Handling editor: Phanikrishna Thota

Nonlinear and Complex Systems Laboratory Pohang University of Science & Technology in Pohang, Korea by Seunghwan Kim Department of Physics, POSTECH

The Nonlinear and Complex Systems Laboratory (NCSL) was established in 1990 in the Department of Physics of the Pohang University of Science & Technology in Pohang, Korea. Its goals are to pursue interdisciplinary research on the basic understanding and applications of nonlinear dynamics and complex systems. From the 1990s, NCSL has operated as one of the key centers of nonlinear science in Korea with three professors and 20 PhD students, developing the fundamental methodology of nonlinear dynamics, studying pattern formation, self-organization, and chaos in nonlinear physical and biological systems. Since July 1997, NCSL has participated in a national research project on brain science as a key laboratory with a focus on neurodynamics and information processing of the nervous system. In June 2000, NCSL was selected as a National Research Laboratory (NRL) by the Ministry of Science and Technology (MOST) in Korea. The NCSL as an NRL has also been working on prediction of complex time series based on chaos and complex system theory and applications to biomedical and economic time series. The NCSL operates as one of the key members of the Basic Science Research Institute and the Brain Research Center at POSTECH and has been cooperating with hospitals and research centers around Korea including Samsung Medical School, Asan Medical Hospital, and Seoul National University Hospital.

NCSL group photo; back row from left to right: Joonyoung Moon, Sungyun Kim, Sunghoon Kim, Kyeyeon Hur, Hongseok Kim, Jeongkyu Shin; front row from left to right: Eunjin Hwang, Seunghwan Kim, Jeongeun Hwang, Dongmyeong Lee; insets from top to bottom: Myoung Won Cho, Gabjin Oh, and Chang-Woo Shin.

The main current research interests of NCSL are the development of the fundamental methodology of nonlinear dynamics and the understanding of self-organization and pattern formation of complex systems through modeling and analysis of biological complex networks, neural networks of the brain, and economic systems. The key mathematical techniques involve bifurcation theory, nonlinear time series analysis, and computational modeling. The research projects of our focus are:

Biophysics of neurons and neural networks

The brain is one of the most challenging complex systems. The neurons, massively inter-connected with each other, show highly complex and correlated responses to external stimuli, which help the brain to extract relevant patterns from sensory inputs, coordinate movements and control behaviors. To understand the complexity of the nervous system we need to characterize its network structure on which the spatio-temporal firing activities are supported.
		The brain as a complex network of neurons.
Recent studies of complex systems have shown that the synchronization of oscillators including neuronal ones is faster, stronger, and more efficient in small-world networks than in regular or random networks, and many studies are based on the assumption that the brain may utilize the small-world and scale-free network structure. Our study shows that the functional structures in the brain are self-organized to both small-world and scale-free networks by synaptic re-organization of the spike timing dependent synaptic plasticity (STDP), which is hardly achieved with conventional Hebbian learning rules. Here, the balance between excitatory and inhibitory synaptic inputs is critical in the formation of the functional structure, which is in a self-organized critical state.

In the case of conventional Hebbian networks, all synaptic connections between neurons increase under the common external stimulus, whereas the others are weakened. However, the STDP networks show that the neurons under common stimulus need not be fully connected; only a small portion of the strengthened synapses forms a sparse small-world scale-free network, which is dynamically more effective and structurally more robust. This neural mechanism may be utilized in modeling and controlling the neural networks more efficiently. Furthermore, this work provides insight into the formation of functional complex networks in the brain due to the activity of dependent synaptic plasticity, and the developmental processes of neural circuits, as in learning and memory models.

Functional self-organization in brain map development

How can we explain the different patterns in the visual maps of mammals such as Macaque Monkey, cats, and tree shrews? This highly ordered structure in the mammalian visual cortex has attracted much attention from theoretical neurobiologists and has been thoroughly studied with the expectation of providing the basis for neural dynamics and computational models. The visual maps on the cortex exhibit diverse ordered patterns, the most fundamental of which is provided by the ocular dominance and orientation preference columns. Though most of the models of the visual map formation are based on common postulates such as Hebbian synapses, connections, or competition between neighboring neurons and synaptic normalization, there are quite a number of successful models with unique mechanisms. The Hamiltonian models with spin variables are proposed for the visual map formation that exhibit a striking analogy with the physical systems such as magnetism.

