• Title/Summary/Keyword: Vanishing

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HOMOLOGY AND SERRE CLASS IN D(R)

  • Zhicheng, Wang
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.23-32
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    • 2023
  • Let 𝓢 be a Serre class in the category of modules and 𝖆 an ideal of a commutative Noetherian ring R. We study the containment of Tor modules, Koszul homology and local homology in 𝓢 from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when TorR𝓼+t(R/𝖆, X) ≅ TorR𝓼(R/𝖆, H𝖆t(X)).

CERTAIN STUDY OF GENERALIZED B CURVATURE TENSOR WITHIN THE FRAMEWORK OF KENMOTSU MANIFOLD

  • Rahuthanahalli Thimmegowda Naveen Kumar;Basavaraju Phalaksha Murthy;Puttasiddappa Somashekhara;Venkatesha Venkatesha
    • Communications of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.893-900
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    • 2023
  • In the present study, we consider some curvature properties of generalized B-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized B curvature tensor on Kenmostu manifold. Later we formulate generalized B pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized B ϕ-recurrent Kenmotsu manifold.

LARGE TIME CONVERGENCE FOR A CHEMOTAXIS MODEL WITH DEGENERATE LOCAL SENSING AND CONSUMPTION

  • Philippe Laurencot
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.2
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    • pp.479-488
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    • 2024
  • Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is C1-smooth on [0, ∞), vanishes at zero, and is positive on (0, ∞). A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.

A Survey on Neural Networks Using Memory Component (메모리 요소를 활용한 신경망 연구 동향)

  • Lee, Jihwan;Park, Jinuk;Kim, Jaehyung;Kim, Jaein;Roh, Hongchan;Park, Sanghyun
    • KIPS Transactions on Software and Data Engineering
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    • v.7 no.8
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    • pp.307-324
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    • 2018
  • Recently, recurrent neural networks have been attracting attention in solving prediction problem of sequential data through structure considering time dependency. However, as the time step of sequential data increases, the problem of the gradient vanishing is occurred. Long short-term memory models have been proposed to solve this problem, but there is a limit to storing a lot of data and preserving it for a long time. Therefore, research on memory-augmented neural network (MANN), which is a learning model using recurrent neural networks and memory elements, has been actively conducted. In this paper, we describe the structure and characteristics of MANN models that emerged as a hot topic in deep learning field and present the latest techniques and future research that utilize MANN.

Study on the Effective Compensation of Quantization Error for Machine Learning in an Embedded System (임베디드 시스템에서의 양자화 기계학습을 위한 효율적인 양자화 오차보상에 관한 연구)

  • Seok, Jinwuk
    • Journal of Broadcast Engineering
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    • v.25 no.2
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    • pp.157-165
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    • 2020
  • In this paper. we propose an effective compensation scheme to the quantization error arisen from quantized learning in a machine learning on an embedded system. In the machine learning based on a gradient descent or nonlinear signal processing, the quantization error generates early vanishing of a gradient and occurs the degradation of learning performance. To compensate such quantization error, we derive an orthogonal compensation vector with respect to a maximum component of the gradient vector. Moreover, instead of the conventional constant learning rate, we propose the adaptive learning rate algorithm without any inner loop to select the step size, based on a nonlinear optimization technique. The simulation results show that the optimization solver based on the proposed quantized method represents sufficient learning performance.

A Study for Depth-map Generation using Vanishing Point (소실점을 이용한 Depth-map 생성에 관한 연구)

  • Kim, Jong-Chan;Ban, Kyeong-Jin;Kim, Chee-Yong
    • Journal of Korea Multimedia Society
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    • v.14 no.2
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    • pp.329-338
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    • 2011
  • Recent augmentation reality demands more realistic multimedia data with the mixture of various media. High-technology for multimedia data which combines existing media data with various media such as audio and video dominates entire media industries. In particular, there is a growing need to serve augmentation reality, 3-dimensional contents and realtime interaction system development which are communication method and visualization tool in Internet. The existing services do not correspond to generate depth value for 3-dimensional space structure recovery which is to form solidity in existing contents. Therefore, it requires research for effective depth-map generation using 2-dimensional video. Complementing shortcomings of existing depth-map generation method using 2-dimensional video, this paper proposes an enhanced depth-map generation method that defines the depth direction in regard to loss location in a video in which none of existing algorithms has defined.

