arXiv subjects

B. Kahng

Publications and source records attributed to B. Kahng.

At least 37 records · Page 2Linked to original sources

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

Prediction and mitigation of nonlocal cascading failures using graph neural networks

Cascading failures (CFs) in electrical power grids propagate nonlocally; After a local disturbance, the second failure may be distant. To study the avalanche dynamics and mitigation strategy of nonlocal CFs, numerical simulation is necessary; however, computational complexity is high. Here, we first propose an avalanche centrality (AC) of each node, a measure related to avalanche size, based on the Motter and Lai model. Second, we train a graph neural network (GNN) with the AC in small networks. Next, the trained GNN predicts the AC ranking in much larger networks and real-world electrical grids. This result can be used effectively for avalanche mitigation. The framework we develop can be implemented in other complex processes that are computationally costly to simulate in large networks.

physics.soc-ph↗

arXiv2022

Resolving mean-field solutions of dissipative phase transitions using permutational symmetry

Phase transitions in dissipative quantum systems have been investigated using various analytical approaches, particularly in the mean-field (MF) limit. However, analytical results often depend on specific methodologies. For instance, Keldysh formalism shows that the dissipative transverse Ising (DTI) model exhibits a discontinuous transition at the upper critical dimension, $d_c= 3$, whereas the fluctuationless MF approach predicts a continuous transition in infinite dimensions ($d_\infty$). These two solutions cannot be reconciled because the MF solutions above $d_c$ should be identical. This necessitates a numerical verification. However, numerical studies on large systems may not be feasible because of the exponential increase in computational complexity as $\mathcal{O}(2^{2N})$ with system size $N$. Here, we note that because spins can be regarded as being fully connected at $d_\infty$, the spin indices can be permutation invariant, and the number of quantum states can be considerably contracted with the computational complexity $\mathcal{O}(N^3)$. The Lindblad equation is transformed into a dynamic equation based on the contracted states. Applying the Runge--Kutta algorithm to the dynamic equation, we obtain all the critical exponents, including the dynamic exponent $z\approx 0.5$. Moreover, since the DTI model has $\mathbb{Z}_2$ symmetry, the hyperscaling relation has the form $2β+γ=ν(d+z)$, we obtain the relation $d_c+z=4$ in the MF limit. Hence, $d_c\approx 3.5$; thus, the discontinuous transition at $d=3$ cannot be treated as an MF solution. We conclude that the permutation invariance at $d_\infty$ can be used effectively to check the validity of an analytic MF solution in quantum phase transitions.

cond-mat.stat-mech↗

arXiv2021

Link overlap influences opinion dynamics on multiplex networks: spin model approach

Consider a multiplex network formed by two layers indicating social interactions: the first layer is a friendship network and the second layer is a network of business relations. In this duplex network each pair of individuals can be connected in different ways: they can be connected by a friendship but not connected by a business relation, they can be connected by a business relation without being friends, or they can be simultaneously friends and in a business relation. In the latter case we say that the links in different layers overlap. These three types of connections are called multilinks and the multidegree indicates the sum of multilinks of a given type that are incident to a given node. Previous models of opinion formation on multilayer networks have mostly neglected the effect of link overlap. Here we show that link overlap can have important effects in opinion formation. Indeed, emerging pattern of opinion formation can be significantly influenced by the statistical properties of multilinks, and in particular by the multidegree distribution. To quantitatively address this problem, we study a simple spin model, called the Ashkin-Teller model including 2-body and 4-body interactions between nodes in different layers. Here we fully investigate the rich phase diagram of this model which includes a large variety of phase transitions (PTs). Indeed the phase digram or the model displays continuous, discontinuous, successive discontinuous, and hybrid PTs.

physics.soc-ph↗

arXiv2021

Machine learning approaches for Kuramoto coupled oscillator systems

Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing collective behaviors, synchronization phase transitions, chaotic behaviors and so on. Even though traditional approaches such as analytical and numerical methods enable to understand diverse properties of such systems, some properties still remain unclear. Here, we applied the ML approach to such systems particularly described by the Kuramoto model, with the aim of resolving the following intriguing problems, namely determination of the transition point and criticality of a hybrid synchronization transition; understanding network structures from chaotic patterns; and comparison of ML algorithms for the prediction of future chaotic behaviors. The proposed method is expected to be useful for further problems such as understanding a neural network structure from electroencephalogram signals.

cond-mat.stat-mech↗

arXiv2021

A hybrid percolation transition at a finite transition point in scale-free networks

Percolation transition (PT) means the formation of a macroscopic-scale large cluster, which exhibits a continuous transition. However, when the growth of large clusters is globally suppressed, the type of PT is changed to a discontinuous transition for random networks. A question arises as to whether the type of PT is also changed for scale-free (SF) network, because the existence of hubs incites the formation of a giant cluster. Here, we apply a global suppression rule to the static model for SF networks, and investigate properties of the PT. We find that even for SF networks with the degree exponent $2 < λ<3$, a hybrid PT occurs at a finite transition point $t_c$, which we can control by the suppression strength. The order parameter jumps at $t_c^-$ and exhibits a critical behavior at $t_c^+$.

