• 제목/요약/키워드: General tensor

검색결과 70건 처리시간 0.031초

CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD

  • De, Uday Chand;Mantica, Carlo Alberto
    • 대한수학회논문집
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    • 제29권2호
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    • pp.319-329
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    • 2014
  • In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.

Time Series Classification of Cryptocurrency Price Trend Based on a Recurrent LSTM Neural Network

  • Kwon, Do-Hyung;Kim, Ju-Bong;Heo, Ju-Sung;Kim, Chan-Myung;Han, Youn-Hee
    • Journal of Information Processing Systems
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    • 제15권3호
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    • pp.694-706
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    • 2019
  • In this study, we applied the long short-term memory (LSTM) model to classify the cryptocurrency price time series. We collected historic cryptocurrency price time series data and preprocessed them in order to make them clean for use as train and target data. After such preprocessing, the price time series data were systematically encoded into the three-dimensional price tensor representing the past price changes of cryptocurrencies. We also presented our LSTM model structure as well as how to use such price tensor as input data of the LSTM model. In particular, a grid search-based k-fold cross-validation technique was applied to find the most suitable LSTM model parameters. Lastly, through the comparison of the f1-score values, our study showed that the LSTM model outperforms the gradient boosting model, a general machine learning model known to have relatively good prediction performance, for the time series classification of the cryptocurrency price trend. With the LSTM model, we got a performance improvement of about 7% compared to using the GB model.

Injury of the Thalamocortical Pathway Between the Mediodorsal Nuclei and the Prefrontal Cortex in a Patient with Traumatic Brain Injury

  • Sang Seok Yeo
    • The Journal of Korean Physical Therapy
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    • 제35권6호
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    • pp.190-194
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    • 2023
  • Purpose: Traumatic brain injury (TBI) refers to brain damage caused by external forces or trauma. TBIs can vary in severity and result from accidents, falls, sports injuries, assaults, or other forms of physical trauma. The prefrontal cortex (PFC) is known have roles in various cognitive functions. We report on a patient with traumatic brain injury who showed prefrontal symptoms after injury of thalamocortical connections between mediodorsal nuclei (MD) of thalamus and PFC. Methods: A 54-year-old, male patient suffered a TBI as a result of a heavy object falling on his head. After onset of TBI, he showed typical symptoms of prefrontal lobe injury, including personality changes, memory impairment, and general cognition problem. The thalamocortical connections between MD and PFC (ventrolateral prefrontal cortex (VLPFC), dorsolateral prefrontal cortex (DLPFC), and obrbitofrontal cortex (OFC)) were reconstructed using diffusion tensor tractography. In terms of fractional anisotropy value, the right thalamocortical connections to the OFC were significantly lower than those of control subjects. Results: The value of mean diffusivity in the right thalamocortical connections to the DLPFC was significantly higher than that of control subjects. By contrast, both VLPFC and left OFC showed significant decrement in the tract volume of thalamocortical connections compared with that of control subjects. Conclusion: We reported on a patient who showed cognitive and neuropsychiatric impairment due to global injury of the thalamocoritcal connections between MD and PFC following TBI.

GENERAL RELATIVISTIC RADIATION HYDRODYNAMICS: FREQUENCY-INTEGRATED RADIATION MOMENT FORMALISM

  • Park, Myeong-Gu
    • 천문학회지
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    • 제45권4호
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    • pp.101-110
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    • 2012
  • I present here one approach to general relativistic radiation hydrodynamics. It is based on covariant tensor conservation equations and considers only the frequency-integrated total energy and momentum exchange between matter and the radiation field. It is also a mixed-frame formalism in the sense that, the interaction between radiation and matter is described with quantities in the comoving frame in which the interaction is often symmetric in angle while the radiation energy and momentum equations are expressed in the fixed frame quantities in which the derivatives are simpler. Hence, this approach is intuitive enough to be applied straightforwardly to any spacetime or coordinate. A few examples are provided along with caveats in this formalism.

