Search results for: high dimensional data

Authors: Malay Bhattacharyya, Saparya Suresh

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The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

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Authors: Meng Su

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High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.

Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis

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Authors: Bharat Singh Om Prakash Vyas

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Now a day’s applications deal with High Dimensional Data have tremendously used in the popular areas. To tackle with such kind of data various approached has been developed by researchers in the last few decades. To tackle with such kind of data various approached has been developed by researchers in the last few decades. One of the problems with the NMF approaches, its randomized valued could not provide absolute optimization in limited iteration, but having local optimization. Due to this, we have proposed a new approach that considers the initial values of the decomposition to tackle the issues of computationally expensive. We have devised an algorithm for initializing the values of the decomposed matrix based on the PSO (Particle Swarm Optimization). Through the experimental result, we will show the proposed method converse very fast in comparison to other row rank approximation like simple NMF multiplicative, and ACLS techniques.

Keywords: ALS, NMF, high dimensional data, RMSE

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Authors: Chen Zhang, Nan Chen

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High-dimensional process monitoring becomes increasingly important in many application domains, where usually the process distribution is unknown and much more complicated than the normal distribution, and the between-stream correlation can not be neglected. However, since the process dimension is generally much bigger than the reference sample size, most traditional nonparametric multivariate control charts fail in high-dimensional cases due to the curse of dimensionality. Furthermore, when the process goes out of control, the influenced variables are quite sparse compared with the whole dimension, which increases the detection difficulty. Targeting at these issues, this paper proposes a new nonparametric monitoring scheme for high-dimensional processes. This scheme first projects the high-dimensional process into several subprocesses using random projections for dimension reduction. Then, for every subprocess with the dimension much smaller than the reference sample size, a local nonparametric control chart is constructed based on the spatial rank test to detect changes in this subprocess. Finally, the results of all the local charts are fused together for decision. Furthermore, after an out-of-control (OC) alarm is triggered, a diagnostic framework is proposed. using the square-root LASSO. Numerical studies demonstrate that the chart has satisfactory detection power for sparse OC changes and robust performance for non-normally distributed data, The diagnostic framework is also effective to identify truly changed variables. Finally, a real-data example is presented to demonstrate the application of the proposed method.

Keywords: random projection, high-dimensional process control, spatial rank, sequential change detection

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Authors: Mohammed Abdullah Alshahrani

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The research focuses on investigating the use of partial least squares (PLS) methodology for addressing challenges associated with high-dimensional correlated data. Recent technological advancements have led to experiments producing data characterized by a large number of variables compared to observations, with substantial inter-variable correlations. Such data patterns are common in chemometrics, where near-infrared (NIR) spectrometer calibrations record chemical absorbance levels across hundreds of wavelengths, and in genomics, where thousands of genomic regions' copy number alterations (CNA) are recorded from cancer patients. PLS serves as a widely used method for analyzing high-dimensional data, functioning as a regression tool in chemometrics and a classification method in genomics. It handles data complexity by creating latent variables (components) from original variables. However, applying PLS can present challenges. The study investigates key areas to address these challenges, including unifying interpretations across three main PLS algorithms and exploring unusual negative shrinkage factors encountered during model fitting. The research presents an alternative approach to addressing the interpretation challenge of predictor weights associated with PLS. Sparse estimation of predictor weights is employed using a penalty function combining a lasso penalty for sparsity and a Cauchy distribution-based penalty to account for variable dependencies. The results demonstrate sparse and grouped weight estimates, aiding interpretation and prediction tasks in genomic data analysis. High-dimensional data scenarios, where predictors outnumber observations, are common in regression analysis applications. Ordinary least squares regression (OLS), the standard method, performs inadequately with high-dimensional and highly correlated data. Copy number alterations (CNA) in key genes have been linked to disease phenotypes, highlighting the importance of accurate classification of gene expression data in bioinformatics and biology using regularized methods like PLS for regression and classification.

