• Title/Summary/Keyword: computational mathematics

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A divide-oversampling and conquer algorithm based support vector machine for massive and highly imbalanced data (불균형의 대용량 범주형 자료에 대한 분할-과대추출 정복 서포트 벡터 머신)

  • Bang, Sungwan;Kim, Jaeoh
    • The Korean Journal of Applied Statistics
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    • v.35 no.2
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    • pp.177-188
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    • 2022
  • The support vector machine (SVM) has been successfully applied to various classification areas with a high level of classification accuracy. However, it is infeasible to use the SVM in analyzing massive data because of its significant computational problems. When analyzing imbalanced data with different class sizes, furthermore, the classification accuracy of SVM in minority class may drop significantly because its classifier could be biased toward the majority class. To overcome such a problem, we propose the DOC-SVM method, which uses divide-oversampling and conquers techniques. The proposed DOC-SVM divides the majority class into a few subsets and applies an oversampling technique to the minority class in order to produce the balanced subsets. And then the DOC-SVM obtains the final classifier by aggregating all SVM classifiers obtained from the balanced subsets. Simulation studies are presented to demonstrate the satisfactory performance of the proposed method.

An algebraic multigrids based prediction of a numerical solution of Poisson-Boltzmann equation for a generation of deep learning samples (딥러닝 샘플 생성을 위한 포아즌-볼츠만 방정식의 대수적 멀티그리드를 사용한 수치 예측)

  • Shin, Kwang-Seong;Jo, Gwanghyun
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.26 no.2
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    • pp.181-186
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    • 2022
  • Poisson-Boltzmann equation (PBE) is used to model problems arising from various disciplinary including bio-pysics and colloid chemistry. Therefore, to predict a numerical solution of PBE is an important issue. The authors proposed deep learning based methods to solve PBE while the computational time to generate finite element method (FEM) solutions were bottlenecks of the algorithms. In this work, we shorten the generation time of FEM solutions in two directions. First, we experimentally find certain penalty parameter in a bilinear form. Second, we applied algebraic multigrids methods to the algebraic system so that condition number is bounded regardless of the meshsize. In conclusion, we have reduced computation times to solve algebraic systems for PBE. We expect that algebraic multigrids methods can be further employed in various disciplinary to generate deep learning samples.

A computational investigation on flexural response of laminated composite plates using a simple quasi-3D HSDT

  • Draiche, Kada;Selim, Mahmoud M.;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bourada, Fouad;Tounsi, Abdeldjebbar;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.41 no.5
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    • pp.697-711
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    • 2021
  • In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.

Computational intelligence models for predicting the frictional resistance of driven pile foundations in cold regions

  • Shiguan Chen;Huimei Zhang;Kseniya I. Zykova;Hamed Gholizadeh Touchaei;Chao Yuan;Hossein Moayedi;Binh Nguyen Le
    • Computers and Concrete
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    • v.32 no.2
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    • pp.217-232
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    • 2023
  • Numerous studies have been performed on the behavior of pile foundations in cold regions. This study first attempted to employ artificial neural networks (ANN) to predict pile-bearing capacity focusing on pile data recorded primarily on cold regions. As the ANN technique has disadvantages such as finding global minima or slower convergence rates, this study in the second phase deals with the development of an ANN-based predictive model improved with an Elephant herding optimizer (EHO), Dragonfly Algorithm (DA), Genetic Algorithm (GA), and Evolution Strategy (ES) methods for predicting the piles' bearing capacity. The network inputs included the pile geometrical features, pile area (m2), pile length (m), internal friction angle along the pile body and pile tip (Ø°), and effective vertical stress. The MLP model pile's output was the ultimate bearing capacity. A sensitivity analysis was performed to determine the optimum parameters to select the best predictive model. A trial-and-error technique was also used to find the optimum network architecture and the number of hidden nodes. According to the results, there is a good consistency between the pile-bearing DA-MLP-predicted capacities and the measured bearing capacities. Based on the R2 and determination coefficient as 0.90364 and 0.8643 for testing and training datasets, respectively, it is suggested that the DA-MLP model can be effectively implemented with higher reliability, efficiency, and practicability to predict the bearing capacity of piles.

