Search results for: simple linear correlation

Authors: Guorong Sui, Xingwei Jia, Fei Tong, Xiumin Gao

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Camera calibration is a fundamental issue of high precision noncontact measurement. And it is necessary to analyze and study the reliability and application range of its linear model which is often used in the camera calibration. According to the imaging features of monocular cameras, a camera model which is based on the image pixel coordinates and three dimensional space coordinates is built. Using our own customized template, the image pixel coordinate is obtained by the subpixel corner detection method. Without considering the aberration of the optical system, the feature extraction and linearity analysis of the line segment in the template are performed. Moreover, the experiment is repeated 11 times by constantly varying the measuring distance. At last, the linearity of the camera is achieved by fitting 11 groups of data. The camera model measurement results show that the relative error does not exceed 1%, and the repeated measurement error is not more than 0.1 mm magnitude. Meanwhile, it is found that the model has some measurement differences in the different region and object distance. The experiment results show this linear model is simple and practical, and have good linearity within a certain object distance. These experiment results provide a powerful basis for establishment of the linear model of camera. These works will have potential value to the actual engineering measurement.

Keywords: camera linear model, geometric imaging relationship, image pixel coordinates, three dimensional space coordinates, sub-pixel corner detection

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: D. Chronopoulos, I. Antoniadis, V. Spitas, D. Koulocheris, V. Polenta

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A concept of a simple linear oscillator, incorporating a negative stiffness element is demonstrated to exhibit extraordinary damping properties. This oscillator shares the same overall (static) stiffness, the same mass and the same damping element with a reference classical linear SDOF oscillator. However, it differs from the original SDOF oscillator by appropriately redistributing the component spring stiffness elements and by re-allocating the damping element. Despite the fact that the proposed oscillator incorporates a negative stiffness element, it is designed to be both statically and dynamically stable. Once such an oscillator is optimally designed, it is shown to exhibit an extraordinary apparent damping ratio, which is even several orders of magnitude higher than that of the original SDOF system, especially in cases where the original damping of the SDOF system is low. This damping behavior is not a result of a novel additional extraordinary energy dissipation mechanism, but a result of the phase difference between the positive and the negative stiffness elastic forces, which is in turn a consequence of the proper re-distribution of the stiffness and the damper elements. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the excitation forces. Next, Acoustic or Phononic Meta-materials are considered, in which one atom is replaced by the concept of the above simple linear oscillator. The results indicate that not only the damping of the meta-material verifies and exceeds the one expected from the so-called "meta-damping" behavior, but also that the band gap of the meta-material can be significantly increased.

Keywords: wave propagation, periodic structures, wave damping, mechanical engineering

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Authors: Joel Mintz, Kyle Huntley, Waseem Wahood, Samuel Raine, Farzanna Haffizulla

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The effect of different state government interventions on COVID-19 health outcomes is currently unknown. Stay at home (SAH) orders, all non-essential business closures and school closures in the Northeastern US were examined. A linear correlation between the peak number of new daily COVID-19 positive tests, hospitalizations and deaths per capita and the elapsed time between government issued guidance and a fixed number of COVID-19 deaths in each state was performed. Earlier government interventions were correlated with lower peak healthcare burden. Statewide closures of schools and non-essential businesses showed significantly greater (p<.001) correlation to peak COVID-19 disease burden as compared to a statewide SAH. The implications of these findings require further study to determine the effectiveness of these interventions.

Keywords: Coronavirus, epidemiology, government intervention, public health, social distancing

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Authors: Khodzhaberdi Allaberdiev