cond-mat.stat-mech↗

arXiv2021

Betweenness centrality of teams in social networks

Betweenness centrality (BC) was proposed as an indicator of the extent of an individual's influence in a social network. It is measured by counting how many times a vertex (i.e., an individual) appears on all the shortest paths between pairs of vertices. A question naturally arises as to how the influence of a team or group in a social network can be measured. Here, we propose a method of measuring this influence on a bipartite graph comprising vertices (individuals) and hyperedges (teams). When the hyperedge size varies, the number of shortest paths between two vertices in a hypergraph can be larger than that in a binary graph. Thus, the power-law behavior of the team BC distribution breaks down in scale-free hypergraphs. However, when the weight of each hyperedge, for example, the performance per team member, is counted, the team BC distribution is found to exhibit power-law behavior. We find that a team with a widely connected member is highly influential.

physics.soc-ph↗

arXiv2021

Absorbing phase transition with a continuously varying exponent in a quantum contact process: a neural network approach

Phase transitions in dissipative quantum systems are intriguing because they are induced by the interplay between coherent quantum and incoherent classical fluctuations. Here, we investigate the crossover from a quantum to a classical absorbing phase transition arising in the quantum contact process (QCP). The Lindblad equation contains two parameters, $ω$ and $κ$, which adjust the contributions of the quantum and classical effects, respectively. We find that in one dimension when the QCP starts from a homogeneous state with all active sites, there exists a critical line in the region $0 \le κ< κ_*$ along which the exponent $α$ (which is associated with the density of active sites) decreases continuously from a quantum to the classical directed percolation (DP) value. This behavior suggests that the quantum coherent effect remains to some extent near $κ=0$. However, when the QCP in one dimension starts from a heterogeneous state with all inactive sites except for one active site, all the critical exponents have the classical DP values for $κ\ge 0$. In two dimensions, anomalous crossover behavior does not occur, and classical DP behavior appears in the entire region of $κ\ge 0$ regardless of the initial configuration. Neural network machine learning is used to identify the critical line and determine the correlation length exponent. Numerical simulations using the quantum jump Monte Carlo technique and tensor network method are performed to determine all the other critical exponents of the QCP.

cond-mat.stat-mech↗

arXiv2021

Homological percolation transitions in growing simplicial complexes

Simplicial complex (SC) representation is an elegant mathematical framework for representing the effect of complexes or groups with higher-order interactions in a variety of complex systems ranging from brain networks to social relationships. Here, we explore the homological percolation transitions (HPTs) of growing SCs using empirical datasets and a model proposed. The HPTs are determined by the first and second Betti numbers, which indicate the appearance of one- and two-dimensional macroscopic-scale homological cycles and cavities, respectively. A minimal SC model with two essential factors, namely, growth and preferential attachment, is proposed to model social coauthorship relationships. This model successfully reproduces the HPTs and determines the transition types as infinite order (the Berezinskii--Kosterlitz--Thouless type) with different critical exponents. In contrast to the Kahle localization observed in static random SCs, the first Betti number continues to increase even after the second Betti number appears. This delocalization is found to stem from the two aforementioned factors and arises when the merging rate of two-dimensional simplexes is less than the birth rate of isolated simplexes. Our results can provide topological insight into the maturing steps of complex networks such as social and biological networks.

physics.soc-ph↗

arXiv2020

Covid-19 epidemic under the K-quarantine model: Network approach

The Covid-19 pandemic is ongoing worldwide, and the damage it has caused is unprecedented. For prevention, South Korea has adopted a local quarantine strategy rather than a global lockdown. This approach not only minimizes economic damage, but it also efficiently prevents the spread of the disease. In this work, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to isolated people are disconnected and then reinstated when they are released. This link dynamics leads to time-dependent reproduction number. Numerical simulations are performed on networks with reaction rates estimated from empirical data. The temporal pattern of the cumulative number of confirmed cases is then reproduced. The results show that a large number of asymptomatic infected patients are detected as they are quarantined together with infected patients. Additionally, possible consequences of the breakdowns of local quarantine measures and social distancing are considered.

physics.soc-ph↗

arXiv2020

Hysteresis and criticality in hybrid percolation transitions

Phase transitions (PTs) are generally classified into second-order and first-order transitions, each exhibiting different intrinsic properties. For instance, a first-order transition exhibits latent heat and hysteresis when a control parameter is increased and then decreased across a transition point, whereas a second-order transition does not. Recently, hybrid percolation transitions (HPTs) are issued in diverse complex systems, in which the features of first-order and second-order PTs occur at the same transition point. Thus, the question whether hysteresis appears in an HPT arises. Herein, we investigate this fundamental question with a so-called restricted Erdős--Rényi random network model, in which a cluster fragmentation process is additionally proposed. The hysteresis curve of the order parameter was obtained. Depending on when the reverse process is initiated, the shapes of hysteresis curves change, and the critical behavior of the HPT is conserved throughout the forward and reverse processes.