횡등방성 암석의 강도 이방성 모사를 위한 강도정수 공간분포함수 (Spatial Distribution Functions of Strength Parameters for Simulation of Strength Anisotropy in Transversely Isotropic Rock)

  • 이연규
    • 터널과지하공간
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    • 제26권2호
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    • pp.100-109
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    • 2016
  • 이 연구에서는 횡등방성 암석파괴함수의 개발에 활용할 수 있는 3가지 강도정수 공간분포함수를 제안하였다. 제안된 분포함수는 편구(oblate spheroid)분포함수, 지수분포함수, 강도정수텐서 방향투영함수이며 모두 2개의 모델파라미터로 정의된다. 제안된 분포함수들을 점착력과 마찰각의 공간분포함수로 활용하여 횡등방성 Mohr-Coulomb 파괴함수를 유도한 후 이를 활용하여 수치삼축시험을 모사하였다. 연약면의 경사각과 구속압의 변화에 따른 파괴축응력 변화 및 파괴면 방향 변화를 계산한 결과 3개의 분포함수을 적용한 경우 모두 실제 실험에서 관찰되는 이방성 파괴특성을 재현하고 있음을 확인하였다. 3개의 분포함수 중 강도정수텐서 방향투영함수를 채용한 경우가 가장 큰 파괴축강도를 계산하였으며 지수분포함수, 편구분포함수 순으로 낮은 파괴축강도 값을 예측하였다.

다중 층간 분리부가 내재된 복합재 쉘 고차 지그재그 모델의 유한요소 해석 (A Finite Element Analysis based on Higher-Order Zig-Zag Shell Theory for Laminated Composites with Multiple Delamination)

  • 오진호;조맹효
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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    • pp.229-236
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    • 2004
  • A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection. which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the buckling problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The accuracy of the present element is demonstrated in the prediction of buckling loads and buckling modes of shells with multiple delaminations. The present shell element should serve as a powerful tool in the prediction of buckling loads and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

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다중 층간분리부가 있는 복합재 원통쉘의 지그재그 고차이론에 기초한 유한요소 진동해석 (A Finite Element Analysis based on Higher-Order Zig-Zag Shell Theory for Laminated Composites Cylinderical Shell with Multiple Delaminations)

  • 조맹효;오진호;김흥수
    • 한국복합재료학회:학술대회논문집
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    • 한국복합재료학회 2004년도 추계학술발표대회 논문집
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    • pp.69-72
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    • 2004
  • A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

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효과적인 3차원 기하학적 구조 추정 및 모델링을 위한 텐서 보팅 기반 영역 분할 (Efficient 3D Geometric Structure Inference and Modeling for Tensor Voting based Region Segmentation)

  • 김상균;박순영;박종현
    • 대한전자공학회논문지SP
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    • 제49권3호
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    • pp.10-17
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    • 2012
  • 이미지 기반 3차원 장면은 비전 시스템, 게임, 가상현실 체험 등의 분야에서 쉽게 찾아볼 수 있다. 본 논문은 단일 영상으로부터 자동으로 3차원 가상 장면을 생성하기 위한 방법을 제안한다. 제안된 방법은 어린이용 도서의 팝업 이미지의 생성과 유사하다. 특히, 단일 외부 영상으로부터 장면의 3차원 기하학적 구조를 평가하기 위한 과분할 영상을 얻기 위해 텐서 보팅을 적용하였다. 텐서 보팅은 이미지의 균질 영역을 더욱더 부드러운 영역에 가깝게 만들며 영역 중심의 토큰은 매우 큰 saliency 값을 갖게 된다. 그리고 각 분할된 영역을 지면, 하늘, 수직성분 등의 대략적인 카테고리로 분류하고 라벨을 부여한다. 이 라벨은 간단한 가정 하에서 이미지를 팝업 모델로 변환시키기 위한 "잘라내기"와 "접기" 로 이용된다. 실험결과 제안된 방법은 복잡한 자연 영상에서도 성공적으로 영역 분할을 수행하였으며 분할된 영역 정보를 기반으로 구조 정보를 추론하여 3차원 팝업 영상으로 모델링하였다.

Software development for the visualization of brain fiber tract by using 24-bit color coding in diffusion tensor image