Keywords: partial least square regression, genetics data, negative filter factors, high dimensional data, high correlated data

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Authors: Yoonsuh Jung

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As DNA microarray data contain relatively small sample size compared to the number of genes, high dimensional models are often employed. In high dimensional models, the selection of tuning parameter (or, penalty parameter) is often one of the crucial parts of the modeling. Cross-validation is one of the most common methods for the tuning parameter selection, which selects a parameter value with the smallest cross-validated score. However, selecting a single value as an "optimal" value for the parameter can be very unstable due to the sampling variation since the sample sizes of microarray data are often small. Our approach is to choose multiple candidates of tuning parameter first, then average the candidates with different weights depending on their performance. The additional step of estimating the weights and averaging the candidates rarely increase the computational cost, while it can considerably improve the traditional cross-validation. We show that the selected value from the suggested methods often lead to stable parameter selection as well as improved detection of significant genetic variables compared to the tradition cross-validation via real data and simulated data sets.

Keywords: cross validation, parameter averaging, parameter selection, regularization parameter search

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: local nonlinear estimation, LWPR algorithm, online training method, locally weighted projection regression method

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Authors: Cheng Zeng, George Michailidis, Hitoshi Iyatomi, Leo L. Duan

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The conditional density characterizes the distribution of a response variable y given other predictor x and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant work on the problem of Conditional Density Estimation (CDE) for a low-dimensional response in the presence of a high-dimensional predictor, little work has been done for a high-dimensional response such as images. The promising performance of normalizing flow (NF) neural networks in unconditional density estimation acts as a motivating starting point. In this work, the authors extend NF neural networks when external x is present. Specifically, they use the NF to parameterize a one-to-one transform between a high-dimensional y and a latent z that comprises two components [zₚ, zₙ]. The zₚ component is a low-dimensional subvector obtained from the posterior distribution of an elementary predictive model for x, such as logistic/linear regression. The zₙ component is a high-dimensional independent Gaussian vector, which explains the variations in y not or less related to x. Unlike existing CDE methods, the proposed approach coined Augmented Posterior CDE (AP-CDE) only requires a simple modification of the common normalizing flow framework while significantly improving the interpretation of the latent component since zₚ represents a supervised dimension reduction. In image analytics applications, AP-CDE shows good separation of 𝑥-related variations due to factors such as lighting condition and subject id from the other random variations. Further, the experiments show that an unconditional NF neural network based on an unsupervised model of z, such as a Gaussian mixture, fails to generate interpretable results.

Keywords: conditional density estimation, image generation, normalizing flow, supervised dimension reduction

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Authors: S. Habte, K. Ouazzane, P. Patel, S. Patel

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The dynamic and highly competitive nature of the consumer electronics retail industry means that businesses in this industry are experiencing different decision making challenges in relation to pricing, inventory control, consumer satisfaction and product offerings. To overcome the challenges facing retailers and create opportunities, we propose a generic data warehousing solution which can be applied to a wide range of consumer electronics retailers with a minimum configuration. The solution includes a dimensional data model, a template SQL script, a high level architectural descriptions, ETL tool developed using C#, a set of APIs, and data access tools. It has been successfully applied by ASK Outlets Ltd UK resulting in improved productivity and enhanced sales growth.

Keywords: consumer electronics, data warehousing, dimensional data model, generic, retail industry

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Authors: Hongfang Ma, Mingchuan Zhou, Haitao Zhang, Weiyong Ying

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One dimensional pseudo-homogenous modeling has been performed for methanol steam reforming reactor. The results show that the models can well predict the industrial data. The reactor had minimum temperature along axial because of endothermic reaction. Hydrogen productions and temperature profiles along axial were investigated regarding operation conditions such as inlet mass flow rate and mass fraction of methanol, inlet temperature of external thermal oil. Low inlet mass flow rate of methanol, low inlet temperature, and high mass fraction of methanol decreased minimum temperature along axial. Low inlet mass flow rate of methanol, high mass fraction of methanol, and high inlet temperature of thermal oil made cold point forward. Low mass fraction, high mass flow rate, and high inlet temperature of thermal oil increased hydrogen production. One dimensional models can be a guide for industrial operation.

