KSIAM 2020 Annual Meeting - C O N T EN TS -

>> Plenary Talks Stochastic Optimization in Mathematical - Moran Ki ······························································· 2 Finance II - Eun-Jae Park (KSIAM-KUMGOK Award) ······· 3 - yun Jin Jang ······················································ 45 - Hyung Hee Cho ················································· 5 - Hyungbin Park ·················································· 46 - Minsuk Kwak ····················································· 47 - Geonwoo Kim ··················································· 48 >> KSIAM Awards Deep Learning and Image Process - Yongho Choi ····················································· 12 - Han-Soo Choi ··················································· 50 - Junseok Kim ······················································ 13 - Hyomin Ahn ······················································ 51 - Sun Xiang ··························································· 14 - Geonho Hwang ················································· 52 - Yea Chan Park ·················································· 53 >> Special Session Finance·Fishery·Manufacture Industrial Mathematics Center on Big Data Math for Public Safety based on Modeling - Changsin Kim ···················································· 55 and Data analysis - Seong-Uk Nam ················································· 59 - Hyuk Kang ························································· 17 - Yuanmeng Hu ··················································· 60 - Hark soo Song ················································· 18 - Sat byul Seo ······················································ 61 - Jieun Kim ···························································· 19 - Sang-hyup Seo ················································· 62 - Young Jin Kim ·················································· 20 Deep Learning for Digital Dentistry Numerical methods for the Hyperbolic - Sung Ho Kang ·················································· 64 conservation laws - Hye sun Yun ····················································· 65 - Kunmin Sung ····················································· 22 - Taejun Jang ······················································· 66 - Youngsoo Ha ···················································· 23 - Hyeon Cheol Jo ················································ 67 - Hyuntae Cho ····················································· 25 Domain Decomposition Methods and - Hojun You ·························································· 26 Related Methods I Stochastic Optimization in Mathematical - Dongho Kim ······················································ 69 Finance I - Jongho Park ······················································ 71 - Junkee Jeon ······················································· 29 - YoungKyu Lee ··················································· 72 - Kyunghyun Park ··············································· 30 - Hyea Hyun Kim ················································ 73 - Kum Hwan Rho ················································ 31 Regularity and singularity of some partial - Yong Hyun Shin ··············································· 32 differential equations related to fluid flows The Challenges of Mathematical Modeling - Sukjung Hwang ················································ 75 of the Spread of COVID-19 - Jinmyoung Seok ··············································· 76 - Jong-Hoon Kim ················································ 34 - Minsuk Yang ····················································· 77 - Hee-Sung Kim ··················································· 35 - In-Jee Jeong ······················································ 78 - Woo-Sik Son ····················································· 36 Deep Learning for Medical Imaging - Il Hyo Jung ························································ 37 - Hyoung Suk Park ············································· 80 Some cases in Industrial Mathematics - Chang Min Hyun ············································· 81 - Byung Chun Kim ·············································· 39 - Seong Hyeon Baek ·········································· 82 - Hyunju Lee ························································· 41 - Seo Taek Kong ················································· 83 - Minjung Gim ····················································· 42 - Minwon Na ························································ 43 KSIAM 2020 Annual Meeting - C O N T EN TS -

Domain Decomposition Methods and General Session Ⅵ Related Methods II - Soyoung Jeong ··············································· 125 - Eun-Hee Park ···················································· 85 - Eo-Jin Lee ························································ 126 - Hee Jun Yang ··················································· 86 - Sungjin Lee ······················································ 128 - Dong-wook ························································ 87 - Seungil Kim ······················································· 88 >> Poster Session Nonlinear differential equations modeling of collective motion - Hyundong Kim ··············································· 131 - Seok-bae Yun ···················································· 90 - JongHyuk Kang ·············································· 132 - Woojoo Shim ···················································· 91 - Bongyeong Koo ·············································· 133 - Jinwook Jung ····················································· 92 - EuiMin Jeong ·················································· 134 - Hansol Park ······················································· 93 - Eun Hae Cho ·················································· 135 - Jungho Park ···················································· 136 >> General Session - Sangmin Park ·················································· 137 - Malik Muhammad Ibrahhim ························ 138 General Session Ⅰ - Donghyun Kim ················································ 139 - Duk-Soon Oh ···················································· 96 - Yun Min Song ················································ 140 - Byungjoon Lee ·················································· 97 - Junhui U ··························································· 141 - Heejae Han ························································ 98 - Mijin Ha ··························································· 143 - Chohong Min ···················································· 99 - Mannan Jamshaid ·········································· 144 General Session Ⅱ - Dae Wook Kim ··············································· 145 - Hayeong Koh ·················································· 101 - TaeKyung Ki ···················································· 146 - Hyeuknam Kwon ············································ 102 - Sanghee Lee ···················································· 147 - Young Ju Lee ·················································· 104 - Hyukpyo Hong ··············································· 148 - Won-Kwang Park ··········································· 105 - Jongmin Lee ···················································· 149 General Session Ⅲ - Youngsuk Ko ··················································· 150 - Sehun Chun ····················································· 107 - Meiyan Jiang ··················································· 151 - Myeongmin Kang ·········································· 108 - Nu Ree Song ·················································· 152 - Gwanghyun Jo ················································ 109 - Soobin Kwak ··················································· 153 - Seryoong Ahn ················································· 110 - Yeon Ju Lee ···················································· 154 General Session Ⅳ - Juyeb Yeo ························································ 155 - Donggu Lee ···················································· 112 - Seokjoo Chae ·················································· 156 - Jiyeon Suh ······················································· 113 - Sungyeon Kim ················································ 157 - Hyunwoo Cho ················································· 115 - GyuSang Han ·················································· 158 - Seyeon Lee ······················································ 116 - Junghyun Lee ·················································· 159 General Session Ⅴ - Hoin Jung ························································ 160 - Eunha Shim ····················································· 118 - DongHeon Seong, GyoungMin Lim ·········· 161 - Taeyong Lee ···················································· 119 - Hyeonseong Jin ·············································· 162 - Yunjeong Lee ·················································· 120 - Masud M A ····················································· 122 Plenary Talks

Moran Ki (National Cancer Center Graduate school of

Cancer Science and Policy)

Eun-Jae Park (Yonsei University)

Hyung Hee Cho (Yonsei University) KSIAM 2020 Annual Meeting ------

  



   

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- 2 - KSIAM 2020 Annual Meeting ------

Computational Paradigms: Old and New

Eun-Jae Park 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, Korea

Corresponding Author : Eun-Jae Park, [email protected]

ABSTRACT Galerkin finite element methods based on simplicial/cubical meshes have been studied over the past half century and their mathematical analysis and computational engineering applica- tions are well understood. Recently, polygonal/polytopal finite element methods have received considerable attention. This is because general meshes offer a very convenient framework for mesh generation, mesh deformations, fracture problems, composite materials, topology opti- mizations, mesh refinements and coarsening; for instance, to handle hanging nodes, different cell shapes within the same mesh and non-matching interfaces. Such a flexibility represents a powerful tool towards the efficient solution of problems with complex inclusions as in geo- physical applications or posed on very complicated or possibly deformable geometries as en- countered in basin and reservoir simulations, in fluid-structure interaction, crack propagation or contact problems. In this talk, a new computational paradigm for discretizing PDEs is presented via staggered Galerkin method on general meshes. First, a class of locally conservative, lowest order stag- gered discontinuous Galerkin method on general quadrilateral/polygonal meshes for elliptic problems are proposed. The method can be flexibly applied to rough grids such as highly dis- torted meshes. Next, adaptive mesh refinement is an attractive tool for general meshes due to their flexibility and simplicity in handling hanging nodes. We derive a simple residual-type er- ror estimator. Numerical results indicate that optimal convergence can be achieved for both the potential and vector variables, and the singularity can be well-captured by the proposed error estimator. Then, some applications to diffusion equations, Stokes equations, and linear elasticity equations are considered. Finally, we extend this approach to high-order polynomial approxi- mations on general meshes. This is joint work with Dohyun Kim, Dong-wook Shin, and Lina Zhao.

REFERENCES

1. S. Anita, M. Iannelli, M.-Y. Kim, E.-J. Park, Optimal harvesting for periodic age-dependent population dynamics, SIAM J. Appl. Math. 58 (1998), 1648-1666 2. E.-J. PARK, Mixed finite element methods for generalized Forchheimer flow in porous media, Numer. Methods Partial Differential Equations 21 (2005), no. 2, 213–228. 3. L. Zhao and E.-J. Park, A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes, SIAM J. Sci. Comput. 40, (2018), no. 4, A2543-A2567.

- 3 - KSIAM 2020 Annual Meeting ------4. L. Zhao and E.-J. Park, A staggered cell-centered DG method for linear elasticity on polygonal meshes. SIAM J. Sci. Comput. 42 (2020), no. 4, A2158-A2181. 5. Dohyun Kim, L. Zhao, and E.-J. Park, Staggered DG Methods for the Pseudostress-Velocity Formulation of the Stokes Equations on General Meshes. SIAM J. Sci. Comput. 42 (2020), no. 4, A2537-A2560. 6. L Zhao, E Chung, E.-J. Park, G Zhou, Staggered DG method for coupling of the Stokes and Darcy-Forchheimer problems, arXiv preprint arXiv:1906.06652; SIAM J. Numer. Anal. Accepted.

- 4 - KSIAM 2020 Annual Meeting ------

  

                           



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- 10 - KSIAM Awards

Yongho Choi (Daegu University)

Junseok Kim (Korea University)

Sun Xiang (Yonsei University) KSIAM 2020 Annual Meeting ------

Numerical Study and Application of Partial Differential Equations on 3D Surfaces

Yongho Choi

Department of Mathematics and Big Data, Daegu University, Gyeongsan-si, Gyeongsangbuk-do 38453, Republic of Korea

Corresponding Author : Yongho Choi, yongho [email protected]

ABSTRACT Numerical studies of partial differential equations(PDEs) on three-dimensional surfaces have a variety of applications such as pattern formation, convection phenomenon, medical fields, diblock copolymer, fluid mechanics. Since an exact solution is not always exist, accurate and efficient numerical approximation is needed. In this talk, I will explain some methods(narrow band domain, closest points method, Laplace–Beltrami operator) of numerically solving PDEs on a three-dimensional surface, and introduce the currently working on researches: Compari- son spherical Laplacian and Laplace–Beltrami operator, Effect of curvature on sphere, Optimal scaffold shape, etc.

REFERENCES

1. Y Choi, D Jeong, S Lee, M Yoo, J Kim, “Motion by mean curvature of curves on surfaces using the Allen–Cahn equation.” International Journal of Engineering Science 97 (2015): 126-132. 2. J Kim, D Jeong, SD Yang, Y Choi, “A finite difference method for a conservative Allen–Cahn equation on non-flat surfaces.” Journal of Computational Physics 334 (2017): 170-181. 3. Macdonald, Colin B., Jeremy Brandman, and Steven J. Ruuth. “Solving eigenvalue problems on curved surfaces using the closest point method.” Journal of Computational Physics 230.22 (2011): 7944-7956. 4. Xu, Guoliang. “Discrete Laplace–Beltrami operators and their convergence.” Computer aided geometric design 21.8 (2004): 767-784. 5. Chen, Sheng-Gwo, and Jyh-Yang Wu. “Discrete conservation laws on curved surfaces.” SIAM Journal on Scientific Computing 35.2 (2013): A719-A739.

- 12 - KSIAM 2020 Annual Meeting ------

A NEW MATHEMATICAL EPIDEMIC MODEL FOR COMPUTING UNIDENTIFIED INFECTED PEOPLE FOR COVID-19

Chaeyoung LEE 1 ,YibaoLI2 and Junseok KIM 1

1) Department of Mathematics, Korea University, Seoul 02841, KOREA 2) School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, CHINA

Corresponding Author : Junseok KIM, [email protected]

ABSTRACT In this talk, we present a new mathematical epidemic model for computing unidentified infected people for coronavirus disease 2019 (COVID-19) in China. We define the unidentified infected people by the infected but not identified population. To compute the number of the unidentified infected people, we calculate the optimal model parameter values which best fit the confirmed case data in the least-squares sense. The proposed mathematical epidemic model is simple but potentially practical in computing the unidentified infected people to monitor the effect of in- terventions.

ACKNOWLEDGEMENT

The corresponding author (J.S. Kim) was supported by Korea University Future Research Grant.

REFERENCES

1. Lee C, Li Y, Kim J, ”The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19.” Chaos, Solitons & Fractals 139 (2020): 110090. 2. Zhao S, Musa SS, Lin Q, Ran J, Yang G, Wang W, et al. Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak. J Clin Med 2020;9(2):388. 3. Novel Coronavirus (2019-nCoV) situation reports. Available online: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/. 4. Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW, et al. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health 2020;8(4):e488–e496. 5. Kucharski AJ, Russell TW, Diamond C, Liu Y, Edmunds J, Funk S, et al. Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis 2020;20:553–558.

- 13 - KSIAM 2020 Annual Meeting ------

GLOBAL SENSITIVITY ANALYSIS FOR MULTIVARIATE OUTPUTS USING POLYNOMIAL CHAOS-BASED SURROGATE MODEL

Xiang SUN 1 , Yun Young CHOI 1 and Jung-Il CHOI 1 1) Department of Computational Science and Engineering, Yonsei University, Seoul 03722, KOREA We propose an efficient global sensitivity analysis method for multivariate outputs that ap- plies polynomial chaos-based surrogate models to vector projection-based sensitivity indices. These projection-based sensitivity indices, which are powerful measures of the comprehensive effects of uncertain model inputs on multiple outputs, are conventionally estimated by the Monte Carlo simulations that incur prohibitive computational costs for many practical problems. Here, the projection-based sensitivity indices are efficiently estimated via two polynomial chaos- based surrogates: sparse polynomial chaos expansion and a proper orthogonal decomposition- based polynomial chaos expansion. Compared to the Monte Carlo simulations, the sparse poly- nomial chaos expansion usually approximates the original model with only a few number of samples. Furthermore, there is no more extra cost on the estimation of the sensitivity indices because the sensitivity indices are a function of polynomial chaos expansion coefficients. How- ever, this approach can be computationally intensive if the number of the model outputs is large and, in some cases, can seriously reduce the applicability of this approach to realistic problems. To address this, we developed a new polynomial chaos expansion based on proper orthogonal decomposition, which can reduce the dimension of the model output and can estimate the sta- tistical quantities as easily as the general polynomial chaos expansion. The new method reduces the computational cost by projecting the model output into a low-dimension space expanded by its principle components using proper orthogonal decomposition, and approximating the projec- tion coefficients using a polynomial chaos expansion. Several numerical examples with various types of outputs are tested to validate the proposed methods; the results demonstrate that the polynomial chaos-based surrogates are more efficient than Monte Carlo simulations at estimat- ing the sensitivity indices, even for models with a large number of outputs. Furthermore, for models with only a few outputs, polynomial chaos expansion alone is preferable, whereas for models with a large number of outputs, implementation with proper orthogonal decomposition is the best approach. Additionally, the results indicate that the estimated vector projection based sensitivity indices can efficiently and reasonably quantify the input uncertainty contributions to the whole output domain. This implies that the present global sensitivity analysis can potential- ly be used to design practical experiments, or to improve experimental design or mathematical models in engineering problems.

- 14 - Special Session

Math for Public Safety based on Modeling and Data analysis Numerical methods for the Hyperbolic conservation laws Stochastic Optimization in Mathematical Finance I The Challenges of Mathematical Modeling of the Spread of COVID-19 Some cases in Industrial Mathematics Stochastic Optimization in Mathematical Finance II Deep Learning and Image Process Finance·Fishery·Manufacture Industrial Mathematics Center on Big Data Deep Learning for Digital Dentistry Domain Decomposition Methods and Related Methods I Regularity and singularity of some partial differential equations related to fluid flows Deep Learning for Medical Imaging Domain Decomposition Methods and Related Methods II Nonlinear differential equations modeling of collective motion Special Session

Math for Public Safety based on Modeling and Data analysis

Hyuk Kang (NIMS)

Hark soo Song (NIMS)

Jieun Kim (NIMS)

Young Jin Kim (NIMS) KSIAM 2020 Annual Meeting ------

REPRODUCTION OF MODULATION PROCESS OF HUMAN BLOOD GLUCOSE LEVEL THROUGH THE MATHEMATICAL MODELING

Hyuk KANG1, Minha YOO1, Jong-Ho KIM1, Sang Soo KIM2,3, Jeong Mi KIM2,3, Min Hee JANG2,3, Wook YI2,3, Soree RYANG2,3, Minsoo KIM2, In Joo KIM2,3 and Jinmi KIM4

1) Division of Basic Researches for Industrial Mathematics, National Institute for Mathematical Sciences, Daejeon 34047, KOREA 2) Division of Endocrinology and Metabolism, Department of Internal Medicine, Pusan National University Hospital, Busan 49241, KOREA 3) Biomedical Research Institute, Pusan National University Hospital, Busan 49241, KOREA 4) Department of Biostatistics, Clinical Trial Center, Biomedical Research Institute, Pusan National University Hospital, Busan 49241, KOREA

Corresponding Author: Hyuk KANG [email protected]

ABSTRACT

In order to maintain the life, the human body supplies glucose, which is an important energy source, to each organ of the human body through the blood, maintaining higher than a certain level. However, when the concentration of glucose in the blood is too high, various harmful actions to the human body appear. Therefore, maintaining the proper level of blood sugar in the human body is indispensable for maintaining vital phenomena. Therefore, numerous studies have been conducted on the process of regulating blood sugar in the human body, and mathematical models to theoretically investigate this phenomenon have also been developed. This study explains the mathematical mechanism that regulates the blood sugar level in the human body, and shows what dynamics it has to efficiently maintain the appropriate level of blood sugar. Particularly in the early stages of diabetes, it explains the action of increasing insulin secretion, which is taken to compensate for the defect in the blood sugar control function caused by insulin resistance of the human body organs. In addition, it suggests the theoretical hypothesis that can explain how to provide information on the onset or progression stage of diabetes in the subject who has the mathematical model for controlling blood sugar with the specific parameter set on the diabetes development pathway.

- 17 - KSIAM 2020 Annual Meeting ------

Analysis of important factors in diabetes using machine learning algorithms and KoGES (Korean Genome and Epidemiology Study) data

Hark Soo SONG1, Hynk KANG1, Young Jin KIM1, Ruda RHEE, KIM Sang Soo2,3, KIM Jeong Mi2,3, JANG Min Hee2,3, YI Wook2,3, RYANG Soree2,3, KIM Minsoo2,3, KIM In Joo2,3, KIM Jinmi4

1) Division of Basic Researches for Industrial Mathematics, Daejeon 34-047, KOREA 2) Division of Endocrinology and Metabolism, Department of Internal Medicine, Pusan National University Hospital, Pusan 49-241, KOREA 3) Biomedical Research Institute, Pusan National University Hospital, Pusan 49-241, KOREA 4) Division of Biostatistics, Clinical Trial Center, Biomedical Research Institute, Pusan National University Hospital, Pusan 49-241, KOREA

Corresponding Author: Hark Soo SONG, hssong @gwmail.nims.re.kr

ABSTRACT

Recently, as the average life span of humans is prolonged due to the development of medical technology and the evolution of individuals' awareness of health, the prevalence of chronic diseases or complex diseases is rapidly increasing. In particular, in the case of chronic diseases such as diabetes and diseases that cause complications at the same time, the modern people's dietary habits and lifestyle patterns change, leading to a rapid upward curve. In this study, we aim to use machine learning methods to predict how the transition to diabetes will progress in the future if type 2 diabetes patients maintain their current diet and lifestyle. The data used in this study are large-scale medical examination records data, which is a Korean genome epidemiology study (KoGES, The Korean Genome and Epidemiology Study) conducted by the Korea Centers for Disease Control and Prevention. We had to improve the quality of the data in order to use machine learning methods. Improving the quality of the data is because it guarantees the accuracy of predictions and describes the reality well. We will introduce methods and results for extracting variables closely related to diabetes and the process of data purification in order to extract statistical rules and useful information from large amounts of unrefined data through data mining methods.