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Aromaticity, one of the most important concepts in organic chemistry, has attracted considerable interest from both experimentalists and theoreticians. The geometry optimization of p-substituted o-(N-dialkyl)aminomethylphenols, o-DEAMPH XC₆ H₅CH ₂Y (X=p-OCH₃, CH₃, H, F, Cl, Br, COCH₃, COOCH₃, CHO, CN and NO₂, Y=o-N (C₂H₅)₂, o-DEAMPHs have been performed in the gas phase using the B3LYP/6-311+G(d,p) level. Aromaticities of the considered molecules were investigated using different indices included geometrical (HOMA and Bird), electronic (FLU, PDI and SA) magnetic (NICS(0), NICS(1) and NICS(1)zz indices. The linear dependencies were obtained between some aromaticity indices. The best correlation is observed between the Bird and PDI indices (R² =0.9240). However, not all types of indices or even different indices within the same type correlate well among each other. Surprisingly, for studied molecules in which geometrical and electronic cannot correctly give the aromaticity of ring, the magnetism based index successfully predicts the aromaticity of systems. 1H NMR spectra of compounds were obtained at B3LYP/6–311+G(d,p) level using the GIAO method. Excellent linear correlation (R²= 0.9996) between values the chemical shift of hydrogen atom obtained experimentally of 1H NMR and calculated using B3LYP/6–311+G(d,p) demonstrates a good assignment of the experimental values chemical shift to the calculated structures of o-DEAMPH. It is found that the best linear correlation with the Hammett substituent constants is observed for the NICS(1)zz index in comparison with the other indices: NICS(1)zz =-21.5552+1,1070 σp- (R²=0.9394). The presence intramolecular hydrogen bond in the studied molecules also revealed changes the aromatic character of substituted o-DEAMPHs. The HOMA index predicted for R=NO2 the reduction in the π-electron delocalization of 3.4% was about double that observed for p-nitrophenol. The influence intramolecular H-bonding on aromaticity of benzene ring in the ground state (S0) are described by equations between NICS(1)zz and H-bond energies: experimental, Eₑₓₚ, predicted IR spectroscopical, Eν and topological, EQTAIM with correlation coefficients R² =0.9666, R² =0.9028 and R² =0.8864, respectively. The NICS(1)zz index also correlates with usual descriptors of the hydrogen bond, while the other indices do not give any meaningful results. The influence of the intramolecular H-bonding formation on the aromaticity of some substituted o-DEAMPHs is criteria to consider the multidimensional character of aromaticity. The linear relationships as well as revealed between NICS(1)zz and both pyramidality nitrogen atom, ΣN(C₂H₅)₂ and dihedral angle, φ CAr – CAr -CCH₂ –N, to characterizing out-of-plane properties.These results demonstrated the nonplanar structure of o-DEAMPHs. Finally, when considering dependencies of NICS(1)zz, were excluded data for R=H, because the NICS(1) and NICS(1)zz values are the most negative for unsubstituted DEAMPH, indicating its highest aromaticity; that was not the case for NICS(0) index.

Keywords: aminomethylphenols, DFT, aromaticity, correlations

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

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This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, linear mixed model, multivariate conditional autoregressive model, spatial time series

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Authors: Dibakar Chandra Deka, Anamika Kalita Deka

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Fermented alcoholic beverage production has its own stand among the tribal communities of North-East India. This biological oxidation method is followed by Ahom, Dimasa, Nishi, Miri, Bodo, Rabha tribes of this region. Bodo tribes among them not only prepare fermented alcoholic beverage but also store it for various time periods like 3 months, 6 months, 9 months, 12 months and 15 months etc. They prepare alcoholic beverage Jou (rice beer) following the fermentation of Oryza sativa with traditional yeast culture Amao. Saccharomyces cerevisiae is the main domain strain present in Amao. Dongphangrakep (Scoparia dulcis), Mwkhna (Clerodendrum viscosum), Thalir (Musa balbisina) and Khantal Bilai (Ananas cosmos) are the main plants used for Amao preparation. The stored Jou is known as Joufinai. They store the fermented mixture (rice and Amao) in anaerobic conditions for the preparation of Joufinai. We observed a successive increase in alcohol content from 3 months of storage period with 11.79 ± 0.010 (%, v/v) to 15.48 ± 0.070 (%, v/v) at 15 months of storage by a simple, reproducible and solution based colorimetric method. A positive linear correlation was also observed between pH and ethanol content with storage having correlation coefficient 0.981. Here, we optimised the detection of change in constituents of Joufinai during storage using reverse phase HPLC method. We found acetone, ethanol, acetic acid, glycerol as main constituents present in Joufinai. A very good correlation was observed from 3 months to 15 months of storage periods with its constituents. Increase in glycerol content was also detected with storage periods and hence Joufinai can be use as a precursor of above stated compounds. We also observed antioxidant activities increase from 0.056 ±2.80 mg/mL for 3 months old to 0.078± 5.33 mg/mL (in ascorbic acid equivalents) for 15 month old beverage by DPPH radical scavenging method. Therefore, we aimed for scientific validation of storage procedure used by Bodos in Joufinai production and to convert the Bodos’ traditional alcoholic beverage to a commercial commodity through our study.

