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Periodicity and Chaos of High-Order Lorenz Systems
Moon, Sungju,Han, Beom-Soon,Park, Junho,Seo, Jaemyeong Mango,Baik, Jong-Jin World Scientific Publishing Company 2017 International journal of bifurcation and chaos in Vol.27 No.11
<P>High-order Lorenz systems with five, six, eight, nine, and eleven equations are derived by choosing different numbers of Fourier modes upon truncation. For the original Lorenz system and for the five high-order Lorenz systems, solutions are numerically computed, and periodicity diagrams are plotted on <TEX>$ (\sigma ,r)$</TEX> parameter planes with <TEX>$ \sigma ,r \in [0, 1000]$</TEX>, and <TEX>$ b = 8/3$</TEX>. Dramatic shifts of patterns are observed among periodicity diagrams of different systems, including the appearance of expansive areas of period 2 in the fifth-, eighth-, ninth-, and 11th-order systems and the disappearance of the onion-like structure beyond order 5. Bifurcation diagrams along with phase portraits offer a closer look at the two phenomena.</P>
High-Dimensional Lorenz Systems, Atmospheric Predictability, and Data Assimilation: An Overview
Sungju Moon 한국기상학회 2021 한국기상학회 학술대회 논문집 Vol.2021 No.10
In this talk, I will give a broad overview of my PhD project. The primary aim has been to investigate chaotic or nonlinear dynamical behavior of certain high-dimensional extensions of the Lorenz system and to explore potential implications pertaining to the study and modeling of Earth"s atmosphere and its predictability. To this end, two distinct approaches to extending the Lorenz system were employed: 1. incorporating additional physical ingredients in the governing equations, leading to the 6-dimensional physically extended Lorenz system and 2. including higher wavenumber modes before truncating the series expansions in the derivation, yielding the (3N)- and (3N+2)-dimensional generalized Lorenz systems for any positive integer N. The newly derived systems are thoroughly analyzied, utilizing various tools borrowed from the study of dynamical systems. I will first go over the results deemd most important from the chaos theoretic point of view, which includes the discovery of a new chaotic attractor, analysis of coexisting attractors, and some new insights into chaos synchronization in these systems. Inspired in particular by the chaos synchronization result, I will then argue that the generalized systems can be used as a testbed model for assessing data assimilation methods with some distinctive advantages compared to other conventional testbed models. Predictability has also been an important theme; more specifically, my aim has been to explore and establish deviation time as the measure of predictability more in tune with the chaos inherent to Earth"s atmosphere, which has thus far been overlooked in favor of other notions of predictability. Upon testing the deviation time concept on the generalized Lorenz systems as well as on realistic simulations of a precipitating case over East Asia by the Weather Research and Forecast (WRF) Model, it was suggested that atmospheric predictability may not necessarily respond monotonically to refinements of vertical resolution. I will conclude the talk with suggestions for future research.
The Generalized Lorenz Systems: A New Testbed Model for Data Assimilation
Sungju Moon,Jong-Jin Baik 한국기상학회 2021 한국기상학회 학술대회 논문집 Vol.2021 No.10
The feasibility of using a (3N)-dimensional generalization of the Lorenz system in testing a data assimilation method is explored through numerical experiments. The generalization extends the Lorenz system, known as the Lorenz "63 model, into a (3N)-dimensional nonlinear system for any positive integer N, which is known to exhibit chaos synchronization. Because the extension involves inclusion of additional wavenumber modes, raising the dimension allows the system to resolve smaller-scale motions, a unique characteristic of the present generalization that can be relevant to real modeling scenarios. Accordingly, model imperfections are simulated by assuming a high-dimensional generalized Lorenz system as the true system and a generalized system of dimension less than or equal to the dimension of the true system as the model system. The Ensemble Kalman filter data assimilation method is tested. Different scenarios relevant to data assimilation practices are simulated by varying the dimensional differences between the model and true systems, ensemble size, and observation frequency and accuracy. The results indicate that this generalization of the Lorenz system is a viable and flexible tool for evaluating the effectiveness of data assimilation methods and, therefore, a meaningful addition to the portfolio of testbed systems that includes the Lorenz "63 and "96 models, especially considering its relationship with the Lorenz "63 model
A Practical Implementation of Fuzzy Fingerprint Vault
( Sungju Lee ),( Yongwha Chung ),( Daesung Moon ),( Sung Bum Pan ),( Chang-ho Seo ) 한국인터넷정보학회 2011 KSII Transactions on Internet and Information Syst Vol.5 No.10
Recently, a cryptographic construct, called fuzzy vault, has been proposed for crypto-biometric systems, and some implementations for fingerprint have been reported to protect the stored fingerprint template by hiding the fingerprint features. In this paper, we implement the fuzzy fingerprint vault, combining fingerprint verification and fuzzy vault scheme to protect fingerprint templates. To implement the fuzzy fingerprint vault as a complete system, we have to consider several practical issues such as automatic fingerprint alignment, verification accuracy, execution time, error correcting code, etc. In addition, to protect the fuzzy fingerprint vault from the correlation attack, we propose an approach to insert chaffs in a structured way such that distinguishing the fingerprint minutiae and the chaff points obtained from two applications is computationally hard. Based on the experimental results, we confirm that the proposed approach provides higher security than inserting chaffs randomly without a significant degradation of the verification accuracy, and our implementation can be used for real applications.
이성주 ( Sungju Lee ),정승환 ( Seunghwan Jung ),문대성 ( Daesung Moon ),최성백 ( Sungback Choi ),양성현 ( Sunghyun Yang ),정용화 ( Yongwha Chung ) 한국정보처리학회 2006 한국정보처리학회 학술대회논문집 Vol.13 No.1
생체정보를 이용한 사용자 인증시스템은 편리함과 동시에 강력한 보안을 제공할 수 있다. 그러나 사용자 인증을 위해 저장된 중요한 생체정보가 타인에게 도용된다면 심각한 문제를 일으킨다. 따라서 타인에게 유출되더라도 재사용이 불가능하도록 하기 위하여 사용자의 생체정보에 역변환이 불가능한 함수를 적용하여 저장하고 변환된 상태에서 인증과정을 수행할 수 있는 방법이 필요하다. 본 논문에서는 최근 지문 템플릿(Fingerprint Template)을 보호하기 위해 암호학적 방법으로 연구되어지고 있는 퍼지볼트(Fuzzy Vault) 이론을 이용하여 안전하게 지문 템플릿을 보호하는 방법을 제안한다. 특히, 지문 템플릿에 퍼지볼트 이론을 단순 적용할 경우 기준점 부재로 인하여 야기되는 지문 정렬(alignment) 문제를 해결하기 위하여 기하학적 해싱(Geometric Hashing)방법을 사용하였다. 실험을 통하여 제안한 지문 퍼지볼트(Fuzzy Fingerprints Vault) 기법은 추가적인 정보없이 변환된 도메인에서 자동으로 지문 정렬을 수행하여 안전한 지문 템플릿 보호 및 인증이 가능하다는 것을 확인하였다.