Stony Brook University Applied Mathematics and Statistics

Speaker: Xiaolin Li Location: C107 Date and Time: April 25 (Fri), 12:00 PM - 1:00 PM KST About the Speaker: Dr. Xiaolin Li • Professor, Dept. of Applied Mathematics and Statistics | Stony Brook University • Assistant Professor, Dept. of Mathematics and Dept. of Computer Science | Indiana University-Purdue University at Indianapolis • Assistant Professor, Department of Mathematics | New Jersey Institute of Technology • Associate Research Scientist | Courant Institute of Mathematical Sciences • Ph.D. in Applied Mathematics | Columbia University • M.S. in Applied Mathematics | Columbia University • B.S. in Physics | Wuhan University Abstract This work presents a story of mathematical modeling through the development of a mesoscale dual-stress spring model, derived using Rayleigh-Ritz analysis, to represent the fabric surface of a parachute as an elastic membrane. The elastic structure is coupled with a fluid solver via the impulse method to capture fluid-structure interactions. We describe the implementation of this coupled system on a front-tracking computational platform, leveraging its data structures and core functionalities. Key challenges in this multi-physics simulation are addressed, including turbulence modeling, fabric collision, parachutist-body-fluid interaction, and computational parallelization. We also provide numerical evidence of convergence, along with verification and validation of the model components. Finally, we discuss the software architecture designed to support simulations of various air-delivery systems.    

Speaker: Xiaolin Li Location: B205 Date and Time: March 21 (Fri), 12:00 PM - 1:00 PM KST About the Speaker: Dr. Xiaolin Li Professor, Dept. of Applied Mathematics and Statistics | Stony Brook University Assistant Professor, Dept. of Mathematics and Dept. of Computer Science | Indiana University-Purdue University at Indianapolis Assistant Professor, Department of Mathematics | New Jersey Institute of Technology Associate Research Scientist | Courant Institute of Mathematical Sciences Ph.D. in Applied Mathematics | Columbia University M.S. in Applied Mathematics | Columbia University B.S. in Physics | Wuhan University Abstract Nonlinear hyperbolic PDEs, due to the intersection of characteristics, lead to either multivalued solutions or discontinuities. In physics, only the latter is acceptable. These discontinuities fall under the category of "weak solutions," which satisfy the integral form of the PDE rather than the pointwise form. The front tracking method is specifically designed to handle such discontinuities within finite difference and finite element schemes for numerically solving PDEs. In two and three dimensions, the challenge extends beyond coupling the interior solution with the discontinuity—we must also manage topological bifurcations. In this talk, we will discuss the implementation of this method and its applications to physical phenomena such as fluid interface instabilities, jet mixing, and deposition and erosion.  

The AMS Department is proud to recognize and celebrate the outstanding accomplishments of the Fall 2024 graduating class!   Bachelor of Science: Han, Jiwon | Magna Cum Laude Kim, Yul A (Elisa) | Summa Cum Laude Lee, Geon Myeong | Cum Laude Park, Suyoung Son, Minwoo   Congratulations on reaching this incredible milestone! Your hard work and dedication have truly paid off, and we couldn’t be more excited to see all that you’ll accomplish.      

The AMS Department is thrilled to formally celebrate the achievements of the Graduating Class of Spring 2024!   Bachelor of Science: Choo, Sieun | Magna Cum Laude Ochiai, Kotone | Magna Cum Laude Shin, Ji Woo | Magna Cum Laude Jung, Hyewon | Cum Laude Park, Cheayoung | Cum Laude Choi, Hyeonseok Kim, Jung Hwan Yang, Ui Jung   As you step into the next phase of your journey, remember that the skills and knowledge you've gained here will serve as a strong foundation for your future endeavors. We wish you all the best and look forward to the bright lives you will continue to live!     

[AMS Seminar III] Math in Music by Professor Hongshik Ahn  

[AMS Seminar II] Two-Stage Ransomware Detection Using Dynamics Analysis and Machine Learning Techniques by Professor Jinsoo Hwang  

Speaker: Jinsoo Hwang   Location: B105 Date and Time: April 22 (Mon), 6:30 PM - 7:30 PM in KST About the Speaker: Dr. Jinsoo Hwang Adjunct Professor, Dept. of Applied Mathematics and Statistics | SUNY Korea Dean, College of Natural Sciences | Inha University Assistant Professor, Department of Mathematical Sciences | Arizona State University Ph.D. in Statistics | Purdue University M.S. in Statistics | Seoul National University B.S. in Statistics & Computer Science | Seoul National University Abstract Detecting ransomware is harder than general malware because of the ever-increasing number of ransomwares with different signatures, which makes traditional signature-based detection technique powerless against ransomware. Current ransomware detection techniques usually build a complex model that incorporates various behavioral traits. The traits include suspicious file activities, API call pattern or frequency, registry keys, file extensions, etc. In this paper, we build a two-stage mixed ransomware detection model, Markov model and Random Forest model. First, we focus on Windows API call sequence pattern and build a Markov model to capture the characteristics of ransomware. Next, we build Random Forest machine learning model to the remaining data to control both false positive (FPR) and false negative (FNR) error rates. As a result of our two-stage mixed detection method we can achieve overall accuracy 97.3% with 4.8% FPR and 1.5% FNR.    