Keywords: Amao, correlation, beverage, joufinai

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Authors: Badreddine Chemali, Boualem Tiliouine

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This article presents the main results of a numerical investigation on the uncertainty of dynamic response of structures with statistically correlated random damping Gamma distributed. A computational method based on a Linear Statistical Model (LSM) is implemented to predict second order statistics for the response of a typical industrial building structure. The significance of random damping with correlated parameters and its implications on the sensitivity of structural peak response in the neighborhood of a resonant frequency are discussed in light of considerable ranges of damping uncertainties and correlation coefficients. The results are compared to those generated using Monte Carlo simulation techniques. The numerical results obtained show the importance of damping uncertainty and statistical correlation of damping coefficients when obtaining accurate probabilistic estimates of dynamic response of structures. Furthermore, the effectiveness of the LSM model to efficiently predict uncertainty propagation for structural dynamic problems with correlated damping parameters is demonstrated.

Keywords: correlated random damping, linear statistical model, Monte Carlo simulation, uncertainty of dynamic response

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Authors: Soltani Amir, Hu Jiaxin

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Determination of optimal parameters of a passive control system device is the primary objective of this study. Expanding upon the use of control devices in wind and earthquake hazard reduction has led to development of various control systems. The advantage of non-linearity characteristics in a passive control device and the optimal control method using LQR algorithm are explained in this study. Finally, this paper introduces a simple approach to determine optimum parameters of a nonlinear viscous damper for vibration control of structures. A MATLAB program is used to produce the dynamic motion of the structure considering the stiffness matrix of the SDOF frame and the non-linear damping effect. This study concluded that the proposed system (variable damping system) has better performance in system response control than a linear damping system. Also, according to the energy dissipation graph, the total energy loss is greater in non-linear damping system than other systems.

Keywords: passive control system, damping devices, viscous dampers, control algorithm

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Authors: Ghazal Doostmohammadi, Susan Rahimzadeh

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Aim: This research aimed to investigate the relationship between empathy and interpersonal trust and recognize the mediating role of loneliness between them in both genders. Methods: With a correlational descriptive design, 192 university students (130 female and 62 male) responded to the questionnaires on “empathy quotient,” “loneliness,” and “interpersonal trust” tests. These tests were designed and validated by experts in the field. Data were analysed using Pearson correlation and path analysis, which is a statistical technique that uses standard linear regression equations to determine the degree of conformity of a theoretical causal model with reality. Results: The data analysis showed that there was no significant correlation between interpersonal trust, both with loneliness (t=0.169) and empathy (t=0.186), while there was a significant negative correlation (t=0.359) between empathy and loneliness. This means that there is an inverse correlation between empathy and loneliness. The path analysis confirmed the hypothesis of the research about the mediating role of loneliness between empathy and interpersonal trust. But gender did not play a role in this relationship. Conclusion: As an outcome, clinical professionals and education trainers should pay more attention to interpersonal trust as a basic need and try to recreate and shape it to prevent people's social breakdown, and on the other hand, self-disclosure training (especially in Men), expression of feelings and courage should be given double importance to prevent the consequences of loneliness.

Keywords: empathy, loneliness, interpersonal trust, gender

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Authors: Adriana de Paula Lacerda Santos, Bruna Godke, Mauro Lacerda Santos Filho

