• Journal of Korean Neurosurgical Society
• /
• v.64 no.1
• /
• pp.110-119
• /
• 2021

Objective : Preoperative prediction of the arachnoid membrane descent in pituitary surgery is useful for achieving gross total removal and avoiding cerebrospinal fluid leakage resulting from tearing of the arachnoid membrane in the chiasmatic cistern. In this study, we analyzed the patterns of arachnoid membrane descent during or after pituitary tumor surgery and identified the factors related to this descent. Methods : Analysis was restricted to pituitary macroadenomas not extending into the third ventricle or over the internal carotid artery. To minimize confounding factors, patients who underwent revision surgery, those who had a torn arachnoid during operation or small medial diaphragma sellae (DS) opening, and subtotal resections were excluded. We enrolled 41 consecutive patients in this retrospective analysis. The degree of arachnoid descent was categorized using intraoperative videos. Preoperative magnetic resonance findings, including tumor height, suprasellar extension, and variables including DS area and medial opening size, tumor composition, and displacement of the pituitary stalk and gland were evaluated to determine their correlations with arachnoid membrane descent. Results : Arachnoid membrane descent was significantly correlated with DS area and medial opening size. Based on T2-weighted images (T2WI) magnetic resonance (MR) images, tumor composition was significantly associated with arachnoid membrane descent. Other factors were not significantly correlated with arachnoid membrane descent. Conclusion : T2WI of tumor composition and preoperative MR imaging of DS area and medial opening provided valuable information regarding arachnoid membrane descent. These parameters may serve as fundamental measures to facilitate complete resection of pituitary macroadenomas.

• Journal of Practical Engineering Education
• /
• v.14 no.2
• /
• pp.305-312
• /
• 2022

In this paper, we focused on training to create and optimize a basic data prediction model. And we proposed a gradient descent training method of machine learning that is widely used to optimize data prediction models. It visually shows the entire operation process of gradient descent used in the process of optimizing parameter values required for data prediction models by applying the differential method and teaches the effective use of mathematical differentiation in machine learning. In order to visually explain the entire operation process of gradient descent, we implement gradient descent SW in a spreadsheet. In this paper, first, a two-variable gradient descent training method is presented, and the accuracy of the two-variable data prediction model is verified by comparison with the error least squares method. Second, a three-variable gradient descent training method is presented and the accuracy of a three-variable data prediction model is verified. Afterwards, the direction of the optimization practice for gradient descent was presented, and the educational effect of the proposed gradient descent method was analyzed through the results of satisfaction with education for non-majors.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.19 no.2
• /
• pp.58-63
• /
• 2011

A Continuous Descent Approach(CDA) is defined as a simple, cost-effective, noise and emission abatement technique for any powered aircraft on approach. CDA also can be optimised within energy, speed and safety constraints by avoiding unnecessary flap, air brake and engine thrust. This study includes comparison on fuel consumption between Continuous Descent type and Step Down type by using flight data. In particular, we investigated fuel flow per hour, calibrated airspeed and pressure altitude for all flight time. During descent flight, the fuel consumption of Continuous Descent type was less than the fuel consumption of Step Down type.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.239-254
• /
• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.12
• /
• pp.7277-7282
• /
• 2014

In this study, the gradient descent algorithm was used for FLC analysis and the algorithm was used to represent the effects of nonlinear parameters, which alter the antecedent and consequence fuzzy variables of FLC. The controller parameters choose the control variable by iteration for gradient descent algorithm. The FLC consists of 7 membership functions, 49 rules and a two inputs - one output system. The system adopted the Min-Max inference method and triangle type membership function with a 13 quantization level.

• Communications of Mathematical Education
• /
• v.37 no.3
• /
• pp.467-482
• /
• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.

• Proceedings of the KIEE Conference
• /
• 1987.07b
• /
• pp.1595-1597
• /
• 1987

Two gradient methods, steepest descent method and conjugate gradient descent method, are compar ed through application to vector linear predictors. It is found that the convergence rate of the conju-gate gradient descent method is much faster than that of the steepest descent method.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.21 no.2
• /
• pp.189-194
• /
• 2020

This paper analyzes the gradient descent method, which is the one most used for learning neural networks. Learning means updating a parameter so the loss function is at its minimum. The loss function quantifies the difference between actual and predicted values. The gradient descent method uses the slope of the loss function to update the parameter to minimize error, and is currently used in libraries that provide the best deep learning algorithms. However, these algorithms are provided in the form of a black box, making it difficult to identify the advantages and disadvantages of various gradient descent methods. This paper analyzes the characteristics of the stochastic gradient descent method, the momentum method, the AdaGrad method, and the Adadelta method, which are currently used gradient descent methods. The experimental data used a modified National Institute of Standards and Technology (MNIST) data set that is widely used to verify neural networks. The hidden layer consists of two layers: the first with 500 neurons, and the second with 300. The activation function of the output layer is the softmax function, and the rectified linear unit function is used for the remaining input and hidden layers. The loss function uses cross-entropy error.

• East Asian mathematical journal
• /
• v.32 no.2
• /
• pp.193-215
• /
• 2016

There are three subjects in the study. First, after investigating the development process of the method of infinite descent and the reduction to absurdity, we prove them to be equivalent each other. Second, we apply the method of infinite descent to some problems in textbook and compare it with the reduction to absurdity. Finally, we discuss on teaching proofs with the method of infinite descent.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.31 no.2
• /
• pp.1-6
• /
• 2023

When landing an aircraft descent-speed, wind around the airport, and regulations are important indicators for the pilot to decide whether to land in the Final Approach. In this study, in order to maintain a decent angle accessible to the airport, the pilot predicts an appropriate decent rate suitable for wind direction, wind speed, and speed to make a stable landing. To confirm this, the decent rate according to the speed and speed of wind was calculated using the information actually measured on the B737NG aircraft and compared with the theoretical figures. The purpose of this study is to ensure that the pilot can make a stable landing at a given FPM (Feet Per Minute) when a visual approach and non-normal approach is required at an airport designed with a somewhat higher descent angle.