• Title, Summary, Keyword: projections

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STRUCTURAL PROJECTIONS ON A JBW-TRIPLE AND GL-PROJECTIONS ON ITS PREDUAL

  • Hugli, Remo-V.
    • Journal of the Korean Mathematical Society
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    • v.41 no.1
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    • pp.107-130
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    • 2004
  • A $JB^{*}-triple$ is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ can be defined in a canonical way. If A is also the dual of some Banach space $A_{*}$, then A is said to be a JBW triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, }holds. On $JBW^{*}-triples$, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual $A_{*}$ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.

Homotopy of projections in C^*-algebras

  • Kim, Sang-Og
    • Communications of the Korean Mathematical Society
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    • v.12 no.1
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    • pp.75-78
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    • 1997
  • We show that if a simple $C^*$-algebra A satisfies certain $K_1$-group conditions, then two unitarily equivalent projections are homotopic. Also we show that the equivalence of projections determined by a dimension function is a homotopy.

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The Upper Ascending Reticular Activating System between Intralaminar Thalamic Nuclei and Cerebral Cortex in the Human Brain

  • Jang, Sungho;Kwak, Soyoung
    • The Journal of Korean Physical Therapy
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    • v.29 no.3
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    • pp.109-114
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    • 2017
  • Purpose: The ascending reticular activating system (ARAS) is responsible for regulation of consciousness. In this study, using diffusion tensor imaging (DTI), we attempted to reconstruct the thalamocortical projections between the intralaminar thalamic nuclei and the frontoparietal cortex in normal subjects. Methods: DTI data were acquired in 24 healthy subjects and eight kinds of thalamocortical projections were reconstructed: the seed region of interest (ROI) - the intralaminar thalamic nuclei and the eight target ROIs - the medial prefrontal cortex, dorsolateral prefrontal cortex, ventrolateral prefrontal cortex, orbitofrontal cortex, premotor cortex, primary motor cortex, primary somatosensory cortex, and posterior parietal cortex. Results: The eight thalamocortical projections were reconstructed in each hemisphere and the pathways were visualized: projections to the prefrontal cortex ascended through the anterior limb and genu of the internal capsule and anterior corona radiata. Projections to the premotor cortex passed through the genu and posterior limb of the internal capsule and middle corona radiata; in contrast, projections to the primary motor cortex, primary somatosensory cortex, and posterior parietal cortex ascended through the posterior limb of the internal capsule. No significant difference in fractional anisotropy, mean diffusivity, and fiber volume of all reconstructed thalamocortical projections was observed between the right and left hemispheres (p>0.05). Conclusion: We reconstructed the thalamocortical projections between the intralaminar thalamic nuclei and the frontoparietal cortex in normal subjects. We believe that our findings would be useful to clinicians involved in the care of patients with impaired consciousness and for researchers in studies of the ARAS.

PROJECTIONS OF PSEUDOSPHERE IN THE LORENTZ 3-SPACE

  • Birman, Graciela S.;Desideri, Graciela M.
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.483-492
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    • 2007
  • In this paper, we study the map projections from pseudo-sphere $S_1^2$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $L^3$, with curvature zero. We show geometrical means and properties of $\mathbb{R}{\times}S_1^1-cylindrical$, $S^1{\times}L-cylindrical$ and $\mathbb{R}{\times}H_0^1-cylindrical$ projections defined on $S_1^2$ to cylinders $\mathbb{R}{\times}S_1^1,\;S^1{\times}L$ and $\mathbb{R}{\times}H_0^1$, respectively, and orthographic and stereographic projections on $S_1^2$ to Lorentzian plane, $L^2$.

