Search results for: premise variable

Authors: U. Chattaraj, K. Dhusiya, M. Raviteja

Abstract:

Perception reaction time of drivers is an outcome of human thought process, which is vague and approximate in nature and also varies from driver to driver. So, in this study a fuzzy logic based model for prediction of the same has been presented, which seems suitable. The control factors, like, age, experience, intensity of driving of the driver, speed of the vehicle and distance of stimulus have been considered as premise variables in the model, in which the perception reaction time is the consequence variable. Results show that the model is able to explain the impacts of the control factors on perception reaction time properly.

Keywords: driver, fuzzy logic, perception reaction time, premise variable

Procedia PDF Downloads 270

Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen

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Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.

Keywords: natural language inference, explanation generation, variational auto-encoder, generative model

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Authors: Ritu Rani

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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.

Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: auxiliary variable, dynamic programming technique, nonlinear programming problem, optimum stratification, uniform distribution

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Authors: Jaya Mathew

Abstract:

Many organizations are faced with the challenge of how to analyze and build Machine Learning models using their sensitive telemetry data. In this paper, we discuss how users can leverage the power of R without having to move their big data around as well as a cloud based solution for organizations willing to host their data in the cloud. By using ScaleR technology to benefit from parallelization and remote computing or R Services on premise or in the cloud, users can leverage the power of R at scale without having to move their data around.

Keywords: predictive maintenance, machine learning, big data, cloud based, on premise solution, R

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Authors: C. A. Akaash Emmanuel Raj, V. R. Sanal Kumar

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In this paper using smart materials we have proposed a specially manufactured variable volume spin tub for loading clothes for negating the vibration to a certain extent for getting better operating performance. Additionally, we have recommended a variable spinning speed rotor for handling varieties of garments for an efficient washing, aiming for increasing the life span of both the garments and the machine. As a part of the conflicting dynamic constraints and demands of the customer friendly design optimization of a lucrative and cosmetic washing machine we have proposed a drier and a desalination system capable to supply desirable heat and a pleasing fragrance to the garments. We thus concluded that while incorporating variable volume and variable spinning speed tub integrated with a drier and desalination system, the washing machine could meet the varieties of domestic requirements of the customers cost-effectively.

Keywords: customer friendly washing machine, drier design, quick cloth cleaning, variable tub volume washing machine, variable spinning speed washing machine

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Yong-Jun Kim, Jae-Hyun Ro, Chang-Bin Ha, Hyoung-Kyu Song

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Because current wireless communication requires high reliability in a limited bandwidth environment, this paper proposes the variable modulation scheme based on the codebook. The variable modulation scheme adjusts transmission power using the codebook in accordance with hannel state. Also, if the codebook is composed of many bits, the reliability is more improved by the proposed scheme. The simulation results show that the performance of proposed scheme has better reliability than the the performance of conventional scheme.

Keywords: MIMO-OFDM, variable modulation, codebook, channel state

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Authors: S. A. Alotaibi, M. A. Al-Ajmi

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This work introduces a new concept for controlling the mechanical vibrations via variable stiffness coil spring. The concept relies on fitting a screw though the spring to change the number of active spring coils. A prototype has been built and tested with promising results toward an innovation in the field of vibration control.

Keywords: variable stiffness, coil spring, vibration control, computer science

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Authors: I. Algul, G. Akgun, H. Kurtaran

Abstract:

Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: differential quadrature method, doubly curved panels, laminated composite materials, small displacement

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Authors: Daniel E. Martin, Chenghai Yang

Abstract:

Variable-rate aerial application systems are becoming more readily available; however, aerial applicators typically only use the systems for constant-rate application of materials, allowing the systems to compensate for upwind and downwind ground speed variations. Much of the resistance to variable-rate aerial application system adoption in the U.S. pertains to applicator’s trust in the systems to turn on and off automatically as desired. The objectives of this study were to evaluate a commercially available variable-rate aerial application system under field conditions to demonstrate both the response and accuracy of the system to desired application rate inputs. This study involved planting oats in a 35-acre fallow field during the winter months to establish a uniform green backdrop in early spring. A binary (on/off) prescription application map was generated and a variable-rate aerial application of glyphosate was made to the field. Airborne multispectral imagery taken before and two weeks after the application documented actual field deposition and efficacy of the glyphosate. When compared to the prescription application map, these data provided application system response and accuracy information. The results of this study will be useful for quantifying and documenting the response and accuracy of a commercially available variable-rate aerial application system so that aerial applicators can be more confident in their capabilities and the use of these systems can increase, taking advantage of all that aerial variable-rate technologies have to offer.