cond-mat.stat-mech↗

arXiv2020

Competing synchronization on random networks

The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(ω)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs, $K_1 < 0$ and $K_2 > 0$, to the $1-p$ and $p$ fractions of nodes, respectively. This model has a rich phase diagram that includes incoherent, $π$, and traveling wave (TW) phases and a hybrid phase transition with abnormal properties that occurs through an intermediate metastable $π$ state. Here, we consider the competing Kuramoto model on Erdős--Rényi (ER) random networks. Numerical simulations and the mean-field solution based on the annealed network approximation reveal that in this case, when the mean degree of the random networks is large, the features of the phase diagram and transition types are consistent overall with those on completely connected networks. However, when the mean degree is small, the mean-field solution is not consistent with the numerical simulation results; specifically, the TW state does not occur, and thus the phase diagram is changed, owing to the strong heterogeneity of the local environment. By contrast, for the original Kuramoto oscillators, the annealed mean-field solution is consistent with the numerical simulation result for ER networks.

cond-mat.stat-mech↗

arXiv2020

Effective potential approach to hybrid synchronization transitions

The Kuramoto model exhibits different types of synchronization transitions depending on the type of natural frequency distribution. To obtain these results, the Kuramoto self-consistency equation (SCE) approach has been used successfully. However, this approach affords only limited understanding of more detailed properties such as the stability and finite size effect. Here, we extend the SCE approach by introducing an effective potential, that is, an integral version of the SCE. We examine the landscape of this effective potential for second-order, first-order, and hybrid synchronization transitions in the thermodynamic limit. In particular, for the hybrid transition, we find that the minimum of effective potential displays a plateau across the region in which the order parameter jumps. This result suggests that the effective free energy can be used to determine a type of synchronization transition. For finite systems, the effective potential contains local minima at which the system can be trapped. Using numerical simulations, we determine the stability of the system as a function of system size and simulation time.

cond-mat.stat-mech↗

arXiv2020

Synchronization in leader-follower switching dynamics

The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization models. However, such models do not take into account asynchronous and adaptive updating of an individual's status at each time. Here, we modify the Kuramoto model slightly by classifying oscillators as leaders or followers, according to their angular velocity at each time, where individuals interact asymmetrically according to their leader/follower status. As the angular velocities of the oscillators are updated, the leader and follower status may also be reassigned. Owing to this adaptive dynamics, oscillators may cooperate by taking turns acting as a leader or follower. This may result in intriguing patterns of synchronization transitions, including hybrid phase transitions, and produce the leader-follower switching pattern observed in bird migration patterns.

nlin.AO↗

arXiv2020

Tricritical directed percolation with long-range interaction in one and two dimensions

Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited $s$ state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the $d$ state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of $\sim 1/r^{d+σ}$ (denoted as LTDP), where $r$ is the separation, $d$ is the spatial dimension, and $σ$ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension $d_c=$ min$(3,\,1.5σ)$. We numerically obtain a set of critical exponents in the LTDP class and determine the interval of $σ$ for the LTDP class. Finally, we construct a diagram of universality classes in the space ($d$, $σ$).

cond-mat.stat-mech↗

arXiv2019

Simplicial SIS model in scale-free uniform hypergraph

The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior such as the spread of information or disease. Recently, a simplicial contagion problem was introduced and considered using a simplicial susceptible-infected-susceptible (SIS) model. Although recent studies have investigated random hypergraphs with a Poisson-type facet degree distribution, hypergraphs in the real world can have a power-law type of facet degree distribution. Here, we consider the SIS contagion problem on scale-free uniform hypergraphs and find that a continuous or hybrid epidemic transition occurs when the hub effect is dominant or weak, respectively. We determine the critical exponents analytically and numerically. We discuss the underlying mechanism of the hybrid epidemic transition.

physics.soc-ph↗

arXiv2019

Entropy production and fluctuation theorems on complex networks

Entropy production (EP) is known as a fundamental quantity for measuring the irreversibility of processes in thermal equilibrium and states far from equilibrium. In stochastic thermodynamics, the EP becomes more visible in terms of the probability density functions of the trajectories of a particle in the state space. Inspired by a previous result that complex networks can serve as state spaces, we consider a data packet transport problem on complex networks. Entropy is produced owing to the complexity of pathways as the packet travels back and forth between two nodes. The EPs are exactly enumerated along the shortest paths between every pair of nodes, and the functional form of the EP distribution is determined by extreme value analysis. The asymptote of the accumulated EP distribution is found to follow the Gumbel distribution.

cond-mat.stat-mech↗

arXiv2019

Interevent time distribution, burst, and hybrid percolation transition

Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order transitions, depend on the processes. The HPT induced by cluster merging is more intrigue and little understood than the other. Here, we construct a theoretical framework using the so-called restricted percolation model. In this model, clusters are ranked by size and partitioned into small- and large-cluster sets. As the cluster rankings are updated by cluster coalescence, clusters may move back and forth across the set boundary. The inter-event time (IET) between two consecutive crossing times have two distributions with power-law decays, which in turn characterize the criticality of the HPT. A burst of such crossing events occurs and signals the upcoming transition. We discuss a related phenomenon to this critical dynamics.

cond-mat.stat-mech↗