Biomedical subjects

Jae Dong Noh

Publications and source records attributed to Jae Dong Noh.

12 recordsLinked to original sources

PubMed2006

Random field Ising model on networks with inhomogeneous connections.

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent gamma. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for gamma<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for gamma>3. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

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PubMed2005

Stationary and dynamical properties of a zero-range process on scale-free networks.

We study the condensation phenomenon in a zero-range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase transition between a condensed phase and an uncondensed phase, and the phase diagram is obtained analytically. As for the dynamical property, we find that the relaxation dynamics depends on the global structure of underlying networks. The relaxation time follows the power law tau approximately Lz with the network size L in the condensed phase. The dynamic exponent z is found to take a different value depending on whether underlying networks have a tree structure or not.

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PubMed2005

Complete condensation in a zero range process on scale-free networks.

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.

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PubMed2005

Asymmetrically coupled directed percolation systems.

We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species A and B are coupled asymmetrically in that A particles branch B particles, whereas B particles prey on A particles. This model may describe epidemic spreading controlled by reactive immunization agents. We study nonequilibrium phase transitions with attention focused on the multicritical point where both species undergo the absorbing phase transition simultaneously. In one dimension, we find that the inhibitory coupling from B to A is irrelevant and the model belongs to the unidirectionally coupled directed percolation class. On the contrary, a mean-field analysis predicts that the inhibitory coupling is relevant and a new universality appears with a variable dynamic exponent. Numerical simulations on small-world networks confirm our predictions.

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PubMed2005

Growing network model for community with group structure.

We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time step. The new member then creates a new group or joins one of the groups of the introducer. We investigate the emerging community structure analytically and numerically. The group size distribution shows a power-law distribution for a variety of growth rules, while the activity distribution follows an exponential or a power law depending on the details of the growth rule. We also present an analysis of empirical data from online communities the "Groups" in http://www.yahoo.com and the "Cafe" in http://www.daum.net, which show a power-law distribution for a wide range of group sizes.

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PubMed2004

Scale-free trees: the skeletons of complex networks.

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing the total weight of the edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. Especially, in ubiquitous scale-free networks, it is found that the scale-free spanning tree shows very robust betweenness centrality distributions and the remaining shortcuts characterize the properties of the original network, such as the clustering coefficient and the classification of scale-free networks by the betweenness centrality distribution.

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PubMed2004

Constrained spin-dynamics description of random walks on hierarchical scale-free networks.

We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule, which allows an analytic approach. We show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes N as T--N(z). From a scaling argument, we also show the power-law decay of the autocorrelation function C(sigma)(t)--t(-alpha), which is the probability to find the Ising spins in the initial state sigma after t time steps, with the state-dependent nonuniversal exponent alpha. It turns out that the power-law scaling behavior has its origin in a quasiultrametric structure of the configuration space.

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PubMed2004

Random walks on complex networks.

We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.

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PubMed2004

Universality class of absorbing transitions with continuously varying critical exponents.

The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a different type of critical phenomenon distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

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PubMed2003

Exact scaling properties of a hierarchical network model.

We report on the exact results for the degree K, the diameter D, the clustering coefficient C, and the betweenness centrality B of a hierarchical network model with a replication factor M. Such quantities are calculated exactly with the help of recursion relations. Using the results, we show that (i). the degree distribution follows a power law P(K) approximately K-gamma with gamma=1+ln M/ln(M-1), (ii). the diameter grows logarithmically as D approximately ln N with the number of nodes N, (iii). the clustering coefficient of each node is inversely proportional to its degree, C proportional, variant 1/K, and the average clustering coefficient is nonzero in the infinite N limit, and (iv). the betweenness centrality distribution follows a power law P(B) approximately B-2. We discuss a classification scheme of scale-free networks into the universality class with the clustering property and the betweenness centrality distribution.

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PubMed2002

Stability of shortest paths in complex networks with random edge weights.

We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies the spanning tree such that some edges are activated and the network diameter is increased. With analytic random-walk mappings and numerical analysis, we find that the spanning tree is unstable to the introduction of disorder and displays a phase-transitionlike behavior at zero disorder strength epsilon =0. In the infinite network-size limit (N--> infinity ), we obtain a continuous transition with the density of activated edges Phi growing like Phi approximately epsilon (1) and with the diameter-expansion coefficient Upsilon growing like Upsilon approximately epsilon (2) in the regular network, and first-order transitions with discontinuous jumps in Phi and Upsilon at epsilon=0 for the small-world (SW) network and the Barabási-Albert scale-free (SF) network. The asymptotic scaling behavior sets in when N>>N(c), where the crossover size scales as N(c) approximately epsilon (-2) for the regular network, N(c) approximately exp(alpha epsilon (-2)) for the SW network, and N(c) approximately exp(alpha|ln epsilon | epsilon (-2)) for the SF network. In a transient regime with N<<N(c), there is an infinite-order transition with Phi approximately Upsilon approximately exp[-alpha/(epsilon (2)ln N)] for the SW network and approximately exp[-alpha/(epsilon (2)ln N/ln ln N)] for the SF network. It shows that the transport pattern is practically most stable in the SF network.

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PubMed2002

Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential.

We study the roughening transition of a (3+1)-dimensional elastic manifold, which is driven by the competition between a periodic pinning potential and a random impurity potential. The elastic manifold is modeled by a solid-on-solid-type interface model, and the universal properties of the transition from a flat phase (for strong periodic potential) to a rough phase (for strong random potential) are investigated at zero temperature using a combinatorial optimization algorithm technique. We find that the transition is a continuous one. Critical exponents are estimated numerically, and compared with analytic results and those for a periodic elastic medium.

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