- 18 - KSIAM 2020 Annual Meeting ------

Fully and robust unsupervised detection of epileptic seizure from long-term EEG recordings

Jieun Kim1, Dong-Uk Hwang1, Edwin J. Son1, Whansun Kim1, and Sang Hoon Oh1

1) Division of Basic Researches for Industrial Mathematics, National Institute for Mathematical Sciences, Daejeon 34047, KOREA

Corresponding Author: Dong Uk Hwang, [email protected]

ABSTRACT

According to the World Health Organization (WHO), epilepsy is a neurological disease that affects about 6.5 million people, and it affects 3.52 out of every 1,000 people in Korea. About 30% of them are difficult to treat with drugs, so surgery must be treated. For this, it is important to accurately estimate the location of the epileptic lesion. Electroencephalography (EEG) plays an important role in monitoring brain activity and diagnosing epilepsy in patients with epilepsy, but detecting epilepsy activity requires a specialist analyzing long-term measured EEG records. However, this method is time consuming and requires a tedious process, and it is expensive to train experts. Therefore, we developed an algorithm aiming at fully automatic detection of seizures in long-term EEG data using the K-means clustering method, an unsupervised learning method. The automatic detection algorithm developed so far requires training data, that is, data labeled by an expert. Although detection is performed by unsupervised learning, there are cases where the false positive rate is very bad. In threshold-based analysis, there is a trade-off between sensitivity and false positives rate. Other studies do not have an automatic artifact removal method. In order to solve these problems, we developed an algorithm for automatically detecting and removing artifacts in the preprocessing stage, extracting features of ictal waves that appear during seizures, applying k- means classification, and extracting events continuously detected in the post-processing stage. As a characteristic of the ictal wave, the average power spectral density (PSD) of two frequency bands of 1 to 5 Hz and 6 to 13 Hz was used. We have defined three artifacts that interfere with finding the seizure in EEG; Power line noise, slow sleep wave, inter-ictal spikes. Artifacts were detected and removed using the features of each artifact. The ictal wave signal and the background signal were classified using curvature from clear data scattered in 2D. To solve the unbalanced data, oversampling was used and then k-mean clustering was performed. In the post-processing step, only events detected continuously were filtered. In this process, we applied an adjusted threshold and obtained a sensitivity of 84.9% and a 0.093 false positive rate/hour for 21 subjects in the CHB-MIT data set. Our study showed superior results compared to previous actual unsupervised seizure detection studies.

- 19 - KSIAM 2020 Annual Meeting ------

Sea level rise estimation near the Korean peninsula using CEEMDAN

Young Jin Kim 1 , Harksoo Song 1 , Jongho Kim 1 and Hyuk Kang 1

1) Public Problem Research Team, NIMS, Daejeon 34047, Korea

Lead Author : Young Jin Kim, [email protected] Corresponding Author : Hyuk Kang, [email protected]

ABSTRACT The sea level rise due to global warming is an issue at a global level and its causes already have been studied clearly in early times. IPCC creates scenarios for greenhouse gas emissions and predicts global average sea level rise accordingly. Ice Sheet System Model is a numerical model of ice sheet dynamics process caused by the loss of ice sheets in polar regions. In particular, the global sea level rise prediction through the Glacial Isostatic Adjustment provides seawater flows from the ice sheet at a macroscopic scale. However, this global scale modeling has limitations in insufficient mesh size due to computation speed and makes it difficult to predict local differences in sea level rise in microscopic scale and complex terrain. In particular, in the Korean Peninsula, high sea level rise rate differences between tidal stations have been reported in microscopic areas (∼ 100 km). In this study, we study regression and empirical mode decomposition for sea level rise prediction using tidal data near Korean Peninsula. And we also analyze correlation, causality, and volatility to understand the difference between tidal stations.

- 20 - Special Session

Numerical methods for the Hyperbolic conservation laws

Kunmin Sung (Seoul National University)

Youngsoo Ha (Seoul National University)

Hyuntae Cho (Seoul National University)

Hojun You (Seoul National University) KSIAM 2020 Annual Meeting ------

HYBRID WENO METHOD WITH ANTI-DIFFUSIVE FLUX

Kunmin Sung 1 , Youngsoo Ha 1 and Myungjoo Kang 1

1) Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT In this paper, we present a hybrid weighted essentially non-oscillatory (WENO) method with anti-diffusive flux for solving the hyperbolic conservation laws. The WENO scheme [1] is very popular method for problems having discontinuities. It shows a good resolution in shocks, but has a relatively poor resolution in contact discontinuities. Many researchers have been studied to enhance the resolution of contact discontinuities. Despres` and Lagoutiere´ [2] proposed the downwind scheme, which maintain the sharpness in linear advection. Bouchut [3] modified this scheme to satisfy the entropy condition. Xu and Shu [4] applied this scheme for the high order WENO scheme. The resulting scheme shows enhanced resolution at contact discontinuities. However, it requires more computational costs than the original WENO methods. The hybrid WENO schemes selectively adopt the high-order linear upwind scheme or the WENO scheme to avoid the local characteristic decompositions and calculations of the nonlinear weights in smooth regions. We developed the MVP troubled-cell indicator [5] which does not need any variable parameter to detect the discontinuities. In this paper, we adopt the anti-diffusive flux on only near discontinuities, also the high order linear upwind scheme on smooth regions. The results shows the good resolution with essential computational cost.

REFERENCES

1. Jiang, G.-S. and Shu, C.-W., “Efficient Implementation of Weighted ENO Schemes”, Journal of Computational Physics, Vol. 126, No 1, 1996, pp. 202–228. 2. Despres,` B. and Lagoutiere,´ F., “Contact Discontinuity Capturing Schemes for Linear Advection and Compressible Gas Dynamics”, Journal of Scientific Computing, Vol. 16, No. 4, 2001, pp. 479–524. 3. Bouchut, F., “An Antidiffusive Entropy Scheme for Monotone Scalar Conservation Laws”, Journal of Scientific Computing, Vol. 21, No. 1, 2004, pp. 1–30. 4. Xu, Z. and Shu, C. W., “Anti-diffusive flux corrections for high order finite difference WENO schemes”, Journal of Computational Physics, Vol. 205, No. 2, 2005, pp. 458–485. 5. Sung, K., Ha, Y. and Kang, M., “Troubled-Cell Indicator based on Mean Value Property for Hybrid WENO schemes”, Communications in Computational Physics, Vol. 27, No 4, 2020, pp. 949–975.

- 22 - KSIAM 2020 Annual Meeting ------

Improving accuracy of the fifth-order WENO scheme by using the exponential approximation space

Youngsoo Ha 1 , Chang Ho Kim 2 , Hyoseon Yang 3 and Jungho Yoon 4

1) Dept. of Math. Sciences, Seoul National University, Seoul, KOREA 2) Dept. of Software Technology, Glocal Campus, Konkuk University, Chungju, KOREA 3) Dept. of Computational Math. Science and Engineering, Michigan State Univ. East Lansing, MI, USA 4) Dept. of Math., Ewha Womans University, Seoul, KOREA

Corresponding Author : Youngsoo Ha, [email protected]

ABSTRACT The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to fit the the specific feature of the data, yielding better results compared to the polynomial approximation space. However, finding an optimal tension parameter is a very important and difficult problem, indeed a topic of active research. In this regard, this study introduces a practical approach to determine an optimal tension parameter by taking into account the relationship between the tension parameter and the accuracy of the exponential polynomial interpolation under the setting of the fifth- order WENO scheme. As a result, the proposed WENO scheme attains an improved order of accuracy (that is, sixth-order) better than other fifth-order WENO methods without loss of accuracy at critical points. A detailed analysis is provided to verify the improved convergence rate. Further, we present modified nonlinear weights based on L1-norm approach along with a new global smoothness indicator. The proposed nonlinear weights reduce numerical dissipation significantly, while attaining better resolution in smooth regions. Some experimental results for various benchmark test problems are presented to demonstrate the ability of the new scheme.

INTRODUCTION

Hyperbolic systems are used for a wide range of scientific and engineering applications such as meteorology, gas dynamics, shallow water modeling, astrophysics models, and multiphase flow problems. The space of algebraic polynomials is the most well-established tool to reconstruct nu- merical flux. However, the interpolation method cannot be regulated according to the trait of the given data such that it causes excessive numerical dissipation when approximating rapidly varying data (e.g., sharp gradients or high oscillations). To circumvent this limitation, this study exploits the interpolation method based on the space of exponential polynomials of the form

k λx φ(x)=x e ,k∈ Z+,λ∈ R ∪ iR (1)

- 23 - KSIAM 2020 Annual Meeting ------that allows an environment to fit the approximation to the characteristic of the given prob- lem. For a given exponential polynomial space, the choice of the tension (or shape) parameter λ has a significant impact on the accuracy of interpolation. A well-selected parameter can yield better results compared to the polynomial-based method for various types of PDEs [1,2,3,4,5]. However, selecting an optimal parameter is an important and difficult problem, indeed a topic of active research. Most studies end up finding the tension parameter by using trial and error or minimization problem. In this regards, the goal of this study is first to present a specific type of exponential approximation space for the construction of numerical fluxes under the setting of the fifth-order WENO scheme. We then introduce a practical approach to determine an optimal parameter by taking into account the relation between the value of the tension parameter and the accuracy of the exponential polynomial interpolation. As a result, the proposed WENO scheme (termed as WENO-H) provides an improved order of accuracy better than the other fifth- order WENO methods. In fact, we will observe that the sixth-order accuracy can be achieved by the WENO-H technique, without loss of accuracy at critical points. A rigorous analysis is provided to prove the improved convergence rate. Further, a modified smoothness indicator based on L1-norm approach is presented along with a new global smoothness indicator. Accordingly, the proposed WENO scheme reduces numerical dissipation significantly, while attaining better resolution in smooth regions. Some experimental results for various benchmark test problems are given to illustrate the performance of the WENO-H scheme.

REFERENCES

1. Y. Ha, Y.J. Lee and J. Yoon, “Modified essentially non-oscillatory scheme based on exponential polynomial interpolation for hyperbolic conservation laws,”, SIAM J. Numer. Analy., Vol. 52, 2012, pp. 864-893. 2. Y. Ha, C. H. Kim, Y. H. Yang, and J. Yoon, “Sixth-order weighted essentially non- oscillatory schemes based on exponential polynomials,”, SIAM J. Sci. Comput., Vol. 38, 2016, pp. A1987-A2017. 3. L. Yuan and C.W. Shu, “Discontinuous Galerkin method based on non-polynomial approximation spaces,”, J. Sci. Comput., Vol. 218, 2006, pp. 295-323. 4. J. Zhu and J. Qiu, “Trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory problems,”, Commun. Comput. Phys., Vol. 8, 2010, pp. 1242-1263. 5. J. Zhu and J. Qiu, “WENO schemes and their application as limiters for RKDG methods based on Trigonometric approximation spaces,”, J. Sci. Comput., Vol. 55, 2013, pp. 606- 644.

- 24 - KSIAM 2020 Annual Meeting ------

Fully implicit and accurate treatment of jump conditions for two-phase incompressible Navier–Stokes equation

Hyuntae Cho 1 and Myungjoo Kang 1

1) Department of Mathematical Sciences, Seoul National University, Seoul, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT We present a numerical method for two-phase incompressible Navier–Stokes equation with jump discontinuity in the normal component of the stress tensor and in the material properties. Although the proposed method is only first-order accurate, it does capture discontinuity sharply, not neglecting nor omitting any component of the jump condition. Discontinuities in velocity gradient and pressure are expressed using a linear combination of singular force and tangen- tial derivatives of velocities to handle jump conditions in a fully implicit manner. The linear system for the divergence of the stress tensor is constructed in the framework of the ghost fluid method, and the resulting saddle-point system is solved via an iterative procedure using recently introduced techniques by Egan and Gibou [2]. Numerical results support the inference that the proposed method converges in L∞ norms even when velocities are not smooth across the inter- face and can handle a large density ratio that is likely to appear in a real-world simulation.

REFERENCES

1. Hyuntae Cho, Myungjoo Kang, Fully implicit and accurate treatment of jump conditions for two-phase incompressible Navier–Stokes equation, submitted to Journal of Computational Physics 2. Raphael Egan, Frederic Gibou, xGFM: Recovering convergence of fluxes in the ghost fluid method, Journal of Computational Physics Volume 409, 15 May 2020, 109351

- 25 - KSIAM 2020 Annual Meeting ------

High-performance Large Eddy Simulation using High-order Discontinuous Galerkin Method

Hojun You1, Juhyun Kim1, and Chongam Kim1,2

1) Department of Aerospace Engineering, Seoul National University, Seoul 08826, KOREA 2) Institute of Advanced Aerospace Technology, Seoul National University, Seoul 08826, KOREA

Corresponding Author: Chongam Kim, [email protected]

ABSTRACT

The direct reconstruction method (DRM) is applied to the high-order discontinuous Galerkin (DG) method for solving multi-dimensional compressible Navier-Stokes (NS) equations [1-3]. In the DRM-DG method, flux functions in spatial integrals of DG weak formulation are represented via generalized reconstruction that is a generalized concept of interpolation in which the number of reconstruction nodes is larger than the number of interpolants. As a result, each spatio-temporal flux is decomposed into spatial and temporal terms separately. The integral of the spatial term is then precomputed in a pre-processing step. This approach significantly reduces computational costs compared with the conventional quadrature-based DG method when high-order mixed-curved meshes are employed. To validate the DRM-DG method, transitional flows (Figs. 1 and 2) are solved by the large eddy simulation (LES). For time-marching, both explicit and implicit Runge-Kutta (RK) multi-stage methods are considered, and the generalized minimal residual (GMRES) method with the incomplete lower- upper factorization (ILU) preconditioner is considered as a linear system solver for the implicit RK method. Computed results confirm that the DRM-DG method successfully resolves the physical characteristics of transitional flows and significantly improves the computational performance of LES compared to the quadrature-based DG method.

Figure 1. LES analysis of a transitional flow over a circular cylinder.

- 26 - KSIAM 2020 Annual Meeting ------

Figure 2. LES analysis of a transitional flow over the SD7003 airfoil.

REFERENCES

1. You, H. and Kim, C., “Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes I. Volume integration,” Journal of Computational Physics, Vol. 395, 2019, pp. 223-246. 2. You, H. and Kim, C., “Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes II. Surface integration,” Journal of Computational Physics, Vol. 416, 2020, 109514. 3. You, H. and Kim, C., “Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes III. Code optimization via tensor contraction,” Submitted to Computers and Fluids.

- 27 - Special Session

Stochastic Optimization in Mathematical Finance I

Junkee Jeon (Kyung Hee University)

Kyunghyun Park (Seoul National University)

Kum Hwan Rho (Hannam University)

Yong Hyun Shin (Sookmyung Women’s University) KSIAM 2020 Annual Meeting ------

Intertemporal Preference with Loss Aversion: Consumption and Risk-Attitude

Kyoung Jin Choi 1 , Junkee Jeon 2 and Hyeng Keun Koo 3

1) Haskayne School of Business, University of Calgary, Canada. 2) Department of Applied Mathematics, Kyung Hee University, Korea. 3) School of Business, Ajou University, Korea.

ABSTRACT We study the consumption and portfolio selection problem of an agent who faces consumption irreversibility: there is disutility from changing consumption levels. The derived preference exhibits loss aversion toward a consumption gamble with the previous consumption level being the reference point. The optimization problem involves the non-monotonic and non-concave utility function. By combining a duality method and the super-contact principle, we derive the closed-form solution. We show that the consumption policy involves an inaction interval for the consumption-wealth ratio, which can explain the four stylized facts about consumption at once. The optimal portfolio choice exhibits a U-shape in the inaction interval, which sheds light on the empirical debate on the relationship between a household’s financial wealth and the share invested in risky assets.

- 29 - KSIAM 2020 Annual Meeting ------

PORTFOLIO SELECTION WITH DRAWDOWN CONSTRAINT ON CONSUMPTION: A GENERALIZATION MODEL

Junkee JEON 1 and Kyunghyun PARK 2

1) Department of Applied Mathematics & Institute of Natural Science, Kyung Hee University, KOREA 2) Department of Mathematical Sciences, Seoul National University, KOREA

Corresponding Author : Kyunghyun PARK, [email protected]

ABSTRACT In this study, we generalize the results of Arun (2013) on the optimal consumption and invest- ment problem of an infinitely lived agent who does not accept her consumption falling below a fixed proportion of her historically highest level, the so-called drawdown constraint on con- sumption. We extend the results to a general class of utility functions. We use the martingale method to study the dual problem, which involves the choice of a maximum consumption pro- cess. The dual problem can be formulated as a two-dimensional singular control problem, with the free boundary depending on a state variable of the maximum process. We establish the duality theorem and provide semi-closed form solutions regarding the optimal strategies. To highlight our methodology, we present some special cases of utility functions that do not allow for the dimension reduction considered in Arun (2013).

- 30 - KSIAM 2020 Annual Meeting ------

An Optimal Consumption and Investment Problem with a Subsistence Consumption Contraint and Quadratic-Featured General Utility

Kum-Hwan Roh 1 and Yong Hyun Shin 2

1) Department of Mathematics, Hannam University, Daejeon 34430, Korea. 2) Department of Mathematics, Sookmyung Women’s University, Seoul 04310, Korea.

Presentation Author : Kum-Hwan Roh, E-mail: [email protected]

ABSTRACT We study optimal consumption and investment problem of an economic agent who has a general utility function with pre-fixed bliss level of consumption and subsistence constraints. We use a dual transform method for obtaining an explict solution of optimization problem. And we show that our result is a general version of the quadratic utility case.

Keywords: Portfolio selection, subsistence consumption constraint, general utility, dual trans- form method

- 31 - KSIAM 2020 Annual Meeting ------

An Optimal Consumption, Investment and Retirement Choice Problem with Quadratic Utility and Subsistence Consumption Constraints

Kum-Hwan Roh 1 , Hyeng Keun Koo 2 and Yong Hyun Shin 3

1) Department of Mathematics, Hannam University, Daejeon 34430, Korea. 2) Department of Financial Engineering, Ajou University, Suwon 16499, Korea. 3) Department of Mathematics, Sookmyung Women’s University, Seoul 04310, Korea.

Presentation Author : Yong Hyun Shin, E-mail: [email protected]

ABSTRACT We investigate the optimal consumption, investment and retirement time choice problem with quadratic utility. In this model, the agent faces the subsistence consumption constraints be- fore/after retirement. We use the duality approach to derive the closed-form solutions of this optimization problem. Also we observe the effects of the constraints on the optimal strategies.

Keywords: Portfolio selection, voluntary retirement, quadratic utility, subsistence consumption constraints, duality approach

- 32 - Special Session

The Challenges of Mathematical Modeling of the Spread of COVID-19

Jong-Hoon Kim (International Vaccine Institute)

Hee-Sung Kim (Chungbuk National University)

Woo-Sik Son (NIMS)

Il Hyo Jung (Pusan National University) KSIAM 2020 Annual Meeting ------

TWO IMPORTANT FINDINGS IN THE CORONAVIRUS DISEASE 2019 (COVID-19) SPREAD IN KOREA

Jong-Hoon KIM

Epidemiology, Public Health, Impact, Clinical Development, International Vaccine Institute, Seoul 08826, KOREA

Corresponding Author: Jong-Hoon KIM, [email protected]

ABSTRACT

We present two important findings about coronavirus disease 2019 (COVID-19) transmission in Korea. The first finding is rapid transmission of COVID-19 observed in the Shincheonji Church of Jesus, a religious sect in South Korea. The index case was confirmed on Feb 18, 2020 in Daegu City, and within two weeks, 3,081 connected cases were identified. A stochastic model fitted to the time series of confirmed cases suggests that the basic reproduction number (R0) of COVID-19 was 9.0 [95% credible interval (CrI): 7.5, 12.2] among the church members, whereas R0=2.7 [95% CrI: 0.6, 7.6] in the rest of the population of Daegu City. The Shincheonji Church cluster is likely to be emblematic of other outbreak- prone populations where R0 of COVID-19 is higher. Understanding and subsequently limiting the risk of transmission in such high-risk places is key to effective control. The second finding is reduced incidence of acute respiratory tract infections (ARTI). For the first half of 2020 when the COVID-19 is spreading, incidence of eight major ARTIs including influenza dropped substantially in Korea. The change points in the time series data of the weekly incidence were almost identical to those detected in human mobility patterns extracted from mobile phone data, a potential proxy for social distancing. Unlike COVID-19, historic incidence records are available for ARTIs and this makes the ARTIs better examples in which the impact of social distancing on their transmissions can be evaluated. Insights from analyses of ARTIs will help evaluate the impact of social distancing and design better strategies.

- 34 - KSIAM 2020 Annual Meeting ------

The experiences and limitations of infectious disease physician on COVID-19 management

Hee-Sung Kim

Department of Internal Medicine, Chungbuk National University College of Medicine, Cheongju, Korea

Corresponding Author: Hee-Sung Kim, [email protected]

ABSTRACT

In the era of COVID 19 pandemic, infectious disease physicians participate in the treatment of COVID 19 patients and the management of nosocomial infections to keep the hospital environment safe from COVID 19. In order to manage unknown infectious diseases, a mathematical models that can assist in decision-making by making projections regarding which intervention effectively control COVID-19 is a valuable tool for infection control in hospitals and communities. I would like to share my experiences on the themes, issues and difficulties of convert real world problem in a mathematical form.

- 35 - KSIAM 2020 Annual Meeting ------

 








   
   







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- 36 - KSIAM 2020 Annual Meeting ------

A FORECAST MODEL OF COVID-19 SPREADING IN SOUTH KOREA

Sungchan Kim and Il Hyo Jung*

Department of Mathematics, Pusan National University, Busan 46241, South Korea *Finance Fishery Manufacture Industrial Mathematics Center on Big Data, Pusan National University, Busan 46241, South Korea

Corresponding Author: Il Hyo Jung, [email protected]

ABSTRACT

The number of people with COVID-19 in South Korea continues to increase. In this talk, we introduce to several forecast models of the spread of COVID-19 in the U.S. and then we consider a real time forecast model of COVID-19 spreading in South Korea using bayesian and a compartment model. Such model can be used the real-time application of a collaborative ensemble to forecast deaths and cases attributable to COVID-19 in South Korea.

