arXiv subjects

D. -S. Lee

Publications and source records attributed to D. -S. Lee.

At least 19 recordsLinked to original sources

arXiv2026

Structure and dynamics jointly stabilize the international trade hypergraph

To understand how fluctuations arise and are distributed in international trade, a question crucial for economic risk assessment and policymaking, we analyze strong adverse fluctuations-collapsed trades-defined as individual trades with sharp annual volume declines. Adopting a hypergraph framework for a fine-scale trade-centric representation of international trade, we find that collapsed trades (hyperedges) are clustered and their occurrence decays algebraically with trade volume (weight), which suggests inhomogeneous, epidemic-like spreading of collapse in the international trade hypergraph. Modeling collapse propagation as a contagion process and analyzing its dynamics, we show that a positive degree-weight correlation and a volume-decaying collapse rate synergistically suppress the onset of global collective collapse. Notably, the degree-weight correlation persisted but the volume-decay of the collapse rate weakened during the 2008-2009 global economic recession, resulting in a broader collapse spread. Our study shows how the interplay between structure and dynamics stabilizes complex systems.

physics.soc-ph↗

arXiv2025

Equilibrium-preserving Laplacian renormalization group

Diffusion over networks has recently been used to define spatiotemporal scales and extend Kadanoff block spins of Euclidean space to supernodes of networks in the Laplacian renormalization group (LRG). Yet, its ad hoc coarse-graining procedure remains underdeveloped and unvalidated, limiting its broader applicability. Here we rigorously formulate an LRG preserving the equilibrium state, offering a principled coarse-graining procedure. We construct the renormalized Laplacian matrix preserving dominant spectral properties using a proper, quasi-complete basis transformation and the renormalized adjacency matrix preserving mean connectivity from equilibrium-state flows among supernodes. Applying recursively this equilibrium-preserving LRG to various hypergraphs, we find that in hypertrees with low spectral dimensions vertex degree and hyperedge cardinality distributions flow toward Poissonian forms, while in hypergraphs lacking a finite spectral dimension they broaden toward power-law forms when starting from Poissonian ones, revealing how informational, structural, and dynamical scale-invariances are interrelated.

cond-mat.stat-mech↗

arXiv2024

Entropy-Induced Phase Transitions in a Hidden Potts Model

A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. Using the Ginzburg-Landau formalism in the mean-field limit, we explore the $q$-state Potts model with extra $r$ hidden states. We analytically demonstrate that when $1 < q \le 2$, the model exhibits a rich phase diagram comprising a variety of phase transitions such as continuous, discontinuous, two types of hybrids, and two consecutive second- and first-order transitions; moreover, several characteristics such as critical, critical endpoint, and tricritical point are identified. The critical line and critical end lines merge in a singular form at the tricritical point. Those complex critical behaviors are not wholly detected in previous research because the research is implemented only numerically. We microscopically investigate the origin of the discontinuous transition; it is induced by the competition between the interaction and entropy of the system in the Ising limit, whereas by the bi-stability of the hidden spin states in the percolation limit. Finally, we discuss the potential applications of the hidden Potts model to social opinion formation with shy voters and the percolation in interdependent networks.

cond-mat.stat-mech↗

arXiv2018

Essentiality landscape of metabolic networks

Local perturbations of individual metabolic reactions may result in different levels of lethality, depending on their roles in metabolism and the size of subsequent cascades induced by their failure. Moreover, essentiality of individual metabolic reactions may show large variations within and across species. Here we quantify their essentialities in hundreds of species by computing the growth rate after removal of individual and pairs of reactions by flux balance analysis. We find that about 10% of reactions are essential, i.e., growth stops without them, and most of the remaining reactions are redundant in the metabolic network of each species. This large-scale and cross-species study allows us to determine ad hoc ages of each reaction and species. We find that when a reaction is older and contained in younger species, the reaction is more likely to be essential. Such correlations of essentiality with the ages of reactions and species may be attributable to the evolution of cellular metabolism, in which alternative pathways are recruited to ensure the stability of important reactions to various degrees across species.

q-bio.MN↗

arXiv2018

Recent advances of percolation theory in complex networks

During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous transitions, the percolation transitions occurring in complex systems are often of different types such as discontinuous, hybrid, and infinite-order phase transitions. Thus, percolation has received considerable attention in network science community. Here we present a very brief review of percolation theory recently developed, which includes those types of phase transitions, critical phenomena, and finite-size scaling theory. Moreover, we discuss potential applications of theoretical results and several open questions including universal behaviors.

