• Title/Summary/Keyword: Matrix algebra

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Ex Vivo MR Diffusion Coefficient Measurement of Human Gastric Tissue (인체의 위 조직 시료에서 자기공명영상장치를 이용한 확산계수 측정에 대한 기초 연구)

  • Mun Chi-Woong;Choi, Ki-Sueng;Nana Roger;Hu, Xiaoping P.;Yang, Young-Il;Chang Hee-Kyung;Eun, Choong-Ki
    • Journal of Biomedical Engineering Research
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    • v.27 no.5
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    • pp.203-209
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    • 2006
  • The aim of this study is to investigate the feasibility of ex vivo MR diffusion tensor imaging technique in order to observe the diffusion-contrast characteristics of human gastric tissues. On normal and pathologic gastric tissues, which have been fixed in a polycarbonate plastic tube filled with 10% formalin solution, laboratory made 3D diffusion tensor Turbo FLASH pulse sequence was used to obtain high resolution MR images with voxel size of $0.5{\times}0.5{\times}0.5mm^3\;using\;64{\times}32{\times}32mm^3$ field of view in conjunction with an acquisition matrix of $128{\times}64{\times}64$. Diffusion weighted- gradient pulses were employed with b values of 0 and $600s/mm^2$ in 6 orientations. The sequence was implemented on a clinical 3.0-T MRI scanner(Siemens, Erlangen, Germany) with a home-made quadrature-typed birdcage Tx/Rx rf coil for small specimen. Diffusion tensor values in each pixel were calculated using linear algebra and singular value decomposition(SVD) algorithm. Apparent diffusion coefficient(ADC) and fractional anisotropy(FA) map were also obtained from diffusion tensor data to compare pixel intensities between normal and abnormal gastric tissues. The processing software was developed by authors using Visual C++(Microsoft, WA, U.S.A.) and mathematical/statistical library of GNUwin32(Free Software Foundation). This study shows that 3D diffusion tensor Turbo FLASH sequence is useful to resolve fine micro-structures of gastric tissue and both ADC and FA values in normal gastric tissue are higher than those in abnormal tissue. Authors expect that this study also represents another possibility of gastric carcinoma detection by visualizing diffusion characteristics of proton spins in the gastric tissues.

Use of ChatGPT in college mathematics education (대학수학교육에서의 챗GPT 활용과 사례)

  • Sang-Gu Lee;Doyoung Park;Jae Yoon Lee;Dong Sun Lim;Jae Hwa Lee
    • The Mathematical Education
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    • v.63 no.2
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    • pp.123-138
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    • 2024
  • This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.