Keywords: COVID-19, SARS-CoV-2, Epidemic model, Compartment model

- 37 - Special Session

Some cases in Industrial Mathematics

Byung Chun Kim (NIMS)

Hyunju Lee (NIMS)

Minjung Gim (NIMS)

Minwon Na (NIMS) KSIAM 2020 Annual Meeting ------

Extension of pQSAR: ensemble model generated by Random Forest and Partial Least Squares Regressions

Byung Chun Kim 1 , Dosang Joe 1 , Youngho Woo 1 , Yongkuk Kim 2 and Gangjoon Yoon 1

1) National Institute for Mathematical Science, 70, Yuseong-daero 1689 beon-gil, Yuseong-gu, Daejeon 34047 Korea 2) Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566 Korea

Speaker : Byung Chun Kim, [email protected]

ABSTRACT Quantitative structure-activity relationship (QSAR) regression models are mathematical ones which relate the structural properties of chemicals to the potencies of the biological activities of the chemicals. In QSAR models, the physical and chemical information of the molecules is en- coded into quantitative numbers called descriptors. Recently, experimental test results (profiles) have been used as descriptors of chemicals. Profile QSAR 2.0 (pQSAR) model suggested by Martin et. al, is a multitask, two step machine learning prediction method with a combination of random forest regressions (RFRs) and partial least squares regression (PLSR). In pQSAR model, one fills the profile table’s missing values with RFRs and then builds PLSR using the profile predictions. Note that in the second step of the pQSAR method, PLSR’s predictor vari- ables are profiles; so activity values, and the response variables are also activity values. Thus we can use the PLSRs to update the profile table and then repeat the second step. In this work, we propose an extended model of pQSAR generated by RFRs and PLSRs. Experiment of up- dating the given full initially predicted profile table by two kinds of prediction models, RFRs and PLSRs, has been conducted iteratively for the PKIS and ChEMBL data sets. Even though prediction performance of individual combination of RFRs and PLSRs varies, the average of the all possible predicted profile tables for given iteration shows better performance. This en- semble model has better prediction performance in sense of Pearson’s R2 compared to that of the pQSAR model.

- 39 - KSIAM 2020 Annual Meeting ------

Figure 1. R2 distribution for the ChEMBL data. The graph was plotted in descending order of R2 values for the three models. Table 1 R2 performance comparison for the ChEMBL assay data. R2 ave. median ≥ 0.3 ≥ 0.5 ≥ 0.6 ≥ 0.7 RF (M) 0.13462 0.11148 10 1 0 0 pQSAR 0.5269 0.55026 148 99 63 13 PLS-RF iter. 1 0.58411 0.61225 149 122 87 39 iter. 2 0.59104 0.61787 149 119 88 42 iter. 3 0.59925 0.62822 151 121 88 49 iter. 4 0.59808 0.62380 149 121 91 48 iter. 5 0.60058 0.62868 150 123 93 49

REFERENCES

1. E. J. Martin and V. R. Polyakov and X. Zhu and L. Tian and P. Mukherjee and X. Liu, “All-Assay-Max2 pQSAR: Activity Predictions as Accurate as Four-Concentration IC50s for 8558 Novartis Assays”, Journal of Chemical Information and Modeling, Vol. 59 (10), 2019, pp. 4450-4459. 2. A. P. A. Janssen, S. H. Grimm, R. H. M. Wijdeven, E. B. Lenselink, J. Neefjes, C. A. A. van Boeckel, G. J. P. van Westen, and M. van der Stelt, “Drug Discovery Maps, a Machine Learning Model That Visualizes and Predicts Kinome–Inhibitor Interaction Landscapes”, Journal of Chemical Information and Modeling, Vol. 59 (3), 2019, pp. 1221-1229

- 40 - KSIAM 2020 Annual Meeting ------

An uncoupled approach to online state of charge and state of health estimation for a Lithium-ion battery

Hyunju LEE 1 , Sun Woo PARK 1 and Yong Sul WON 2

1) Division of Advanced Researches for Industrial Mathematics, National Institute for Mathematical Sciences, Daejeon, 34047, KOREA 2) Division of Medical Mathematics, National Institute for Mathematical Sciences, Daejeon, 34047, KOREA

Corresponding Author : Yong Sul WON, ys [email protected]

ABSTRACT Real time monitoring and health managements of the battery require reliable estimation al- gorithms equipped with efficient adaptive schemes. In this talk, we introduce two forecasting models to track separately each fundamental state of the Lithium-ion battery known as the state of charge (SOC) and state of health (SOH) during real time operations. We separate the estimations by modeling battery degradation upon mathematical concepts. This replaces the traditional ageing parameters such as cycle numbers with a new variable that, together with ter- minal measured voltage, constitutes the SOC and SOH equations. Especially, the SOC model is constructed by fitting data to a logistic curve. We then split the corresponding domain into several regions to incorporate the corrections of local fluctuations and the health related factors via linear regression. Moreover, the SOH equation is simply determined as a linear equation of the ageing parameter without requiring any prior knowledge of SOC. Finally, we discuss the ad- vantages of such uncoupled approaches, regarding the predictability and the real time adaption. One particular merit of the proposed methodologies is comprehensive applicability to Lithium- ion batteries even with arbitrary usage profiles. The manuscript of the paper has been submitted for publication.

REFERENCES

1. Weng, C., Cui, Y., Sun, J., and Peng, H., “On-board State of Health monitoring of Lithium- ion batteries using incremental capacity analysis with support vector regression”, J. Power Sources, vol. 235, pp. 36-44, Aug. 2013. 2. Huang, S. C., Tseng, K. H., Liang, J. W., Chang, C. L., and Pecht, M. G., “An online SOC and SOH estimation model for Lithium-ion batteries”, Energies, vol. 10, no. 4, Apr. 2017. 3. Le, D. and Tang, X., “Lithium-ion battery State of Health estimation using Ah-V characterization”, Annual Conference of the Prognostics and Health Management Society 2011, vol. 235, pp. 367-373, Montreal, Quebec, Canada, Aug. 2011. 4. Rahimi-Eichi, H., Baronti, F., and Chow, M., “Online adaptive parameter identification and State-of-Charge coestimation for Lithium-polymer battery cells,” IEEE Transaction Industrial Electronics, vol. 61, no. 4, pp. 2053-2061, Apr. 2014.

- 41 - KSIAM 2020 Annual Meeting ------

ANOMALY DETECTION IN SENSING DATA BASED ON RRCF

Minjung Gim 1 , Jin-Hwan Cho 1 and Dong Heon Cheo 1

1) National Institute for Mathematical Sciences, KOREA

ABSTRACT Anomaly detection problem is an important problem for various industries and remains to be research branches. In this talk, we deal with some case of solving industrial problem regarding anomaly detection of a Takyon Tech company. The company is a smart factory-related solution development start-up company and requested an industrial problem to improve the sensor data anomaly detection solution. We introduce the problem requested by NIMS and the method to solve it mathematically. In addition, a mathematical explanation of the Robust random cut for- est(RRCF) algorithm and a method to use effectively use RRCF for anomaly detection. Finally, we will present the results of the performance comparison of the improved RRCF algorithm with the existing classic anomaly detection algorithm.

REFERENCES

1. S. Guha, N. Mishra, G. Roy, O. Schrijvers, “Robust random cut forest based anomaly detection on streams”, Proceedings of the 33rd International conference on machine learning, 2016, pp. 2712-2721. 2. F. T. Liu, K. M. Ting, Z. Zhou “Isolation Forest”, 2008 Eighth IEEE International Conference on Data Mining, 2008, pp. 413-422. 3. R. Dominguesa, M. Filipponea, P. Michiardia, J. Zouaouib “A comparative evaluation of outlier detection algorithms: Experiments and analyses ”, Pattern Recognition , Vol 74, February 2018, pp. 406-421.

- 42 - KSIAM 2020 Annual Meeting ------

          

     

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- 43 - Special Session

Stochastic Optimization in Mathematical Finance II

Hyun Jin Jang (UNIST)

Hyungbin Park (Seoul National University)

Minsuk Kwak (Hankuk University of Foreign Studies)

Geonwoo Kim (Seoul National University of Science and

Technology) KSIAM 2020 Annual Meeting ------Optimal Market-Making Strategies Under Synchronised Order Arrivals with Deep Neural Networks

So Eun CHOI1, Hyun Jin JANG 2 , Kyungsub LEE3, and Harry ZHENG4

1) Samsung Electronics, Suwon, KOREA 2) Department of Business Administration, UNIST, Ulsan, KOREA 3) Department of Statistics, Yeungnam University, Gyeongsan, KOREA 4) Department of Mathematics, Imperial College, London, UNITED KINGDOM

Corresponding Author: Hyun Jin JANG, [email protected]

ABSTRACT

This study investigates the optimal execution strategy of market-making for market and limit order arrival dynamics under a novel framework that includes a synchronised factor between buy and sell order arrivals. Using statistical tests, we empirically confirm that a synchrony propensity appears in the market, where a buy order arrival tends to follow the sell order's long-term mean level and vice versa. This is presumably closely related to the drastic increase in the influence of high-frequency trading activities in markets. To solve the high-dimensional Hamilton–Jacobi–Bellman equation, we propose a deep neural network approximation and theoretically verify the existence of a network structure that guarantees a sufficiently small loss function. Finally, we implement the terminal profit and loss profile of market-making using the estimated optimal strategy and compare its performance distribution with that of other feasible strategies. We find that our estimation of the optimal market-making placement allows significantly stable and steady profit accumulation over time through the implementation of strict inventory management.

- 45 - KSIAM 2020 Annual Meeting ------

                  

   

                 

    



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- 46 - KSIAM 2020 Annual Meeting ------

Real Options with Endogenous Payoff

Kyoung Jin Choi 1 and Minsuk Kwak 2

1) Haskayne School of Business, University of Calgary, AB, Canada 2) Department of Mathematics, Hankuk University of Foreign Studies, Yongin 17035, Korea

Corresponding Author : Minsuk Kwak, [email protected]

ABSTRACT This paper studies a model of irreversible investment decisions in which the exercise payoff is endogenously determined by the firm’s risk management choice. By obtaining the explicit solution of a non-linear free boundary problem with a stochastic control, we present the impli- cations for the optimal investment timing and the associated optimal risk management strategy. The firm’s optimal risk management strategy exhibits risk-seeking: it increases the insurance as- set holdings that provide rewards (damages) when there is good (bad) news for the underlying price. As a result of the risk-seeking insurance strategy, in our model, in contrast to the standard models, investment can be hastened as the underlying uncertainty increases, depending on the economic conditions. The main force driving these results is that the firm’s risk management is designed to optimize the risk-return tradeoff of the endogenous payoff.

- 47 - KSIAM 2020 Annual Meeting ------

Note on option pricing model with credit risk

Geonwoo Kim

School of Liberal Arts, Seoul National University of Science and Technology, Korea.

E-mail: [email protected]

Abstract

Credit risk is undoubtedly one of the most important issues for researchers and practitioners in the financial market. Therefore, credit risk should be considered when the option is priced. In fact, there have been many researches on the pricing of option with credit risk which is called vulnerable option. In this talk, we introduce the recent results on the vulnerable option pricing and discuss the future work on vulnerable option.

Keywords Credit risk, Vulnerable option, Review

- 48 - Special Session

Deep Learning and Image Process

Han-Soo Choi (Seoul National University)

Hyomin Ahn (Seoul National University)

Geonho Hwang (Seoul National University)

Yea Chan Park (Seoul National University) KSIAM 2020 Annual Meeting ------

Squeezed Fire Segmentation Model using Deep Learning for Outdoor Images on Mobile Device

Kyungmin Song 1 Han-Soo Choi 2 and Myungjoo Kang 31

1) Department of Computational Science and Technology, Seoul National University, Seoul 151-742, KOREA 2) Research institute of Mathematics, Seoul National University, Seoul 151-742, KOREA 3) Department of Mathematical Sciences, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT Image-based fire events prediction is widely applied, but the current predictive methods are difficult to implement because of low performance and high specifications. In this paper, to we propose binary semantic segmentation for fire images by employing deep learning that can be applied to embedded devices such as Jetson TX2. Here, we propose the confusion block that the model can be executed more active training proceed. From these study, we achieved a significantly small-sized network for fire segmentation with the highest performance.

REFERENCES

1. Yuan, Feiniu and Zhang, Lin and Xia, Xue and Wan, Boyang and Huang, Qinghua and Li, Xuelongg. Deep smoke segmentation. Neurocomputing, Vol. 357, pp. 248–260. 2019 2. Tuba, Viktor and Capor-Hrosik, Romana and Tuba, Eva. Forest Fires Detection in Digital Images Based on Color Features. International Journal of Education and Learning Systems, Vol. 2, 2017 3. Quan, Tran Minh and Hildebrand, David GC and Jeong, Won-Ki. Fusionnet: A deep fully residual convolutional neural network for image segmentation in connectomics. arXiv preprint arXiv:1612.05360. 2016 4. Drozdzal, Michal and Chartrand, Gabriel and Vorontsov, Eugene and Shakeri, Mahsa and Di Jorio, Lisa and Tang, An and Romero, Adriana and Bengio, Yoshua and Pal, Chris and Kadoury, Samuel. Learning normalized inputs for iterative estimation in medical image segmentation. Medical image analysis, Vol. 44, pp. 1-13. 2018

1 1, 2 : equally contribution

- 50 - KSIAM 2020 Annual Meeting ------

Dynamic Background Subtraction With Masked RPCA

Hyomin Ahn 1 ,Myungjoo Kang 1

1) Department of Mathematics, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Hyomin Ahn, [email protected]

ABSTRACT Robust principal component analysis(RPCA) has been proven effective in modeling the static background of videos. However, because a dynamic background cannot be represented by a low-rank matrix, measures additional to the RPCA are required. In this thesis, we propose masked RPCA to process backgrounds containing moving textures. First-order Marcov ran- dom field is used to generate a mask that roughly labels moving objects and backgrounds. To estimate the background, the rank minimization process is then applied with the mask multi- plied. During the iteration, the background rank increases as the object mask expands, and the weight of the rank constraint term decreases, which increases the accuracy of the background. We compared the proposed method with state-of-art, end-to-end non-deep learning methods to demonstrate its advantages.

- 51 - KSIAM 2020 Annual Meeting ------

Discrete Conditioned Continuous Variational Autoencoder

Jaewoong Choi 1 , Geonho Hwang 1 and Myungjoo Kang 1

1) Department of Mathematical Sciences, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT Recently, several attempts have been made to integrate the discreteness of data into the dis- entangling frame in the VAE based disentangling models. However, most of the attempts had a limitation assuming statistical independence between continuous and discrete variables. We treat this problem by conditioning the continuous variable by the discrete variable which can model the disentanglement inside each class and universal variations across all classes.

- 52 - KSIAM 2020 Annual Meeting ------

Rainy Image Restoration with Hierarchical Structure

Yeachan Park 1 Myeongho Jeon 1 and Junho Lee 1

1) Department of Mathematical Science, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang [email protected]

ABSTRACT We present a new image restoration method of rainy images. We propose a wide range of non- local method and hierarchical structure. We also apply a new data augmentation strategy. Ex- perimental results show that our proposed model outperforms other models.

- 53 - Special Session

Finance, Fishery, Manufacture Industrial Mathematics Center on Big Data

Changsin Kim (National Institute of Fisheries Science)

Seong-Uk Nam (Pusan National University)

Yuanmeng Hu (Pusan National University)

Sat byul Seo (Kyungnam University)

Sang-hyup Seo (NIMS) KSIAM 2020 Annual Meeting ------

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- 55 - KSIAM 2020 Annual Meeting ------

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- 57 - KSIAM 2020 Annual Meeting ------

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- 58 - KSIAM 2020 Annual Meeting ------

COST SENSITIVE MACHINE LEARNING MODEL FOR CREDIT CARD DELIQUENCY PREDICTION

Seong-Uk Nam 1

1) Department of Mathematics, Pusan National University, KOREA

Corresponding Author : Seong-Uk Nam, [email protected]

ABSTRACT In recent years, there has been an increasing tendency to use machine learning models in various fields. In this paper, we would like to examine the example of Busan Bank of the financial field. The problem we are trying to solve is to distinguish a delinquent among credit card users, Further, we are more interested in credit card users who has spent more on credit card payments. The cost sensitive machine learning model are used in here. By using the cost sensitive model, we could put more weight on credit card users who spent more money than others. A study for cost sensitive model use the Bayes minimum risk classifier[1], but in here, we simply use the cost sensitive learning model by defining the empirical loss as:

1 n Remp(h)= wi ∗ L(h(xi),yi) (1) n i=1 , where h is a hypothesis function, L() is a loss function, xi is a i-th pattern, yi is a i-th label, and wi is a weight for i-th sample. As a result, we was able to design a model that took into account actual costs. How to utilize it remained as a challenge.

REFERENCES

1. Almhaithawi, Doaa and Jafar, Assef and Aljnidi, Mohamad, Example-dependent cost- sensitive credit cards fraud detection using SMOTE and Bayes minimum risk, SN Applied Science, Springer, 2020.

- 59 - KSIAM 2020 Annual Meeting ------





   
 
  
  

 
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- 60 - KSIAM 2020 Annual Meeting ------


 
  

 
  
  

  
 

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- 61 - KSIAM 2020 Annual Meeting ------

OPHTHALMIC DISEASE DIAGNOSIS BASED ON CONVOLUTIONAL NEURAL NETWORK

Sang-hyup SEO 1 , Youngho WOO 2 and Hyojung LEE 1

1) Busan Center for Medical Mathematics, National Institute for Mathematical Science, Busan 49241, Republic of Korea 2) National Institute for Mathematical Science, Daejeon 34047, Republic of Korea

Corresponding Author : Sang-hyup SEO, [email protected]

ABSTRACT Recently, old people with ophthalmic diseases have been increased in Korea. Diabetic retinopa- thy(DR), aged macular degeneration(AMD), and glaucoma are major ophthalmic diseases, which can lead to the vision damage. The old people need regular checkup for these diseases with a fundus camera for eyes. However, it is difficult to be inspected in advance and regularly, due to the limited medical environment including the number of doctors and tertiary-care hospi- tals. Here, an Artificial Intelligence (A.I.) is developed through the research project. Early detec- tion and diagnosis are available by employing the A.I. for ophthalmic diseases using the image data of fundi of eyes. Moreover, the diagnosis results obtained from the A.I. model will help both non-ophthalmic doctors and ophthalmic doctors to give suitable suggestions to patients. Finally, it can be useful for the regular checkup and early diagnosis of ophthalmic diseases. In this talk, we will introduce the developed A.I. model and the training process to identify the main three ophthalmic diseases from the image data.

REFERENCES

1. Yoo, Hyeong-gon and Lee, Jae-hong, Funduscopic Examination, Naewae-haksool, 2013.

- 62 - Special Session

Deep Learning for Digital Dentistry

Sung Ho Kang (NIMS)

Hye sun Yun (Yonsei University)

Taejun Jang (Yonsei University)

Hyeon Cheol Jo (Yonsei University) KSIAM 2020 Annual Meeting ------

Automatic three-dimensional cephalometric landmark detection system using volume projection rendering image-based reinforcement learning

Sung Ho Kang 1, Kiwan Jeon 1 and Sang-Hwy Lee2

1) Division of Medical Mathematics, National Institute of Mathematical Science, Daejeon, Republic of Korea 2) Department of Oral and Maxillofacial Surgery, Oral Science Research Center, College of Dentistry, Yonsei University, Seoul, Republic of Korea

Corresponding Author: Sung Ho Kang, [email protected]

ABSTRACT

This talk presents a new approach to automatic three-dimensional (3D) cephalometric landmark detection system for diagnosis, surgical planning, and treatment evaluation. Manual annotation of such landmarks is a time consumed task and can lead to expert errors. In particular, 3D cephalometric landmark detection methods have been limited to computational complexity and computing performance. We propose a volume projection rendering image- based reinforcement learning(RL) which use various anatomical view with transparency preprocessing. Since the proposed method uses a volume rendering technique, there is no need for prior segmentation to create a 3D mesh object. In the initial or post-op cephalometric diagnosis, it is possible to check the reference planes using the 3D prediction point through acquiring CT data simultaneously.

- 64 - KSIAM 2020 Annual Meeting ------

 
 
 
  

 

 




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- 65 - KSIAM 2020 Annual Meeting ------

A fully automated method for 3D individual tooth identification and segmentation in dental CBCT

Tae Jun Jang1, Kang Cheol Kim1, Hyeon Cheol Jo1, and Jin Keun Seo1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, KOREA

Corresponding Author: Kang Cheol Kim

ABSTRACT

Accurate and automatic segmentation of three-dimensional (3D) individual teeth from cone- beam computerized tomography (CBCT) images is a challenging problem because of the difficulty in separating an individual tooth from adjacent teeth and its surrounding alveolar bone. Thus, this paper proposes a fully automated method of identifying and segmenting 3D individual teeth from dental CBCT images. The proposed method addresses the aforementioned difficulty by developing a deep learning-based hierarchical multi-step model. First, it automatically generates upper and lower jaws panoramic images to overcome the computational complexity caused by high-dimensional data and the curse of dimensionality associated with limited training dataset. The obtained 2D panoramic images are then used to identify 2D individual teeth and capture loose- and tight- regions of interest (ROIs) of 3D individual teeth. Finally, accurate 3D individual tooth segmentation is achieved using both loose and tight ROIs. Experimental results showed that the proposed method achieved an F1 score of 94.19% for tooth identification and a Dice score of 94.55% for individual 3D tooth segmentation. The results demonstrate that the proposed method provides an effective clinical and practical framework for digital dentistry.