Keywords: variable-rate, aerial application, remote sensing, precision application

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Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Philippe Larvet

Abstract:

This paper presents the concept of an object-based programming language where tests (if... then... else) and control structures (while, repeat, for...) disappear and are replaced by conditions on data. According to the object paradigm, by using this concept, data are still embedded inside objects, as variable-value couples, but object methods are expressed into the form of logical propositions (‘conditions on data’ or COD).For instance : variable1 = value1 AND variable2 > value2 => variable3 = value3. Implementing this approach, a central inference engine turns and examines objects one after another, collecting all CODs of each object. CODs are considered as rules in a rule-based system: the left part of each proposition (left side of the ‘=>‘ sign) is the premise and the right part is the conclusion. So, premises are evaluated and conclusions are fired. Conclusions modify the variable-value couples of the object and the engine goes to examine the next object. The paper develops the principles of writing CODs instead of complex algorithms. Through samples, the paper also presents several hints for implementing a simple mechanism able to process this ‘COD language’. The proposed approach can be used within the context of simulation, process control, industrial systems validation, etc. By writing simple and rigorous conditions on data, instead of using classical and long-to-learn languages, engineers and specialists can easily simulate and validate the functioning of complex systems.

Keywords: conditions on data, logical proposition, programming without code, object-oriented programming, system simulation, system validation

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Authors: Kimiyo Shimomai, Mihoko Harada

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This study is a literature review of the psychological reactions that occur in end-of-life cancer patients who are nearing death. It searched electronic databases and selected literature related to psychological studies of end-of-life patients. There was no limit on the search period, and the search was conducted until the second week of December 2021. The keywords were specified as “death and dying”, “terminal illness”, “end-of-life”, “palliative care”, “psycho-oncology” and “research”. These literatures referred to Holly (2017): Comprehensive Systematic Review for Advanced Practice Nursing, P268 Figure 10.3 to ensure quality. These literatures were selected with a dissertation score of 4 or 5. The review was conducted in two stages with reference to the procedure of George (2002). First, these references were searched for keywords in the database, and then relevant references were selected from the psychology and nursing studies of end-of-life patients. The number of literatures analyzed was 76 for overseas and 17 for domestic. As for the independent variables, "physical variable" was the most common in 36 literatures (66.7%), followed by "psychological variable" in 35 literatures (64.8%), "spiritual variable" in 21 literatures (38%), and "social variable" in 17 literatures. (31.5%), "Variables related to medical care / treatment" were 16 literatures (29.6%). To summarize the relationship between these independent variables and the dependent variable, when the dependent variable is "psychological variable", the independent variables are "psychological variable", "social variable", and "physical variable". Among the independent variables, the physical variables were the most common. The psychological responses that occur in end-stage cancer patients who are nearing death are mutually influenced by psychological, social, and physical variables. Therefore, it supported the "total pain" advocated by Cicely Saunders.

Keywords: cancer patient, end-of-life, literature review, psychological process

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Authors: Priya Kedia, Kiranmoy Das

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There is a rich literature on variable selection in regression setting. However, most of these methods assume normality for the response variable under consideration for implementing the methodology and establishing the statistical properties of the estimates. In many real applications, the distribution for the response variable may be non-Gaussian, and one might be interested in finding the best subset of covariates at some predetermined quantile level. We develop dynamic Bayesian approach for variable selection in quantile regression framework. We use a zero-inflated mixture prior for the regression coefficients, and consider the asymmetric Laplace distribution for the response variable for modeling different quantiles of its distribution. An efficient Gibbs sampler is developed for our computation. Our proposed approach is assessed through extensive simulation studies, and real application of the proposed approach is also illustrated. We consider the data from health and retirement study conducted by the University of Michigan, and select the important predictors when the outcome of interest is out-of-pocket medical cost, which is considered as an important measure for financial risk. Our analysis finds important predictors at different quantiles of the outcome, and thus enhance our understanding on the effects of different predictors on the out-of-pocket medical cost.

