Statistics, Optimization & Information Computing

Globally Optimal Dense and Sparse Spanning Trees, and their Applications

2020-05-28T00:53:53+08:00

Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of dense ( sparse ) tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large) sum of distances between vertices. We show that finding DST and SST reduces to solving the discrete optimization problems. New and efficient approaches to find such spanning trees is achieved by imposing certain conditions on the vertex degrees which are then used to define an objective function that is minimized over all spanning trees of the graph under consideration. Solving this minimization problem exactly may be prohibitively time consuming for large graphs. Hence, we propose to use genetic algorithm (GA) which is one of well known metaheuristics methods to solve DST and SST approximately. As far as we are aware this is the first time GA has been used in this context.We also demonstrate on a number of applications that GA approach is well suited for these types of problems both in computational efficiency and accuracy of the approximate solution. Furthermore, we improve the efficiency of the proposed method by using Kruskal s algorithm in combination with GA. The application of our methods to several practical large graphs and networks is presented. Computational results show that they perform faster than previously proposed heuristic methods and produce more accurate solutions. Furthermore, the new feature of the proposed approach is that it can be applied recursively to sub-trees or spanning trees with additional constraints in order to further investigate the graphical properties of the graph and/or network. The application of this methodology on the gene network of a cancer cell led to isolating key genes in a network that were not obvious from previous studies.

Time Series Components Separation Based on Singular Spectral Analysis Visualization: an HJ-biplot Method Application

2020-05-28T00:53:54+08:00

The extraction of essential features of any real-valued time series is crucial for exploring, modeling and producing, for example, forecasts. Taking advantage of the representation of a time series data by its trajectory matrix of Hankel constructed using Singular Spectrum Analysis, as well as of its decomposition through Principal Component Analysis via Partial Least Squares, we implement a graphical display employing the biplot methodology. A diversity of types of biplots can be constructed depending on the two matrices considered in the factorization of the trajectory matrix. In this work, we discuss the called HJ-biplot which yields a simultaneous representation of both rows and columns of the matrix with maximum quality. Interpretation of this type of biplot on Hankel related trajectory matrices is discussed from a real-world data set.

A Modified Algorithm for the Computation of the Covariance Matrix Implied by a Structural Recursive Model with Latent Variables Using the Finite Iterative Method

2020-05-28T00:53:54+08:00

Structural Equation Modeling (SEM) is a statistical technique that assesses a hypothesized causal model by
showing whether or not, it fits the available data. One of the major steps in SEM is the computation of the covariance matrix implied by the specified model. This matrix is crucial in estimating the parameters, testing the validity of the model and, make useful interpretations. In the present paper, two methods used for this purpose are presented: the J¨oreskog’s formula and the finite iterative method. These methods are characterized by the manner of the computation and based on some apriori assumptions. To make the computation more simplistic and the assumptions less restrictive, a new algorithm for the computation of the implied covariance matrix is introduced. It consists of a modification of the finite iterative method. An illustrative example of the proposed method is presented. Furthermore, theoretical and numerical comparisons between the exposed methods with the proposed algorithm are discussed and illustrated

Assessing the effect of fungicide treatment on Cocoa black pod disease in Ghana: Insight from mathematical modeling

2020-05-28T00:53:55+08:00

Black pod disease is caused by fungi of the species Phytophthora palmivora or Phytophthora megakarya. The disease causes darkening of affected areas of cocoa trees and/or fruits and leads to significant reduction in crop yields and decreases lifespan of the plant. This study presents a simple S_1S_2IT-type model with variable population size to assess the impact of fungicide treatment on the dynamics of the black pod disease. We do both theoretical studies and numerical simulations of the model. In particular, we analyze the existence of equilibrium points and their stability, simulate the model using data on reported black pod cases from Ghana. In addition, we perform sensitivity analysis of the basic reproduction number with respect to the model parameters. The results show that the top three parameters that govern the dynamics of the black pod disease are the treatment rate, transmission rate, and planting rate of new trees

Applying Multivariate and Univariate Analysis of Variance on Socioeconomic, Health, and Security Variables in Jordan

2020-05-28T00:53:55+08:00

Many researchers have studied socioeconomic, health, and security variables in the developed countries; however, very few studies used multivariate analysis in developing countries. The current study contributes to the scarce literature about the determinants of the variance in socioeconomic, health, and security factors. Questions raised were whether the independent variables (IVs) of governorate and year impact the socioeconomic, health, and security dependent variables (DVs) in Jordan, whether the marginal mean of each DV in each governorate and in each year is significant, which governorates are similar in difference means of each DV, and whether these DVs vary. The main objectives were to determine the source of variances in DVs, collectively and separately, testing which governorates are similar and which diverge for each DV.