Effective ChatGPT Prompts in Mathematical Problem Solving : Focusing on Quadratic Equations and Quadratic Functions (수학 문제 해결에서 효과적인 ChatGPT의 프롬프트 고찰: 이차방정식과 이차함수를 중심으로)

  • Oh, Se Jun
    • Communications of Mathematical Education
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    • v.37 no.3
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    • pp.545-567
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    • 2023
  • This study investigates effective ChatGPT prompts for solving mathematical problems, focusing on the chapters of quadratic equations and quadratic functions. A structured prompt was designed, following a sequence of 'Role-Rule-Example Solution-Problem-Process'. In this study, an artificial intelligence model combining GPT-4, Wolfram plugin, and Advanced Data Analysis was utilized. Wolfram was used as the primary tool for calculations to reduce computational errors. When using the structured prompt, the accuracy rate for problems from nine high school mathematics textbooks on quadratic equations and quadratic functions was 91%, showing higher performance compared to zero-shot prompts. This confirmed the effectiveness of the structured prompts in solving mathematical problems. The structured prompts designed in this study can contribute to the development of intelligent information systems for personalized and customized education.

Geometry optimization of a double-layered inertial reactive armor configured with rotating discs

  • Bekzat Ajan;Dichuan Zhang;Christos Spitas;Elias Abou Fakhr;Dongming Wei
    • Advances in Computational Design
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    • v.8 no.4
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    • pp.309-325
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    • 2023
  • An innovative inertial reactive armor is being developed through a multi-discipline project. Unlike the well-known explosive or non-explosive reactive armour that uses high-energy explosives or bulging effect, the proposed inertial reactive armour uses active disc elements that is set to rotate rapidly upon impact to effectively deflect and disrupt shaped charges and kinetic energy penetrators. The effectiveness of the proposed armour highly depends on the tangential velocity of the impact point on the rotating disc. However,for a single layer armour with an array of high-speed rotating discs, the tangential velocity is relatively low near the center of the disc and is not available between the gap of the discs. Therefore, it is necessary to configure the armor with double layers to increase the tangential velocity at the point of impact. This paper explores a multi-objective geometry design optimization for the double-layered armor using Nelder-Mead optimization algorithm and integration tools of the python programming language. The optimization objectives include maximizing both average tangential velocity and high tangential velocity areas and minimizing low tangential velocity area. The design parameters include the relative position (translation and rotation) of the disc element between two armor layers. The optimized design results in a significant increase of the average tangential velocity (38%), increase of the high tangential velocity area (71.3%), and decrease of the low tangential velocity area (86.2%) as comparing to the single layer armor.

A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND B-MODE POLARIZATION WITH POLARBEAR

  • ADE, P.A.R.;AKIBA, Y.;ANTHONY, A.E.;ARNOLD, K.;ATLAS, M.;BARRON, D.;BOETTGER, D.;BORRILL, J.;CHAPMAN, S.;CHINONE, Y.;DOBBS, M.;ELLEFLOT, T.;ERRARD, J.;FABBIAN, G.;FENG, C.;FLANIGAN, D.;GILBERT, A.;GRAINGER, W.;HALVERSON, N.W.;HASEGAWA, M.;HATTORI, K.;HAZUMI, M.;HOLZAPFEL, W.L.;HORI, Y.;HOWARD, J.;HYLAND, P.;INOUE, Y.;JAEHNIG, G.C.;JAFFE, A.H.;KEATING, B.;KERMISH, Z.;KESKITALO, R.;KISNER, T.;JEUNE, M. LE;LEE, A.T.;LEITCH, E.M.;LINDER, E.;LUNGU, M.;MATSUDA, F.;MATSUMURA, T.;MENG, X.;MILLER, N.J.;MORII, H.;MOYERMAN, S.;MYERS, M.J.;NAVAROLI, M.;NISHINO, H.;ORLANDO, A.;PAAR, H.;PELOTON, J.;POLETTI, D.;QUEALY, E.;REBEIZ, G.
    • Publications of The Korean Astronomical Society
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    • v.30 no.2
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    • pp.625-628
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    • 2015
  • POLARBEAR is a ground-based experiment located in the Atacama desert of northern Chile. The experiment is designed to measure the Cosmic Microwave Background B-mode polarization at several arcminute resolution. The CMB B-mode polarization on degree angular scales is a unique signature of primordial gravitational waves from cosmic inflation and B-mode signal on sub-degree scales is induced by the gravitational lensing from large-scale structure. Science observations began in early 2012 with an array of 1.274 polarization sensitive antenna-couple Transition Edge Sensor (TES) bolometers at 150 GHz. We published the first CMB-only measurement of the B-mode polarization on sub-degree scales induced by gravitational lensing in December 2013 followed by the first measurement of the B-mode power spectrum on those scales in March 2014. In this proceedings, we review the physics of CMB B-modes and then describe the Polarbear experiment, observations, and recent results.