Keywords: variable selection, quantile regression, Gibbs sampler, asymmetric Laplace distribution

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Authors: Ehsan Motamedian

Abstract:

Finding all optimal flux distributions of a metabolic model is an important challenge in systems biology. In this paper, a new algorithm is introduced to identify all alternate optimal solutions of a large scale metabolic network. The algorithm reduces the model to decrease computations for finding optimal solutions. The algorithm was implemented on the Escherichia coli metabolic model to find all optimal solutions for lactate and acetate production. There were more optimal flux distributions when acetate production was optimized. The model was reduced from 1076 to 80 variable fluxes for lactate while it was reduced to 91 variable fluxes for acetate. These 11 more variable fluxes resulted in about three times more optimal flux distributions. Variable fluxes were from 12 various metabolic pathways and most of them belonged to nucleotide salvage and extra cellular transport pathways.

Keywords: flux variability, metabolic network, mixed-integer linear programming, multiple optimal solutions

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Authors: Nguyen J. M., Lucas G., Brunner M., Ruan S., Antonioli D.

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Deep learning based on convolutional neural networks (CNN) is a very powerful technique for classifying information from an image. We propose a new method, DeepNic, to transform each variable of a tabular dataset into an image where each pixel represents a set of conditions that allow the variable to make an error-free prediction. The contrast of each pixel is proportional to its prediction performance and the color of each pixel corresponds to a sub-family of NICs. NICs are probabilities that depend on the number of inputs to each neuron and the range of coefficients of the inputs. Each variable can therefore be expressed as a function of a matrix of 2 vectors corresponding to an image whose pixels express predictive capabilities. Our objective is to transform each variable of tabular data into images into an image that can be analysed by CNNs, unlike other methods which use all the variables to construct an image. We analyse the NIC information of each variable and express it as a function of the number of neurons and the range of coefficients used. The predictive value and the category of the NIC are expressed by the contrast and the color of the pixel. We have developed a pipeline to implement this technology and have successfully applied it to genomic expressions on an Affymetrix chip.

Keywords: tabular data, deep learning, perfect trees, NICS

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Authors: Amitha Puranik, V. S. Binu, Seena Biju

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Missing data is a common problem in spatial analysis especially at the aggregate level. Missing can either occur in covariate or in response variable or in both in a given location. Many missing data techniques are available to estimate the missing data values but not all of these methods can be applied on spatial data since the data are autocorrelated. Hence there is a need to develop a method that estimates the missing values in both response variable and covariates in spatial data by taking account of the spatial autocorrelation. The present study aims to develop a model to estimate the missing data points at the aggregate level in spatial data by accounting for (a) Spatial autocorrelation of the response variable (b) Spatial autocorrelation of covariates and (c) Correlation between covariates and the response variable. Estimating the missing values of spatial data requires a model that explicitly account for the spatial autocorrelation. The proposed model not only accounts for spatial autocorrelation but also utilizes the correlation that exists between covariates, within covariates and between a response variable and covariates. The precise estimation of the missing data points in spatial data will result in an increased precision of the estimated effects of independent variables on the response variable in spatial regression analysis.

Keywords: spatial regression, missing data estimation, spatial autocorrelation, simulation analysis

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Authors: E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glele Kakai, E. M. Qannari

