arXiv subjects

Deok-Sun Lee

Publications and source records attributed to Deok-Sun Lee.

At least 19 recordsLinked to original sources

arXiv2026

Ecological networks of viable species with degree-dependent interaction

The generalized Lotka-Volterra (GLV) framework, recently advanced by dynamical mean-field theory, enables the systematic analysis of large ecological networks. When combined with structured interaction topologies, previous studies have shown that the viability of species, defined by having a positive stationary abundance, depends on the number of their interacting neighbors or the "degree." While such model studies usually assume that interaction strengths follow an identical distribution across all connected pairs, real ecological communities often exhibit correlations between interaction strength and a species' degree. To capture this overlooked feature, we introduce degree-dependent interaction strengths into a generalized random LV model. We identify two distinct regimes: a hub-favored phase, where highly connected species survive preferentially, and a hub-suppressed phase, where they face higher extinction risks. We analytically derive the phase boundary where these degree-dependent strengths precisely balance the connectivity effect, leaving all species equally susceptible. Crucially, these phases induce opposing shifts in the degree-degree correlation or "assortativity" of the network of viable species: the hub-favored phase enhances disassortativity by selectively removing the interactions between low-degree species, whereas the hub-suppressed phase reduces it as the interactions involving hub species tend to disappear. Ultimately, our findings demonstrate that degree-dependent interactions are a fundamental mechanism not only for shaping species survival, but for naturally reproducing the wide range of assortativity values observed in real ecological networks.

q-bio.PE↗

arXiv2026

Competing heterogeneities shape ordering via higher-order interactions

Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while degree heterogeneity softens it as hubs cooperatively seed ordering with non-hubs. Under either type of heterogeneity, continuous--discontinuous double transitions can arise, where the symmetry-breaking continuous transition is driven by pairs or by hubs, respectively. When both heterogeneities coexist, cross-order degree correlations further modulate the phase diagram, with anticorrelation delaying the group-driven discontinuous jump and broadening the hysteretic region. Our results reveal the intricate interplay between size and degree heterogeneities in collective phenomena beyond pairwise interactions.

cond-mat.stat-mech↗

arXiv2026

Reinforcement Learning for Microcanonical Graph Ensemble with Assortativity Constraints

How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties. Canonical approaches, formulated as exponential random graph models (ERGMs), enforce constraints only in expectation, allowing individual realizations to fluctuate around the target. Conversely, microcanonical ensembles impose hard constraints exactly, but practical sampling methods beyond fixing the degree sequence have remained out of reach. Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning (RL) framework that transforms any given graph through degree-preserving rewirings to exactly reach a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. Instead of relying on the entropically dominated Metropolis--Hastings dynamics of the ERGM, DMGG employs a policy-guided search that maximally alters the joint-degree matrix. This eliminates exhaustive parameter tuning and accelerates generation by at least an order of magnitude while preserving configurational diversity. As DMGG generalizes across various graph sizes, sparsities, and topologies, it provides exact null models that allow for the quantitative isolation of secondary observables, such as the clustering coefficient. These results establish RL as a practical and powerful paradigm for generating hard-constrained graphs, opening avenues to investigate structure-function relationships free from ensemble artifacts.

cs.LG↗

arXiv2026

Watch your neighbors: Training statistically accurate chaotic systems with local phase space information

Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a good surrogate model for chaotic dynamics is. Prior work has largely focused either on reproducing the Jacobian of the underlying dynamics, which governs local expansion and contraction rates, or on training surrogate models that reproduce the ground-truth dynamics' long-term statistical behavior. In this work, we propose a new framework that aims to bridge these two paradigms by training surrogate dynamics models with accurate Jacobians and long-term statistical properties. Our method constructs a local covering of a chaotic attractor in phase space and analyzes the expansion and contraction of these coverings under the dynamics. The surrogate model is trained by minimizing the maximum mean discrepancy between the pushforward distributions of the coverings under the surrogate and ground-truth dynamics. Experiments show that our method significantly improves Jacobian accuracy while remaining competitive with state-of-the-art statistically accurate dynamics learning methods. Our code is fully available at https://anonymous.4open.science/r/neighborwatch.

