Asymmetric Network Properties of Bipartite Ecological Networks

맹성은,이재우 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.58 No.4

The asymmetric properties of bipartite ecological networks were studied by analyzing the interaction of seven plant-pollinator mutualistic networks. The data in this work were collected from published papers and web sites. The frequencies of pollinators’ visits to various plant species in a certain area were measured during a season. The visiting frequency was considered the interaction strength. The cumulative probability distribution function (CDF) of the plants was found to follow a stretched exponential function for both degree and strength. However, the CDF of the pollinators followed a power law. The average strength showed a nonlinear dependence on the degree. The average disparity followed a power law dependence on the degree of the networks. The disparity showed that the weights were distributed heterogeneously on the links of the mutualistic networks.

고등학교 과학 교육에서 혼돈 이론을 도입하는 방안에 대한 연구

김민희,맹성은,이재우 한국물리학회 2012 새물리 Vol.62 No.12

This paper introduces the basic concepts of chaos theory and develops learning contents that can be applied to education in high-school science. We introduce logistic maps, attractors,self-similarity, butterfly effects (sensitivity to initial conditions), Lyapunov exponents, fractals, and fractal dimensions. The chaotic examples can be applied to high-school science in the following areas; the simple harmonic oscillator in mechanics, the population dynamics in biology, and the weather and the motion of the planets. To induce interests in science, teachers should introduce chaos theory by using the methods of computer simulation. 본 연구는 고등학교 과학 교육에 적용할 수 있는 혼돈 이론 학습내용을소개하고 학습 자료를 개발함으로써 고등학교 과학과 교육과정에혼돈현상을 도입하는 방안을 모색한다. 혼돈 이론을 이해하는데 필요한로지스틱 사상, 끌개, 자기 유사성, 나비효과(초기조건의 민감성),리아프노프 지수, 프랙탈에 대한 정의와 프랙탈 차원에 대해 알아보았다. 고등학교 과학 교육에서 혼돈 이론의 필요성과 단원별 연계성을제시하였다. 혼돈 현상은 고등학교 과학 교과의 `역학에서 단진동',`생물학의 인구동력학', `기상현상과 행성의 운동' 등의 단원에서 도입할수 있다. 컴퓨터 활동을 활용하여 혼돈이론을 학습하게 함으로써학생들의 과학에 대한 친근감과 흥미를 높인다. 교사들이 실제 수업에활용할 수 있는 이론과 학습자료를 제공한다.

Scaling of Nestedness in Complex Networks

이덕선,맹성은,이재우 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.60 No.4

Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the neighbors of the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of species in ecological communities exhibit such nestedness, which is known to support the network’s robustness. Despite such importance, the quantitative characteristics of nestedness are little understood. Here, we take a graph-theoretic approach to derive the scaling properties of nestedness in various model networks. Our results show how the heterogeneous connectivity patterns enhance nestedness. Also, we find that the nestedness of bipartite networks depends sensitively on the fraction of different types of nodes, causing nestedness to scale differently for nodes of different types.

Self-organized Criticality of a Simple Integrate-and-fire Neural Model

최형욱,맹성은,이재우 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.60 No.4

We consider a simple integrate-and-fire neural model without synaptic plasticity. In this model, the membrane potential propagates to the nearest neighbor neurons when that potential is greater than a threshold value. When a neuron is fired, the propagating potential is leaky. Therefore, the sum of the received potential is less than the presynaptic potential. We simulated this simple model on a fully-connected network. We identified the critical membrane strength, Jc = 4.71(1). At the critical membrane strength, we observed that the probability distribution function of the avalanche shows a power law, P(s) ≈ s−τ, with the critical exponent τ = 1.414(5). The lifetime of the avalanche also showed a power law. The power law behaviors imply that this model shows self-organized criticality.

Scaling and Non-scaling Behaviors of Seismic Time Series for Korean Earthquakes

최형욱,맹성은,이재우 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.59 No.1

Seismic time series for the Korean peninsula are considered for data over the last 33 years. Korean earthquakes follow the Gutenberg-Richter law, log_(10) N(M > m) ~ -bm, with b = 0.78(1) where N(M > m) denotes the cumulative number of earthquakes of magnitude M greater than a threshold magnitude m. The cumulative probability distribution function P_>(T), of the inter-occurrence time follows an exponential function, P_>(T) ~ exp(-aT), with a = 2.60 (1), up to an inter-occurrence time of T = 40,000 min. The occurrence rate n(t), is also considered as a function of time, with a time interval, Δt. The cumulative probability distribution function of the occurrence rate follows a power law P_>(n) ~ n^(−α), with α = 1.20 (2), regardless of the length of the time interval Δt. The persistence distribution function of the seismic time series is also analyzed. Positive (or negative) persistence times are defined as intervals when earthquake magnitudes remain above (or below) the initial magnitude, m(t_o), from time t_o to a time t_o + s, where s is the persistence time. The cumulative persistence probability Q_> (s), follows a power law, Q_> (s) ~ s^(−θ), with θ = 0.93 (3).