Keywords: reactor, modeling, methanol, steam reforming

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Authors: Nirmala Lama

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The construction of high dams has led to significant challenges in managing flow rates discharging over spillways, resulting in cavitation damages on hydraulic surfaces. To address this, aerator devices were designed and installed to promote fore aeration, thereby controlling and mitigating damages caused by cavitation. Consequently, these aerator types, three-dimensional aerators (3DAEs), have demonstrated superior efficiency in introducing forced air into the flow.This research focuses on the installation and evaluation of three-dimensional aerator devices at the high discharge spillway surface. In the laboratory, the air concentration downstream of the hydraulic structures was extensively measured, and the data were analyzed in details.Multiple flow scenarios and structural arrangements of the aerators were adopted for the study. The outcomes of these experiments are listed as In terms of air concentration value, the comparison between 3 DAE (three-dimensional aerator) with offset only and offset with ramp reveals significant differences. The concentration value on the side wall was justified. The side cavity length was found to increase with higher approach Froude numbers and lateral enlargement widths. Furthermore, 3DAE exhibited shorter side cavity lengths compared to three-dimensional aerator devices without ramps (3DAD), a beneficial features for controlling water fins. An empirical formula to express the side cavity length was derived from the measured data. Also, the comparison were made on the basis of water fin formation between the different arrangements of 3D aerators. In conclusion, this research provides valuable insights into the performance of three-dimensional aerators in mitigating cavitation damages and controlling water fins in high dam spillways. The findings offer practical implications for designers and engineers seeking to enhance the efficiency and safety of hydraulic structures subjected to high flow rates.

Keywords: three-dimension aerator, cavity, water fin, air entrainment

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Authors: M. A. Rubio, A. Urquia

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Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.

Keywords: optimization, sensitivity, genetic algorithms, model calibration

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Authors: Xin Chen

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It has been widely observed that marine food webs have significantly larger predator–prey body-size ratios compared with their terrestrial counterparts. A number of hypotheses have been proposed to account for such difference on the basis of primary productivity, trophic structure, biophysics, bioenergetics, habitat features, energy efficiency, etc. In this study, an alternative explanation is suggested based on the difference in the spatial dimensions of foraging arenas: terrestrial animals primarily forage in two dimensional arenas, while marine animals mostly forage in three dimensional arenas. Using 2-dimensional and 3-dimensional random walk simulations, it is shown that marine predators with 3-dimensional foraging would normally have a greater foraging efficiency than terrestrial predators with 2-dimensional foraging. Marine prey with 3-dimensional dispersion usually has greater swarms or aggregations than terrestrial prey with 2-dimensional dispersion, which again favours a greater predator foraging efficiency in marine animals. As an analytical tool, a Lotka-Volterra based adaptive dynamical model is developed with the predator-prey ratio embedded as an adaptive variable. The model predicts that high predator foraging efficiency and high prey conversion rate will dynamically lead to the evolution of a greater predator-prey ratio. Therefore, marine food webs with 3-dimensional foraging space, which generally have higher predator foraging efficiency, will evolve a greater predator-prey ratio than terrestrial food webs.

Keywords: predator-prey, body size, lotka-volterra, random walk, foraging efficiency

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Authors: S. Y. Cicekli

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In this study, tree-dimensional model of tree was created by using terrestrial close range photogrammetry. For this close range photos were taken. Photomodeler Pro 5 software was used for camera calibration and create three-dimensional model of trees. In first test, three-dimensional model of a tree was created, in the second test three-dimensional model of three trees were created. This study aim is creating three-dimensional model of trees and indicate the use of close-range photogrammetry in forestry. At the end of the study, three-dimensional model of tree and three trees were created. This study showed that usability of close-range photogrammetry for monitoring tree and forests three-dimensional model.