cs.LG↗

arXiv2026

Scale-freeness under node removal: a finite-size scaling perspective

In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While robustness to random failures and targeted attacks has been extensively studied, most analyses have focused on connectivity loss or degree distribution, rather than on how scale-invariant organization emerges and evolves with system size. Here we examine how scale-free structure evolves under progressive degree-dependent node removal, systematically varying the hub-protection strength $θ$. Starting from scale-free networks, we apply the recently developed finite-size scaling (FSS) analysis to node-removed networks and compare the results with those from Kullback-Leibler (KL) divergence-based classification. We find that under random ($θ=0$) and hub-protecting removal ($θ>0$), the two criteria largely agree, whereas under hub-preferential removal ($θ<0$), networks may appear scale-free according to the KL criterion while failing the FSS test of scaling collapse. This discrepancy indicates that similarity to a reference degree distribution does not guarantee the persistence of scale-invariant organization across system sizes. The two diagnostics thus probe complementary aspects of network structure, and their joint use provides a more complete characterization of structural degradation.

physics.soc-ph↗

arXiv2026

Optimality in group-driven social dynamics on hypergraphs

We explore the role of intrinsic structural properties of hypergraphs in governing group-driven social dynamics with social reinforcement. First, we analyze simplicial contagion dynamics on random hypergraphs in which the level of hyperedge nestedness is systematically controlled. By developing the facet-based approximate master equation (FAME) method, we demonstrate that hyperedge nestedness induces a non-monotonic change in the outbreak threshold for simplicial contagion, displaying the lowest threshold at an intermediate level of hyperedge nestedness due to competition between simple and higher-order contagion processes. Next, we formulate the group-driven voter model (GVM) and investigate the consensus time for the GVM on hypergraphs with N nodes. Focusing on a representative case of the GVM, we show that the consensus time scales logarithmically with the system size as A ln N, where the prefactor A displays the fastest consensus formation at an intermediate level of social reinforcement due to competition between group-constraint and nonlinearity factors. Taken together, our results highlight the importance of competing effects arising from higher-order interactions in shaping optimality in group-driven social dynamical processes.

physics.soc-ph↗

arXiv2026

Discontinuous Wealth-Gradient Transition Driving Cooperation

The universal prevalence of cooperation is puzzling, as defection typically yields higher payoffs than cooperation, motivating searches for hidden pathways to cooperation. Here we study a game-theoretic model on a lattice structured population in which interaction payoffs are scaled by the minimum of participants' accumulated wealth, reflecting real-world heterogeneity and incorporating the influence of past strategic choices. This wealth scaling allows frequent cooperators to surpass defectors in payoffs through their greater wealth even at high cooperation costs where defection would otherwise dominate. At the elevated critical cost-benefit ratio, the wealth gradient at the cooperator-defector boundary in one dimension exhibits a discontinuous transition. We show that slowing and effective stalling of the boundary trigger an explosive buildup of the wealth gradient, driving the dominance of cooperation below the critical ratio. Remarkably, this promotion of cooperation is stronger at higher temperatures, revealing a constructive role of fluctuations.

physics.soc-ph↗

arXiv2026

Age structure alters optimal hospital allocation for reducing tuberculosis fatalities in South Korea

Optimal healthcare allocation requires accounting for spatial heterogeneity in disease burden, while demographic heterogeneity may further alter local vulnerability when outcomes vary strongly with age. Tuberculosis (TB) provides a useful case because treatment requires sustained access to care and fatality risk rises markedly with age. In South Korea, TB incidence remains relatively high, while regional incidence, mortality, and hospital data are systematically recorded, allowing these effects to be examined empirically. Finer spatial resolution provides more local observations, helping reveal regional heterogeneity and spatial patterns. However, due to privacy concerns, official district-level TB statistics are provided only in age-aggregated form, whereas age-specific statistics are available at province level. We therefore propose a method to reconstruct age-resolved TB cases and fatalities across 228 districts for 2014--2022 by combining province-level age distributions with district-level totals, using the finest available age and spatial information. Building on an existing hospital-allocation framework, we incorporate age-dependent vulnerability into the fatality-minimization objective. We find that age-aware and age-agnostic optimizations yield similar total minimized fatalities but distinct district-level allocations. The oldest age group's rescaled patient density is strongly associated with this difference and the direction of hospital redistribution. Age-weighting schemes clarify how countervailing contributions across age groups affect optimization.

physics.soc-ph↗

arXiv2024

Competition between group interactions and nonlinearity in voter dynamics on hypergraphs