- 66 - KSIAM 2020 Annual Meeting ------

AI based digital platform integrating 3D multi modal Hyeon Cheol Jo 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, KOREA

Corresponding Author: Jin Keun Seo, [email protected]

ABSTRACT

In this study, we developed AI based digital platform integrating CBCT data and oral scan data and others. This platform enables fast accurate and convenient future dental treatment by building a digital workflow.

- 67 - Special Session

Domain Decomposition Methods and Related Methods I

Dongho Kim (Yonsei University)

Jongho Park (KAIST)

YoungKyu Lee (KAIST)

Hyea Hyun Kim (Kyung Hee University) KSIAM 2020 Annual Meeting ------

ADAPTIVE MULTI-LEVEL ALGORITHM FOR NONLINEAR PROBLEMS

Dongho KIM 1 , Eun-Jae PARK 2 and Boyoon SEO 3

1) University College, Yonsei University, Seoul 03722, KOREA 2) Department of Computational Science and Engineering, Yonsei University, Seoul 03722, KOREA 3) Department of Mathematics, Yonsei University, Seoul 03722, KOREA

Corresponding Author : Dongho KIM, [email protected]

ABSTRACT In this paper, we derive a unified a posteriori error estimate for the approximate solutions of the multi-level algorithm developed in D. Kim, E.-J. Park & B. Seo [1] for a class of nonlinear problems. The multi-level algorithm using a two-grid idea is an efficient numerical method designed to resolve nonlinearities. The two-grid algorithm is first applied and in the subsequent process, uniform mesh refinement is exploited to deliver a desired accuracy and convergence; as the mesh is being refined, the solution on a given mesh is exploited as an accurate starting iterate for solutions on the next mesh level. The multi-level algorithm has quadratic convergence in the sense of (3). We apply this strategy to efficiently compute numerical solutions by adaptive mesh refinement. We emphasize that the multi-level algorithm on the adaptive meshes retains quadratic convergence of Newton’s method across different mesh levels, which is validated from the numerical results presented in the last section. In particular, existing a posteriori error estimates for the linear problem can be utilized to find reliable error estimators for the nonlinear problem. We mention that this approach is quite general and can be applied to any numerical scheme for a class of nonlinear problems. As applications, we consider the pseudostress-velocity formulation of the stationary Navier- Stokes equations (NSE) and the standard Galerkin formulation of a semilinear elliptic equations (SEE). The mixed finite element methods for the pseudostress-velocity formualtion have been recently established in for the Stokes [2] & [3] and the Navier-Stokes equations [4] & [5]. The pseudostress-velocity formualtion has several advantages: The pseudostress is nonsymmetric unlike stress tensor and approximated by the RTk elements, Raviart-Thomas elements of index k  0. Moreover, the approximation of the pressure, the velocity gradient, or even the stress can be algebraically obtained from the approximate value of the pseudostress.

MULTI-LEVEL ALGORITHM

For given C2 map G :Λ× X → Y , we consider the following nonlinear problem: Find (ν, φ) ∈ Λ × X such that

F (ν, φ):=φ + SG(ν, φ)=0, (1)

- 69 - KSIAM 2020 Annual Meeting ------where S ∈ L (Y ; X ) is a linear operator independent of ν. The approximation of nonlinear problem (1) is to find φh ∈ X such that

h h h Fh(ν, φ ):=φ + ShG(ν, φ )=0. (2)

Algorithm: Multi-level Algorithm Step 1: (Nonlinear Solver) Solve nonlinear system on initial mesh Find φ0(ν) ∈ X0 such that F0(ν, φ0(ν)) = 0. Step 2: (Linear Solver) Update on each mesh level j with one Newton iteration For j =1, 2, ···, find φj(ν) ∈ Xj such that DφFj(ν, φj−1(ν))(φj(ν)−φj−1(ν)) = −Fj(ν, φj−1(ν)).

Theorem 1 (a priori error bound) Assume that (H1)-(H4) hold. Let φhj (ν) be nonsingular solutions of (2) on Xj. And let φj(ν) be solutions obtained from Step 2 of Algorithm.Then ¯ ∗ ∗ hj there exist ξ>0 with ξ  ξ and h0 > 0 such that for hj  h0, φ (ν) ∈ B(φ(ν),ξ/2) and h φj(ν) belongs to the ball B(φ j (ν),ξ/2) for j  1. Moreover, for positive constants K2 & K3 independent of mesh sizes hj and ν, we have the following quadratic relation

hj hj 2 φ (ν) − φj(ν)X  K2φ (ν) − φj−1(ν)X , (3) and we have an a priori estimate  2 φ(ν) − φj(ν)X K3 (S − Sj)G(ν, φ(ν))X + (S − Sj)G(ν, φ(ν))X  2 + φ(ν) − φj−1(ν)X .

Theorem 2 (a posteriori error bound) Assume that (H1)-(H4) hold. Let φ(ν) be a nonsingular solution of (1) and let φj(ν) be the approximate solution produced by Algorithm. Then, there ex- ∗ ∗ ∗ hj ists 0

−1 φ(ν) − φj(ν)X  2DφF (ν, φj(ν)) X ;X F (ν, φj(ν))X  K1F (ν, φj(ν))X .

REFERENCES

1. D. Kim, E.-J. Park, and B. Seo, Convergence of Multi-level Algorithms for a Class of Nonlinear Problems, J. Sci. Comput. 84 (2020), no. 2, 34. 2. Z. Cai and Y. Wang, A multigrid method for the pseudostress formulation of Stokes problems, SIAM J. Sci. Comput., 29 (2007), No. 5, pp. 2078–2095. 3. C. Carstensen, D, Kim, and E. J. Park, A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem, SIAM J. Numer. Anal., 49 (2011), No. 6, pp. 2501–2523. 4. Z. Cai, C. Wang, and S. Zhang, Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations, SIAM J. Numer. Anal., 48 (2010), No. 1, pp. 79–94. 5. D. Kim, E.-J. Park, and B. Seo, Optimal error estimates for the pseudostress formulation of the Navier-Stokes equations, Applied Mathematics Letters, 78 (2018), pp. 24–30

- 70 - KSIAM 2020 Annual Meeting ------

Accelerated Additive Schwarz Methods for Convex Optimization

Jongho Park 1

1) Department of Mathematical Sciences, KAIST, Daejeon 34141, KOREA

Corresponding Author : Jongho Park, [email protected]

ABSTRACT Based on an observation that additive Schwarz methods for general convex optimization can be interpreted as gradient methods [3], we propose an acceleration scheme for additive Schwarz methods. Adopting acceleration techniques developed for gradient methods such as momen- tum and adaptive restarting [1,2], the convergence rate of additive Schwarz methods is greatly improved. The proposed acceleration scheme does not require any a priori information on the levels of smoothness and sharpness of a target energy functional, so that it can be applied to various convex optimization problems. Numerical results for linear elliptic problems, nonlinear elliptic problems, nonsmooth problems, and nonsharp problems are provided to highlight the superiority and the broad applicability of the proposed scheme.

REFERENCES

1. Beck, A. and Teboulle, M. “A fast iterative shrinkage-thresholding algorithm for linear inverse problems”, SIAM Journal on Imaging Sciences, Vol 2, 2008, pp. 183–202. 2. O’Donoghue, B. and Candes, E., “Adaptive restart for accelerated gradient schemes”, Foundations of Computational Mathematics, Vol. 15, 2015, pp. 715–732. 3. Park, J., “Additive Schwarz methods for convex optimization as gradient methods”, SIAM Journal on Numerical Analysis, Vol. 58, 2020, pp. 1495–1530.

- 71 - KSIAM 2020 Annual Meeting ------

Parareal neural networks emulating a parallel-in-time algorithm

Youngkyu Lee 1 , Jongho Park 1 and Chang-Ock Lee 1

1) Department of Mathematical Sciences, KAIST, Daejeon 34141, KOREA

Corresponding Author : Chang-Ock Lee, [email protected]

ABSTRACT As deep neural networks (DNNs) [2] become deeper, the training time increases. In this per- spective, multi-GPU parallel computing has become a key tool in accelerating the training of DNNs. In this paper, we introduce a novel methodology to construct a parallel neural network that can utilize multiple GPUs simultaneously from a given DNN. We observe that layers of the DNN can be interpreted as time steps of a time-dependent problem and can be parallelized by emulating a parallel-in-time algorithm called parareal [3]. The parareal algorithm consists of fine structures which can be implemented in parallel and a coarse structure which gives suitable approximations to the fine structures. By emulating it, the layers of the DNN are torn to form a parallel structure, which is connected using a suitable coarse network. We report accelerated and accuracy-preserved results of the proposed methodology applied to ResNet-1001 [1] on various datasets.

REFERENCES

1. He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian, “Identity mappings in deep residual networks", European Conference on Computer Vision, pp 630–645, Springer, Cham, 2016. 2. LeCun, Yann and Bengio, Yoshua and Hinton, Geoffrey, “Deep learning”, Nature, Vol. 521, 2015, pp. 436-444. 3. Lions, Jacques-Louis and Maday, Yvon and Turinici, Gabriel, “Résolution d’EDP par un schéma en temps «pararéel»", Comptes Rendus de l’Académie des Sciences-Series I- Mathematics, Vol. 332, 2001, pp. 661-668.

- 72 - KSIAM 2020 Annual Meeting ------

An adaptive BDDC algorithm for three dimensional problems with an enhanced edge eigenvalue problem

Hyea Hyun Kim 1 and Junxian Wang 2

1) Department of Applied Mathematics, College of Applied Science, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 17104, Republic of Korea 2) Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, P.R.China

Corresponding Author : Hyea Hyun Kim, [email protected]

ABSTRACT An adaptive BDDC (Balancing Domain Decomposition by Constraints) preconditioner is con- sidered for three dimensional elliptic problems with coefficients of high contrast and random variation. For such problems, the classical primal unknowns in the BDDC preconditioner, such as values at subdomain vertices, and average values over subdomain edges or faces, are not enough to give a scalable coarse problem. Specially designed eigenvalue problems related to the estimate of condition numbers are considered and problematic eigenvectors are selected from the eigenvalue problems to enrich the set of primal unknowns so as to make the resulting coarse problem in the preconditioner more scalable. In three dimensions, eigenvalue problems are formed on each face or edge nodal equivalence classes. For the case of edges, proposed eigenvalue problems in previous studies are not satisfactory while those for faces perform very effectively. For the case of edges, the eigenvalues are not clearly separated in contrast to the case of faces and most eigenvectors are thus often selected in practice, see [1–3]. The eigen- value problems can be enhanced by utilizing prior selected primal constraints as proposed in [4]. In this paper, this new idea is adopted when forming edge eigenvalue problems. The primal un- knowns at subdomain vertices and the adaptive primal unknowns chosen from face eigenvalue problems are included when forming edge eigenvalue problems. For the BDDC preconditioner with the enhanced edge eigenvalue problems, the bound of condition numbers is shown to be dependent on the given tolerance value, that is used to select the problematic eigenvectors from face and edge eigenvalue problems, but independent of the contrast in the coefficients of the model problem. In addition, numerical results are provided to verify that the new edge eigen- value problem gives a more optimal set of primal unknowns compared to those in the previous studies.

REFERENCES

1. Calvo, J. C., and Widlund, O. B. “An adaptive choice of primal constraints for BDDC domain decomposition algorithms”, Electron. Trans. Numer. Anal., Vol. 45, 2016, pp. 524- 544. 2. Klawonn, A., Kuhn, M., and Rheinbach, O., “Adaptive coarse spaces for FETIDP in three dimensions”, SIAM J. Sci. Comput., Vol. 38, 2016, pp. A2880-A2911. 3. Kim, H. H., Chung, E., and Wang, J, “BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients”, Journal of Computational Physics, Vol. 349, 2017, pp. 191-214. 4. Pechstein, C., and Dohrmann, C. R., “A unified framework for adaptive BDDC”, Electron. Trans. Numer. Anal., Vol. 46, 2017, pp. 273-336. Special Session

Regularity and singularity of some partial differential eqauations related to fluid flows

Sukjung Hwang (Yonsei University)

Jinmyoung Seok (Kyonggi University)

Minsuk Yang (Yonsei University)

In-Jee Jeong (KIAS) KSIAM 2020 Annual Meeting ------

Regularity of nonlinear heat equations

Sukjung HWANG 1

1) Department of Mathematics, Yonsei University, Seoul, SOUTH KOREA

Corresponding Author : Sukjung HWANG [email protected] or [email protected]

ABSTRACT In this talk, I would like to explain the Holder¨ continuity on local solutions to equations of p−Laplacian type and porous medium type and discuss recent development.

ACKNOWLEDGEMENT

This author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Tech- nology (2020R1I1A1A0107011511).

REFERENCES

1. K. Adimurthi, S. Hwang, “Uniform boundedness for weak solutions of quasilinear parabolic equations”, Proc. Amer. Math. Soc. , Vol. 148 (2020), pp. 653-665. 2. Y. Chung, S. Hwang, K. Kang, J. Kim, “ Holder¨ continuity of Keller-Segel equations of porous medium type coupled to fluid equations”, J. Differential Equations, Vol. 263, 2017, pp. 2157-2212. p q 3. S, Hwang, Y.Zhang, “Continuity results for degenerate diffusion equations with Lt Lx drifts ”, arXiv:1906.04961.

- 75 - KSIAM 2020 Annual Meeting ------

DYNAMICAL STABILITY OF UNIFORMLY ROTATING BINARY STARS AND GALAXIES

Juhi JANG 1 and Jinmyoung SEOK 2

1) Department of Mathematics, University of South California, Los Angeles, CA, USA 2) Department of Mathematics, Kyonggi University, Suwon 16227, KOREA

Corresponding Author : Jinmyoung SEOK, [email protected]

ABSTRACT In this talk, we are concerned with dynamically stability of uniformly rotating binary stars and galaxies, which are represented as stationary solutions to Euler-Poisson equations and Vlasov- Poisson equations respectively. These solutions were constructed as minimizers of suitable vari- ational problems by McCann [2] in which some kind of structural stability on them is discussed. This talk focuses on the nonlinear dynamical stability of them, based on Cazenave-Lions type arguments [1] exploiting variational characterization of stationary solutions. We will see that the uniqueness of a minimizer, which is one of main results of our work, plays a indispensable role in analysis.

REFERENCES

1. Cazenave, T. and Lions, P.-L., “Orbital stability of standing waves for some nonlinear Schrodinger¨ equations”, Comm. Math. Phys., 85 (1982), no. 4, 549–561. 2. McCann, Robert J., “Stable rotating binary stars and fluid in a tube”, Houston J. Math.,32 (2006), no. 2, 603–631.

- 76 - KSIAM 2020 Annual Meeting ------

New regularity criterion for suitable weak solutions of the surface growth model

Jongkeun Choi 1 and Minsuk Yang 2

1) Department of Mathematics Education, Pusan National University, Busan 46241, Korea 2) Department of Mathematics, Yonsei University, 50 Yonseiro, Seodaemungu, Seoul 03722, Korea

Corresponding Author : Minsuk Yang, [email protected]

ABSTRACT We present a new regularity criterion for suitable weak solutions of the one-dimensional surface growth initial-value problem in terms of mixed Lebesgue norms.

REFERENCES

1. Choi, J. and Yang, M., “New regularity criterion for suitable weak solutions of the surface growth model”, Applied Mathematics Letters, Vol. 112, 2021, 106720.

- 77 - KSIAM 2020 Annual Meeting ------

           

   

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- 78 - Special Session

Deep Learning for Medical Imaging

Hyoung Suk Park (NIMS)

Chang Min Hyun (Yonsei University)

Seong Hyeon Baek (Yonsei University)

Seo Taek Kong (VUNO Inc.) KSIAM 2020 Annual Meeting ------

A Penalized Weighted Least Squares Method with a Deep Learning Prior

Hyoung Suk Park 1 Kyungsang Kim 2 Kiwan Jeon 1

1) National Institute for Mathematical Sciences, Daejeon, 34047, Korea 2) Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114 USA.

Corresponding Author : Hyoung Suk Park, e-mail : [email protected]

ABSTRACT In low-dose computed tomography (LDCT), a penalized weighted least squares (PWLS) ap- proach that incorporates the Poisson statistics of X-ray photons can significantly reduce exces- sive quantum noise. To improve the quality of LDCT images, prior information such as the total variation, Markov random field, and nonlocal mean, can be imposed onto the target im- age. However, this information may be limited to reflect the characteristics of the target images, thereby resulting in unexpected side effects (e.g. blurry images). In this talk, we introduce a PWLS method by combining it with a deep learning prior [1] to improve the image quality in LDCT. We found that our method reduced quantum noise in LDCT images and improved legion visibility, thereby outperforming other PLWS methods, by imposing existing priors such as the total variation and the nonlocal mean.

REFERENCES

1. H.S. Park, K. Kim, and K. Jeon, “Low-Dose CT Image Reconstruction With a Deep Learning Prior”, IEEE Access, Vol. 8, pp. 158647–158655, 2020.

- 80 - KSIAM 2020 Annual Meeting ------

Metal Artifact Reduction in Low-Dose Dental CBCT

Chang Min Hyun 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, KOREA

Corresponding Author: Chang Min Hyun, [email protected]

ABSTRACT

This talk presents a beam hardening artifact correction method for low-dose dental cone beam computerized tomography (CBCT). In dental CBCT applications, it is important to improve the quality of maxillofacial imaging, where soft tissue details are not required. Compared to standard CT, the additional difficulty of dental CBCT comes from the problems caused by offset detector, FOV truncation, and low signal-to-noise ratio due to low X-ray irradiation. To address these problems, we proposed a method that primarily performs a sinogram adjustment in the direction of enhancing data consistency, considering the situation according to the FOV truncation and offset detector. This sinogram correction algorithm significantly reduces beam hardening artifacts caused by high-density materials such as teeth, bones, and metal implants, while tending to amplify special types of noise. To suppress such noise, a deep convolutional neural network is complementarily used, where CT images adjusted by the sinogram correction are used as the input of the neural network. If time is permitted, the photon starvation issue would be discussed.

- 81 - KSIAM 2020 Annual Meeting ------



    
 
  

   
 
 

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- 82 - KSIAM 2020 Annual Meeting ------

ALLEVIATING ANNOTATION COSTS BY COMBINING ACTIVE AND SEMI-SUPERVISED LEARNING

Seo Taek Kong1,*, Soomin Jeon1, and Kyu-Hwan Jung1

1) VUNO Inc., Seoul, Korea

[email protected]

ABSTRACT

Training deep neural networks (DNNs) requires excessive amounts of labeled data, which is prohibitively expensive for medical imaging. Statistical learning theory and algorithms have attempted to alleviate this annotation cost by either actively interacting with the dataset and querying those considered most important or utilizing unlabeled data which is usually more accessible. Deep learning-based active learning (AL) algorithms have been developed with the former objective, but their performances can only outperform random sampling, or passive learning, by a modest margin. In contrast, the latter approach has seen great success with semi- supervised learning (SSL) algorithms, performing on par with fully-supervised models with far less labeled samples. Motivated by empirical pessimism of AL algorithms and success of SSL, we propose to shift the objective of AL. Rather than querying instances that help generalize upon labeling, we propose to design AL to ease optimization and use SSL to constrain the hypothesis class to those that generalize well. In this direction, we designed a novel AL algorithm using neural tangent kernels and demonstrated its efficacy to enhancing the sample complexities associated with deep learning.

REFERENCES

1. Jacot, A., Gabriel, F., and Hongler, C., “Neural tangent kernel: Convergence and generalization in neural networks,” Advances in Neural Information Processing Systems, 31, pp. 8571–8580. Curran Associates, Inc., 2018. 2. G¨opfert, C., Ben-David, S., Bousquet, O., Gelly, S., Tolstikhin, I., and Urner, R., “When can unlabeled data improve the learning rate?” Conference on Learning Theory, 2019. 3. Huang, J., Child, R., Rao, V. Liu, H., Satheesh, S., and Coates, A., “Active learning for speech recognition: the power of gradients.” arXiv preprint arXiv:1612.03226, 2016. 4. Sohn, K., Berthelot, D., Li, C., Zhang, Z., Carlini, N., Cubuk, E.D., Kurakin, A., Zhang, H., and Raffel, C., “Fixmatch: Simplifying semi-supervised learning with consistency and confidence.” arXiv preprint arXiv:2001.07685, 2020. 5. D. Wang and Y. Shang. “A new active labeling method for deep learning”. International Joint Conference on Neural Networks (IJCNN), pp. 112–119, 2014.