  • Oh, Jung-Su;Song, In-Chan;Ik hwan Cho;Kim, Jong-Hyo;Chang, Kee-Hyun;Park, Kwang-Suk
    • 대한자기공명의과학회:학술대회논문집
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    • 대한자기공명의과학회 2002년도 제7차 학술대회 초록집
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    • pp.133-133
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    • 2002
  • Purpose: The purpose of paper is to implement software to visualize brain fiber tract using a 24-bit color coding scheme and to test its feasibility. Materials and Methods: MR imaging was performed on GE 1.5 T Signa scanner. For diffusion tensor image, we used a single shot spin-echo EPI sequence with 7 non-colinear pulsed-field gradient directions: (x, y, z):(1,1,0),(-1,1,0),(1,0,1),(-1,0,1),(0,1,1),(0,1,-1) and without diffusion gradient. B-factor was 500 sec/$\textrm{mm}^2$. Acquisition parameters are as follows: TUTE=10000ms/99ms, FOV=240mm, matrix=128${\times}$128, slice thickness/gap=6mm/0mm, total slice number=30. Subjects consisted of 10 normal young volunteers (age:21∼26 yrs, 5 men, 5 women). All DTI images were smoothed with Gaussian kernel with the FWHM of 2 pixels. Color coding schemes for visualization of directional information was as follows. HSV(Hue, Saturation, Value) color system is appropriate for assigning RGB(Red, Green, and Blue) value for every different directions because of its volumetric directional expression. Each of HSV are assigned due to (r,$\theta$,${\Phi}$) in spherical coordinate. HSV calculated by this way can be transformed into RGB color system by general HSV to RGB conversion formula. Symmetry schemes: It is natural to code the antipodal direction to be same color(antipodal symmetry). So even with no symmetry scheme, the antipodal symmetry must be included. With no symmetry scheme, we can assign every different colors for every different orientation.(H =${\Phi}$, S=2$\theta$/$\pi$, V=λw, where λw is anisotropy). But that may assign very discontinuous color even between adjacent yokels. On the other hand, Full symmetry or absolute value scheme includes symmetry for 180$^{\circ}$ rotation about xy-plane of color coordinate (rotational symmetry) and for both hemisphere (mirror symmetry). In absolute value scheme, each of RGB value can be expressed as follows. R=λw|Vx|, G=λw|Vy|, B=λw|Vz|, where (Vx, Vy, Vz) is eigenvector corresponding to the largest eigenvalue of diffusion tensor. With applying full symmetry or absolute value scheme, we can get more continuous color coding at the expense of coding same color for symmetric direction. For better visualization of fiber tract directions, Gamma and brightness correction had done. All of these implementations were done on the IDL 5.4 platform.

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Diffusion Tensor-Derived Properties of Benign Oligemia, True "at Risk" Penumbra, and Infarct Core during the First Three Hours of Stroke Onset: A Rat Model

  • Chiu, Fang-Ying;Kuo, Duen-Pang;Chen, Yung-Chieh;Kao, Yu-Chieh;Chung, Hsiao-Wen;Chen, Cheng-Yu
    • Korean Journal of Radiology
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    • 제19권6호
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    • pp.1161-1171
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    • 2018
  • Objective: The aim of this study was to investigate diffusion tensor (DT) imaging-derived properties of benign oligemia, true "at risk" penumbra (TP), and the infarct core (IC) during the first 3 hours of stroke onset. Materials and Methods: The study was approved by the local animal care and use committee. DT imaging data were obtained from 14 rats after permanent middle cerebral artery occlusion (pMCAO) using a 7T magnetic resonance scanner (Bruker) in room air. Relative cerebral blood flow and apparent diffusion coefficient (ADC) maps were generated to define oligemia, TP, IC, and normal tissue (NT) every 30 minutes up to 3 hours. Relative fractional anisotropy (rFA), pure anisotropy (rq), diffusion magnitude (rL), ADC (rADC), axial diffusivity (rAD), and radial diffusivity (rRD) values were derived by comparison with the contralateral normal brain. Results: The mean volume of oligemia was $24.7{\pm}14.1mm^3$, that of TP was $81.3{\pm}62.6mm^3$, and that of IC was $123.0{\pm}85.2mm^3$ at 30 minutes after pMCAO. rFA showed an initial paradoxical 10% increase in IC and TP, and declined afterward. The rq, rL, rADC, rAD, and rRD showed an initial discrepant decrease in IC (from -24% to -36%) as compared with TP (from -7% to -13%). Significant differences (p < 0.05) in metrics, except rFA, were found between tissue subtypes in the first 2.5 hours. The rq demonstrated the best overall performance in discriminating TP from IC (accuracy = 92.6%, area under curve = 0.93) and the optimal cutoff value was -33.90%. The metric values for oligemia and NT remained similar at all time points. Conclusion: Benign oligemia is small and remains microstructurally normal under pMCAO. TP and IC show a distinct evolution of DT-derived properties within the first 3 hours of stroke onset, and are thus potentially useful in predicting the fate of ischemic brain.