Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics

A forbidden zone theorem, hypothesis, and applied mathematical method and model are introduced in the present article. The method and model are based on the forbidden zones and hypothesis. The article is initiated by the well-known generic problems concerned with the mathematical description of the behavior of a man. The essence of the problems consists in biases of preferences and decisions of a man in comparison with predictions of the probability theory. The model is uniformly and successfully applied for different domains. The ultimate goal of the research is to solve some generic problems of behavioral economics, decision theories, and the social sciences.

Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

Building a Predictive Model for Gynecologic Cancer Using Levels of Data Analytics

The four levels of data analytics techniques (descriptive, diagnostic, predictive, and perspective) were used as a methodology. We also used data mining techniques to predict Gynecologic cancer before any lab test or surgical intervention. Influencing and associating between factors are used to cover hidden relationships or unknown patterns. We focused on three types of Gynecologic cancer (cervical, endometrial, and ovarian cancer). We collected an initial examination of 513 (228 benign and 285 malignant) patients from King Abdulaziz University Hospital (Saudi Arabia). Data were collected during the period of 16 years (2000-2016). After examining many models, we found that the classification trees C5 and CHAID beside the Support Vector Machine (SVM) algorithm give the highest accuracy, with the values of 87.33 %, 79.53%, and 78.36 % respectively. The sensitivity and specificity were found to be 86.18 % and 89.00 % for C5. The corresponding values for CHAID were found to be to equals to 82.20 % and 76.72 % while for support vector machine (SVM) the values were found to be 83.74 % and 77.10 %.

The Modified Increment Method for Eigenspace Model

Eigenspace is a convenient way to represent sets of observations with widespread applications, so it is necessary to accurately calculate the eigenspace of data. With the advent of the era of big data, the increasing and updating of data bring great challenges to the solution of eigenspace. Hall, et al. [1], proposed that the incremental method could update the eigenspace of data online, which reduces computational costs and storage space. In this paper, the updating coefficient of the sample covariance matrix in an incremental method is modified. Numerical analysis shows that the modified updating form has better performance.

Auto-Transformations of the Probability Density Functions

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into some similar functions having smaller sizes of their domains. 2) To research and outline basic features of these auto-transformations of PDFs. Particularly, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences.

Landing Trajectory Design for UAV Considering Control Restrictions and Landing Speed

The article presents a method for designing the trajectory of the UAV in space, taking into account the restriction on control. The chosen optimal controls are namely normal overload with restrictions, tangential overload with restrictions, and lateral overload. The Pontryagin maximum principle allows the transition of the optimal control problem to a boundary value problem. The parameter continuation method is applied to solve the boundary problem. The article results reveal reference trajectories in different cases of UAV landing. This result allows the design of reference trajectories for the UAV to attain the highest landing efficiency.

Application of Bayesian Networks of Genotype by Environment Interaction Evaluation Under Plant Disease, Soil Types and Climate Condition-using Bayesia Lab

Genotype by environment interaction (GEI) linked to plant disease, soil properties and climate conditions add potential value for a breeding program to underpin decision making. In understanding genotype x environment interaction, the most challenging factors are the identification of genetic variation for a range of traits and their responsiveness to the climate change factors. In order to study the complex relationships with genetic and non-genetic factors, the application of Bayesian network tools will help understand and accelerate plant breeding progress and improve the efficiency of crop production. In this study, we proposed the application of Bayesian networks (BNs) to evaluate genotype by environment interaction under plant diseases, soil type, and climate variables. An adapted to simulate multiple environmental trial (MET) data of maize (corn) was used to examine the performance of the BN predictive modeling using BayesiaLab for deriving knowledge and graphical structure for exploring GEI diagnosis and analysis. The results highlighted that genotypes have the same probability and the frequentist of rainfall, temperature, soil type, and disease type occurred as <=88 (46%), 35 (37%), clay (27%), and MB (47%) respectively, which have to monitor reflects in each discretization. This study provided a roadmap to knowledge modeling of GEI using BayesiaLab software. On a broader scale, this study helps predict the yield of crop varieties by understanding agronomic and environmental factors under farm conditions rather than conducting long-term agricultural testing under well-controlled conditions of the on-station trials. Future improvements of BNs application of METs should consider working on a larger and more detailed soil and irrigation system linked to agro system.

Stochastic Stability and Analytical Solution with Homotopy Perturbation Method of Multicompartment Non-Linear Epidemic Model with Saturated Rate

In this work, we consider a nonlinear epidemic model with a saturated incidence rate. we consider a population of size N(t) at time t, this population is divided into six subclasses, with N(t)=S(t)+I(t)+I₁(t)+I₂(t)+I₃(t)+Q(t). Where S(t), I(t), I₁(t), I₂(t), I₃(t), and Q(t) denote the sizes of the population susceptible to disease, infectious members, and quarantine members, respectively. We have made the following contributions: 1. The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determined by the ratio called the basic reproductive number. 2. We find the analytical solution of the nonlinear epidemic model by Homotopy perturbation method. 3. Finally the stochastic stabilities. The study of its sections are justified with theorems and demonstrations under certain conditions. In this work, we have used the different references cited in different studies in the three sections already mentioned.

Different Types of Curvature and Their Vanishing Conditions

In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.

1-D Optimum Path Problem and Its Application

The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-point variable reduces to vector integral equations of Fredhom / Volterra type and is hard to solve. Translating it to scalar components equations would be an easier way of solving it. Here, the solution of the optimum path problem is recommended by connecting it with the Principle of minimum Energy Release (PMER). A lot of optimum path problems with path function E=cu2, where E is the released energy, u is the velocity, c is constant, can be solved by PMER, e.g., the Great Earthquake, the denotation of a nuclear weapon, the strategy of sports games. The one end-point fixed, the other end-point variable is studied for wing moving. High lights: The pulse-mode of nuclear denotation releasing energy is the same as Earthquake, Yun [1], shows that the derivative of wind velocity with respect to time in proportion to the derivative of temperature with respect to the track. Which conforms with the weather forecast in winter that strong wind companies with low temperature for cold wave coming, and also suits for the motion of mushroom cloud [2].