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Several dams in the world have already collapsed, causing environmental, social and economic damage. The concern to avoid future disasters has stimulated the creation of a great number of laws and rules in many countries. In Brazil, Law 12.334/2010 was created, which establishes the National Policy on Dam Safety. Overall, this policy requires the dam owners to invest in the maintenance of their structures and to improve its monitoring systems in order to provide faster and straightforward responses in the case of an increase of risks. As monitoring tools, visual inspections has provides comprehensive assessment of the structures performance, while auscultation’s instrumentation has added specific information on operational or behavioral changes, providing an alarm when a performance indicator exceeds the acceptable limits. These limits can be set using statistical methods based on the relationship between instruments measures and other variables, such as reservoir level, time of the year or others instruments measuring. Besides the design parameters (uplift of the foundation, displacements, etc.) the dam instrumentation can also be used to monitor the behavior of defects and damage manifestations. Specifically in concrete gravity dams, one of the main causes for the appearance of cracks, are the concrete volumetric changes generated by the thermal origin phenomena, which are associated with the construction process of these structures. Based on this, the goal of this research is to propose a monitoring process of the thermal cracking behavior in concrete gravity dams, through the instrumentation data analysis and the establishment of control values. Therefore, as a case study was selected the Block B-11 of José Richa Governor Dam Power Plant, that presents a cracking process, which was identified even before filling the reservoir in August’ 1998, and where crack meters and surface thermometers were installed for its monitoring. Although these instruments were installed in May 2004, the research was restricted to study the last 4.5 years (June 2010 to November 2014), when all the instruments were calibrated and producing reliable data. The adopted method is based on simple linear correlations procedures to understand the interactions among the instruments time series, verifying the response times between them. The scatter plots were drafted from the best correlations, which supported the definition of the limit control values. Among the conclusions, it is shown that there is a strong or very strong correlation between ambient temperature and the crack meters and flowmeters measurements. Based on the results of the statistical analysis, it was possible to develop a tool for monitoring the behavior of the case study cracks. Thus it was fulfilled the goal of the research to develop a proposal for a monitoring process of the behavior of thermal cracking in concrete gravity dams.

Keywords: concrete gravity dam, dams safety, instrumentation, simple linear correlation

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Authors: Merrimi El Bekkaye, El Bikri Khalid, Benamar Rhali

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In the present paper, the problem of geometrically non-linear free vibration of symmetrically and asymmetrically laminated composite beams (LCB) resting on nonlinear Pasternak elastic Foundation with immovable ends is studied. A homogenization procedure has been performed to reduce the problem under consideration to that of the isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the LCB has been studied. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Keywords: large vibration amplitudes, laminated composite beam, Pasternak foundation, composite beams

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Authors: G. I. Onwuka, A. Danbaba, S. U. Gulumbe

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This study investigated of Infant Mortality Rate as observed at a general hospital in Kaduna-South, Kaduna State, North West Nigeria. The causes of infant Mortality were examined. The data used for this analysis were collected at the statistics unit of the Hospital. The analysis was carried out on the data using Multiple Linear regression Technique and this showed that there is linear relationship between the dependent variable (death) and the independent variables (malaria, measles, anaemia, and coronary heart disease). The resultant model also revealed that a unit increment in each of these diseases would result to a unit increment in death recorded, 98.7% of the total variation in mortality is explained by the given model. The highest number of mortality was recorded in July, 2005 and the lowest mortality recorded in October, 2009.Recommendations were however made based on the results of the study.

Keywords: infant mortality rate, multiple linear regression, diseases, serial correlation

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Authors: Ahmed Abdelghany, Bernard Uguen, Christophe Moy, Dominique Lemur

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The Internet of Things (IoT) is developed to ensure monitoring and connectivity within different applications. Thus, it is critical to study the channel propagation characteristics in Low Power Wide Area Network (LPWAN), especially Long Range Wide Area Network (LoRaWAN). In this paper, an in-depth investigation of the reciprocity between the uplink and downlink Channel State Information (CSI) is done by performing an outdoor measurement campaign in the area of Campus Beaulieu in Rennes. At each different location, the CSI reciprocity is quantified using the Pearson Correlation Coefficient (PCC) which shows a very high linear correlation between the uplink and downlink CSI. This reciprocity feature could be utilized for the physical layer security between the node and the gateway. On the other hand, most of the CSI shapes from different locations are highly uncorrelated from each other. Hence, it can be anticipated that this could achieve significant localization gain by utilizing the frequency hopping in the LoRa systems by getting access to a wider band.

Keywords: IoT, LPWAN, LoRa, effective signal power, onsite measurement

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Authors: Ali Nourollah, Mohsen Movahedinejad

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In this paper a new algorithm to generate random simple polygons from a given set of points in a two dimensional plane is designed. The proposed algorithm uses a genetic algorithm to generate polygons with few vertices. A new merge algorithm is presented which converts any two polygons into a simple polygon. This algorithm at first changes two polygons into a polygonal chain and then the polygonal chain is converted into a simple polygon. The process of converting a polygonal chain into a simple polygon is based on the removal of intersecting edges. The merge algorithm has the time complexity of O ((r+s) *l) where r and s are the size of merging polygons and l shows the number of intersecting edges removed from the polygonal chain. It will be shown that 1 < l < r+s. The experiments results show that the proposed algorithm has the ability to generate a great number of different simple polygons and has better performance in comparison to celebrated algorithms such as space partitioning and steady growth.