Keywords: close- range photogrammetry, forest, tree, three-dimensional model

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Authors: Abdelhamid Zerroug, Mlle Ismahene Sehili

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Spectral methods are usually applied to solve uni-dimensional boundary value problems. With the advantage of the creation of multidimensional basis, we propose a new spectral method for bi-dimensional problems. In this article, we start by creating bi-spectral basis by different ways, we developed also a new relations to determine the expressions of spectral coefficients in different partial derivatives expansions. Finally, we propose the principle of a new bi-spectral method for the bi-dimensional problems.

Keywords: boundary value problems, bi-spectral methods, bi-dimensional Legendre basis, spectral method

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Authors: Mr. P. Suryaprasad, R. Lalitha

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This paper presents an efficient area and delay architectures for the implementation of one dimensional and two dimensional discrete cosine transform (DCT). These are supported to different lengths (4, 8, 16, and 32). DCT blocks are used in the different video coding standards for the image compression. The 2D- DCT calculation is made using the 2D-DCT separability property, such that the whole architecture is divided into two 1D-DCT calculations by using a transpose buffer. Based on the existing 1D-DCT architecture two different types of 2D-DCT architectures, folded and parallel types are implemented. Both of these two structures use the same transpose buffer. Proposed transpose buffer occupies less area and high speed than existing transpose buffer. Hence the area, low power and delay of both the 2D-DCT architectures are reduced.

Keywords: transposition buffer, video compression, discrete cosine transform, high efficiency video coding, two dimensional picture

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Authors: Gaelle Candel, David Naccache

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t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embeddings. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n²) to O(n²=k), and the memory requirement from n² to 2(n=k)², which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution, and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning

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Authors: Nacer Eddine Chelbi, Ayet Bagane, Annie Saleh, Claude Sauvageau, Denis Gingras

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As recently stated by National Highway Traffic Safety Administration (NHTSA), to demonstrate the expected performance of a highly automated vehicles system, test approaches should include a combination of simulation, test track, and on-road testing. In this paper, we propose a new validation method for autonomous vehicles involving on-road tests (Field Operational Tests), test track (Test Matrix) and simulation (Worst Case Scenarios). We concentrate our discussion on the simulation aspects, in particular, we extend recent work based on Importance Sampling by using a Metropolis-Hasting algorithm (MHS) to sample collected data from the Safety Pilot Model Deployment (SPMD) in lane-change scenarios. Our proposed MH sampling method will be compared to the Importance Sampling method, which does not perform well in high-dimensional problems. The importance of this study is to obtain a sampler that could be applied to high dimensional simulation problems in order to reduce and optimize the number of test scenarios that are necessary for validation and certification of autonomous vehicles.

Keywords: automated driving, autonomous emergency braking (AEB), autonomous vehicles, certification, evaluation, importance sampling, metropolis-hastings sampling, tests

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Authors: Laura Pytel, Georg Baumann, Gregor Gstrein, Corina Klug

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Premium cars often coat the instrument panels with a bilaminate consisting of a soft foam and a plastic skin. The coating is torn open during the passenger airbag deployment under high strain rates. Characterizing and simulating the top coat layer is crucial for predicting the attenuation that delays the airbag deployment, effecting the design of the restrain system and to reduce the demand of simulation adjustments through expensive physical component testing.Up to now, bilaminates used within cars either have been modelled by using a two-dimensional shell formulation for the whole coating system as one which misses out the interaction of the two layers or by combining a three-dimensional formulation foam layer with a two-dimensional skin layer but omitting the foam in the significant parts like the expected tear line area and the hinge where high compression is expected. In both cases, the properties of the coating causing the attenuation are not considered. Further, at present, the availability of material information, as there are failure dependencies of the two layers, as well as the strain rate of up to 200 1/s, are insufficient. The velocity of the passenger airbag flap during an airbag shot has been measured with about 11.5 m/s during first ripping; the digital image correlation evaluation showed resulting strain rates of above 1500 1/s. This paper provides a high strain rate material characterization of a bilaminate consisting of a thin polypropylene foam and a thermoplasctic olefins (TPO) skin and the creation of validated material models. With the help of a Split Hopkinson tension bar, strain rates of 1500 1/s were within reach. The experimental data was used to calibrate and validate a more physical modelling approach of the forced ripping of the bilaminate. In the presented model, the three-dimensional foam layer is continuously tied to the two-dimensional skin layer, allowing failure in both layers at any possible position. The simulation results show a higher agreement in terms of the trajectory of the flaps and its velocity during ripping. The resulting attenuation of the airbag deployment measured by the contact force between airbag and flaps increases and serves usable data for dimensioning modules of an airbag system.