The research design was time series and cross-sectional analysis. The main hypotheses are that IVs affect DVs collectively and separately. We carried out Multivariate and univariate analyses of variance to test these hypotheses. The population of 12 governorates in Jordan and the available data of 15 years (2000–2015) accrued from several Jordanian statistical yearbooks. We investigated the effect of two factors of governorate and year on the four DVs of divorce, mortality, unemployment, and crime. We used the rate of divorce, mortality, and crime, and the percentage of unemployment in the analyses. We transformed all DVs to multivariate normal distribution. We calculated descriptive statistics for each DV in each governorate and each year. We provided visual and numerical inspection of how each DV changed over time in each governorate compared with DV change in other governorates.

Based on the multivariate analysis of variance, we found a significant effect in IVs on DVs with p < .001. Based on the univariate analysis, we found a significant effect of IVs on each DV with p < .001, except the effect of the year factor on unemployment, was not significant with p = .642. The grand and marginal means of each DV in each governorate and each year were significant based on a 95% confidence interval. Most governorates are not similar in DVs with p < .001.

We concluded that the two factors produce significant effects on DVs, collectively and separately. Based on these findings, the government can distribute its financial and physical resources to governorates more efficiently. By identifying the sources of variance that contribute to the variation in DVs, insights can help inform focused variation prevention efforts.

Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems

2020-05-28T00:53:56+08:00

This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values. Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient method. Finally, some numerical results are reported to show the efficiency of our algorithm.

Active Effects Selection which Considers Heredity Principle in Multi-Factor Experiment Data Analysis

2020-05-28T00:53:56+08:00

The sparsity principle suggests that the number of effects that contribute significantly to the response variable of an experiment is small. It means that the researchers need an efficient selection procedure to identify those active effects. Most common procedures can be found in literature work by considering an effect as an individual entity so that selection process works on individual effect. Another principle we should consider in experimental data analysis is the heredity principle. This principle allows an interaction effect is included in the model only if the correspondence main effects are there in. This paper addresses the selection problem that takes into account the heredity principle as Yuan et al. (2007) did using least angle regression (LARS). Instead of selecting the effects individually, the proposed approach perform the selection process in groups. The advantage our proposed approach, using genetic algorithm, is on the opportunity to determine the number of desired effect, which the LARS approach cannot.

Bayesian Unit Root Test for AR(1) Model with Trend Approximated

2020-05-28T00:53:57+08:00

The objective of present study is to develop a time series model for handling the non-linear trend process using a spline function. Spline function is a piecewise polynomial segment concerning the time component. The main advantage of spline function is the approximation, non linear time trend, but linear time trend between the consecutive join points. A unit root hypothesis is projected to test the non stationarity due to presence of unit root in the proposed model. In the autoregressive model with linear trend, the time trend vanishes under the unit root case. However, when non-linear trend is present and approximated by the linear spline function, through the trend component is absent under the unit root case, but the intercept term makes a shift with r knots. For decision making under the Bayesian perspective, the posterior odds ratio is used for hypothesis testing problems. We have derived the posterior probability for the assumed hypotheses under appropriate prior information. A simulation study and an empirical application are presented to examine the performance of theoretical outcomes.

Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates

2020-05-28T00:53:58+08:00

This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.

Extended Search Planning for Multiple Moving Targets Incorporating Search Priorities

2020-05-28T00:53:58+08:00

This article deals with a one-searcher multi-target search problem where targetswith different detection priorities move in Markov processes in each discrete time interval over agiven space search area, and the total number of search time intervals is fixed. A limitedsearch resource is available in each search time interval and an exponential detection functionis assumed. The searcher can obtain a target detection reward, if the target is detected, whichrepresents the detection priority of target and does not increase with respect to time. The objective is toestablish the optimal search plan that allocates the search resource effort over the search areasin each time interval in order to maximize the total detection reward. The analysis shows that the given problem can be decomposed into interval-wise individualsearch problems, each being treated as a single stationary target problem for each timeinterval. Thus, an iterative procedure is derived to solve a sequence of stationary targetproblems. The computational results show that the proposed algorithm guaranteesoptimality.

Progressively Type-II Right Censored Order Statistics from Hjorth Distribution and Related Inference

2020-05-28T00:53:59+08:00

In this paper some recurrence relations satisfied by single and product moments of progressive Type-II right censored order statistics from Hjorth distribution have been obtained. Then we use these results to compute the moments for all sample sizes and all censoring schemes (R1,R2,...,Rm),m ≤ n, which allow us to obtain BLUEs of location and scale parameters based on progressive type-II right censored samples.