- 83 - Special Session

Domain Decomposition Methods and Related Methods II

Eun-Hee Park (Kangwon National University)

Hee Jun Yang (Kyung Hee University)

Dong-wook Shin (Myongji University)

Seungil Kim (Kyung Hee University) KSIAM 2020 Annual Meeting ------

DD solvers for the Stokes problem with a varying viscosity coefficient

Hyea Hyun Kim 1 , Eun-Hee Park 2

1) Department of Applied Mathematics, Kyung Hee University, Yongin 17104, South Korea 2) Division of Liberal Studies, Kangwon National University, Samcheok 25913, South Korea

Corresponding Author : Eun-Hee Park, [email protected]

ABSTRACT In this talk we will discuss domain decomposition solvers for the Stokes problem with a varying viscosity coefficient. A FETI-DP algorithm for the Stokes problem with a constant viscosity was proposed in the previous work by the authors. In a similar manner, a finite element discrete problem is obtained by adopting the inf-sup stable finite element space where the functions in the pressure space can be discontinuous across the element boundary. First based on a non- overlapping subdomain partition, a multi-domain problem is considered, which is equipped with the continuity constraint across the subdomain interface. Then a FETI-DP formulation is derived by introducing Lagrange multipliers to enforce the continuity constraint. For iterations on the dual problem in FETI-DP formulation, preconditioners are proposed, where the scaling procedure is employed to treat the ill-conditioned property in connection with the presence of a discontinuous viscosity. Finally, Theoretical results for the condition number estimate of the preconditioned problem will be presented along with numerical results.

REFERENCES

1. X. Xie, J. Xu, and G. Xue, Uniformly-stable finite element methods for Darcy-Stokes- Brikman models, J. Comput. Math. 26(2008), pp. 437–455. 2. H.H. Kim, C.-O. Lee, and E.-H. Park, A FETI-DP formulation for the Stokes problem without primal pressure components, SIAM J. Numer. Anal. 47(2010), pp. 4142–4162. 3. X. Tu, and J. Li, A unified dual-primal fintie element tearing and interconnecting approach for imcompressible Stokes equations, Internat. J. Numer. Methods Engrg., 94(2013), pp. 128–149.

- 85 - KSIAM 2020 Annual Meeting ------

EFFICIENT MESH GENERATION UTILIZING ADAPTIVE INITIAL GRIDS AND DOMAIN DECOMPOSITION PRECONDITIONERS

Hee Jun Yang 1 , Kiwan Jeon 2 and Hyea Hyun Kim 3

1) Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Republic of Korea 2) Division of Medical Mathematics, National Institute for Mathematical Sciences, Yuseong-daero 1689beon-gil 70, Yuseong-gu, Daejeon, 34047, Republic of Korea 3) Department of Applied Mathematics, College of Applied Science, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 17104, Republic of Korea

Corresponding Author : Hyea Hyun Kim, [email protected]

ABSTRACT To generate a mesh in a physical domain, an initial mesh of a polygonal domain that approxi- mates the physical domain is introduced. An optimization problem by utilizing a mesh quality function is considered for the displacement on the initial body centered cubic (BCC) mesh points with constraints on the boundary of physical domain, which maintains a good quality of triangles while aiming at fitting the initial mesh to the boundary of the physical domain. The BCC mesh can give a more efficient node ordering for the matrix vector multiplication and the constraints are provided by the level set function of the physical domain [1]. The solution to the optimization problem can be obtained by using the Frechet´ derivative of the objective func- tion. The resulting nonlinear algebraic system can be solved by the Picard or Newton method. To handle a physical domain with a complex boundary such as a human organ or body, a very fine initial mesh is often required but the solution time for the nonlinear algebraic system be- comes problematic. To overcome this limitation, adaptively refined grid cells for the initial BCC mesh can be used and the algebraic system in the Picard or Newton method can be solved ef- ficiently by an iterative method using preconditioners [2,3]. The use of iterative solvers with domain decomposition preconditioners gives a parallel meshing algorithm that makes the pro- posed scheme more efficient for large scale problems. Numerical results for various test models are included.

REFERENCES

1. Teran, J., Molino, N., Fedkiw, R., and Bridson, R, ”Adaptive physics based tetrahedral mesh generation using level sets”, Engineering with Computers, Vol. 21, 2005, pp. 2-18. 2. Li, J., and Widlund, O. B, ”FETI-DP, BDDC, and block Cholesky methods”, International journal for numerical methods in engineering, Vol. 66.2 2006, pp. 250-271. 3. Kim, H. H., Chung, E., and Wang, J, ”BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients”, Journal of Computational Physics, Vol. 349, 2017, pp. 191-214.

- 86 - KSIAM 2020 Annual Meeting ------

A hybrid difference method and postprocessing

Dong-wook Shin∗, 1 , Youngmok Jeon 2 and Eun-Jae Park 3

1) Department of Mathematics, Myongji University, Yongin 17058, KOREA Email: [email protected]. 2) Department of Mathematics, Ajou University, Suwon 16499, KOREA 3) Department of Computational Science and Engineering, Yonsei University, Seoul 03722, KOREA

ABSTRACT In this talk, we consider a hybrid difference method (HDM) which was introduced and ana- lyzed by Jeon-Park-Shin (Comput. Methods Appl. Math., 2017) for the second-order elliptic problems. This method can be viewed as a finite difference version of hybrid discontinuous Galerkin methods (Jeon-Park, SIAM J. Numer. Anal., 2010). The HDM is a locally conserva- tive method and it allows high-order approximations. Also, the method has great reduction in global degrees of freedom and its convergence is proved in the discrete energy norm. Since a few node points in each element are not used, the approximation value is evaluated on the axis parallel lines constructed by the node points of the HDM in Rd (d =2, 3). In the present work, the error estimate is analyzed by introducing a projection operator to obtain the optimal rate of convergence. Also, the HDM is developed and generalized to be a conforming method by introducing a postprocessing. Numerical results are presented to show the performance of the proposed method, which support our theoretical findings.

*Speaker

- 87 - KSIAM 2020 Annual Meeting ------

Convergence analysis of a double sweep domain decomposition method for solving the Helmholtz equation

Seungil Kim

Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 20447, KOREA

Corresponding Author : Seungil Kim, [email protected]

ABSTRACT Abstract: In this talk we will discuss a double sweep domain decomposition method for solving the Helmholtz equation in waveguides. The double sweep preconditioner is defined in terms of transmission conditions based on high order absorbing boundary conditions such as PML (perfectly matched layer) or CRBC (complete radiation boundary condition). It seeks for an approximate solution in H1 of local subdomains which is discontinuous across interfaces of nonoverlapped subdomains. We show the convergence of approximate solutions to the problem in both continuous level and discontinuous level.

- 88 - Special Session

Nonlinear differential eqautions : modeling of collective motion

Seok-bae Yun (Sungkyunkwan University)

Woojoo Shim (Seoul National University)

Jinwook Jung (Seoul National University)

Hansol Park (Seoul National University) KSIAM 2020 Annual Meeting ------

Entropy production esimate of the ES-BGK model below the critical Prandtl parameter

Doheon Kim 1 , Meongsu Lee ?? and Seok-bae Yun 2

1) School of Mathematics, Korea Institutefor Advanced Study, Seoul 02455, Korea 2) Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

Corresponding Author : Seok-Bae Yun, [email protected]

ABSTRACT Ellipsoidal BGK model (ES-BGK) is a general version of the BGK model where the local Maxwellian is generalized to a ellipsoidal Gaussian with a Prandtl parameter so that the model can produce the correct transport coefficient in the Navier-Stokes limit. The correct Prandtl number is obtained when the Prandtl parameter is -1/2, but various familiar structure of the original BGK model breaks down in this case, which give rise to various interesting mathemati- cal issues. In this talk, we consider our recent result on the entropy-entropy production estimate of the ES-BGK model. Unexpected is that the estimate holds even below the critical Prandtl parameter -1/2.

- 90 - KSIAM 2020 Annual Meeting ------

A CUCKER-SMALE INSPIRED DETERMINISTIC MEAN FIELD GAME WITH VELOCITY INTERACTIONS

Filippo SANTAMBROGIO 1 and Woojoo SHIM 2

1) Universite´ Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne, France and Institut Universitaire de France 2) The Research Institute of Basic Sciences, Seoul National University, Seoul, KOREA

Corresponding Author : Filippo SANTAMBROGIO, [email protected]

ABSTRACT We introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference between their own velocity and that of the other agents they meet. We aims at proposing a simple model which is a bridge between some collective motion models such as the well-studied Cucker- Smale model, mainly applied to flock behavior, and the theory of Mean Field Games. We prove existence of an equilibrium in a Lagrangian setting by using its variational structure, and then study its properties and regularity.

- 91 - KSIAM 2020 Annual Meeting ------

ON THE CAUCHY PROBLEM FOR THE PRESSURELESS EULER–NAVIER–STOKES SYSTEM IN THE WHOLE SPACE

Young-Pil CHOI 1 and Jinwook JUNG 2

1) Department of Mathematics, Yonsei University, Seoul 03722, KOREA 2) Research Institute of Basic Sciences, Seoul National University, Seoul 08826, KOREA

Corresponding Author : Jinwook JUNG, [email protected]

ABSTRACT In this talk, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier–Stokes equations where the cou- pling of two equations is through the drag force. We establish the global-in-time existence and uniqueness of classical solutions for that system when the initial data are sufficiently small and regular. Main difficulties arise in the absence of pressure in the Euler equations. In order to resolve it, we properly combine the large-time behavior of classical solutions and the bootstrap- ping argument to construct the global-in-time unique classical solutions.

- 92 - KSIAM 2020 Annual Meeting ------

A Dynamical Systems Approach for the Shape Matching of Polytopes Along Rigid-Body Motions

Seung-Yeal Ha 1,2 Hansol Park 1

1) Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea 2) Korea Institute for Advanced Study, Hoegiro 85, 02455, Seoul Republic of Korea

Corresponding Author : Hansol Park, [email protected]

ABSTRACT We present a dynamical systems approach for geometric matchings in an ensemble of poly- topes along rigid-body motions. Each polytope can be characterized by a vertex set and edge or faces determined by vertices, and polygons and simplexes correspond to a polytope. For a geometric matching, we propose a system of dynamical system for the evolution of centroids and rotations of polytopes to match the vertices under rigid-body motions which can be de- composed as a composition of translation and rotations. Our proposed dynamical system acts on the product space (Rd × SO(d))N . The evolution of centroids can be described by the cou- pled linear second-order dynamical system with diffusive linear couplings, whereas rotations for the matching of vertices are described by the Lohe matrix model on SO(d)N . In particular, the Lohe matrix model has been derived from some set of physical principles compared to pre- vious works in which the Lohe matrix model were employed as a system dynamics. This is a contrasted difference between earlier works on the Lohe matrix model which has been adopted a priori for an aggregate modeling of matrices. We also provide an analytical result leading to the complete shape matchings for an ensemble of congruent polytopes, and several numerical examples to illustrate analytical results visually.

- 93 - General Sessions

General Session Ⅰ

General Session Ⅱ

General Session Ⅲ

General Session Ⅳ

General Session Ⅴ

General Session Ⅵ General Sessions

General Session I

Duk-Soon Oh (Chungnam National University)

Byungjoon Lee (The Catholic University of Korea)

Heejae Han (Seoul National University)

Chohong Min (Ehwa Woman University) KSIAM 2020 Annual Meeting ------

A Multigrid Method for 3D H(curl) Problems

Duk-Soon Oh 1

1) Department of Mathematics, Chungnam National University, Daejeon 34134, KOREA

[email protected]

ABSTRACT We design a V-cycle multigrid for problems arising from the edge elements in three dimensions. Since the smoothers in the traditional multigrid methods do not perform well for H(curl) vec- tor fields, special techniques for the smoothers are necessary. We introduce a new smoothing method which involves a domain decomposition preconditioner based on substructuring.

- 96 - KSIAM 2020 Annual Meeting ------

Optimal Preconditioners on Solving the Poisson equation with Neumann boundary conditions

Byungjoon Lee and Chohong Min October 20, 2020

Abstract We review Relaxed ILU and Perturbed MILU preconditioners in the case of Neumann boundary conditions, and present empirical results which indicate that the former is optimal in two dimensions and the latter is optimal in two and three dimensions. There is little difference in coding the optimal preconditioners and the conventional ones. A slight code change from the conventional to the optimal can result in significant speed ups in computational time. In our fluid simulation, the speed up reached about 3.3 and 2.0 with respect to Jacobi and ILU, respectively. To the best of our knowledge, these empirical results have not been rigorously verified yet. We present a formal proof for the optimality of Relaxed ILU in rectangular domains, and discuss its possible extension to general smooth domains and Perturbed MILU.

1 - 97 - KSIAM 2020 Annual Meeting ------

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- 98 - KSIAM 2020 Annual Meeting ------

GRADIENT EXPLOSION FREE ALGORITHM FOR TRAINING RECURRENT NEURAL NETWORKS

SEOYOUNG HONG1, HYERIN JEON1 , BYUNGJOON LEE2, AND CHOHONG MIN1

1) Department of Mathematics, Ewha Womans University, South Korea 2) Department of Mathematics, The Catholic University of Korea, South Korea

Corresponding Author: CHOHONG MIN,[email protected]

ABSTRACT

Exploding gradient is a widely known problem in training recurrent neural networks. The explosion problem has often been coped with cutting off the gradient norm by some fixed value. However, this strategy, commonly referred to norm clipping, is an ad hoc approach to attenuate the explosion. In this research, we opt to view the problem from a different perspective, the discrete-time optimal control with infinite horizon for a better understanding of the problem. Through this perspective, we fathom the region at which gradient explosion occurs. Based on the analysis, we introduce a gradient-explosion-free algorithm that keeps the training process away from the region. Numerical tests show that this algorithm is at least three times faster than the clipping strategy.

- 99 - General Sessions

General Session II

Hayeong Koh (Yonsei University)

Hyeuknam Kwon (Yonsei University)

Young Ju Lee (Texas State University)

Won-Kwang Park (Kookmin University) KSIAM 2020 Annual Meeting ------

PAC-BAYESIAN MARGIN BOUNDS WITH RANDOM INPUT NOISES

Hayeong Koh 1 , Jimin Lee 2 and Hi Jun Choe 1

1) Department of Mathematics Yonsei University Seoul 03722, Republic of Korea 2) Institute of Mathematical Sciences Ewha Womans University Seoul 03760, Republic of Korea

Corresponding Author : Hayeong Koh, [email protected]

ABSTRACT Machine learning shows state-of-the-art performance in various fields, but there are short theo- retical understandings of the process of how machine learning works. We especially wondered on the role of margin in the perturbations of inputs. And we present a generalization bound of classifiers with input noise using margin loss function and related terms to perturbation of input and parameters. For this, we assume that the input noises are random values following Gaus- sian distribution and apply the PAC-Bayesian framework. The additional generalization term caused by random noises is related to margin and exponentially inversely proportional to the noise level. We consider random noises and margin together, and it will be helpful to a better understanding of model sensitivity and the construction of robust generalization.

REFERENCES

1. Bartlett, Peter L and Foster, Dylan J and Telgarsky, Matus J, “Spectrally-normalized margin bounds for neural networks”, Advances in Neural Information Processing Systems 30, 2017, pp. 6240-6249. 2. Langford, John and Shawe-Taylor, John, “PAC-Bayes & margins”, Advances in neural information processing systems, 2003, pp. 439-446. 3. McAllester, David, “PAC-Bayesian model averaging”, Proceedings of the twelfth annual conference on Computational learning theory, 1999, pp. 164-170. 4. McAllester, David, “Simplified PAC-Bayesian margin bounds”, Learning theory and Kernel machines, 2003, pp. 203-215. 5. Neyshabur, Behnam and Bhojanapalli, Srinadh and Srebro, Nathan, “A pac-bayesian approach to spectrally-normalized margin bounds for neural networks”, International Conference on Learning Representations, 2018.

- 101 - KSIAM 2020 Annual Meeting ------

NUMERICAL METHOD FOR CRACK LOCALIZATION IN A CONCRETE MODEL USING ACOUSTIC EMISSION

Dong Geon Lim 1 , Byung Il Lee 2 and Hyeuknam Kwon 1

1) Department of Mathematics, Yonsei University, Wonju 26493, KOREA 2) Integrity Diagnostics Korea, Daejeon 34028, KOREA

Corresponding Author : Hyeuknam Kwon, [email protected]

ABSTRACT We developed numerical method to localize crack in a concrete domain. Cracks in a domain Ω cause acoustic waves (as shown in Fig. 1)) which reach to the boundary of Ω [1]. The waves are measured at a finite number of points on ∂Ω (as shown in Fig. 1). Using the measured waves on

Domain

measured signal

source signal

Figure 1. Appearance of crack causes wave source represented as red star. We measured the wave signal at some points of the boundary of the domain, represented as blue dots. ∂Ω, the goal is to find position of cracks in Ω. Under the assumption of homogeneous medium, we consider a velocity of wave propagation is constant. With the constant velocity, we can find the position of crack by minimizing the cost function ϕ(x, y, t)= ϕi,j(x, y, t) where ϕi,j is discrepancy of velocity at i- and j-th measurement, (x, y) is position of and t is time when crack occurs.   2 2 2 2 2 2 2 ϕi,j(x, y, t)= (t − tj) ((x − xi) +(y − yi) ) − (t − ti) ((x − xj) +(y − yj) )

We compared the proposed method with the conventional time reverse modeling (TRM) method [2,3]. In TRM, the measured signals are re-emitted numerically into a domain in a time-reversed manner by solving the linear anisotropic elastic wave equation for the displacement field ui(x,t) ∈ Rd (d =2in this paper) which reads:

ρg∂ttui = ∂j(cijkl∂luk)+fi in Ω × [0,T]

- 102 - KSIAM 2020 Annual Meeting ------where fi represents wave force caused by crack, gravitational density is given by ρg and cijkl denotes the stiffness tensor, which gives the momentum tensor by mij = cijkl∂kuk [4]. To com- pare and verify performance in various situations, we perform several numerical experiments. Most of cases both methods are capable of localizing AE activity in concrete. However when the measurements are only on one side, TRM fails to localize crack position while suggested method is still able to localizing crack position (Fig. 2). conventional TRM method suggested method on all 4 sides

source position estimated source position measurements on left side only measurements

Figure 2. Comparison of ‘conventional TRM method’ and ‘suggested method’. Two different numerical experiments are performed; with measurements on all 4 sides and with measurements only on left side. Blue dots represent position of measurements, red circles are source positions, and green squares denote estimated source positions.

ACKNOWLEDGMENT

This work was supported by Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government (MOTIE) (과제번호 20191510301470, 원자로 격납건 물 등의 대형구조물 해체 시실시간 안전 진단을위한 10Msps 속도 급의 AET 다채널 임베디 드 인공지능 시스템 개발)

REFERENCES

1. Schechinger, B., and Vogel, t., “Acoustic emission for monitoring a reinforced concrete beam subject to four-point-bending”, Constr. Build. Mater, Vol. 21, 2007, pp. 483–490. 2. Saenger, E. H., Kocur, G. K., Jud, R. and Torrilhon, M., “Application of time reverse modeling on ultrasonic non-destructive testing of concrete”, Applied Mathematical Modelling, Vol. 35, 2011, pp. 807-816. 3. Kocur, G. K., Saenger, E. H., Grosse, C. U., and Vogel, T., “Time reverse modeling of acoustic emissions in a reinforced concrete beam”, Ultrasonics, Vol. 65, 2016, pp. 96-104. 4. Fink, M., “Time reversal of ultrasonic fields – part 1: basic principles”, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, Vol. 39, 1992, pp. 555–566.

2 - 103 - KSIAM 2020 Annual Meeting ------

Helicity-conservative finite element discretization for MHD systems

Kaibo Hu 1 Young Ju Lee 2 and Jinchao Xu 3

1) Department of Mathematics, University of Minnesota 2) Department of Mathematics, Texas State University 3) Department of Mathematics, Pennsylvania State University

ABSTRACT We construct finite element methods for the magnetohydrodynamics (MHD) system that pre- cisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level. The variables are discretized as discrete differential forms fitting in a discrete de Rham complex. We present numerical tests to show the properties of the algorithm.

- 104 - KSIAM 2020 Annual Meeting ------

Application of Orthogonality Sampling Method for Identifying Small Anomaly From Scattering Parameters

Seongje CHAE 1 , Chi Young AHN 2 and Won-Kwang PARK 1

1) Department of Mathematics, Kookmin University, Seoul, 02707, KOREA 2) National Institute for Mathematical Sciences, Daejeon, 34047, KOREA

Corresponding Author : Won-Kwang PARK, [email protected]

ABSTRACT We consider the application of orthogonality sampling method (OSM) in microwave imaging for a fast localization of small anomalies from measured scattering parameters. For this, we design an indicator function of OSM defined on Lebesgue space to test the orthogonality re- lation between the Hankel function and the measurement data. This is based on an application of the Born approximation and the integral equation formula for scattering parameters in the presence of a small anomaly. We then examine that the indicator function consists of a combi- nation of an infinite series of Bessel functions of integer order, an antenna configuration, and material properties. Simulation results with synthetic data are presented to show the feasibility and limitations of designed OSM.