physics.soc-ph↗

arXiv2018

Relevance of the minimum degree to dynamic fluctuation in strongly heterogeneous networks

The fluctuation of dynamic variables in complex networks is known to depend on the dimension and the heterogeneity of the substrate networks. Previous studies, however, have reported inconsistent results for the scaling behavior of fluctuation in strongly heterogeneous networks. To understand the origin of this conflict, we study the dynamic fluctuation on scale-free networks with a common small degree exponent but different mean degrees and minimum degrees constructed by using the configuration model and the static model. It turns out that the global fluctuation of dynamic variables diverges algebraically and logarithmically with the system size when the minimum degree is one and two, respectively. Such different global fluctuations are traced back to different, linear and sub-linear, growth of local fluctuation at individual nodes with their degrees, implying a crucial role of degree-one nodes in controlling correlation between distinct hubs.

physics.soc-ph↗

arXiv2017

Urn model for products' shares in international trade

International trade fluxes evolve as countries revise their portfolios of trade products towards economic development. Accordingly products' shares in international trade vary with time, reflecting the transfer of capital between distinct industrial sectors. Here we analyze the share of hundreds of product categories in world trade for four decades and find a scaling law obeyed by the annual variation of product share, which informs us of how capital flows and interacts over the product space. A model of stochastic transfer of capital between products based on the observed scaling relation is proposed and shown to reproduce exactly the empirical share distribution. The model allows analytic solutions as well as numerical simulations, which predict a pseudo-condensation of capital onto few product categories and when it will occur. At the individual level, our model finds certain products unpredictable, the excess or deficient growth of which with respect to the model prediction is shown to be correlated with the nature of goods.

q-fin.TR↗

arXiv2014

Origin of the hub spectral dimension in scale-free networks

The return-to-origin probability and the first passage time distribution are essential quantities for understanding transport phenomena in diverse systems. The behaviors of these quantities typically depend on the spectral dimension $d_s$. However, it was recently revealed that in scale-free networks these quantities show a crossover between two power-law regimes characterized by $ d_s $ and the so-called hub spectral dimension $d_s^{\textrm{(hub)}}$ due to the heterogeneity of connectivities of each node. To understand the origin of $d_s^{\textrm{(hub)}}$ from a theoretical perspective, we study a random walk problem on hierarchical scale-free networks by using the renormalization group (RG) approach. Under the RG transformation, not only the system size but also the degree of each node changes due to the scale-free nature of the degree distribution. We show that the anomalous behavior of random walks involving the hub spectral dimension $d_s^{\textrm{(hub)}}$ is induced by the conservation of the power-law degree distribution under the RG transformation.

cond-mat.stat-mech↗

arXiv2014

Fast Algorithm for Relaxation Processes in Big-data Systems

Relaxation processes driven by a Laplacian matrix can be found in many real-world big-data systems, for example, in search engines on the World-Wide-Web and the dynamic load balancing protocols in mesh networks. To numerically implement such processes, a fast-running algorithm for the calculation of the pseudo inverse of the Laplacian matrix is essential. Here we propose an algorithm which computes fast and efficiently the pseudo inverse of Markov chain generator matrices satisfying the detailed-balance condition, a general class of matrices including the Laplacian. The algorithm utilizes the renormalization of the Gaussian integral. In addition to its applicability to a wide range of problems, the algorithm outperforms other algorithms in its ability to compute within a manageable computing time arbitrary elements of the pseudo inverse of a matrix of size millions by millions. Therefore our algorithm can be used very widely in analyzing the relaxation processes occurring on large-scale networked systems.

cond-mat.stat-mech↗

arXiv2013

External magnetic fields and the chiral phase transition in QED at nonzero chemical potential

Inspired by recent discussions of inverse magnetic catalysis in the literature, we examine the effects of a uniform external magnetic field on the chiral phase transition in quenched ladder QED at nonzero chemical potential. In particular, we study the behaviour of the effective potential as the strength of the magnetic field is varied while the chemical potential is held constant. For a certain range of the magnetic field, the effective potential develops a local maximum. Inverse magnetic catalysis is observed at this maximum, whereas the usual magnetic catalysis is observed at the true minimum of the effective potential.