Keywords: Divide and conquer, genetic algorithm, merge polygons, Random simple polygon generation.

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Authors: S. Khan, A. Khan, Abdul R. Soomrani, Raja F. Zafar, A. Waqas, G. Akbar

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This paper proposes a low-complexity image interpolation method. Image interpolation is used to convert a low dimension video/image to high dimension video/image. The objective of a good interpolation method is to upscale an image in such a way that it provides better edge preservation at the cost of very low complexity so that real-time processing of video frames can be made possible. However, low complexity methods tend to provide real-time interpolation at the cost of blurring, jagging and other artifacts due to errors in slope calculation. Non-linear methods, on the other hand, provide better edge preservation, but at the cost of high complexity and hence they can be considered very far from having real-time interpolation. The proposed method is a linear method that uses gradient orientation for slope calculation, unlike conventional linear methods that uses the contrast of nearby pixels. Prewitt edge detection is applied to separate uniform regions and edges. Simple line averaging is applied to unknown uniform regions, whereas unknown edge pixels are interpolated after calculation of slopes using gradient orientations of neighboring known edge pixels. As a post-processing step, bilateral filter is applied to interpolated edge regions in order to enhance the interpolated edges.

Keywords: edge detection, gradient orientation, image upscaling, linear interpolation, slope tracing

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Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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Authors: John Kabuba

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The study investigated the implementation of the Neural Network (NN) techniques for prediction of the loading of Cu ions onto clinoptilolite. The experimental design using analysis of variance (ANOVA) was chosen for testing the adequacy of the Neural Network and for optimizing of the effective input parameters (pH, temperature and initial concentration). Feed forward, multi-layer perceptron (MLP) NN successfully tracked the non-linear behavior of the adsorption process versus the input parameters with mean squared error (MSE), correlation coefficient (R) and minimum squared error (MSRE) of 0.102, 0.998 and 0.004 respectively. The results showed that NN modeling techniques could effectively predict and simulate the highly complex system and non-linear process such as ion-exchange.

Keywords: clinoptilolite, loading, modeling, neural network

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Authors: Zizouni Khaled, Fali Leyla, Sadek Younes, Bousserhane Ismail Khalil

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In structural vibration caused principally by an earthquake excitation, the most vibration’s attenuation system used recently is the semi active control with a Magneto Rheological Damper device. This control was a subject of many researches and works in the last years. The big challenges of searchers in this case is to propose an adequate controller with a robust algorithm of current or tension adjustment. In this present paper, a linear controller is proposed to control the MR damper using to reduce a vibrations of three story structure exposed to El Centro’s 1940 and Boumerdès 2003 earthquakes. In this example, the MR damper is installed in the first floor of the structure. The numerical simulations results of the proposed linear control with a feedback law based on clipped optimal algorithm showed the feasibility of the semi active control to protecting civil structures. The comparison of the controlled structure and uncontrolled structures responses illustrate clearly the performance and the effectiveness of the simple proposed approach.

Keywords: MR damper, seismic vibration, semi-active control

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Authors: David A. Swanson, Lucky M. Tedrow

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Taylor’s Law is a widely observed empirical pattern that relates variances to means in sets of non-negative measurements via an approximate power function, which has found application to human mortality. This study adds to this research by showing that Taylor’s Law leads to a model that reasonably describes the relationship between life expectancy at birth (e0, which also is equal to mean age at death in a life table) and variance at age of death in seven World Bank regional life tables measured at two points in time, 1970 and 2000. Using as a benchmark a non-random sample of four Japanese female life tables covering the period from 1950 to 2004, the study finds that the simple linear model provides reasonably accurate estimates of variance in age at death in a life table from e0, where the latter range from 60.9 to 85.59 years. Employing 2017 life tables from the Human Mortality Database, the simple linear model is used to provide estimates of variance at age in death for six countries, three of which have high e0 values and three of which have lower e0 values. The paper provides a substantive interpretation of Taylor’s Law relative to e0 and concludes by arguing that reasonably accurate estimates of variance in age at death in a period life table can be calculated using this approach, which also can be used where e0 itself is estimated rather than generated through the construction of a life table, a useful feature of the model.