−3 −3 −4 x 10 x 10 x 10 0.1 0.1 3.5 0.1 14 3 3 12 0.05 0.05 0.05 2.5 2.5 10

2 8 0 0 0 2 1.5 6 y−axis (m) y−axis (m) y−axis (m)

1 4 −0.05 1.5 −0.05 −0.05 0.5 2

−0.1 1 −0.1 −0.1 −0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 x−axis (m) x−axis (m) x−axis (m)

ACKNOWLEDGEMENT

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (NRF-2020R1A2C1A01005221) and the National Institute for Mathematical Sciences (NIMS) grant funded by the Korean government (No. NIMS-B20900000).

REFERENCES

1. Potthast, R., “A study on orthogonality sampling”, Inverse Problems, Vol. 26, 2010, Article No. 074015. 2. Chae, S., Ahn, C. Y., and Park, W.-K., “Localization of small anomalies via orthogonality sampling method from scattering parameters”, Electronics, Special issue on photonic and microwave sensing developments and applications, Vol. 9, 2020, Article No. 1119.

- 105 - General Sessions

General Session III

Sehun Chun (Yonsei University)

Myeongmin Kang (Chungnam National University)

Gwanghyun Jo (Kunsan National University)

Seryoong Ahn (Pukyong National University) KSIAM 2020 Annual Meeting ------

Excitation time map for fast multidimensional simulation with ODEs beyond PDEs

Sehun Chun 1 and Jae-Hun Jung 2

1) Underwood International College, Yonsei University, Incheon, South Korea 2) Department of Mathematics, POSTECH, Pohang, South Korea

Corresponding Author : Sehun Chun, [email protected]

ABSTRACT Time has been one of the fundamental concepts in human thinking, but underwent the most dra- matic change of its meaning in the modern era. The old traditional concept of the absolute time was challenged by the relativity theory of Einstein to yield the new understanding of the concept of time in a relativistic measure. The modern quantum theory brings us one step further to deny the physical reality of time, only to be coined as a quantitative device for the order of sequence of events [1]. The core feature of this modern concept of time lies in its individuality and local- ity, in relation to neighboring events. This talk adapts this new point of views on time to devise a new computational scheme which would solve some critical problems in computational sim- ulations, particularly reducing the large-scale computer simulations into a clinically-available time scale. This talk introduces a novel procedure to simulate a diffusion-reaction phenomenon with a dramatic reduction of time without significantly compromising its accuracy and stability. The Laplacian operator is replaced by a priorly-created map, which is called excitation time map T(xi), to approximately indicate the time when the location at xi is “excited”. Then, the gov- erning equation shrinks to an ordinary differential equation to consist of only the reaction func- tion which describes the mechanism of ion channels. In other words, the proposed scheme is to solve ordinary differential equations with the excitation time map for a time-dependent multi- dimensional domain. One of the biggest advantages is the dramatic reduction of time to realize real-time computational simulations in clinical time scale, but it also may open the new horizon in mathematical modeling and computational simulation of physical and biological phenomena in terms of its diversity and efficiency.

REFERENCES

1. Rovelli, Carlo, The order of time, Penguin Random House, 2008.

- 107 - KSIAM 2020 Annual Meeting ------

Inexact version of proximal iteratively reweighted algorithms

Myeongmin Kang 1

1) Department of Mathematics, Chungnam National University, Daejeon 34134, KOREA

Corresponding Author : Myeongmin Kang, [email protected]

ABSTRACT Iteratively reweighted algorithms are popular methods for solving nonconvex minimization problems and have been used in applications such as image processing. They often have a convex subproblem and do not have closed form solutions in general. In this article, we propose inexact versions of proximal iteratively reweighted algorithms. Specifically, we can achieve an approximate solution for the subproblem by applying a computable inexact stopping rule. We prove the convergence of our method based on inexact unified framework. Numerical applica- tions are also presented to validate the effectiveness of the proposed algorithms.

REFERENCES

1. Ochs, P., Dosovitskiy, A., Brox, T. and Pock, T., “On iteratively reweighted algorithms for nonsmooth nonconvex optimization in computer vision”, SIAM Journal on Imaging Sciences, Vol. 8, no. 1, 2015 pp. 331-372. 2. Sun, T., Jiang, H., Cheng, L. and Zhu, W., “A convergence frame for inexact nonconvex and nonsmooth algorithms and its applications to several iterations”, in: arXiv preprint:1709.04072, 2017.

- 108 - KSIAM 2020 Annual Meeting ------Semi-Uniform Multigrid (SUMG) Algorithms for Interface Problems

Jo, Gwanghyun1, Kwak, Do Young2

1) Department of Mathematics, Kunsan National University, Republic of Korea 2) Department of Mathematical Science, KAIST, Daejeon 305-701 KOREA

Corresponding Author: Jo, Gwanghyun [email protected]

ABSTRACT

We develop a new type of multigrid method for interface problems based on the semi- uniform grids, which is obtained by refinement of the uniform grid. The algorithms is based on the subspace correction concept. First, the residual at the semi-uniform grids are restricted to the uniform grid system and then V-cycle multigrid algorithms are solved on the uniform grid system. We provide the contracting analysis of the proposed algorithms and present numerical results supporting the algorithms.

- 109 - KSIAM 2020 Annual Meeting ------  7+(237,0$/&219(56,21%(7:((1-(216(, 720217+/<5(17:,7+%2552:,1* &21675$,176 

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- 110 - General Sessions

General Session IV

Donggu Lee (Konkuk University)

Jiyeon Suh (Yonsei University)

Hyunwoo Cho (Yonsei University)

Seyeon Lee (UNIST) KSIAM 2020 Annual Meeting ------




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- 112 - KSIAM 2020 Annual Meeting ------

Assessing the Impact of Two-Dose Varicella Vaccination on Varicella and Herpes Zoster Incidences in the Republic of Korea

Jiyeon Suh 1 , Sun Hee Park 2 and Jeehyun Lee 3

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, KOREA 2) Division of Infectious Diseases, Department of Internal Medicine, College of Medicine, The Catholic University of Korea, Seoul 06591, KOREA 3) School of Mathematics and Computing (Mathematics), Yonsei University, Seoul 03722, KOREA

Corresponding Author : Jeehyun Lee, [email protected]

ABSTRACT Varicella-zoster virus (VZV) causes two different diseases, varicella and herpes zoster (HZ), known as chickenpox and shingles, respectively. At the first infection, VZV develops varicella which commonly occurs in childhood. After the primary infection, VZV becomes latent and can reactivate, resulting in HZ as the immunity weakens with age. One-dose varicella vaccination was introduced in the national immunity program of Korea in 2005, and it has significantly reduced varicella incidence. However, the varicella outbreak constantly occurs in the group of children who has been vaccinated.[1] Therefore, a two-dose schedule is under consideration, but there is a concern that the additional vaccination can lead to an increase in HZ incidence by reducing the exogenous boosting.[2] In this study, we developed a dynamic compartmental model of VZV and assessed the impact of two-dose varicella vaccination on varicella and HZ disease burden. The model was stratified into age and the WAIFW (who-acquired-infection-from-who) matrix was estimated using the POLYMOD survey and Korean VZV seroprevalence data in 2008.[3,4] We then incorporated dynamically changing population structure into the model using popula- tion projection data between 1960–2065 and estimated the reactivation rate of HZ using the HZ incidence data between 2013–2015. Under four different assumptions on the effectiveness of varicella vaccination (base, moderate, worst, and best), the introduction of second dose vaccination reduced the cumulative varicella incidence over 45 years by a minimum of 3.71% and a maximum of 64.3% compared to the one-dose scenario. Meanwhile, the cumulative HZ incidence was slightly increased after the second dose of vaccination, but within 30 years, it started to decline and reduced by a minimum of 0.22% and a maximum of 2.55% over 45 years. The results showed that the two-dose varicella vaccination significantly reduced varicella inci- dence and the increase in HZ incidence due to the reduced exogenous boosting was relatively small. Moreover, in the long term, the HZ incidence was also declined. Therefore, the two-dose varicella vaccination can effectively reduce both varicella and HZ disease burden.

- 113 - KSIAM 2020 Annual Meeting ------REFERENCES

1. S. S. Chaves, P. Gargiullo, J. X. Zhang, R. Civen, D. Guris, L. Mascola, and J. F. Seward, “Loss of vaccine-induced immunity to varicella over time”, New England Journal of Medicine, Vol. 356, 2007, pp. 1121–1129. 2. B. Ogunjimi, P. Van Damme, and P. Beutels, “Herpes zoster risk reduction through exposure to chickenpox patients: a systematic multidisciplinary review”, PloS one, Vol. 8, 2013, p. e66485. 3. J. Mossong, N. Hens, M. Jit, P. Beutels, K. Auranen, R. Mikolajczyk, M. Massari, S. Salmaso, G. S. Tomba, J. Wallinga, et al., “Social contacts and mixing patterns relevant to the spread of infectious diseases”, PLoS Med, Vol. 5, 2008, p. e74. 4. W. S. Choi, J. Y. Noh, J. Y. Huh, Y. M. Jo, J. Lee, J. Y. Song, W. J. Kim, and H. J. Cheong, “Seroprevalence of varicella-zoster virus in korea”, Journal of medical virology, Vol. 82, no. 12, pp. 2123–2126, 2010.

- 114 - KSIAM 2020 Annual Meeting ------

The impact of Tuberculosis interventions in Korea

Hyunwoo Cho 1, Jeehyun Lee1,2 and Young Ae Kang3,4

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, KOREA 2) School of Mathematics and Computing (Mathematics), Yonsei University, Seoul 03722, KOREA 3) Section of Pulmonary, Critical Care and Sleep Medicine, Department of Internal Medicine, Yale University School of Medicine, New Haven, Connecticut 4)Division of Pulmonology, Department of Internal Medicine, Severance Hospital, Institute of Chest Diseases, Yonsei University College of Medicine, Seoul, Korea.

Corresponding Author: Jeehyun Lee, [email protected]

ABSTRACT

Objectives: Tuberculosis (TB) is an infectious disease, one of the top 10 causes of death worldwide. Despite the effort of government, Korea is still suffering from high mortality rate due to TB, ranking first among OECD countries. This study aimed to evaluate the effects of intervention strategies to control number of incidences of new and retreating TB patients. Method: A deterministic model was developed for the TB transmission in Korea. A SEIT (susceptible-exposed-infectious-treating) model with some additional compartments were constructed. The effects of different intervention strategies such as active case finding, treatments success rate, preventive treatment, and hospital delay control were evaluated. Result: The model suggested that active case finding had biggest impact on reducing incidences and decreasing trend of new cases is expected to slow down. Conclusion: Intervention and efforts reduce number of new cases of TB, but due to large number of low risk latent, dramatic effect of control is not expected. Keywords: Pulmonary Tuberculosis, transmission dynamics, infection control

- 115 - KSIAM 2020 Annual Meeting ------

Agent Based Mathematical Modeling and Control Policy for COVID-19 in Korea

Seyeon Lee and Bongsoo Jang*

Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, KOREA

Corresponding Author : Bongsoo Jang, [email protected]

ABSTRACT Coronavirus disease 2019(COVID-19) caused by severe acute respiratory syndrome coron- avirus 2 (SARS-CoV-2) is an infectious disease which was first detected in Wuhan, China in December 2019. This disease is now affecting more that 200 countries. On March 2020, the World Health Organization defined the spread of COVID-19 as a pandemic. The government employs various control policies to prevent the spread of the disease. Agent based modeling(ABM) is the computational modeling methods and describes various phenomena by the interaction of individuals. In this work, we show the spread of COVID-19 by proposing an agent based mathematical model combined with COVID-19 suppression policies such as self-isolation and contact tracing. In particular, we propose a mathematical model for the control of the spread of COVID-19 in accordance with the social distancing policy used in Korea and shows its effectiveness. Several simulation results show that our model From the various numerical experiments, the mathematical model proposed in this study shows how self-isolation and contact tracing can control the spread of COVID-19 and the importance of public health policies such as social distancing.

- 116 - General Sessions

General Session V

Eunha Shim (Soongsil University)

Taeyong Lee (Yonsei University)

Yunjeong Lee (Yonsei University)

Masud M A (Pusan National University) KSIAM 2020 Annual Meeting ------

Mathematical modeling of COVID-19 transmission potential and intervention strategies
Eunha SHIM1, Amna TARIQ2, Kenji MIZUMOTO2,3, Wongyeong CHOI1, Yiseul LEE2, Gerardo CHOWELL2

Department of Mathematics, Soongsil University, Seoul, 06978.

Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA, 30303, USA


Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, Kyoto 615-8530, Japan

Corresponding Author: Eunha Shim, [email protected]
Abstract
In South Korea, 13,745 cases of coronavirus disease (COVID-19) have been reported as of 19 July, 2020. To examine the spatiotemporal changes in the transmission potential, we present regional estimates of the doubling time and reproduction number (Rt) of COVID-19 in the country [1, 4]. Daily series of confirmed COVID-19 cases in the most affected regions were extracted from publicly available sources. We employed established mathematical and statistical methods to investigate the time-varying reproduction numbers of the COVID-19 in Korea, case fatality, and its doubling time [1, 3]. At the regional level, Seoul and Gyeonggi Province have experienced the first peak of COVID19 in early March, followed by the second wave in early June, with Rt exceeding 3.0 and mean doubling time ranging from 3.6 to 10.1 days [1]. As of 19 July, 2020, Gyeongbuk Province and Daegu are yet to experience a second wave of the disease, where the mean Rt reached 3.5-4.4 and doubling time ranging from 2.8 to 4.6 days during the first wave. Our findings support the effectiveness of control measures against COVID-19 in Korea and we present optimal control strategies [1, 2]. However, the easing of the restrictions imposed by the government in May 2020 facilitated a second wave in the greater Seoul area.

References

1. Shim E, Tariq A, Chowell G., “Spatial variability in reproduction number and doubling time across two waves of the COVID-19 pandemic in South Korea, February to July 2020,” International Journal of Infectious Diseases, Vol. 20, 2020, pp. 32210-4.

2. Choi W, Shim E., “Optimal strategies for vaccination and social Distancing in a game-theoretic epidemiological model,” Journal of Theoretical Biology, Vol. 505, pp. 110422.

3. Shim E, Mizumoto K, Choi W, Chowell G, “Estimating the risk of COVID- 19 death during the course of the outbreak in Korea, February-May 2020,” Journal of Clinical Medicine, Vol. 9(6), 2020, pp. E1641.

4. Shim E, Tariq A, Choi W, Lee Y, Chowell G., “Transmission potential and severity of COVID- 19 in South Korea,” International Journal of Infectious Diseases, Vol. 93, 2020, pp. 339-344

- 118 -

KSIAM 2020 Annual Meeting ------

Optimal treatment of the immune-evading oncolytic virus therapy for Cancer

Φ and Jeehyun Lee1,4,Φ,כ,Taeyong Lee1,#, Adrianne L. Jenner2,#, Peter S. Kim3

1) School of Mathematics and Computing (Mathematics), College of Science, Yonsei University, Seoul, Korea 2) Departement de mathématiques et de statistique, Université de Montréal, Montréal, Canada 3) School of Mathematics and Statistics, University of Sydney, Sydney, Australia 4) School of Mathematics and Computing (Computational Science & Engineering), Yonsei University, Seoul, Korea #,Φ These authors contributed equally to this work.

Corresponding Author: Jeehyun Lee, [email protected]

ABSTRACT

The oncolytic virus is one of the promising therapies for treating cancer. With modifying the genomes of viruses, these infect and destroy the cancer cells. While it has several successful experimental results for overcoming its limitation, such as degradation by the immune-system of host, it is hard to test how effective each perturbation of these viruses is. In this talk, we construct the partial differential equation(PDE) model which describes the relationships between cancer cells and the immune-evading, but delaying-infection virus with multiple coats. We would set a multiple level of coats that are degraded over time and determine an optimal initial proportion of virus. Using this system, we show that a non-trivial mixture of viruses with various thickness of coats is needed for minimizing tumor volume. Moreover, we shall inspect the impactness of different viral clearance. It results in the different outcome of the therapy and gives the different optimal control for minimizing the tumor size. We also consider an optimal control problem with continuous control subject to the ordinary differential equation(ODE) model. Employing various optimization algorithms, we seek to find an optimal injection strategy through time. In this talk, we introduce the concept and plan of this research.

REFERENCES

[1] Lee T, Jenner A.L, Kim P.S, Lee J. Application of control theory in a delayed-infection and immune-evading oncolytic virotherapy. Mathematical Biosciences and Engineering. 2020 Feb 12;17(3):2361-2383. [2] Jenner, A. L., Yun, C. O., Kim, P. S., & Coster, A. C. Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols. Bulletin of Mathematical Biolology. 2018 Jun;80(6) pp.1615-1629. [3] Jenner, A. L., Frascoli, F., Coster, A. C., & Kim, P. S. Enhancing oncolytic virotherapy: Observations from a Voronoi Cell-Based model. Journal of Theoretical Biology. 2020 Jan 21;485:110052. [4] Kim, P. H., Sohn, J. H., Choi, J. W., Jung, Y., Kim, S. W., Haam, S., & Yun, C. O. Active targeting and safety profile of PEG-modified adenovirus conjugated with herceptin. Biomaterials. 2011 Mar;32(9):2314-26.

- 119 -

KSIAM 2020 Annual Meeting ------

Estimation of the Reproduction Number of Influenza A(H1N1)pdm2009 in South Korea Using Heterogeneous Models

Yunjeong LEE 1 , Dong Han LEE 2 , Hee-Dae KWON 3 , Changsoo KIM 4 and Jeehyun LEE 5

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, 03722, KOREA 2) Korea Centers for Disease Control and Prevention, Cheongju-si, 28159, KOREA 3) Department of Mathematics, Inha University, Incheon, 22212, KOREA 4) Department of Preventive Medicine and Public Health, Severance Hospital, Yonsei University College of Medicine, Seoul, 03722, KOREA 5) School of Mathematics and Computing (Mathematics), Yonsei University, Seoul, 03722, KOREA

Corresponding Author : Jeehyun Lee, [email protected]

ABSTRACT The reproduction number is defined as the average number of secondary cases generated by a typical primary case. It is one of the most important parameters, which measures the transmission power of epidemic diseases. It can be used to predict whether a disease spread or not by its value. However, estimating this value is a very challenging task because the contact tracing for all cases is almost impossible and the required information is limited. In this study, we propose mass-action age- and region-structured SIR models to describe the dynamics of influenza A(H1N1)pdm09 in 2009. To compare them with the non-structured SIR model, not only these models but also the basic SIR model is used to fit to daily incident cases from September 1, 2009 to March 30, 2010. They are also used to compute the time- dependent reproduction numbers by changing the terminal times. The structured models show robust estimates of the infectious periods and the reproduction numbers at various terminal times. On the other hand, the basic SIR model shows severe fluctuation of the estimates. Also, the estimated reproduction number is consistent with cumulative incidence of each group for both structured models. Therefore, our results suggest that the introduction of heterogeneity to the population is crucial to describe the characteristics of the disease dynamics.

REFERENCES

1. Cruz-Pacheco G, Duran L, Esteva L, Minzoni AA, Lopez-Cervantes M, Panayotaros P, et al., “Modelling of the influenza A(H1N1) outbreak in Mexico City, April-May 2009, with control sanitary measures”, Euro Surveill, Vol. 14, 2009.

- 120 - KSIAM 2020 Annual Meeting ------2. Fraser C, Donnelly CA, Cauchemez S, Hanage WP, Van Kerkhove MD, Hollingsworth TD, et al., “Pandemic potential of a strain of influenza A (H1N1): early findings”, Science, Vol. 324, 2009, pp. 1557-1561. 3. Cowling BJ, Lau MSY, Ho LM, Chuang SK, Tsang T, Liu SH, et al., “The effective reproduction number of pandemic influenza: prospective estimation”, Epidemiology, Vol. 21, 2010, pp. 842-846.

- 121 - KSIAM 2020 Annual Meeting ------

COVID-19 TRANSMISSION IN BANGLADESH

Masud M A 1,2 and Sangil KIM 2

1) Department of Mathematics and Physics, North South University, Dhaka, BANGLADESH 2) Department of Mathematics, Pusan National University, Busan, KOREA

Corresponding Author : Sangil KIM, [email protected]

ABSTRACT In this study we consider the case of Bangladesh, and fit a simple compartmental model holding a feature to distinguish between identified infected and infectious with time series data using the likelihood approach; prior to which dynamics of the model was analyzed mathematically and the identifiability of the parameters was confirmed. We deduced profile likelihood and 95% confidence interval for each of the estimated parameters. Our analysis shows that the basic re- production number is the key threshold for COVID-19 outbreak and persistence; and it changes with time as a consequence of the change in lock-down strategies and expansion of testing fa- cilities, and was estimated to lie between 1.5 and 12. The results show that the peak of the epidemic may appear around October 2, 2020.