hep-ph↗

arXiv2012

First passage time for random walks in heterogeneous networks

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.

cond-mat.stat-mech↗

arXiv2010

Spectral dimensions of hierarchical scale-free networks with shortcuts

The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractals or non-fractals depending on the weight of shortcuts. Applying the renormalization group (RG) approach to the Gaussian model, we obtain the spectral dimension exactly. While the spectral dimension varies between $1$ and $2$ for the fractal case, it remains at $2$, independent of the variation of network structure for the non-fractal case. The crossover behavior between the two cases is studied through the RG flow analysis. The analytic results are confirmed by simulation results and their implications for the architecture of complex systems are discussed.

cond-mat.stat-mech↗

arXiv2007

Scale-free random branching tree in supercritical phase

We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-γ}$. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number $C=\sum_k k q_k$ is larger than 1. The tree-size distribution $p(s)$ exhibits a crossover behavior when $2 < γ< 3$; A characteristic tree size $s_c$ exists such that for $s \ll s_c$, $p(s)\sim s^{-γ/(γ-1)}$ and for $s \gg s_c$, $p(s)\sim s^{-3/2}\exp(-s/s_c)$, where $s_c$ scales as $\sim (C-1)^{-(γ-1)/(γ-2)}$. For $γ> 3$, it follows the conventional mean-field solution, $p(s)\sim s^{-3/2}\exp(-s/s_c)$ with $s_c\sim (C-1)^{-2}$. The lifetime distribution is also derived. It behaves as $\ell(t)\sim t^{-(γ-1)/(γ-2)}$ for $2 < γ< 3$, and $\sim t^{-2}$ for $γ> 3$ when branching step $t \ll t_c \sim (C-1)^{-1}$, and $\ell(t)\sim \exp(-t/t_c)$ for all $γ> 2$ when $t \gg t_c$. The analytic solutions are corroborated by numerical results.

cond-mat.stat-mech↗

arXiv2006

Synchronization transition of heterogeneously coupled oscillators on scale-free networks

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $λ$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of $\couplingcoeff k_i^{η-1}$. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $η> λ-2$ ($η< λ-2$). We find eight different synchronization transition behaviors depending on the values of $η$ and $λ$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2005

Flow correlated percolation during vascular network formation in tumors

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor, leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.

q-bio.TO↗

arXiv2004

Evolution of scale-free random graphs: Potts model formulation

We study the bond percolation problem in random graphs of $N$ weighted vertices, where each vertex $i$ has a prescribed weight $P_i$ and an edge can connect vertices $i$ and $j$ with rate $P_iP_j$. The problem is solved by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous interactions for all pairs of spins. We apply this approach to the static model having $P_i\propto i^{-μ} (0<μ<1)$ so that the resulting graph is scale-free with the degree exponent $λ=1+1/μ$. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density, and their associated critical exponents are also obtained. Finite-size scaling behaviors are derived using the largest cluster size in the critical regime, which is calculated from the cluster size distribution, and checked against numerical simulation results. We find that the process of forming the giant cluster is qualitatively different between the cases of $λ>3$ and $2 < λ<3$. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite $N$ shows double peaks.

cond-mat.stat-mech↗

arXiv2004

Sandpile avalanche dynamics on scale-free networks

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $γ$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-η}$ with $0\leqη<1$, where $k_i$ is the degree of node $i$. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents $τ$ and $δ$, respectively. They are given as $τ=(γ-2 η)/(γ-1-η)$ and $δ=(γ-1-η)/(γ-2)$ for $γ<3-η$, 3/2 and 2 for $γ>3-η$, respectively. The power-law distributions are modified by a logarithmic correction at $γ=3-η$.

cond-mat.stat-mech↗

arXiv2003

On the evolution of scale-free graphs

We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $γ$. We use the branching process approach to obtain scaling forms for the cluster size distribution and the largest cluster size as functions of the number of edges $L$ and vertices $N$. We find that the process of forming a spanning cluster is qualitatively different between the cases of $γ>3$ and $2<γ<3$. While for the former, a spanning cluster forms abruptly at a critical number of edges $L_c$, generating a single peak in the mean cluster size $ $ as a function of $L$, for the latter, however, the formation of a spanning cluster occurs in a broad range of $L$, generating double peaks in $ $.

cond-mat.stat-mech↗