Model of the visual map formation.

The characteristics of visual maps have been systematically explored through the statistical properties of `vortices' in magnetism. The spinlike Hamiltonian models represent essential ingredients of neural interactions in the visual map formation without paying much attention to particular neural control mechanisms, and can be shown to exhibit common statistical properties of the vortex formation as in other development models.

In animal experiments, the observed orientation preference and ocular dominance columns in the visual cortex of the brain shown various pattern types. We study the different visual map formation in various mammals in the context of the crossover behavior in anisotropic systems composed of orientational and scalar components such as easy-plane Heisenberg models. The transition boundary between different pattern types with anisotropy as a main bifurcation parameter is predicted and shown to be consistent with the classification of experimental observations for visual maps in Macaque Monkey, cats, and tree shrews. This study shows a new possibility for the study of the complex brain in the context of physical models.

Nonlinear analysis of biomedical time series

The biomedical time series is one of the paradigms of complex time series. Biological systems continuously interact with the environment and display complex dynamics. Measurements of biological systems lead to complex time series that are nonstationary, high dimensional, and noisy. We try to develop new nonlinear methods for quantifying the nonlinear characteristics of biomedical time series and apply these to the analysis of EEG and HRVs for the purpose of diagnosis of epilepsy and other pathological brain states. In particular, we have been working with the Samsung Medical School to build the standardized database for the EEG research and developing the seizure diagnosis and prediction system based on nonlinear analysis algorithms.

EEG analysis and prediction system.

The relationships between multichannel sites of the electroencephalogram (EEG) have recently been one of the most interesting subjects of research. To understand their complex and dynamic relationships, various methods such as interdependence, synchronization and information flow between multichannels have been investigated. Epilepsy is a dynamics disease in which self-organization and emergent structures occur dynamically at multiple levels of neuronal integration. Therefore, the transient relationship within multichannel EEGs is crucial for understanding epileptic processes. We study the global relationship within multichannel EEGs to gain more information on the classification of different epilepsy types. The global network structure is determined within channels of the scalp EEG based on the minimum spanning tree method. The topological dissimilarity of the network structures from different types of epilepsy is explored through the divergence rate and applied to the data from patients, for example, with the left and right temporal lobe epilepsy. We find that patients with different epilepsy types exhibit different large-scale network structures, which emerge at the epoch immediately before the seizure onset, not in the preceeding epochs. This suggests that patients with two different epilepsy types display distinct large-scale dynamics networks with characteristic epileptic network structures.

Nonlinear analysis of economic time series

The economic time series is one of the most complex time series, because it is strongly nonstationary and stochastic. Recent market technology led to the accumulation of vast economic data that can be utilized for nonlinear analysis. We propose an approach for analyzing the basic relation between correlation properties of the original signal and its magnitude signal by decomposing the original signal into its positive and negative fluctuation components. We use this relation for understanding the volatility correlation behavior, where the original fluctuation signal is short-range correlated while its magnitude signal is long-range correlated. We find that the difference between the correlation properties of the original and its magnitude signal is induced by the time organization structure of the correlation function between fluctuation magnitudes of positive and negative components. We show that this correlation function can be described well by the stretched exponential function and is related to the nonlinear property and the multifractal structure of the signal.

Complex networks in the stock and foreign exchange data.

We also study the relative market efficiency in diverse financial market data using the approximate entropy method for the quantification of complexity, irregularity and unpredictability in the time series. We used the global foreign exchange market indices and found that on average the approximate entropy for typical mature markets is higher than for typical emerging markets. In particular, the market efficiency or the randomness of the time series diminishes remarkably during a market crisis, for example, during the Asian currency crisis. This study suggests that mature markets have a higher market efficiency than emerging markets.