Nonnegative variance component estimation for mixed-effects models

  • Choi, Jaesung
    • Communications for Statistical Applications and Methods
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    • v.27 no.5
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    • pp.523-533
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    • 2020
  • This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

CODES OVER POLYNOMIAL RINGS AND THEIR PROJECTIONS

  • Park, Young Ho
    • Korean Journal of Mathematics
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    • v.17 no.4
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    • pp.385-397
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    • 2009
  • We study codes over the polynomial ring ${\mathbb{F}}_q[D]$ and their projections to the finite rings ${\mathbb{F}}_q[D]/(D^m)$ and the weight enumerators of self-dual codes over these rings. We also give the formula for the number of codewords of minimum weight in the projections.

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Rebinning-Based Deterministic Image Reconstruction Methods for Compton Camera (컴프턴 카메라를 위한 재배열 기반 확정론적 영상재구성법)

  • Lee, Mi-No;Lee, Soo-Jin;Seo, Hee;Nguyen, Van-Giang
    • Journal of Biomedical Engineering Research
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    • v.32 no.1
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    • pp.15-24
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    • 2011
  • While Compton imaging is recognized as a valuable 3-D technique in nuclear medicine, reconstructing an image from Compton scattered data has been of a difficult problem due to its computational complexity. The most complex and time-consuming computation in Compton camera reconstruction is to perform the conical projection and backprojection operations. To alleviate the computational burden imposed by these operations, we investigate a rebinning method which can convert conical projections into parallel projections. The use of parallel projections allows to directly apply the existing deterministic reconstruction methods, which have been useful for conventional emission tomography, to Compton camera reconstruction. To convert conical projections into parallel projections, a cone surface is sampled with a number of lines. Each line is projected onto an imaginary plane that is mostly perpendicular to the line. The projection data rebinned in each imaginary plane can then be treated as the standard parallel projection data. To validate the rebinning method, we tested with the representative deterministic algorithms, such as the filtered backprojection method and the algebraic reconstruction technique. Our experimental results indicate that the rebinning method can be useful when the direct application of existing deterministic methods is needed for Compton camera reconstruction.

PROJECTIONS OF BOUQUET GRAPH WITH TWO CYCLES

  • Huh, Young-Sik
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1341-1360
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    • 2008
  • In this paper we investigate the projections of bouquet graph B with two cycles. A projection of B is said to be trivial if only trivial embeddings are obtained from the projection. It is shown that, to cover all nontrivial projections of B, at least three embeddings of B are needed. We also show that a nontrivial projection of B is covered by one of some two embeddings if the image of each cycle has at most one self-crossing.

A Study on Center Detection and Motion Analysis of a Moving Object by Using Kohonen Networks and Time Delay Neural Networks

  • Kim, Jong-Young;Hwang, Jung-Ku;Jang, Tae-Jeong
    • 제어로봇시스템학회:학술대회논문집
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    • pp.63.5-63
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    • 2001
  • In this paper, moving objects tracking and dynamic characteristic analysis are studied. Kohonen´s self-organizing neural network models are used for moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation.

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A Study on Center Detection and Motion Analysis of a Moving Object by Using Kohonen Networks and Time Delay Neural Networks (코호넨 네트워크 및 시간 지연 신경망을 이용한 움직이는 물체의 중심점 탐지 및 동작특성 분석에 관한 연구)

  • Hwang, Jung-Ku;Kim, Jong-Young;Jang, Tae-Jeong
    • Journal of Industrial Technology
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    • v.21 no.B
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    • pp.91-98
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    • 2001
  • In this paper, center detection and motion analysis of a moving object are studied. Kohonen's self-organizing neural network models are used for the moving objects tracking and time delay neural networks are used for dynamic characteristic analysis. Instead of objects brightness, neuron projections by Kohonen Networks are used. The motion of target objects can be analyzed by using the differential neuron image between the two projections. The differential neuron image which is made by two consecutive neuron projections is used for center detection and moving objects tracking. The two differential neuron images which are made by three consecutive neuron projections are used for the moving trajectory estimation. It is possible to distinguish 8 directions of a moving trajectory with two frames and 16 directions with three frames.

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