Effects of Intraday Patterns on a Time Series Analysis of the Korean Stock Market Index

김두환,맹성은,방유식,최형욱,차문용,이재우 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.58 No.2

The effects of intraday patterns were considered in a time series analysis of the Korean stock market. One minute tick data from January 2, 2004, to October 30, 2009, on the Korea composite stock price index were studied. The autocorrelation function (ACF) of the absolute return and the probability distribution function (PDF) of returns were calculated by using a time series with the intraday patterns removed. Two methods of eliminating the intraday patterns are suggested: elimination from the index itself and from the absolute returns. The ACF of the absolute return showed a power law with an exponent that did not vary with the method used to eliminate the intraday patterns. Eliminating intraday patterns from the absolute return removed the periodicity of the ACF. However, the periodicity remained if intraday patterns were removed from the index itself. The PDF of returns showed a power law, but its exponents depended on the method of removing the intraday patterns.

Structural Changes in the Minimal Spanning Tree and the Hierarchical Network in the Korean Stock Market around the Global Financial Crisis

Ashadun Nobi,맹성은,하정균,이재우 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.66 No.8

This paper considers stock prices in the Korean stock market during the 2008 global financial crisis by focusing on three time periods: before, during, and after the crisis. Complex networks are extracted from cross-correlation coefficients between the normalized logarithmic return of the stock price time series of firms. The minimal spanning trees (MSTs) and the hierarchical network (HN) are generated from cross-correlation coefficients. Before and after the crisis, securities firms are located at the center of the MST. During the crisis, however, the center of the MST changes to a firm in heavy industry and construction. During the crisis, the MST shrinks in comparison to that before and that after the crisis. This topological change in the MST during the crisis reflects a distinct effect of the global financial crisis. The cophenetic correlation coefficient increases during the crisis, indicating an increase in the hierarchical structure during in this period. When crisis hits the market, firms behave synchronously, and their correlations are higher than those during a normal period.

Persistent and Survival Properties in a Stock Market Index

이재우,차문용,맹성은,방유식 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.56 No.3

We consider the persistent and the survival properties of the Korean stock market index (KOSPI),and investigate the crossing and the persistence probability for a time series of the KOSPI. The crossing probability of the stock index follows a power law, Y (t) ~t−α. The Korean stock market shows weak antipersistent behavior. We also report the survival probability of the stock index. The survival probability S(t) measures the probability of a stock’s price remaining above (or below) a reference value up to a time to + t. We observed that the survival probability in the Korean stock market followed a power law, S(t) ~ -β, where the exponent depended on the reference level. The persistence and the survival of the stock index comes from the correlated memory of the stock index in the market.

Random Matrix Theory and Cross-correlations in Global Financial Indices and Local Stock Market Indices

Ashadun Nobi,맹성은,하경균,이재우 한국물리학회 2013 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.62 No.4

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [λ_-,λ₊], where λ_- and λ₊ are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.

Scaling Behaviors of Plant-Pollinator Mutualistic Networks

이재우,이경은,맹성은,황준경 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.53 No.6

We consider three plant-pollinator mutualistic networks, including a montane forest, a beech forest and a meadow. The plant and the pollinator connect by links of interacting strengths between species. We obtained cumulative distribution functions (CDFs) of the degree and the strength for the networks. The CDFs of the degree for all species, pollinators and plant, follow a power law or a stretched exponential function. The CDF of the degree for a meadow food web, MEM food web (Mommett 1999), is well fitted by a stretched exponential function. However, the CDF of the degree for the montane forest food web, INO food web (Inouye and Pkye 1998) and for the beech forest food web, KAT food web (Kato et al. 1990) show a power law. The CDFs of the strength also follow a power law, except for the CDF of the pollinator for the KAT food web. The CDFs of the degree and the strength for mutualistic networks depend on the types and the locations of the food webs.