Keywords: bilaminate ripping behavior, High strain rate material characterization and modelling, induced material failure, TPO and foam

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Authors: Branci Sarra, Branci Saadia

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Because of the multiplied data growth, many computer science tools have been developed to process and analyze these Big Data. High-performance computing architectures have been designed to meet the treatment needs of Big Data (view transaction processing standpoint, strategic, and tactical analytics). The purpose of this article is to provide a historical and global perspective on the recent trend of high-performance computing architectures especially what has a relation with Analytics and Data Mining.

Keywords: high performance computing, HPC, big data, data analysis

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Authors: Julia Desiree Velastegui Caceres, Luis Alejandro Velastegui Caceres, Oswaldo Padilla, Eduardo Kirby, Francisco Guerrero, Theofilos Toulkeridis

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It is fundamental to conserve sites of natural and cultural heritage with any available technique or existing methodology of preservation in order to sustain them for the following generations. We propose a further skill to protect the actual view of such sites, in which with high technology instrumentation we are able to digitally preserve natural and cultural heritages applied in Ecuador. In this project the use of laser technology is presented for three-dimensional models, with high accuracy in a relatively short period of time. In Ecuador so far, there are not any records on the use and processing of data obtained by this new technological trend. The importance of the project is the description of the methodology of the laser scanner system using the Faro Laser Scanner Focus 3D 120, the method for 3D modeling of geospatial data and the development of virtual environments in the areas of Cultural and Natural Heritage. In order to inform users this trend in technology in which three-dimensional models are generated, the use of such tools has been developed to be able to be displayed in all kinds of digitally formats. The results of the obtained 3D models allows to demonstrate that this technology is extremely useful in these areas, but also indicating that each data campaign needs an individual slightly different proceeding starting with the data capture and processing to obtain finally the chosen virtual environments.

Keywords: laser scanner system, 3D model, cultural heritage, natural heritage

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Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: Yanqin Chen, Chao Jiang, Chongdu Cho

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This research presents the three-dimensional mechanical characteristics of a commercial gas diffusion layer by experiment and simulation results. Although the mechanical performance of gas diffusion layers has attracted much attention, its reliability and accuracy are still a major challenge. With the help of simulation analysis methods, it is beneficial to the gas diffusion layer’s extensive commercial development and the overall stress analysis of proton electrolyte membrane fuel cells during its pre-production design period. Therefore, in this paper, a three-dimensional constitutive model of a commercial gas diffusion layer, including its material stiffness matrix parameters, is developed and coded, in the user-defined material model of a commercial finite element method software for simulation. Then, the model is validated by comparing experimental results as well as simulation outcomes. As a result, both the experimental data and simulation results show a good agreement with each other, with high accuracy.

Keywords: gas diffusion layer, proton electrolyte membrane fuel cell, stiffness matrix, three-dimensional mechanical characteristics, user-defined material model

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Abhijith Asok

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This paper presents a generalized approach for the simple linear data transformation, Y=bX, through an integration of multidimensional coordinate geometry, vector space theory and polygonal geometry. The scaling is performed by adding an additional ’Dummy Dimension’ to the n-dimensional data, which helps plot two dimensional component-wise straight lines on pairs of dimensions. The end result is a set of scaled extensions of observations in any of the 2n spatial divisions, where n is the total number of applicable dimensions/dataset variables, created by shifting the n-dimensional plane along the ’Dummy Axis’. The derived scaling factor was found to be dependent on the coordinates of the common point of origin for diverging straight lines and the plane of extension, chosen on and perpendicular to the ’Dummy Axis’, respectively. This result indicates the geometrical interpretation of a linear data transformation and hence, opportunities for a more informed choice of the factor ’b’, based on a better choice of these coordinate values. The paper follows on to identify the effect of this transformation on certain popular distance metrics, wherein for many, the distance metric retained the same scaling factor as that of the features.