Social dynamics are often driven by both pairwise (i.e., dyadic) relationships and higher-order (i.e., polyadic) group relationships, which one can describe using hypergraphs. To gain insight into the impact of polyadic relationships on dynamical processes on networks, we formulate and study a polyadic voter process, which we call the group-driven voter model (GVM), that incorporates the effect of group interactions by nonlinear interactions that are subject to a group (i.e., hyperedge) constraint. By examining the competition between nonlinearity and group sizes, we show that the GVM achieves consensus faster than standard voter-model dynamics, with an optimal minimizing exit time. We substantiate this finding by using mean-field theory on annealed uniform hypergraphs with $N$ nodes, for which the exit time scales as ${\cal A}\ln N$, where the prefactor ${\cal A}$ depends both on the nonlinearity and on group-constraint factors. Our results reveal how competition between group interactions and nonlinearity shapes GVM dynamics. We thereby highlight the importance of such competing effects in complex systems with polyadic interactions.

physics.soc-ph↗

arXiv2024

Phase Transitions in the Simplicial Ising Model on Hypergraphs

We study the phase transitions in the simplicial Ising model on hypergraphs, in which the energy within each hyperedge (group) is lowered only when all the member spins are unanimously aligned. The Hamiltonian of the model is equivalent to a weighted sum of lower-order interactions, evoking an Ising model defined on a simplicial complex. Using the Landau free energy approach within the mean-field theory, we identify diverse phase transitions depending on the sizes of hyperedges. Specifically, when all hyperedges have the same size $q$, the nature of the transitions shifts from continuous to discontinuous at the tricritical point $q=4$, with the transition temperatures varying nonmonotonically, revealing the ambivalent effects of group size $q$. Furthermore, if both pairwise edges and hyperedges of size $q>2$ coexist in a hypergraph, novel scenarios emerge, including mixed-order and double transitions, particularly for $q>8$. Adopting the Bethe--Peierls method, we investigate the interplay between pairwise and higher-order interactions in achieving global magnetization, illuminating the multiscale nature of the higher-order dynamics.

cond-mat.stat-mech↗

arXiv2024

Bifurcations and multistability in empirical mutualistic networks

Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a theoretical framework still remains to be developed to understand species-level dynamical heterogeneity within a given community, hampering real-world ecosystems' theoretical assessment and management. Here, we consider empirical plant-pollinator mutualistic networks, additionally including all-to-all intragroup competition, where species abundance evolves under a Lotka-Volterra-type equation. Setting the strengths of competition and mutualism to be uniform, we investigate how individual species persist or go extinct under varying the interaction strengths. By employing bifurcation theory in tandem with numerical continuation, we elucidate transcritical bifurcations underlying species extinction and demonstrate that the Hopf bifurcation of unfeasible equilibria and degenerate transcritical bifurcations give rise to multistability, i.e., the coexistence of multiple attracting feasible equilibria. These bifurcations allow us to partition the parameter space into different regimes, each with distinct sets of extinct species, offering insights into how interspecific interactions generate one or multiple extinction scenarios within an ecological network.

q-bio.PE↗

arXiv2024

Incorporating Heterogeneous Interactions for Ecological Biodiversity

Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully-connected structure assumed in these previous studies is not realistic as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the well-mixed system, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.

physics.bio-ph↗

arXiv2024

Correlation-enhanced viable core in metabolic networks

Cellular ingredient concentrations can be stabilized by adjusting generation and consumption rates through multiple pathways. To explore the portion of cellular metabolism equipped with multiple pathways, we categorize individual metabolic reactions and compounds as viable or inviable: A compound is viable if processed by two or more reactions, and a reaction is viable if all of its substrates and products are viable. Using this classification, we identify the maximal subnetwork of viable nodes, referred to as the {\it viable core}, in bipartite metabolic networks across thousands of species. The obtained viable cores are remarkably larger than those in degree-preserving randomized networks, while their broad degree distributions commonly enable the viable cores to shrink gradually as reaction nodes are deleted. We demonstrate that the positive degree-degree correlations of the empirical networks may underlie the enlarged viable cores compared to the randomized networks. By investigating the relation between degree and cross-species frequency of metabolic compounds and reactions, we elucidate the evolutionary origin of the correlations.