Semi-automatic 3D Building Reconstruction from Uncalibrated Images (비교정 영상에서의 반자동 3차원 건물 모델링)

  • Jang, Kyung-Ho;Jang, Jae-Seok;Lee, Seok-Jun;Jung, Soon-Ki
    • Journal of Korea Multimedia Society
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    • v.12 no.9
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    • pp.1217-1232
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    • 2009
  • In this paper, we propose a semi-automatic 3D building reconstruction method using uncalibrated images which includes the facade of target building. First, we extract feature points in all images and find corresponding points between each pair of images. Second, we extract lines on each image and estimate the vanishing points. Extracted lines are grouped with respect to their corresponding vanishing points. The adjacency graph is used to organize the image sequence based on the number of corresponding points between image pairs and camera calibration is performed. The initial solid model can be generated by some user interactions using grouped lines and camera pose information. From initial solid model, a detailed building model is reconstructed by a combination of predefined basic Euler operators on half-edge data structure. Automatically computed geometric information is visualized to help user's interaction during the detail modeling process. The proposed system allow the user to get a 3D building model with less user interaction by augmenting various automatically generated geometric information.

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Extraction of Subject Size in Still Image Using Floor Pattern (바닥 패턴을 이용한 단일영상 내의 피사체 크기 추출)

  • Hwang, Min-Gu;Kim, Dong-Min;Har, Dong-Hwan
    • The Journal of the Korea Contents Association
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    • v.11 no.4
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    • pp.11-17
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    • 2011
  • This paper aims to realize the information of a subject existing in a still image with objective values. To attain the goal, this research takes the vanishing point that a 2D still image has as the basis and recomposes the still image into a 3D image using a 3D program. Also, in order to set up the axis of the camera necessary to recompose a 3D image, this paper used the lens angle of view that the image has and floor patterns as well. The 3D image completed in this way can measure the size and distance of all subjects in the floor patterns if the size value of a particular reference subject is known, and through this, it can be possible to acquire basic information of a subject that can be either a criminal or a clue in the images of CCTVs or some criminal scene.

A High Speed Road Lane Detection based on Optimal Extraction of ROI-LB (관심영역(ROI-LB)의 최적 추출에 의한 차선검출의 고속화)

  • Cheong, Cha-Keon
    • Journal of Broadcast Engineering
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    • v.14 no.2
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    • pp.253-264
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    • 2009
  • This paper presents an algorithm, aims at practical applications, for the high speed processing and performance enhancement of lane detection base on vision processing system. As a preprocessing for high speed lane detection, the vanishing line estimation and the optimal extraction of region of interest for lane boundary (ROI-LB) can be processed to reduction of detection region in which high speed processing is enabled. Image feature information is extracted only in the ROI-LB. Road lane is extracted using a non-parametric model fitting and Hough transform within the ROI-LB. With simultaneous processing of noise reduction and edge enhancement using the Laplacian filter, the reliability of feature extraction can be increased for various road lane patterns. Since outliers of edge at each block can be removed with clustering of edge orientation for each block within the ROI-LB, the performance of lane detection can be greatly improved. The various real road experimental results are presented to evaluate the effectiveness of the proposed method.

Interval Hough Transform For Prominent Line Detection (배경선 추출을 위한 구간 허프 변환)

  • Choi, Jin-Mo;Kim, Changick
    • Journal of Korea Multimedia Society
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    • v.16 no.11
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    • pp.1288-1296
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    • 2013
  • The prominent line at the singe image is the important fact for understanding spatial structure or estimating aesthetic scoring. According to this thesis, the abstraction of the background line helps analyzing vanishing point, reconstitution of 3 dimensions, and determining of image sloppiness. It also makes easy to calculate the rule of thirds. This thesis is composed of section hough transform mapping, prioritizing of the prominent line, and selection of the prominent line. These technologies are departmentalized to be applied abstraction of traffic lane, analyzing of building structure, abstraction of vanishing point, and abstraction of straight line documentation. This gives the choice that users are able to compose technology by considering characteristic of objects and luminous environment. This thesis also can be applied to abstract circle. The interval hough transform is able to select the number of prominent line which users want to abstract. It can analyze important prominent line numbers at the image and then abstract the lines, too. Results of prominent lines by experiments would be show at this thesis.