A Customized Cancer Radiation Treatment Planning Simulation (ccRTPs) System via Web and Network (웹과 네트워크 기술을 이용한 환자 맞춤식 암치료 계획 시뮬레이션 시스템)

  • Khm, O-Yeon
    • Progress in Medical Physics
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    • v.17 no.3
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    • pp.144-152
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    • 2006
  • The telemedicine using independent client-server system via networks can provide high quality normalized services to many hospitals, specifically to local/rural area hospitals. This will eventually lead to a decreased medical cost because the centralized institute can handle big computer hardware systems and complicated software systems efficiently and economically, Customized cancer radiation treatment planning for each patient Is very useful for both a patient and a doctor because it makes possible for the most effective treatment with the least possible dose to patient. Radiation planners know that too small a dose to the tumor can result in recurrence of the cancer, while too large a dose to healthy tissue can cause complications or even death. The best solution is to build an accurate planning simulation system to provide better treatment strategies based on each patient's computerized tomography (CT) image. We are developing a web-based and a network-based customized cancer radiation therapy simulation system consisting of four Important computer codes; a CT managing code for preparing the patients target data from their CT image files, a parallel Monte Carlo high-energy beam code (PMCEPT code) for calculating doses against the target generated from the patient CT image, a parallel linear programming code for optimizing the treatment plan, and scientific data visualization code for efficient pre/post evaluation of the results. The whole softwares will run on a high performance Beowulf PC cluster of about 100-200 CPUs. Efficient management of the hardware and software systems is not an easy task for a hospital. Therefore, we integrated our system into the client-sewer system via network or web and provide high quality normalized services to many hospitals. Seamless communication with doctors is maintained via messenger function of the server-client system.

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Development of a Hydrograph Triggered by Earth-Dam-Break for Compiling a Flood Hazard Map (홍수위험지도 작성을 위한 댐 붕괴 지점에서의 유량곡선 산정)

  • Lee, Khil-Ha;Kim, Sung-Wook;Yu, Soonyoung;Kim, Sang-Hyun;Cho, Jinwoo;Kim, Jin-Man
    • The Journal of Engineering Geology
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    • v.23 no.4
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    • pp.381-387
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    • 2013
  • In compiling flood hazard maps for the case of dam-failure, a scenario-based numerical modeling approach is commonly used, involving the modeling of important parameters that capture peak discharge, such as breach formation and progress. In this study, an earth-dam-break model is constructed assuming an identical mechanism and hydraulic process for all dam-break processes. A focus of the analysis is estimation of the hydrograph at the outlet as a function of time. The constructed hydrograph then serves as an upper boundary condition in running the flood routing model downstream, although flood routing is not considered here. Validation was performed using the record of the Tangjishan dam-break in China. The results were satisfactory, with a coefficient of determination of 0.974, Nash-Sutcliffe Coefficient of Efficiency (NSC) of 0.94, and Root Mean Square Error (RMSE) of $610m^3/sec$. The proposed model will contribute to assessments of potential flood hazards caused by dam-break.

Probable Volcanic Flood of the Cheonji Caldera Lake Triggered by Volcanic Eruption of Mt. Baekdusan (백두산 화산분화로 인해 천지에서 발생 가능한 화산홍수)

  • Lee, Khil-Ha;Kim, Sung-Wook;Yoo, Soon-Young;Kim, Sang-Hyun
    • Journal of the Korean earth science society
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    • v.34 no.6
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    • pp.492-506
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    • 2013
  • The historical accounts and materials about the eruption of Mt. Baekdusan as observed by the geological survey is now showing some signs of waking from a long slumber. As a response of the volcanic eruption of Mt. Baekdusan, water release may occur from the stored water in Lake Cheonjii caldera. The volcanic flood is crucial in that it has huge potential energy that can destruct all kinds of man-made structures and that its velocity can reach up to 100 km $hr^{-1}$ to cover hundreds of kilometers of downstream of Lake Cheonji. The ultimate goal of the study is to estimate the level of damage caused by the volcanic flood of Lake Cheon-Ji caldera. As a preliminary study a scenario-based numerical analysis is performed to build hydrographs as a function of time. The analysis is performed for each scenario (breach, magma uplift, combination of uplift and breach, formation of precipitation etc.) and the parameters to require a model structure is chosen on the basis of the historic records of other volcanos. This study only considers the amount of water at the rim site as a function of time for the estimation whereas the downstream routing process is not considered in this study.