q-bio.MN↗

arXiv2024

Heterogeneous popularity of metabolic reactions from evolution

The composition of cellular metabolism is different across species. Empirical data reveal that bacterial species contain similar numbers of metabolic reactions but that the cross-species popularity of reactions is so heterogenous that some reactions are found in all the species while others are in just few species, characterized by a power-law distribution with the exponent one. Introducing an evolutionary model concretizing the stochastic recruitment of chemical reactions into the metabolism of different species at different times and their inheritance to descendants, we demonstrate that the exponential growth of the number of species containing a reaction and the saturated recruitment rate of brand-new reactions lead to the empirically identified power-law popularity distribution. Furthermore, the structural characteristics of metabolic networks and the species' phylogeny in our simulations agree well with empirical observations.

q-bio.PE↗

arXiv2024

Scaling in local to global condensation of wealth on sparse networks

The prevalence of wealth inequality propels us to characterize its origin and progression, via empirical and theoretical studies. The Yard-Sale(YS) model, in which a portion of the smaller wealth is transferred between two individuals, culminates in the concentration of almost all wealth to a single individual, while distributing rest of the wealth with a power-law of exponent one. By incorporating redistribution to the model, in which the transferred wealth is proportional to the sender's wealth, we show that such extreme inequality is suppressed if the frequency ratio of redistribution to the YS-type exchange exceeds the inverse of the population size. Studying our model on a sparsely-connected population, we find that the wealth inequality ceases to grow for a period, when local rich nodes can no longer acquire wealth from their broke nearest neighbors. Subsequently, inequality resumes growth due to the redistribution effect by allowing locally amassed wealth to move and coalesce. Analyzing the Langevin equations and the coalescing random walk on complex networks, we elucidate the scaling behaviors of wealth inequality in those multiple phases. These findings reveal the influence of network structure on wealth distribution, offering a novel perspective on wealth inequality.

physics.soc-ph↗

arXiv2023

Contagion dynamics on hypergraphs with nested hyperedges

In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is the nestedness: Some hyperedges can be entirely contained (that is, nested) within another larger hyperedge, which itself can also be nested further in a hierarchical manner. Yet the effect of such hierarchical structure of hyperedges on the dynamics has remained unexplored. In this context, here we propose a random nested-hypergraph model with a tunable level of nestedness and investigate the effects of nestedness on a higher-order susceptible-infected-susceptible process. By developing an analytic framework called the facet approximation, we obtain the steady-state fraction of infected nodes on the random nested-hypergraph model more accurately than existing methods. Our results show that the hyperedge-nestedness affects the phase diagram significantly. Monte Carlo simulations support the analytical results.

physics.soc-ph↗

arXiv2023

$(k,q)$-core decomposition of hypergraphs

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential subgroups in hypergraphs, named $(k,q)$-core decomposition. The $(k,q)$-core is defined as the maximal subgraph in which each vertex has at least $k$ hypergraph degrees \textit{and} each hyperedge contains at least $q$ vertices. The method contains a repeated pruning process until reaching the $(k,q)$-core, which shares similarities with a widely used $k$-core decomposition technique in a graph. Second, we analyze the pruning dynamics and the percolation transition with theoretical and numerical methods in random hypergraphs. We set up evolution equations for the pruning process, and self-consistency equations for the percolation properties. Based on our theory, we find that the pruning process generates a hybrid percolation transition for either $k\ge 3$ \textit{or} $q\ge 3$. The critical exponents obtained theoretically are confirmed with finite-size scaling analysis. Next, when $k=q=2$, we obtain a unconventional degree-dependent critical relaxation dynamics analytically and numerically. Finally, we apply the $(k,q)$-core decomposition to a real coauthorship dataset and recognize the leading groups at an early stage.

cond-mat.stat-mech↗

arXiv2022

Structure of international trade hypergraphs

We study the structure of the international trade hypergraph consisting of triangular hyperedges representing the exporter-importer-product relationship. Measuring the mean hyperdegree of the adjacent vertices, we first find its behaviors different from those in the pairwise networks and explain the origin by tracing the relation between the hyperdegree and the pairwise degree. To interpret the observed hyperdegree correlation properties in the context of trade strategies, we decompose the correlation into two components by identifying one with the background correlation remnant even in the exponential random hypergraphs preserving the given empirical hyperdegree sequence. The other component characterizes the net correlation and reveals the bias of the exporters of low hyperdegree towards the importers of high hyperdegree and the products of low hyperdegree, which information is not readily accessible in the pairwise networks. Our study demonstrates the power of the hypergraph approach in the study of real-world complex systems and offers a theoretical framework.

physics.soc-ph↗