Keywords: empirical pattern, mean age at death in a life table, mean age of a stationary population, stationary population

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Authors: Mehdi Jafari Matehkolaee

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In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Tae-Hoon Kim, Kwon-Ha Yoon, Hong Young Jun, Ki-Jong Kim, Young Hwan Lee, Myeung Su Lee, Keum Ha Choi, Ki Jung Yun, Eun Young Cho, Yong-Yeon Jeong, Chung-Hwan Jun

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Purpose: To assess the changes of hepatic metabolite for differentiation between non-alcoholic steatohepatitis (NASH) and simple steatosis on proton magnetic resonance spectroscopy (1H-MRS) in both humans and animal model. Methods: The local institutional review board approved this study and subjects gave written informed consent. 1H-MRS measurements were performed on a localized voxel of the liver using a point-resolved spectroscopy (PRESS) sequence and hepatic metabolites of alanine (Ala), lactate/triglyceride (Lac/TG), and TG were analyzed in NASH, simple steatosis and control groups. The group difference was tested with the ANOVA and Tukey’s post-hoc tests, and diagnostic accuracy was tested by calculating the area under the receiver operating characteristics (ROC) curve. The associations between metabolic concentration and pathologic grades or non-alcoholic fatty liver disease(NAFLD) activity scores were assessed by the Pearson’s correlation. Results: Patient with NASH showed the elevated Ala(p<0.001), Lac/TG(p < 0.001), TG(p < 0.05) concentration when compared with patients who had simple steatosis and healthy controls. The NASH patients were higher levels in Ala(mean±SEM, 52.5±8.3 vs 2.0±0.9; p < 0.001), Lac/TG(824.0±168.2 vs 394.1±89.8; p < 0.05) than simple steatosis. The area under the ROC curve to distinguish NASH from simple steatosis was 1.00 (95% confidence interval; 1.00, 1.00) with Ala and 0.782 (95% confidence interval; 0.61, 0.96) with Lac/TG. The Ala and Lac/TG levels were well correlated with steatosis grade, lobular inflammation, and NAFLD activity scores. The metabolic changes in human were reproducible to a mice model induced by streptozotocin injection and a high-fat diet. Conclusion: 1H-MRS would be useful for differentiation of patients with NASH and simple hepatic steatosis.

Keywords: non-alcoholic fatty liver disease, non-alcoholic steatohepatitis, 1H MR spectroscopy, hepatic metabolites

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Qasim M. Kriri

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Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: parameter linear programming, objective function, sensitivity analysis, optimize profit

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Authors: Yuwaratu Syafira, Wahyu K. Y. Putra, Kusharisupeni Djokosujono

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Background/Objective: Body Mass Index (BMI) serves various purposes, including measuring the prevalence of obesity in a population, and also in formulating a patient’s diet at a hospital, and can be calculated with the equation = body weight (kg)/body height (m)². However, the BMI of an individual with difficulties in carrying their weight or standing up straight can not necessarily be measured. The aim of this study was to form a prediction model for the BMI of young adult students of Public Health Faculty of University of Indonesia. Subject/Method: This study used a cross sectional design, with a total sample of 132 respondents, consisted of 58 males and 74 females aged 21- 30. The dependent variable of this study was BMI, and the independent variables consisted of sex and anthropometric measurements, which included ulna length, arm length, tibia length, knee height, mid-upper arm circumference, and calf circumference. Anthropometric information was measured and recorded in a single sitting. Simple and multiple linear regression analysis were used to create the prediction equation for BMI. Results: The male respondents had an average BMI of 24.63 kg/m² and the female respondents had an average of 22.52 kg/m². A total of 17 variables were analysed for its correlation with BMI. Bivariate analysis showed the variable with the strongest correlation with BMI was Mid-Upper Arm Circumference/√Ulna Length (MUAC/√UL) (r = 0.926 for males and r = 0.886 for females). Furthermore, MUAC alone also has a very strong correlation with BMI (r = 0,913 for males and r = 0,877 for females). Prediction models formed from either MUAC/√UL or MUAC alone both produce highly accurate predictions of BMI. However, measuring MUAC/√UL is considered inconvenient, which may cause difficulties when applied on the field. Conclusion: The prediction model considered most ideal to estimate BMI is: Male BMI (kg/m²) = 1.109(MUAC (cm)) – 9.202 and Female BMI (kg/m²) = 0.236 + 0.825(MUAC (cm)), based on its high accuracy levels and the convenience of measuring MUAC on the field.

