• Bulletin of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.537-557
• /
• 2021

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

• Journal of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.1023-1041
• /
• 2023

In this paper, motivated by the work of Q. S. Zhang in [25], we derive optimal Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Émery Ricci curvature bounded below.

• Journal of Biomedical Engineering Research
• /
• v.20 no.1
• /
• pp.53-58
• /
• 1999

Eddy current in MRI systems degrades gradient field linearity and distorts gradient waveform. When the waveform distortion is spatially variant, it is very difficult to perform special imaging techniques such as the echo planar imaging technique or the fast spin echo imaging technique. In this study, we have developed a new technique to estimate the distorted gradient waveforms at any points inside the imaging region using the finite element method. After obtaining the eddy-current-effect transfer function, which represents magnitude and phase characteristics of the gradient field at a particular point, we have used the transfer function to estimate the actual gradient waveforms at the point. To verify the proposed technique, we have compared the estimated gradient waveforms with the measured ones.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.11
• /
• pp.4355-4371
• /
• 2020

Phase retrieval, recovering a signal from phaseless measurements, is generally considered to be an NP-hard problem. This paper adopts an amplitude-based nonconvex optimization cost function to develop a new stochastic gradient algorithm, named stochastic reweighted phase retrieval (SRPR). SRPR is a stochastic gradient iteration algorithm, which runs in two stages: First, we use a truncated sample stochastic variance reduction algorithm to initialize the objective function. The second stage is the gradient refinement stage, which uses continuous updating of the amplitude-based stochastic weighted gradient algorithm to improve the initial estimate. Because of the stochastic method, each iteration of the two stages of SRPR involves only one equation. Therefore, SRPR is simple, scalable, and fast. Compared with the state-of-the-art phase retrieval algorithm, simulation results show that SRPR has a faster convergence speed and fewer magnitude-only measurements required to reconstruct the signal, under the real- or complex- cases.

• Journal of Fisheries and Marine Sciences Education
• /
• v.20 no.2
• /
• pp.156-167
• /
• 2008

Meorological data have been collected to monitor the wetland area in Goheung bay since 2003 and four intensive observations were conducted to study effects of the atmospheric turbulence on the energy budget and the ecological changes. We improved an algorithm to estimate the sensible heat flux with routine data. The sensible heat flux estimated by gradient method was in good agreement with that measured by precision instruments such as surface layer scintillometer and ultrasonic anemometer. Diurnal variations of sensible heat flux showed analogous tendency to those of temperature gradient. When the vertical wind shear of horizontal wind components was weak, even though temperature gradient was strong, the gradient method underestimated the sensible heat flux. A compensation for the cloud will make this gradient method be a helpful tool to monitor the ecosystem without expensive instruments except for weak wind shear and temperature gradient.

• Journal of Korean Ophthalmic Optics Society
• /
• v.9 no.2
• /
• pp.223-231
• /
• 2004

In most previous studies, the assessment of accommodative convergence to accommodative stimulus (AC/A) ratio was commonly made by measuring gradient AC/A ratio. This study deals with the proximal convergence/accommodation(PC/A)ratio measured by comparing values of the gradient AC/A ratio and the calculated AC/A ratio to prevail the clinical use of the AC/A ratio. Visual acuities of All 124 subjects had been corrected to at least 1.0 with either eye through their habitual refractive correction and the MEM dynamic retinoscopy was performed to estimate their accommodative response. And then the PC/A ratio was calculated by making use of the calculated AC/A ratio and the gradient AC/A ratio. This study showed that the difference between the mean calculated AC/A ratio and the mean gradient AC/A ratio in subgroups may be attributable to proximal convergence. Consequently, further studies on proximity cues including the PC/A ratio could be helpful to prevail the clinical use of the AC/A ratio.

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.2
• /
• pp.93-99
• /
• 2011

In this paper, we propose a policy-gradient routing scheme under Reinforcement Learning that can be used adaptive QoS routing. A policy-gradient RL routing can provide fast learning of network environments as using optimal policy adapted average estimate rewards gradient values. This technique shows that fast of learning network environments results in high success rate of routing. For prove it, we simulate and compare with three different schemes.

• The Journal of Korea Robotics Society
• /
• v.14 no.4
• /
• pp.258-263
• /
• 2019

Some animals have special sensing functions in order to find foods, home and mates. Instead of passively sensing, they discharge signals and then extract necessary information from the response. More importantly, they utilize the gradients of the sensed signal in order to find the destination or objects. In this paper this special strategy is formulated mathematically, i.e., the perturbation and the correlation based gradient estimation is developed. A stereo sensor system using temperature sensors mounted on motors is developed for verification. The proposed method can estimate the gradient of the measured value accurately. Using this method, the direction in the maximum measured value can be estimated accurately, and the position of the heat source can be estimated from the intersection of the directions estimated from both sensors.

• Proceedings of the KOSOMBE Conference
• /
• v.1998 no.11
• /
• pp.92-93
• /
• 1998

In this study, we have established the technique to estimate the gradient waveforms distorted by the eddy current in MRI. After obtaining the eddy current effect transfer function using the finite element method, we have used the transfer function to estimate the output gradient waveforms at any points inside the imaging region. We also present experimental results to be compared with estimated ones.

• ETRI Journal
• /
• v.28 no.1
• /
• pp.59-66
• /
• 2006

Learning behaviors of a radial basis function network (RBFN) using a singular value decomposition (SVD) and stochastic gradient (SG) algorithm, together named RBF-SVD-SG, for odor sensing systems are analyzed, and a fast training method is proposed. RBF input data is from a conducting polymer sensor array. It is revealed in this paper that the SG algorithm for the fine-tuning of centers and widths still shows ill-behaving learning results when a sufficiently small convergence coefficient is not used. Since the tuning of centers in RBFN plays a dominant role in the performance of RBFN odor sensing systems, our analysis is focused on the center-gradient variance of the RBFN-SVD-SG algorithm. We found analytically that the steadystate weight fluctuation and large values of a convergence coefficient can lead to an increase in variance of the center-gradient estimate. Based on this analysis, we propose to use the least mean square algorithm instead of SVD in adjusting the weight for stable steady-state weight behavior. Experimental results of the proposed algorithm have shown faster learning speed and better classification performance.