The NCSL also carries out the study of biophysical models and numerical simulations of diverse biological systems in cooperation with biological laboratories at POSTECH. These problems include circadian rhythms, calcium dynamics in pancreatic cells, and stomatal dynamics in plants. The important breakthroughs in science come from unexplored territories in the interdisciplinary area, leading to the emergence of a new paradigm. Our laboratory aims to go beyond the barriers in the field of nonlinear and complex systems through interdisciplinary cooperations with mathematicians, physicists, biologists, biomedical scientists and economists.

Pohang is located at the Yongilman Bay area of the East Sea and has a population of half million people. Pohang is well known as an industrial city because of the Pohang Steel Company (POSCO) and is now emerging as a science city after the establishment of POSTECH in 1986, the Research Institute of Science and Technology (RIST), the Pohang Accelerator Laboratory and the Synchrotron Light Source, the Pohang Biotech Center, the Pohang Nanotechnology Center, the Asia Pacific Center for Theoretical Physics, the Pohang Robotics Center, and Techno Park. Applicants for the PhD program in the nonlinear science group at the

Department of Physics

at POSTECH will be nominated for an RA fellowship of the Brain Korea Program of the Ministry of Education and Human Resources. Postdoctoral fellowships are available every year and candidates are encouraged to apply to both the Department of Physics at POSTECH and the

Asia Pacific Center for Theoretical Physics

.

Selected publications since 1998:

1.	Gabjin Oh, Cheoljun Eom, and Seunghwan Kim, "Market efficiency in foreign exchange markets," Physica A 382, 209 (2007).
2.	Cheoljun Eom, Gabjin Oh, and Seunghwan Kim, "Deterministic factors of stock networks based on cross-correlation in financial market, Physica A 383, 139 (2007).
3.	Chang-Woo Shin and Seunghwan Kim, "Self-organized criticality and scale-free properties in emergent functional neural networks," Phys. Rev. E (Rapid Comm.) 74, 045101 (2006).
4.	Woo Cheol Jun, Gabjin Oh, and Seunghwan Kim, "Understanding the Volatility Correlation Behavior with Magnitude Cross-correlation Function," Phys. Rev. E 73, 06628 (2006).
5.	Un Cheol Lee, Seunghwan Kim, "Classification of epilepsy types through global network analysis of scalp EEG," Phys. Rev. E 73, 041950 (2006).
6.	Myoung Won Cho and Seunghwan Kim, "Different ocular dominance map formation influenced by orientation preference columns in visual cortices," Phys. Rev. Lett. 94, 168701 (2005).
7.	Un Cheol Lee and Seunghwan Kim, "Event and time-scale characteristics of heart-rate dynamics," Phys. Rev. E 71, 061917 (2005).
8.	Myoung Won Cho and Seunghwan Kim, "Understanding visual map formation through vortex dynamics of spin Hamiltonian models," Phys. Rev. Lett. 92, 18101 (2004).
9.	Sang Wook Kim and Seunghwan Kim, "Internal localized eigenmodes on spin discrete breathers in antiferromagnetic chains with on-site easy-axis anisotropy," Phys. Rev. B 66, 212408 (2002).
10.	Sunghwan Jung, Seunghwan Kim and Byungnam Kahng, "Geometric fractal growth model for scale free networks," Phys. Rev. E 65, 056101 (2002).
11.	Vladimir Astakhov, A. Sabunin, W. Uhm and Seunghwan Kim, "Multistability formation and synchronization loss in coupled Hénon maps: Two sides of the single bifurcational mechanism," Phys. Rev. E 63, 056212 (2001).
12.	Sang Wook Kim and Seunghwan Kim, "Fano resonances in translationally invariant one-dimensional nonlinear chains," Phys. Rev. B 63, 212301 (2001).
13.	Sang Gui Lee and Seunghwan Kim, "Parameter dependence of stochastic resonance in the stochastic FitzHugh-Nagumo neuron," Phys. Rev. E 60, 826 (1999).
14.	Sang Gui Lee, Alexander Neiman and Seunghwan Kim, "Coherence resonance in a Hodgkin-Huxley neuron," Phys. Rev. E 57, 3292 (1998).