Keywords: data transformation, dummy dimension, linear transformation, scaling

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Authors: Ibrahim A. Elshaer, Alaa M. Shaker

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Several previous empirical studies have operationalized service quality as either a multidimensional or unidimensional construct. While few earlier studies investigated some practices of the assumed dimensional structure of service quality, no study has been found to have tested the construct’s dimensionality using confirmatory factor analysis (CFA). To gain a better insight into the dimensional structure of service quality construct, this paper tests its dimensionality using three CFA models (higher order factor model, oblique factor model, and one factor model) on a set of data collected from 390 British tourists visited Egypt. The results of the three tests models indicate that service quality construct is multidimensional. This result helps resolving the problems that might arise from the lack of clarity concerning the dimensional structure of service quality, as without testing the dimensional structure of a measure, researchers cannot assume that the significant correlation is a result of factors measuring the same construct.

Keywords: service quality, dimensionality, confirmatory factor analysis, Egypt

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Authors: Alexandru George Vaduva, Adriana Vlad, Bogdan Badea

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In this research, we conduct a Monte Carlo analysis on a two-dimensional χ2 test, which is used to determine the minimum distance required for independent sampling in the context of chaotic signals. We investigate the impact of transforming initial data sets from any probability distribution to new signals with a uniform distribution using the Spearman rank correlation on the χ2 test. This transformation removes the randomness of the data pairs, and as a result, the observed distribution of χ2 test values differs from the expected distribution. We propose a solution to this problem and evaluate it using another chaotic signal.

Keywords: chaotic signals, logistic map, Pearson’s test, Chi Square test, bivariate distribution, statistical independence

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: D. Henninger, A. Zopey, T. Ihde, C. Mehring

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The dynamic performance of a 4-way solenoid operated hydraulic spool valve has been analyzed by means of a one-dimensional modeling approach capturing flow, magnetic and fluid forces, valve inertia forces, fluid compressibility, and damping. Increased model accuracy was achieved by analyzing the detailed three-dimensional electromagnetic behavior of the solenoids and flow behavior through the spool valve body for a set of relevant operating conditions, thereby allowing the accurate mapping of flow and magnetic forces on the moving valve body, in lieu of representing the respective forces by lower-order models or by means of simplistic textbook correlations. The resulting high-fidelity one-dimensional model provided the basis for specific and timely design modification eliminating experimentally observed valve oscillations.

Keywords: dynamic performance model, high-fidelity model, 1D-3D decoupled analysis, solenoid-operated hydraulic servo valve, CFD and electromagnetic FEA

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Authors: U. Yerlikaya, R. T. Balkan

Abstract:

In this research, a method is developed to obtain high-dimensional configuration space for path planning problems. In typical cases, the path planning problems are solved directly in the 3-dimensional (D) workspace. However, this method is inefficient in handling the robots with various geometrical and mechanical restrictions. To overcome these difficulties, path planning may be formalized and solved in a new space which is called configuration space. The number of dimensions of the configuration space comes from the degree of freedoms of the system of interest. The method can be applied in two ways. In the first way, the point clouds of all the bodies of the system and interaction of them are used. The second way is performed via using the clearance function of simulation software where the minimum distances between surfaces of bodies are simultaneously measured. A double-turret system is held in the scope of this study. The 4-D configuration space of a double-turret system is obtained in these two ways. As a result, the difference between these two methods is around 1%, depending on the density of the point cloud. The disparity between the two forms steadily decreases as the point cloud density increases. At the end of the study, in order to verify 4-D configuration space obtained, 4-D path planning problem was realized as 2-D + 2-D and a sample path planning is carried out with using A* algorithm. Then, the accuracy of the configuration space is proved using the obtained paths on the simulation model of the double-turret system.

Keywords: A* algorithm, autonomous turrets, high-dimensional C-space, manifold C-space, point clouds

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