The Location Parameter Estimation of Spherically Distributions with Known Covariance Matrices

2020-05-28T00:53:59+08:00

This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known.We compared the present estimator with natural estimator by using risk function.We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.

Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

2020-05-28T00:53:59+08:00

In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested in
studying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

A Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data

2020-05-28T00:54:00+08:00

In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.

Iterative Algorithms for a Generalized System of Mixed Variational-Like Inclusion Problems and Altering Points Problem

2020-05-28T00:54:00+08:00

In this article, we introduce and study a generalized system of mixed variational-like inclusion problems involving αβ-symmetric η-monotone mappings. We use the resolvent operator technique to calculate the approximate common solution of the generalized system of variational-like inclusion problems involving αβ-symmetric η-monotone mappings and a fixed point problem for nonlinear Lipchitz mappings. We study strong convergence analysis of the sequences generated by proposed Mann type iterative algorithms. Moreover, we consider an altering points problem associated with a generalized system of variational-like inclusion problems. To calculate the approximate solution of our system, we proposed a parallel S-iterative algorithm and study the convergence analysis of the sequences generated by proposed parallel S-iterative algorithms by using the technique of altering points problem. The results presented in this paper may be viewed as generalizations and refinements of the results existing in the literature.

Modelling of Liquid Flow control system Using Optimized Genetic Algorithm

2020-05-28T00:54:01+08:00

Estimation of a highly accurate model for liquid flow process industry and control of the liquid flow rate from experimental data is an important task for engineers due to its non linear characteristics. Efficient optimization techniques are essential to accomplish this task.In most of the process control industry flowrate depends upon a multiple number of parameters like sensor output,pipe diameter, liquid conductivity ,liquid viscosity & liquid density etc.In traditional optimization technique its very time consuming for manually control the parameters to obtain the optimial flowrate from the process.Hence the alternative approach , computational optimization process is utilized by using the different computational intelligence technique.In this paper three different selection of Genetic Algorithm is proposed & tested against the present liquid flow process.The proposed algorithm is developed based on the mimic genetic evolution of species that allow the consecutive generations in population to adopt their environment.Equations for Response Surface Methodology (RSM) and Analysis of Variance (ANOVA) are being used as non-linear models and these models are optimized using the proposed different selection of Genetic optimization techniques. It can be observed that the among these three different selection of Genetic Algorithm ,Rank selected GA is better than the other two selection (Tournament & Roulette wheel) in terms of the accuracy of final solutions, success rate, convergence speed, and stability.

Decision Making: Rational Choice or Hyper-Rational Choice

2020-05-28T00:54:01+08:00

In this paper, we provide an interpretation of the rationality in game theory in which player consider the profit or loss of the opponent in addition to personal profit at the game.‎ ‎‎The goal of a game analysis with two hyper-rationality players is to provide insight into real-world situations that are often more complex than a game with two rational players where the choices of strategy are only based on individual preferences. The hyper-rationality does not mean perfect rationality but an insight toward how human decision-makers behave in interactive decisions. ‎‎The findings of this research can help to enlarge our understanding of the psychological aspects of strategy choices in games and also provide an analysis of the decision-making process with cognitive economics approach at the same time.‎

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An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

2020-05-28T00:54:02+08:00

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputo
fractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

Heuristics for Winner Prediction in International Cricket Matches

2020-05-28T00:54:02+08:00

Cricket is popularly known as the game of gentlemen. The game of cricket has been introduced to the World by England. Since the introduction till date, it has become the second most ever popular game. In this context, few a data mining and analytical techniques have been proposed for the same. In this work, two different scenario have been considered for the prediction of winning team based on several parameters. These scenario are taken for two different standard formats for the game namely, one day international (ODI) cricket and twenty-twenty cricket (T-20). The prediction approaches differ from each other based on the types of parameters considered and the corresponding functional strategies. The strategies proposed here adopts two different approaches. One approach is for the winner prediction for one-day matches and the other is for predicting the winner for a T-20 match. The approaches have been proposed separately for both the versions of the game pertaining to the intra-variability in the strategies adopted by a team and individuals for each. The proposed strategies for each of the two scenarios have been individually evaluated against existing benchmark works, and for each of the cases the duo of approaches have outperformed the rest in terms of the prediction accuracy. The novel heuristics proposed herewith reflects efficiency and accuracy with respect to prediction of cricket data.

A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020-05-28T00:54:03+08:00

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

2020-05-30T03:05:32+08:00

The problem of mean square optimal estimation of linear functionals which depend on the unknown values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise. Formulas for calculation the mean square errors and the spectral characteristics of the optimal estimates of functionals are derived in the case of spectral certainty, where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, where spectral densities of the sequences are not exactly known while some classes of admissible spectral densities are specified.