METHODS

Table 1 Description of the state variables. Description Symbol Description Symbol Number of susceptible individuals S Number of exposed individuals E Number of infected individuals I Number of isolated infected individuals Q Number of removed individuals R

dS(t) dE(t) dI(t) = π − βIS − μS; = βIS − σE − μE; = σE − γ I − qI − μI; dt dt dt 1 dQ(t) dR(t) = qI − γ Q − μQ − δQ; = γ I + γ Q + δQ − μR dt 2 dt 1 2   E = π , 0, 0, 0, 0 The model exhibits a disease free equilibrium (DFE) , 0 μ  and an endemic kE kI (R0−1)kI μ (R0−1)μ (R0−1)qμ (R0−1)(γ1kQ+γ2q) πβσ E∗ = , , , , R0 = equilibrium (EE), βσ βσ β βkQ μkQ . Here, (σ+μ)(γ1+q+μ)μ is the basic reproduction number. The equilibrium E0 is globally asymptotically stable for R0 < 1, whereas E∗ exists and globally asymptotically stable when R0 > 1. We fit the identi- fied Active Cases, which is calculated in terms of several useful data as follows: Active Cases, y(ti) = Total Identified (ti) - Total Recovered (ti) -Total Dead (ti). The identified cases are con- sidered to be isolated at their residence or at hospital, which corresponds to Q subclass of our

- 122 - KSIAM 2020 Annual Meeting ------model. In the Maximuim Likelihood method, we assume all y(ti) are independent and follow Poission distribution with parameter Y (ti,β,q). Therefore, the negative log likelihood function  NLL(β,q)=− tf y(t )ln(Y (t )) − Y (t ) − lny((t )!) is written as, t1 i i i i Table 2 Parameters for numerical simulation.

Symbol Value(day−1) Reference Symbol Value(day−1) Reference π 6088.3 Total population 1.6e8 μ 3.8052e − 05 72 year life time β −− estimated(fitting) σ 0.2 [1]

γ1 0.04545 [2] q −− estimated(fitting)

γ2 0.062 estimated(data) δ 0.0039 estimated(data)

106 106 104 -9.768 -9.7692 8 Data -9.7685 -9.7694 6 Model

-9.769 -9.7696 Q 4 NLL NLL

-9.7695 -9.7698 2

-9.77 -9.77 0 2345 0.25 0.3 0.35 0.4 0.45 0 20406080 10-9 q t

Figure 1. Data fitting is in the first row. On the second row the dotted line shows the evolution of R0 in β − q space. Comparison between Qmax and Imax for different values of β and q.

REFERENCES

1. Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Nicholas G. Azman, Andrew S.and Reich, and Justin Lessler. The incubation period of coronavirus disease 2019 (covid-19) from publicly reported confirmed cases: Estimation and application. Annals of Internal Medicine, 172(9):577–582, 2020. 2. Fei Zhou, Ting Yu, Ronghui Du, Guohui Fan, Ying Liu, Zhibo Liu, Jie Xiang, Yeming Wang, Bin Song, Xiaoying Gu, Lulu Guan, Yuan Wei, Hui Li, Xudong Wu, Jiuyang Xu, Shengjin Tu, Yi Zhang, Hua Chen, and Bin Cao. Clinical course and risk factors for mortality of adult inpatients with covid-19 in wuhan, china: a retrospective cohort study. The Lancet, 395:1054 – 1062, 03 2020.

- 123 - General Sessions

General Session VI

Soyoung Jeong (Advanced Institute of Convergence

Technology)

Eo-Jin Lee (Kyung Hee University)

Sungjin Lee (Yonsei University) KSIAM 2020 Annual Meeting ------

  

           

 

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- 125 - KSIAM 2020 Annual Meeting ------

               

      

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- 126 - KSIAM 2020 Annual Meeting ------&   &&  F(/!-  &B&  -(  &  0 "  &  %(/  &&   G (2!!  & &  ? "* !1%  , H *( %" C $    '   B (& >E  EE>  & 8:D 8:E& &   &&  -(  &  %(/  &&   G (2!!  & &  ?A%,*%  , "*( . %"  *! "" -! $ 0   "%% !/ $!%2% %0 "!" C (   B (& D  EED  & ::I&

- 127 - KSIAM 2020 Annual Meeting ------

Fundamental solution of second-order parabolic equations in non-divergence form

Seick KIM 1 and Sungjin LEE 2

1) School of Mathematics and Computing, Yonsei University, Seoul 03722, KOREA 2) School of Mathematics and Computing, Yonsei University, Seoul 03722, KOREA

Corresponding Author : Sungjin LEE, [email protected]

ABSTRACT We study Fundamental solution for non-divergence form parabolic equations in cylindrical do- mains. Fundamental solution play an important role in studying parabolic equations. When the coefficients are sufficiently smooth, say Holder¨ continuous, then the existence and pointwise estimates of Fundamental solution are well established. However, when the coefficients are merely continuous, then Fundamental solutions do not necessarily exist as functions. We show that when the mean oscillation of the coefficients satisfies the Dini condition, then the Funda- mental solution exist. We also establish the Gaussian bounds for the Fundamental solution. This work presents a unified approach valid for both the scalar and vectorial cases.

- 128 - Poster Session

Hyundong Kim (Korea University)

JongHyuk Kang (Korea University)

Bongyeong Koo (Seoul National University)

EuiMin Jeong (KAIST)

Eun Hae Cho (Pusan National University)

Jungho Park (Seoul National University)

Sangmin Park (Pusan National University)

Malik Muhammad Ibrahhim (Pusan National University)

Donghyun Kim (Pusan National University) Yun Min Song (KAIST)

Junhui U (Pusan National University)

Mijin Ha (Pusan National University)

Mannan Jamshaid (Pusan National University)

Dae Wook Kim (KAIST)

TaeKyung Ki (Yonsei University)

Sanghee Lee (Yonsei University)

Hyukpyo Hong (KAIST)

Jongmin Lee (Konkuk University)

Youngsuk Ko (Konkuk University)

Meiyan Jiang (Pukyong National University)

Nu Ree Song (Yonsei University)

Soobin Kwak (Korea University)

Yeon Ju Lee (Korea University)

Juyeb Yeo (Chungnam National University)

Seokjoo Chae (KAIST)

Sungyeon Kim (Yonsei University)

GyuSang Han (Korea University)

Junghyun Lee (Seoul National University)

Hoin Jung (Seoul National University)

DongHeon Seong, GyoungMin Lim (Pusan National

University)

Hyeonseong Jin (Jeju National University) KSIAM 2020 Annual Meeting ------

Mathematical modeling and computer simulation of the coffee-ring phenomena using a phase-field method

Junxiang Yang 1, Hyundong Kim 1, Chaeyoung Lee 1, Sangkwon Kim 1, Jian Wang 2, Sungha Yoon 1, Jintae Park 1, Junseok Kim 1

1) Department of Mathematics, Korea University, Seoul 151-742, Republic of KOREA 2) School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

Corresponding Author : Junseok Kim, [email protected]

ABSTRACT We present a mathematical model of the coffee-ring effect and its numerical simulation. The phase-field method and MCS are used in the presented method. To model a drying droplet, the AC equation and a pinning boundary condition are considered. Also, the motion of coffee particles inside the droplet is modeled by the Brownian dynamics under gravity. In the 2D and 3D space, we perform numerical experiments.

ACKNOWLEDGEMENT

This work was supported by Basic Science Research Program through the National Re- search Foundation of Korea (NRF) funded by the Ministry of Education(NRF-2019R1A2C1003053).

REFERENCES

1. Yang, J., Kim, H., Lee, C., Kim, S., Wang, J., Yoon, S., Park, J., Kim, J. (2020). Phase-field modeling and computer simulation of the coffee-ring effect. Theor. Comput. Fluid Dyn. 1–14. 2. Lee, H. G., Yang, J., Kim, J. (2020). Pinning boundary conditions for phase-field models. Commun. Nonlinear Sci. Numeri. Simul. 82, 105060. 3. Saka, H., Bengston, R. D., Reichl, L. E. (2009). Relaxation of Brownian particles in a gravitational field. Am. J. Phys. 77, 240–243. 4. Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R., Witten, T. A. (1997). Capillary flow as the cause of ring stains from dried liquid drops. Nature, 389(6653), 827– 829. 5. Allen, S. M., Cahn, J. W. (1979). A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27, 1085–1095.

- 131 -

KSIAM 2020 Annual Meeting ------

SIMULATIONS OF WATER SURFACE

JungHyuk Kang 1, MinJi Go 1, SuYeon Shin1 JinAh Hwang1 WoonJae Hwang1

1) Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Korea

Corresponding Author: Woonjae Hwang, [email protected]

ABSTRACT

We study the changes in the water surface. We apply moving mesh method to investigate the dynamics of tsunami. We also simulate the problems of 2-D shallow water equations including water droplet on the bathtub, and dam break.

REFERENCES

1. Bobby Minola Ginting, and Ralf-Peter Mundani, “Comparison of Shallow Water Solvers: Applications for Dam-Break and Tsunami Cases with Reordering Strategy for Efficient Vectorization on Modern Hardware”, MDPI, 2019, 1-31 2. CR Robinson, “Shallow Water Equations”, Syracuse University, 2011 3. Tulong Xing, Chi-Wang Shu,"High order finite difference WENO schemes with the exact conservation property for the shallow water equations", Journal of Computational Physics 208, 2005, 206-227. 4. A. Kurganov, G Petrova,"Central-upwind schemes fot two-layer shallow water equations", Journal on Scientific Computing 31(3), 2009, 1742-1773. 5. 1. Huazhong Tang, Tao Tang, “Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws”, SIAM journal on numerical analysis 41, 2003, 487-515

- 132 -

KSIAM 2020 Annual Meeting ------

Dangerous situation detection using deep learning models for construction sites

Donggyu Lee 1 Bongyeong Koo 1 Yeachan Park 1 Hyomin Ahn 1 Junho Lee 2 Han-Soo Choi 3 and Myungjoo Kang 4

1) Department of Mathematical Sciences, Seoul National University, Seoul 151-742, KOREA 2) Department of Computational Science and Technology, Seoul National University, Seoul 151-742, KOREA 3) Research institute of Mathematics, Seoul National University, Seoul 151-742, KOREA 4) Department of Mathematical Sciences, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT Accident prevention is a very important factor in a construction site. Therefore, efforts such as supervision of safety regulations were required. As part of these efforts, this study proposes a deep learning model that can prevent safety accidents in advance. It is expected that more accidents can be prevented by strengthening the supervision of compliance with safety rules through these studies.

REFERENCES

- 133 - KSIAM 2020 Annual Meeting ------

Comparisons of models to analyze each type of repression in a negative feedback system

Eui Min JEONG 1 and Jae Kyoung KIM 1

1) Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, KOREA

Corresponding Author: Jae Kyoung KIM, [email protected]

ABSTRACT

A negative feedback loop (NFL) interacting among activator proteins, repressor proteins, and genes can generate sustained oscillations. In NFL, we distinguish three types of repression: (1) sequestration, in which repressor protein binds to activator protein and sequesters it not to activate gene (2) blocking, in which repressor protein binds to activator protein binding with gene and inhibits activator-dependent transcription (3) displacement, in which repressor protein displaces activator protein from gene. To describe these repression mechanisms, we develop ordinary differential equation (ODE) models based on mass action kinetics. Interestingly, by comparing each of models reduced by a quasi-steady-state approximation (QSSA), we show that their characteristics of transcriptional activity (i.e. ultrasensitivity) are totally different depending on repression types they describe. Furthermore, we argue that this approach may be extended to more complex biological systems regulated by NFL.

- 134 - KSIAM 2020 Annual Meeting ------

                 

     

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- 135 - KSIAM 2020 Annual Meeting ------

Quaternion-valued deep neural network for semantic segmentation

Yeachan PARK 1, Jung Ho PARK 2, Myungjoo KANG 1 1) Department of mathematical science, Seoul National University, Seoul 151-742, KOREA 2) Department of computational science and technology, Seoul National University, Seoul 151- 742, KOREA

Corresponding Author: Myungjoo KANG, [email protected]

ABSTRACT

Semantic segmentation is one of the most popular interested research area in deep learning. In practical, this technology is widely used for many areas like autonomous driving. Quaternion is a notion in mathematics consisting of one real part and seven imaginary parts with some relations. In this paper, we suggest a quaternion-valued deep neural network for semantic segemtation and some experiments.

- 136 - KSIAM 2020 Annual Meeting ------ٻ ٻ ٻṲ⹲ٻ㰖䚲ٻἾ┺Ὃ㯳ٻ㧊㣿䞲ٻ㧊⹎㰖⯒ٻڟڍ ٻ Development of indicators for osteoporosis using 2D images ٻ ٻڌ 㧊㔏䠢ٻڇڅڌ ⹫㌗⹒ٻڇڍ ⪕⹫㩫ٻڇڌ 㧻⁒㑮ٻڇڌ ₖ䌲䡫 ٻ ٻ㑮䞯ὒٻ⿖㌆╖䞯ᾦٻڄڌ ٻ㌆㠛㑮䞯㎒䎆ٻ㩲㫆ٻ㑮㌆ٻ⁞㦋ٻ₆⹮ٻ㧊䎆◆゛ٻڄڍ ٻ ٻۈۊھډۇۄڼۈۂڛڌڍڏڋڎڔۈێۋٻڇ⹫㌗⹒ٻڕ㩖㧦ٻᾦ㔶 ٻ ٻ㣪㟓 ٻ ٻ㧊䎆㢖◆ٻ㩫㌗ٻ㩗㣿䞮㡂ٻ⿚㍳㦚ٻ䎣㓺㻮ٻ㠦ڄڟڨڝڃٻ☚Ἶ⹖ٻ㧊䎆㦮◆ٻⰞ㤆㓺ٻ㡆ῂ㠦㍲⓪ٻ㧊 ٻ㧊䎆◆ ٻ㩲Ệ䞮⓪ ٻṨ㦚 ٻ㧊䞮㦮 ٻ‶䘟 ٻ䞲⡦ ٻډ┺Ṳ⹲䞲 ٻ㰖䚲⯒ ٻῂ⿚䞮⓪ ٻ㧊䎆⯒◆ ٻ㩫㌗゚ ٻ㥶㣿㎇㦚ٻ䔏㎇㦮ٻṗٻ㧊㣿䞮㡂ٻ㦚⻫₆ٻ┳⩂ٻⲎ㔶ٻ㟧䞲┺ٻ⏨㧊ἶٻ㩫䢫☚⯒ٻ䐋䟊ٻ㩚㻮Ⰲ⯒ ٻۏۍۊۋۋېڮ ٻڇ㔲䟟䞮㡖㦒Ⳇ ٻᾦ㹾Ỗ㯳㦚 ڿۇۊہڈۆ ٻ㥚䟊 ٻ⹿㰖䞮₆ ٻ㦚 ۂۉۄۏۏۄہۍۀۑڪ ٻډ┺Ỗ㯳䞲 ٻڇἆὒ ٻ㔺䠮 ٻډ┺㫆㩫䞲 ٻ㧚ἚṨ㦚 ٻ㥚䟊 ٻ䟻㌗㦚 ٻ⓻㎇ ٻ⳾◎㦮 ٻ⿚⮮ ٻڄڨڱڮڃ ٻۀۉۄۃھڼڨ ٻۍۊۏھۀڱ ٻṖ㧻 ٻڇ㢪㦒Ⳇ⋮ ٻ⪲ڀڌڑډڑڔ ٻ㩫䢫☚Ṗ ٻ㦮 ڨڱڮ ٻ䞲╖ ٻ㠦 ێۀھۄۍۏڼۈ ٻۃۏۂۉۀۇ ٻۉېۍ ٻۇۀۑۀۇڈ۔ڼۍڢ ڈ۔ڼۍڢ ٻےۊڧ ٻڇڄڭڰکڧڢڃ ٻۉېۍ ٻۍۊہ ٻ۔ۏۄۈۍۊہۄۉڰڈۉۊکٻۇۀۑۀڧڈ۔ڼۍڢ ٻ⓪ ێۀۍېۏڼۀہ ٻṖ㰖 ٻ㎎ ٻ㭧㣪䞲 ٻٻډ┺㧊ڄګڭڃٻۀۂڼۏۉۀھۍۀګٻۉېڭٻڇڄڠڭڢڧڃٻێۄێڼۃۋۈڠٻۉېڭٻۇۀۑۀڧ ٻ ٻ㺎ἶⶎ䠢

1. R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Transactions on sustems, man, and cybernetics, no. 3, pp. 610-621, 1973. 2. M. M. Galloway, “Texture analysis using gray level run lengths,” Computer Graphics and Image Processing, Vol. 4, no. 2, pp 172-179, 1975. 3. G Thibault, B Fertil, C. Navarro, S Pereira, P Cau, N Lévy, J Sequeira, and J Mari, “Texture indexes and gray level size zone matrix,” in Application to cell nuclei classification 10th Int. Conf. on Pattern Recognition and Information Processing ed V Krasnoproshin, S Ablameyko and R Sadykhov (Minsk: Belarusian State University Publishing Center), pp. 140–5, 2009.

ٻ

- 137 - KSIAM 2020 Annual Meeting ------

Lag synchronization of coupled time-delayed FitzHugh- Nagumo neural networks via feedback control Malik Muhammad Ibrahim 1 and Sangil Kim 1

1) Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

Corresponding Author: Sangil Kim, [email protected]

ABSTRACT

Synchronization plays a tremendous role in information transfer and decision-making by neurons and brain neural networks. Researchers have studied the synchronization mechanism of two coupled time-delayed neurons but not for time-delayed neural networks. This study investigates the synchronization of time-delayed unidirectional and bidirectional ring- structured FitzHugh Nagumo (FHN) neuronal systems. Different gap junctions and delay parameters are used to incorporate time delay dynamics in neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. To assure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. Necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov theory of stability. Finally, numerical simulations for a small network of five time-delayed FHN neurons are conducted to verify the effectiveness of the proposed adaptive control scheme.

- 138 - KSIAM 2020 Annual Meeting ------

The analytic method for pricing of vulnerable external barrier options

Donghyun KIM and Ji-Hun YOON 1

1) Department of Mathematics, Pusan National University, Busan 46241, KOREA

Corresponding Author : Ji-Hun YOON, [email protected]

ABSTRACT External barrier options are financial securities which have two-assets for stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state vari- able so that it determines whether the option is knocked in or out. In this paper, taking into consideration the financial derivatives subject to default risks of the option writer in the over- the-counter markets since the Global Financial Crisis, we use multivariate Mellin transforms and the method of images to investigate an explicit (closed) form pricing formula for the vul- nerable external barrier option prices. Furthermore, we verify that our closed-form solution has been obtained accurately and efficiently by making a comparison between the closed-form so- lution and the solution from the Monte-Carlo simulation. Finally, we examine the behavior and sensitivity of the vulnerable external barrier option prices in terms of model parameters.

- 139 - KSIAM 2020 Annual Meeting ------

Analysis of stochastic and deterministic quasi-steady-state approximation.

Yun Min SONG1 Hyukpyo HONG1 and Jae Kyoung KIM1

1) Department of Mathematical Science, Korea Advanced institute of Science and Technology, Daejeon 34141, KOREA

Corresponding Author: Jae Kyoung KIM, [email protected]

ABSTRACT

The Quasi-Steady-State Approximation (QSSA) is commonly used to reduce deterministic biochemical reaction models with timescale separation. The resulting equations that have the form of non-elementary reaction functions provide a simplified description of the model. Such deterministic reductions are frequently a basis for heuristic stochastic reductions in which the non-elementary reaction functions are used to define reaction propensities. However, it is unclear when such stochastic reductions provide an accurate approximation of the original stochastic simulation. Though it is often assumed that the stochastic reduction is valid whenever its deterministic counterpart is valid, some examples show that it’s not necessarily true. Here we provide the complete analysis for these disparities between the accuracy of the deterministic and the stochastic QSSA.

- 140 - KSIAM 2020 Annual Meeting ------

PRICING PERPETUAL AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY

Junhui U 1 , Ji-Hun Yoon 1 and Sun-Young Choi 2

1) Department of Mathmatics, Pusan National University, Pusan 46241, Republic of Korea 2) Department of Financial Mathematics, Gachon University, Gyeonggi 13120, Republic of Korea

Corresponding Author : Sun-Young Choi, [email protected]

ABSTRACT Against a sizeable movement with unpredictable direction, strangle is a option trading strategy that the traders use in order to reduce the risk of loss by simultaneous trading put and call options with different strike prices but with the same expiration date and underlying assets. Especially, a perpetual American strangle option is a strangle option of which maturity is not limited and it can be exercised at any time during the term of the arrangement by a option holder. Pricing perpetual American Strangle options under stochastic volatility model can be mathematically classified the free boundary problem with two optimal exercise boundaries. In this paper, we investigate the price of a perpetual American strangle options under a stochastic volatility model with fast mean reversion by means of the asymptotic analysis technique.

REFERENCES

1. A. Agarwal, S. Juneja and R. Sircar, American options under stochastic volatility : control variates, maturity randomization and multiscale asymptotics, Quantitative Finance, 16 (2016), pp. 17-30. 2. F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of political economy, 81 (1973), pp. 637-654. 3. S. Boyarchenko, Two-point boundary problems and perpetual american strangles in jump- diffusion models, Available at SSRN 896260, (2006). 4. M.-C. Chang and Y.-C. Sheu, Free boundary problems and perpetual american strangles, Quantitative Finance, 13 (2013), pp. 1149-1155. 5. J. S. Chaput and L. H. Ederington, Volatility trade design, Journal of Futures Markets : Futures, Options and Other Derivative Products, 25 (2005), pp. 243-279. 6. W.-T. Chen and S.-P. Zhu, Pricing perpetual american puts under multi-scale stochastic volatility, Asymptotic Analysis, 80 (2012), pp. 133-148. 7. C. Chiarella and A. Ziogas, Evaluation of american strangles, Journal of Economic Dynamics and Control, 29 (2005), pp. 31-62.