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A new definition of a latent variable associated with a dataset makes it possible to propose variants of the PLS2 regression and the multi-block PLS (MB-PLS). We shall refer to these variants as Rd-PLS regression and Rd-MB-PLS respectively because they are inspired by both Redundancy analysis and PLS regression. Usually, a latent variable t associated with a dataset Z is defined as a linear combination of the variables of Z with the constraint that the length of the loading weights vector equals 1. Formally, t=Zw with ‖w‖=1. Denoting by Z' the transpose of Z, we define herein, a latent variable by t=ZZ’q with the constraint that the auxiliary variable q has a norm equal to 1. This new definition of a latent variable entails that, as previously, t is a linear combination of the variables in Z and, in addition, the loading vector w=Z’q is constrained to be a linear combination of the rows of Z. More importantly, t could be interpreted as a kind of projection of the auxiliary variable q onto the space generated by the variables in Z, since it is collinear to the first PLS1 component of q onto Z. Consider the situation in which we aim to predict a dataset Y from another dataset X. These two datasets relate to the same individuals and are assumed to be centered. Let us consider a latent variable u=YY’q to which we associate the variable t= XX’YY’q. Rd-PLS consists in seeking q (and therefore u and t) so that the covariance between t and u is maximum. The solution to this problem is straightforward and consists in setting q to the eigenvector of YY’XX’YY’ associated with the largest eigenvalue. For the determination of higher order components, we deflate X and Y with respect to the latent variable t. Extending Rd-PLS to the context of multi-block data is relatively easy. Starting from a latent variable u=YY’q, we consider its ‘projection’ on the space generated by the variables of each block Xk (k=1, ..., K) namely, tk= XkXk'YY’q. Thereafter, Rd-MB-PLS seeks q in order to maximize the average of the covariances of u with tk (k=1, ..., K). The solution to this problem is given by q, eigenvector of YY’XX’YY’, where X is the dataset obtained by horizontally merging datasets Xk (k=1, ..., K). For the determination of latent variables of order higher than 1, we use a deflation of Y and Xk with respect to the variable t= XX’YY’q. In the same vein, extending Rd-MB-PLS to the path modeling setting is straightforward. Methods are illustrated on the basis of case studies and performance of Rd-PLS and Rd-MB-PLS in terms of prediction is compared to that of PLS2 and MB-PLS.

Keywords: multiblock data analysis, partial least squares regression, path modeling, redundancy analysis

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Authors: Farid Saeidi, Serkan Dag

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In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, Variable Fiber Spacing, Thermoelasticity, T-stress, Finite Element Method, Fibrous Composite.

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Authors: Shohreh Azizi, Memory Tekere, Wag Nel

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An evaluation of the characteristics of wastewater generated from small communities was carried out in relation to decentralized approach for domestic sewage treatment plant and design of biological nutrient removal system. The study included the survey of the waste from various individual communities such as a hotel, a residential complex, an office premise, and an educational institute. The results indicate that the concentration of organic pollutant in wastewater from the residential complex is higher than the waste from all the other communities with COD 664 mg/l, BOD 370.2 mg/l and TSS 248.8 mg/l. And the waste water from office premise indicates low organic load with COD428 mg/l, BOD 232mg/l and TSS 157mg/l. The wastewater from residential complex was studied under activated sludge process to evaluate this technology for decentralized wastewater treatment. The Activated sludge process was operated at different 12to 4 hrs hydraulic retention times and the optimum 6 hrs HRT was selected, therefore the average reduction of COD (85.92%) and BOD (91.28 %) was achieved. The issue of sludge recycling, maintenance of biomass concentration and high HRT reactor (10 L) volume are making the system non-practical for smaller communities.

Keywords: wastewater, small communities, activated sludge process, decentralized system

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Authors: Georgiana Onicescu, Yuqian Shen

Abstract:

Due to the complex nature of geo-referenced data, multicollinearity of the risk factors in public health spatial studies is a commonly encountered issue, which leads to low parameter estimation accuracy because it inflates the variance in the regression analysis. To address this issue, we proposed a two-stage variable selection method by extending the least absolute shrinkage and selection operator (Lasso) to the Bayesian spatial setting, investigating the impact of risk factors to health outcomes. Specifically, in stage I, we performed the variable selection using Bayesian Lasso and several other variable selection approaches. Then, in stage II, we performed the model selection with only the selected variables from stage I and compared again the methods. To evaluate the performance of the two-stage variable selection methods, we conducted a simulation study with different distributions for the risk factors, using geo-referenced count data as the outcome and Michigan as the research region. We considered the cases when all candidate risk factors are independently normally distributed, or follow a multivariate normal distribution with different correlation levels. Two other Bayesian variable selection methods, Binary indicator, and the combination of Binary indicator and Lasso were considered and compared as alternative methods. The simulation results indicated that the proposed two-stage Bayesian Lasso variable selection method has the best performance for both independent and dependent cases considered. When compared with the one-stage approach, and the other two alternative methods, the two-stage Bayesian Lasso approach provides the highest estimation accuracy in all scenarios considered.

