian information criterion (BIC) is treated as an indicator to determine the well-explained model with its data to ensure correctness. The score shows that the proposed method obtains the highest score compared to the two traditional learning algorithms. Finally, the BMIC is applied to discover the causal correlations from the large dataset on Thai rice price by identifying causality change in the paddy price of Jasmine rice. The experimented results show the proposed BMIC returns the directional relationships with clue to identify the cause(s) and effect(s) on paddy price with better heuristic search.

Bayesian Maximal Information Coefficient (BMIC) to Reason Novel Trends in Large Datasets

Bayesian network (BN) is a probability inference model to describe the explicit relationship of cause and effect, which may examine the complex system of rice price with data uncertainty. However, discovering the optimized structure from a super-exponential number of graphs in the search space is an NP-hard problem. In this paper, Bayesian maximal information coefficient (BMIC) is proposed to uncover the causal correlations from a large dataset in a random system by integrating probabilistic graphical model (PGM) and maximal information coefficient (MIC) with Bayesian linear regression (BLR). First, MIC is to capture the strong dependence between predictor variables and a target variable to reduce the number of variables for the BN structural learning of PGM. Second BLR is to assign orientation in a graph resulting by a posterior probability distribution. It conforms to what BN needs to acquire a conditional probability distribution when given the parents for each node by the Bayes' Theorem. Third, Bayesian information criterion (BIC) is treated as an indicator to determine the well-explained model with its data to ensure correctness. The score shows that the proposed method obtains the highest score compared to the two traditional learning algorithms. Finally, the BMIC is applied to discover the causal correlations from the large dataset on Thai rice price by identifying causality change in the paddy price of Jasmine rice. The experimented results show the proposed BMIC returns the directional relationships with clue to identify the cause(s) and effect(s) on paddy price with better heuristic search.

Estimation of different types of entropies for the Kumaraswamy distribution

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

Bayesian Maximal Information Coefficient (BMIC) to Discover Causal Correlations from Large Dataset in Random System

Bayesian network (BN) is a probability inference model to describe the explicit relationship of cause and effect, which may examine the complex system of rice price with data uncertainty. However, discovering the optimized structure from a super-exponential number of graphs in the search space is an NP-hard problem. In this paper, the Bayesian maximal information coefficient (BMIC) is proposed to uncover the causal correlations from a large dataset in a random system by integrating a probabilistic graphical model (PGM) and maximal information coefficient (MIC) with Bayesian linear regression (BLR). First, MIC is to capture the strong dependence between predictor variables and a target variable for reducing the number of variables during the Bayesian network structural learning. Second BLR is to assign orientation in a graph resulting in a posterior probability distribution. It conforms to what BN needs to acquire a conditional probability distribution when given the parents for each node by the Bayes’ Theorem. Third, the Bayesian information criterion (BIC) is treated as an indicator to determine the well-explained model with its data to ensure correctness. The score shows that the proposed method obtains the highest score compared to the two traditional learning algorithms. Finally, the BMIC is applied to discover the causal correlations from large dataset on Thai rice price by identifying the causality change in the paddy price of Jasmine rice. The experimented results show the BMIC returns the directed relationships with a clue to identify the cause(s) and effect(s) on paddy price with the better heuristic search.