[Spring 2024 AMS Seminar I] A Numerical Conversion from Multiple Decrement Rates to Absolute Rates of Decrements by Prof. Taewon Lee  

Speaker: Taewon Lee   Location: B105 Date and Time: March 25 (Mon), 6:30 PM - 7:30 PM in KST   About the Speaker: Dr. Taewon Lee - (Current) Visiting Professor, Dept. of Applied Math and Statistics, SUNY Korea - Professor, Division of Applied Mathematical Sciences, Korea University, Sejong Campus - Visiting Scholar, Dept. of Statistics and Actuarial Science, University of Waterloo - Ph.D. in Applied Mathematics and Statistics, State University of New York at Stony Brook - MS in Statistics, Seoul National University - BS in Mathematics, Seoul National University   Abstract Modeling interactions of competing risks affecting the occurrence of various decrements such as death or disease is a critical issue in survival analysis and actuarial science. It is essential to incorporate multiple decrements for offerring various coverages in an insurance contract. Popular assumptions for the construction of decrement models are uniform distributions of decrements (UDD) in a multiple decrement table (MDT) and associated single decrement tables (ASDT). Whereas the conversion from absolute rates of decrements in ASDT to multiple decrement rates in MDT under the UDD assumption has an explicit formula, extracting absolute rates from multiple decrement rates becomes solving a system of non-linear equations. A novel numerical algorithm using a fixed point iteration method for searching a solution of the system of equations is proposed. The proposed numerical algorithm to obtain absolute rates of decrement from observed probabilities of decrement makes it possible to estimate a new multiple-decrement table from an old multiple-decrement table with some risk factors to be removed. The algorithm delivers reliable results in terms of efficiency and accuracy. The proposed algorithm is proved to be a stable algorithm that never diverges out of range of probability during the iterations. The self-mapping property in iteration is expected to lead to prove the existence of a solution of the system of equations.  

Welcome aboard, the class of 2028! Congratulations and best wishes on your first semester!  

We have been hosting the Math Competition since 2016. After a pause due to the COVID-19 pandemic, we are thrilled to resume this event. It is wonderful to have this event reactivated and to meet the outstanding students once again.   We had 38 high school students, from 24 different high schools, and 27 SUNY Korea students, not only from the College of Engineering and Applied Sciences from SBU but also from the Fashion Design Department from FIT.    Thank you for all your participation. We’d like to express our sincere congratulations to all the winners! Hope to see more students from various high schools and also from all different departments at SUNY Korea next year.   [Pic.1] 2023 Math Competition Award Ceremony for the winners of 2023! (12/02/2023)   [Pic.2] A Short Lecture delivered by Prof. Hongshik Ahn before the Math Competition (11/23/2023)

SUNY Korea Admissions Team hosted the 2023 SUNY Korea Experience Day on November 25, welcoming all prospective and admitted students. Prof. Hongshik Ahn provided an introduction about the AMS Department, and Prof. Young-Seon Lee gave a mock lecture on the topic of 'Essential Concepts of Integral Calculus' to the students. The Experience Day will be held every semester. All prospective students are welcome to the event. Hope to see many students next year again! Introduction of the AMS Department by Prof. Hongshik Ahn   Mock Lecture <Essential Concepts of Integral Calculus> by Prof. Young-Seon Lee

Fall 2023 AMS Seminars -> Seminar II, Hierarchical Bayesian Spatial Regression Models by Prof. Jaewoo Park from Yonsei University.     -> Seminar III, Accelerated Failure Time Modeling via Nonparametric Mixtures by Prof. Sangwook Kang from Yonsei University.   There will be more interesting seminars coming up next semester, so stay tuned! :) 

Speaker: Sangwook Kang   Location: B105 Date and Time: November 20 (Mon), 10:30 AM - 11:30 AM in KST About the Speaker: Dr. Sangwook Kang - (Current) Professor and Chair, Dept of Applied Statistics, Yonsei University -  Assistant/Associate Professor, Dept of Applied Statistics, Yonsei University -  Visiting Professor, Dept of Statistics, University of Connecticut -  Associate Director, Yonsei Institute of Data Science, Yonsei University -  Assistant Professor, Dept of Statistics, University of Connecticut -  Assistant Professor, Dept of Epidemiology and Biostatistics, University of Georgia Abstract An accelerated failure time (AFT) model assuming a log-linear relationship between failure time and a set of covariates can be either parametric or semi-parametric, depending on the distributional assumption for the error term. Both classes of AFT models have been popular in the analysis of censored failure time data. The semiparametric AFT model is more flexible and robust to departures from the distributional assumption than its parametric counterpart. However, the semiparametric AFT model is subject to producing biased results for estimating any quantities involving an intercept. Estimating an intercept requires a separate procedure. Moreover, a consistent estimation of the intercept requires stringent conditions. Thus, essential quantities such as mean failure times might not be reliably estimated using semiparametric AFT models, which can be naturally done in the framework of parametric AFT models. Meanwhile, parametric AFT models can be severely impaired by misspecifications. To overcome this, we propose a new type of the AFT model using a nonparametric Gaussian-scale mixture distribution. We also provide feasible algorithms to estimate the parameters and mixing distribution. The finite sample properties of the proposed estimators are investigated via an extensive stimulation study. The proposed estimators are illustrated using the well-known PBC dataset.

Speaker: Jaewoo Park   Location: B105 Date and Time: October 30 (Mon), 6:40 PM - 7:40 PM in KST RSVP HERE: https://forms.gle/SJeFVFSNsZRD2yfVA About the Speaker: Dr. Jaewoo Park -  (Current) Assistant Professor, Department of Applied Statistics, Yonsei University -  Ph.D. in Statistics, The Pennsylvania State University -  BA in Applied Statistics, Economics, Yonsei University Abstract Spatial regressions are widely used to study relationships between spatial variables in many scientific domains, such as ecology, epidemiology, and sociology. For a given spatial latent process, hierarchical structures are defined for building complex high-dimensional models from simple and low-dimensional building blocks. Bayesian approaches are popular for hierarchical spatial models due to their computational and inferential advantages. In this talk, I will review the Bayesian framework for hierarchical spatial regression models. I will show how such models can be applied to real datasets, such as confirmed COVID-19 cases in the United States.