- 141 - KSIAM 2020 Annual Meeting ------8. C. Chuang, Valuation of perpetual strangles : A quasi-analytical approach, The Journal of Derivatives, 21 (2013), pp. 64-72. 9. R. J. Elliott and L. Chan, Perpetual american options with fractional brownian motion, Quantitative Finance, 4 (2004), pp. 123-128. 10. J. -P. Fouque and G. Papanicolaous and K. R. Sircar, Derivatives in financial markets with stochastic volatility, Cambridge University Press, 2000. 11. J. Hull et al., Options, futures and other derivatives/John C. Hull., Upper Saddle River, NJ: Prentice Hall, 2009. 12. M. Kang, J. Jeon, H. Han and S. Lee, Analytic solution for american strangle options using laplace-carson transforms, Communications in Nonlinear Science and Numerical Simulation, 47 (2017), pp. 292-307. 13. K. S. Leung, An analytic pricing formula for lookback options under stochastic volatility, Applied Mathematics Letters, 26 (2013), pp. 145-149. 14. R. C. Merton, Theory of rational option pricing, The Bell Journal of economics and management science, (1973), pp. 141-183. 15. R. Panini and R. P. Srivastav, Pricing perpetual options using mellin transforms, Applied Mathematics Letters, 18 (2005), pp. 471-474. 16. A. G. Ramm, A simple proof of the fredholm alternative and a characterization of the fredholm operators, The American Mathematical Monthly, 108 (2001), pp. 855-860. 17. L. Tao, The analyticity and general solution of the cauchy-stefan problem, The Quarterly Journal of Mechanics and Applied Mathematics, 36 (1983), pp. 487-504. 18. J. -H. Yoon, Pricing perpetual american options under multiscale stocahstic elasticity of variance, Chaos, Solitons and Fractals, 70 (2015), pp. 14-26. 19. J. -H. Yoon and J. -H. Kim, A closed-form analytic correction to the black-scholes-merton price for perpetual american options, Applied Mathematics Letters, 26 (2013), pp. 1146- 1150. 20. S. -P. Zhu and W. -T. Chen, Pricing perpetual american options under a stochastic- volatility model with fast mean reversion, Applied Mathematics Letters, 24 (2011), pp. 1663-1669.

- 142 - KSIAM 2020 Annual Meeting ------

            

      

           

  

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- 143 - KSIAM 2020 Annual Meeting ------Optimal cost estimation for PV plant operation with tariff incentive Jamshaid Mannan1, Hyun-Min Kim 1 1) Department of Mathematics, Pusan National University, Busan South Korea.

Corresponding Author: Hyun Min Kim, [email protected] Abstract The Rapidly increasing population at planet earth has created an energy crises and requirement of energy is increasing day by day. Researchers are evaluating different renewable energy sources on the basis of low cost, ease of implementation and continues availability of energy etc. Photovoltaics (PV) systems has put itself at favorable position among other renewable energy resources, due to relatively low cost, clean and environment friendly. In this study a mathematical model for photovoltaic system coupled with storage bank is proposed. A scheme is presented for evaluation of optimal cost on consumer’s shoulder by fulfilling all demand requirement. Different tariff incentive schemes are implemented to comprehensively summarize the effective cost. A detailed statistical analysis have been presented to analyze, import, export betray status and solar energy.

- 144 - KSIAM 2020 Annual Meeting ------

A queueing theory approach to infer reaction kinetics in a non-Markovian biochemical system

Dae Wook KIM1, Hyukpo HONG1 and Jae Kyoung KIM1

1) Department of Mathematical Sciences, KAIST, Daejeon 34141, KOREA

Corresponding Author: Jae Kyoung KIM, [email protected]

ABSTRACT Inferring the characteristics of molecular interactions from experimental data is essential to understand the dynamics of intracellular processes. However, this is challenging because stochasticity within individual cells make the resulting dynamics greatly vary. A further difficulty arises from molecular memory of intracellular processes and heterogeneous cellular environments as it results in non-Markovian reaction dynamics and thus the well-studied Markov theory cannot be used. In this talk, we will introduce an inference approach based on queueing theory, which allows to estimate reaction rates in a non-Markovian biochemical system.

- 145 - KSIAM 2020 Annual Meeting ------

Deep Image Scattering Network with Max-pooling

Taekyung Ki 1 , Youngmi Hur 1

1) School of Mathematics and Computing (Mathematics), Yonsei University, Seoul 03722, KOREA

Corresponding Author : Taekyung Ki, key @yonsei.ac.kr

ABSTRACT Scattering network is a convolutional network, consisting of cascading convolutions with the pre-defined wavelet followed by the modulus operator. Since its introduction in 2012 by S. Mallat, the scattering network is used as one of few mathematical tools in explaining the com- ponents of the convolutional neural networks (CNNs). However, when compared with the con- ventional CNN, the pooling operator, which is one of its main components, is not considered in the original setup of the scattering network. In this paper, we propose a new network, called scattering-m network, integrating the scatter- ing network with the max-pooling operator. The max-pooling outputs maximum values from sub-regions of input. We model continuous max-pooling, apply it to the scattering network, and obtain the scattering-m network. We show that the scattering-m network shares many useful properties of the scattering network such as translation invariance, but with much smaller num- ber of parameters. Numerical experiments show that the use of scattering-m network achieves competitive performance and is much faster than the original one, in image classification tasks.

REFERENCES

1. S. Mallat, “Group invariant scattering”, Communications on Pure and Applied Mathematics, Vol. 65, 2012, pp. 1331-1398.

- 146 - KSIAM 2020 Annual Meeting ------

A Priori and A Posteriori Error Estimation for an Expanded Staggered DG Method

Sanghee Lee 1 , Eun-Jae Park 1 , and Dohyun Kim 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, Korea

Corresponding Author : Eun-Jae Park, [email protected]

ABSTRACT In this poster, we present an expanded staggered discontinuous Galerkin method for solving diffusion problems on general meshes. We introduce an auxiliary variable for the pressure gra- dient, which enables the tensor coefficient not to be inverted. It is desirable especially when a degenerating diffusion coefficient is considered. A priori and A posteriori error estimations are established. A priori error estimation gives the optimal convergence rates in L2-norms for the pressure, flux, and the auxiliary variables. On the other hand, we construct a residual-based error estimator η on the L2-errors of the flux and the auxiliary variables. A posteriori error analysis shows that the estimator is reliable and efficient. Optimal convergence rates for all the variables are successfully achieved in the numerical experiments even for the distorted grids. In particular, a singularity is well-captured by the adaptive mesh refinement process with the error estimator η.

REFERENCES

1. Kim, D. and Park, E.-J., “A Posteriori Error Estimator for Expanded Mixed Hybrid Methods”, Numer. Methods Partial Differential Equations, Vol. 23, 2006, pp. 330-349. 2. Zhao, L. and Park, E.-J., “A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes”, SIAM J. Sci. Comput., Vol. 40, 2018, pp. 2543–2567.

- 147 - KSIAM 2020 Annual Meeting ------

DERIVATION OF STATIONARY DISTRIBUTIONS OF BIOCHEMICAL REACTION NETWORKS VIA STRUCTURE TRANSFORMATION

Hyukpyo HONG1, Jinsu KIM2, Muhammad Ali AL-RADHAWI3, Eduardo SONTAG3 and Jae Kyoung KIM1

1) Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, KOREA 2) Department of Mathematics, University of California, Irvine, CA 92697, United States 3) Departments of Bioengineering and of Electrical and Computer Engineering, Northeastern University, Massachusetts 02115, United States

Corresponding Author: Jae Kyoung KIM, [email protected]

ABSTRACT

Long-term behaviors of biochemical reaction networks are described by steady states in deterministic models, and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions, which are the steady-state solutions of Kolmogorov forward equations, are extremely difficult to derive analytically due to the curse of dimensionality. However, if a network admits so-called a complex balanced steady state where the in- and out- flows of each node are balanced, its stationary distribution can be analytically derived. We develop a method for deriving stationary distributions from steady states by using a network transformation: merging nodes and edges of a network to impose complex balance. Applying our approach to networks that model autophosphorylation of EGFR, PAK1, and Aurora B kinase and a multi- timescale toggle switch, we identify robustness of the number of species to kinetic parameters and multi-modality of stationary distributions. Our method provides an effective tool to understand long-term behaviors of stochastic biochemical systems.

- 148 - KSIAM 2020 Annual Meeting ------

Mathematical modeling of COVID-19 epidemic in Korea and Italy considering behavior changes: comparative analysis of the early stage of epidemic

Jongmin LEE 1, Youngsuk KO 1, Soyoung KIM 2 and Eunok JUNG 1

1) Department of Mathematics, Konkuk University, Seoul 05029, KOREA 2) College of Pharmacy, University of Florida, Florida, United States

Corresponding Author: Eunok JUNG, [email protected]

ABSTRACT

It is obvious that social distancing is effective control measure and can curb down the epidemic. In this study, we focus on the behavior changes of population after disease starts to spread. Using mathematical model, we compare the early stage of COVID-19 epidemics in Korea and Italy. As a result, we found that estimated ߚி, behavior change rate, in Korea is 95 folds of Italy. Behavior changes of population affects the reproductive number to decrease. In Korea and Italia, it takes 13 and 42 days to reproductive number to reach threshold value 1, respectively. Numerical simulation shows that if the behavior change rate in Italy is set as same as Korea, the number of confirmed cases decreases 152600 to 22300. Our research emphasizes how important the rapid rate of behavior changes is in controlling the early COVID-19 outbreak.

REFERENCES

1. Kim, Soyoung, Yu Bin Seo, and Eunok Jung. "Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea," Epidemiology and health, Vol. 42, 2020. 2. Perra, Nicola, Duygu Balcan, Bruno Gonçalves, and Alessandro Vespignani. "Towards a characterization of behavior-disease models," PloS one 6, no. 8, 2011. 3. Carcione JM, Santos JE, Bagaini C and Ba J, "A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model," Front. Public Health, Vol. 8, 2020.

- 149 - KSIAM 2020 Annual Meeting ------

Optimal intermittent social distancing control strategy considering behavior changes: flattening COVID-19 epidemic curve in Korea

Youngsuk Ko1, Soyoung Kim2 and Eunok Jung1

1) Department of Mathematics, Konkuk University, Seoul, Korea 2) College of Pharmacy, University of Florida, Florida, United States

Corresponding Author: Eunok Jung, [email protected]

ABSTRACT

Many researchers have claimed that the intermittent on-off type of social distancing could flatten down epidemic curve and last long. In our study, we developed the COVID-19 model considering behavior change of population and set the social distancing as control measure which suppresses population to be eased. Our goal was to minimize the number of incidence and relative intervention costs in optimal control theory frame. Surprisingly, the optimal control solution came out in on-off type, although we did not assume on-off control but the time-dependent control function. Furthermore, we set intervention cost differently and found that the on-off ratio of optimal control showed relatively small change compare to the change of intervention cost. In last, we suggested suboptimal control which is periodic and has the on-off ratio of optimal control with more applicable duration.

REFERENCES

1. Kim, Soyoung, Yu Bin Seo, and Eunok Jung. "Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea", Epidemiology and health, 2020. 2. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F., “The Mathematical Theory of Optimal Processes”, Wiley, New York, 1962. 3. Kissler, S.M. et al., “Social distancing strategies for curbing the COVID-19 epidemic”, medRxiv, Jan 2020.

- 150 - KSIAM 2020 Annual Meeting ------

  
  

  

 
 

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- 151 - KSIAM 2020 Annual Meeting ------

THE LEAST-SQUARES FINITE ELEMENT METHOD WITH DUAL SYSTEM FOR HELMHOLTZ EQUATION

Nuree Song 1, Eunjung Lee 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, KOREA

Corresponding Author: Eunjung Lee, [email protected]

ABSTRACT

This study employs the least-squares finite element method in a dual system to solve Helmholtz equation for large wavenumber k. The wavenumber, also called spatial frequency, causes oscillatory behaviors of the solution, making it difficult to resolve. In Helmholtz problem, the key is to control ‘pollution effect’, a property that is easily affected by the magnitude of k. We define a model problem on a ring-shaped domain with Robin boundary condition which approximates the Sommerfeld radiation condition to ensure the unique solution. The Helmholtz equation is reconstructed into the first order system by introducing a new variable and scaling factors are inserted to the system to alleviate the dependency on k. -adjoint for this system yields a dual problem and the least squares approach is applied to obtain a variational problem corresponding to residual minimization. By showing the unique existence of weak solution to this dual problem, we have the explicit forms of continuity and coercivity constants which depend on k. The a priori error estimation allows us to choose the proper scaling factors independent of k. Numerical experiments reveal that our approach effectively undermines the pollution effect.

- 152 - KSIAM 2020 Annual Meeting ------

Landscape-dependent computational domains for reaction-diffusion equations

Sangkwon Kim 1 , Jintae Park 1 , Chaeyoung Lee 1 , Darae Jeong 2 , Yongho Choi 3 , Soobin Kwak 1 and Junseok Kim 1

1) Department of Mathematics, Korea University, Seoul 02841, Republic of Korea 2) Department of Mathematics, Kangwon National University, Gangwon-do 24341, Republic of Korea 3) Department of Mathematics and Big Data, Daegu University, Gyeongsan-si, Gyeongsangbuk-do 38453, Republic of Korea

Corresponding Author : Junseok Kim, [email protected]

ABSTRACT The landscape with obstacle is often found in predator-prey systems. In the case of periodic travelling wave solutions, the numerical solution of the reaction-diffusion system in the rectan- gular computational domain leads to a chaotic pattern and the boundary treatment is important. To solve this problem, we propose the landscaping fitted domain defined using a distance func- tion based on obstacles. We apply the proposed algorithm to present good results of various mathematical experiments.

REFERENCES

1. Sherratt JA, Lambin X, Thomas CJ, Sherratt TN, “Generation of periodic waves by landscape features in cyclic predator-prey systems”, Proc R Soc Lond B, 2002;269:32734. 2. Sherratt JA, Lambin X, Sherratt TN, “The effects of the size and shape of landscape features on the formation of traveling waves in cyclic populations”, Am Nat, 2003;162:50313. 3. Smith, Matthew J., Jonathan A. Sherratt, and Nicola J. Armstrong, “The effects of obstacle size on periodic travelling waves in oscillatory reactiondiffusion equations”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464.2090 (2008): 365-390. 4. Yun, A., Shin, J., Li, Y., Lee, S., and Kim, J., “Numerical Study of Periodic Traveling Wave Solutions for the PredatorPrey Model with Landscape Features”, International Journal of Bifurcation and Chaos, 25.09 (2015): 1550117.

- 153 - KSIAM 2020 Annual Meeting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

- 154 - KSIAM 2020 Annual Meeting ------

Gated Recurrent Unit Based Model for Audio Classification

Juyeb Yeo 1 and Myeongmin Kang 1

1) Department of Mathematics, Chungnam National University, Daejeon 34134, KOREA

Corresponding Author : Juyeb Yeo, [email protected]

ABSTRACT For handling time-series data in machine learning, Recurrent Neural Network(RNN) is the most appropriate neural network model and audio data is one of the common time-series data. However in audio classifacation problem, using Convolutional Neural Network(CNN) applied to spectrogram using Mel-frequency Cesptral Coefficient(MFCC) performs better than simple RNN models. In this article we propose a model based on Gated Recurrent Unit(GRU) which is one of the recently suggested recurrent neural network model. We also adopt MFCC and spectrogram as a preprocessing. We validate the superiority of the proposed model in terms of accuracy.

REFERENCES

1. Cho, K.H., van Merrienboer,¨ B., Gulcehre, C., Bougares, F., Schwenk, ., and Bengio, Y., Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation, 2014 2. Radhakrishnan, R., Divakaran, A., and Smaragdis, P., “Audio analysis for surveillance applications”, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pp. 158-161, New Paltz, NY, 2005 3. Lezhenin, I., Bogach, N., and Pyshkin, E., “Urban Sound Classification using Long Short- Term Memory Neural Network,”, 2019 Federated Conference on Computer Science and Information Systems (FedCSIS), pp. 57-60, Leipzig, Germany, 2019.

- 155 - KSIAM 2020 Annual Meeting ------ٻ The data-based inference method reveals the network structure of the SCN

Seokjoo CHAE1, Gosia Malgorzata TYCZYNSKA, Jae Kyoung KIM1

1) KAIST, Daejeon, South Korea, 34141 2) University of South Florida, Tempa, FL, United States, 33612

Corresponding author : Jae Kyoung Kim, [email protected] ٻ Abstract ٻ The suprachiasmatic nucleus (SCN) is the central circadian pacemaker in mammals. Even though SCN is composed of thousands of heterogeneous self-oscillating cells, the SCN can synchronize its component oscillators through the proper network structure among cells. To understand the SCN network structure, previous studies obtained information theory based correlations using the time series data to infer the network structure. However, because of the synchronization among cells, previous methods falsely inferred the network as if all the SCN cells were coupled to each other. To circumvent this, we develop a novel data-based method, which can successfully infer the SCN network from the time series data. In particular, our method accurately infers the SCN network with single-cell resolution bioluminescence data from 2,000 mice SCN cells. Furthermore, our method can infer the directionality of the coupling between SCN cells, consistent with biological results. ٻ

- 156 - KSIAM 2020 Annual Meeting ------

IMPEDANCE SPECTROSCOPY-BASED PARAMETER IDENTIFICATION OF LITHIUM-ION BATTERIES FOR DEGRADATION ANALYSIS

Sungyeon KIM 1 , Seongyoon KIM 1 , and Jung-Il CHOI 1

1) School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul 03722, Republic of Korea

Corresponding Author : Jung-Il CHOI, [email protected]

ABSTRACT Accurate estimation of the internal state of lithium-ion batteries (LIBs) is important to under- stand aging phenomena and enable improvement of future generations of LIBs. We propose parameter identification method of LIBs with impedance-based circuit model for degradation analysis. Electrochemical impedance spectroscopy (EIS) is one of the most attractive diagnostic techniques due to its convenience, quickness, accuracy, and low cost. To figure out the degrada- tion pattern, we identify physical parameters of 12 types of equivalent circuit models (ECMs) from battery impedance spectra using the Levenberg-Marquardt (LM) algorithm. Furthermore, the Akaike information criterion is used to decide the most suitable ECM for fitting EIS data. Ultimately, with the optimized parameters from the best-fitting ECM, we utilize the Gaussian process to predict the state-of-health (SOH) and remaining useful life (RUL) of LIBs. The re- sults demonstrate that the proposed method enables physical interpretation of aging pattern of LIBs and forecasts SOH and RUL accurately.

- 157 - KSIAM 2020 Annual Meeting ------

    

                

  

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- 158 - KSIAM 2020 Annual Meeting ------

ANALYSIS AND IMPROVEMENT OF SOFTMAX-LOSS IN DEEP METRIC LEARNING

Junghyun Lee 1

1) Department of Mathematical Science, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT Deep metric learning is a learning method in the field of image search and face verification. This learning method refers to a method of learning the semantic distance between features while mapping each data to a specific embedding space. In order to learn metrics in the em- bedding space, various loss functions and data sampling methods have been developed so far. In particular, the proxy-based loss function is widely used due to its advantage in computa- tion speed. One of the important factors that determine performance in deep metric learning is intra-class distance and inter-class distance. However, because of the complexity of proxy-based loss function, it is hard to analyze these distance. In this study, we analyzed the softmax loss function, which have been used as a basic frame in proxy-based loss. And using the obtained analysis results, we proposed a new loss that can improve the performance. Finally, we checked an improvement of the performance of our suggested new loss in ResNet-50 model.

- 159 - KSIAM 2020 Annual Meeting ------

Instance segmentation model for tracking building in satellite imagery upon high resolution time-series data

Hoin Jung 1 Han-Soo Choi 2 and Myungjoo Kang 3

1) Department of Computational Science and Technology, Seoul National University, Seoul 151-742, KOREA 2) Research institute of Mathematics, Seoul National University, Seoul 151-742, KOREA 3) Department of Mathematical Sciences, Seoul National University, Seoul 151-742, KOREA

Corresponding Author : Myungjoo Kang, [email protected]

ABSTRACT Satellite imagery analytics have numerous time series applications to respond to human devel- opment and disaster. The SpaceNet 7 Multi-Temporal Urban Development Challenge aims to improve these methods while simultaneously advancing state-of-the-art foundational mapping. We propose an encoder-decoder convolutional network that builds upon residual architecture, where decoder architecture includes the Pixelshuffle method as upsampling to train time-series satellite imagery for instance segmentation. To track individual buildings construction over time to assess urbanization, two years time-spans monthly high resolution satellite imagery covering broad areas for each location. There are a hundred locations of image cubes, 60 areas for train- ing, 20 for validation, 20 for the final test. Although identifying and tracking the small pixel object area upon high object density is a challenging task, we obtained a higher SCOT metric score ameliorated more than the baseline given by the challenge host(15.83)

REFERENCES

- 160 - KSIAM 2020 Annual Meeting ------

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- 161 - KSIAM 2020 Annual Meeting ------                  !!!!  "!# !$ "                   

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