Keywords: body mass index, mid-upper arm circumference, prediction model, ulna length

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Amin Salighehdar, Ziwen Ye, Mingzhe Liu, Ionut Florescu, Alan F. Blumberg

Abstract:

Storm surge is an abnormal water level caused by a storm. Accurate prediction of a storm surge is a challenging problem. Researchers developed various ensemble modeling techniques to combine several individual forecasts to produce an overall presumably better forecast. There exist some simple ensemble modeling techniques in literature. For instance, Model Output Statistics (MOS), and running mean-bias removal are widely used techniques in storm surge prediction domain. However, these methods have some drawbacks. For instance, MOS is based on multiple linear regression and it needs a long period of training data. To overcome the shortcomings of these simple methods, researchers propose some advanced methods. For instance, ENSURF (Ensemble SURge Forecast) is a multi-model application for sea level forecast. This application creates a better forecast of sea level using a combination of several instances of the Bayesian Model Averaging (BMA). An ensemble dressing method is based on identifying best member forecast and using it for prediction. Our contribution in this paper can be summarized as follows. First, we investigate whether the ensemble models perform better than any single forecast. Therefore, we need to identify the single best forecast. We present a methodology based on a simple Bayesian selection method to select the best single forecast. Second, we present several new and simple ways to construct ensemble models. We use correlation and standard deviation as weights in combining different forecast models. Third, we use these ensembles and compare with several existing models in literature to forecast storm surge level. We then investigate whether developing a complex ensemble model is indeed needed. To achieve this goal, we use a simple average (one of the simplest and widely used ensemble model) as benchmark. Predicting the peak level of Surge during a storm as well as the precise time at which this peak level takes place is crucial, thus we develop a statistical platform to compare the performance of various ensemble methods. This statistical analysis is based on root mean square error of the ensemble forecast during the testing period and on the magnitude and timing of the forecasted peak surge compared to the actual time and peak. In this work, we analyze four hurricanes: hurricanes Irene and Lee in 2011, hurricane Sandy in 2012, and hurricane Joaquin in 2015. Since hurricane Irene developed at the end of August 2011 and hurricane Lee started just after Irene at the beginning of September 2011, in this study we consider them as a single contiguous hurricane event. The data set used for this study is generated by the New York Harbor Observing and Prediction System (NYHOPS). We find that even the simplest possible way of creating an ensemble produces results superior to any single forecast. We also show that the ensemble models we propose generally have better performance compared to the simple average ensemble technique.

Keywords: Bayesian learning, ensemble model, statistical analysis, storm surge prediction

Procedia PDF Downloads 285

Authors: Gang Li, Ghulam Mubashar Hassan, Arcady Dyskin, Cara MacNish

Abstract:

Digital image correlation (DIC) is a contactless full-field displacement and strain reconstruction technique commonly used in the field of experimental mechanics. Comparing with physical measuring devices, such as strain gauges, which only provide very restricted coverage and are expensive to deploy widely, the DIC technique provides the result with full-field coverage and relative high accuracy using an inexpensive and simple experimental setup. It is very important to study the natural patterns effect on the DIC technique because the preparation of the artificial patterns is time consuming and hectic process. The objective of this research is to study the effect of using images having natural pattern on the performance of DIC. A systematical simulation method is used to build simulated deformed images used in DIC. A parameter (subset size) used in DIC can have an effect on the processing and accuracy of DIC and even cause DIC to failure. Regarding to the picture parameters (correlation coefficient), the higher similarity of two subset can lead the DIC process to fail and make the result more inaccurate. The pictures with good and bad quality for DIC methods have been presented and more importantly, it is a systematic way to evaluate the quality of the picture with natural patterns before they install the measurement devices.

Keywords: Digital Image Correlation (DIC), deformation simulation, natural pattern, subset size

Procedia PDF Downloads 391