Keywords: Lasso, Bayesian analysis, spatial analysis, variable selection

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

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This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control

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Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: Selvakumar Ulaganathan, Ivo Couckuyt, Francesco Ferranti, Tom Dhaene, Eric Laermans

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Variable-fidelity surrogate modelling offers an efficient way to approximate function data available in multiple degrees of accuracy each with varying computational cost. In this paper, a Kriging-based variable-fidelity surrogate modelling approach is introduced to approximate such deterministic data. Initially, individual Kriging surrogate models, which are enhanced with gradient data of different degrees of accuracy, are constructed. Then these Gradient enhanced Kriging surrogate models are strategically coupled using a recursive CoKriging formulation to provide an accurate surrogate model for the highest fidelity data. While, intuitively, gradient data is useful to enhance the accuracy of surrogate models, the primary motivation behind this work is to investigate if it is also worthwhile incorporating gradient data of varying degrees of accuracy.

Keywords: Kriging, CoKriging, Surrogate modelling, Variable- fidelity modelling, Gradients

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Authors: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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Authors: Mohamed Raouf Benmakrelouf, Joseph Rynkiewicz

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Targeted maximum likelihood estimation (TMLE) is well-established method for causal effect estimation with desirable statistical properties. TMLE is a doubly robust maximum likelihood based approach that includes a secondary targeting step that optimizes the target statistical parameter. A causal interpretation of the statistical parameter requires assumptions of the Rubin causal framework. The causal effect of binary variable, E, on outcomes, Y, is defined in terms of comparisons between two potential outcomes as E[YE=1 − YE=0]. Our aim in this paper is to present an adaptation of TMLE methodology to estimate the causal effect of a non-binary categorical variable, providing a large application. We propose coding on the initial data in order to operate a binarization of the interest variable. For each category, we get a transformation of the non-binary interest variable into a binary variable, taking value 1 to indicate the presence of category (or group of categories) for an individual, 0 otherwise. Such a dummy variable makes it possible to have a pair of potential outcomes and oppose a category (or a group of categories) to another category (or a group of categories). Let E be a non-binary interest variable. We propose a complete disjunctive coding of our variable E. We transform the initial variable to obtain a set of binary vectors (dummy variables), E = (Ee : e ∈ {1, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when its category is not present, and the value of 1 when its category is present, which allows to compute a pairwise-TMLE comparing difference in the outcome between one category and all remaining categories. In order to illustrate the application of our strategy, first, we present the implementation of TMLE to estimate the causal effect of non-binary variable on outcome using simulated data. Secondly, we apply our TMLE adaptation to survey data from the French Political Barometer (CEVIPOF), to estimate the causal effect of education level (A five-level variable) on a potential vote in favor of the French extreme right candidate Jean-Marie Le Pen. Counterfactual reasoning requires us to consider some causal questions (additional causal assumptions). Leading to different coding of E, as a set of binary vectors, E = (Ee : e ∈ {2, ..., |E|}), where each vector (variable), Ee, takes the value of 0 when the first category (reference category) is present, and the value of 1 when its category is present, which allows to apply a pairwise-TMLE comparing difference in the outcome between the first level (fixed) and each remaining level. We confirmed that the increase in the level of education decreases the voting rate for the extreme right party.

Keywords: statistical inference, causal inference, super learning, targeted maximum likelihood estimation

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Authors: Jossitt Williams Vargas Cruz, Aura Jazmín Pérez Ríos

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The variations of solar dynamics have become a relevant topic of study due to the effects of climate changes generated on the earth. One of the most disconcerting aspects is the variability that the sun has on the climate is the role played by sunspots (extra-atmospheric variable) in the modulation of the Cosmic Rays CR (extra-atmospheric variable). CRs influence the earth's climate by affecting cloud formation (atmospheric variable), and solar cycle influence is associated with the presence of solar storms, and the magnetic activity is greater, resulting in less CR entering the earth's atmosphere. The different methods of climate prediction in Colombia do not take into account the extra-atmospheric variables. Therefore, correlations between atmospheric and extra-atmospheric variables were studied in order to implement a Python code based on neural networks to make the prediction of the extra-atmospheric variable with the highest correlation.

Keywords: correlations, cosmic rays, sun, sunspots and variations.

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Authors: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Saba Riaz, Syed A. Hussain

Abstract:

This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

Procedia PDF Downloads 193