arXiv subjects

Euijun Song

Publications and source records attributed to Euijun Song.

4 recordsLinked to original sources

arXiv2024

Quantum walk on simplicial complexes for simplicial community detection

Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization of graph structures. Simplicial complexes, encoding higher-order interactions through simplices, offer a richer topological representation of complex systems. Since the conventional classical random walk cannot directly detect community structures, we present a quantum walk algorithm to detect higher-order community structures called simplicial communities. We utilize the Fourier coin to produce entangled translation states among adjacent simplices in a simplicial complex. The potential of our quantum algorithm is tested on Zachary's karate club network. This study may contribute to understanding complex systems at the intersection of algebraic topology and quantum walk algorithms.

quant-ph↗

arXiv2023

Persistent homology analysis of type 2 diabetes genome-wide association studies in protein-protein interaction networks

Genome-wide association studies (GWAS) involving increasing sample sizes have identified hundreds of genetic variants associated with complex diseases, such as type 2 diabetes (T2D); however, it is unclear how GWAS hits form unique topological structures in protein-protein interaction (PPI) networks. Using persistent homology, this study explores the evolution and persistence of the topological features of T2D GWAS hits in the PPI network with increasing P-value thresholds. We define an $n$-dimensional persistent disease module as a higher-order generalization of the largest connected component (LCC). The 0-dimensional persistent T2D disease module is the LCC of the T2D GWAS hits, which is significantly detected in the PPI network (196 nodes and 235 edges, P$<$0.05). In the 1-dimensional homology group analysis, all 18 1-dimensional holes (loops) of the T2D GWAS hits persist over all P-value thresholds. The 1-dimensional persistent T2D disease module comprising these 18 persistent 1-dimensional holes is significantly larger than that expected by chance (59 nodes and 83 edges, P$<$0.001), indicating a significant topological structure in the PPI network. Our computational topology framework potentially possesses broad applicability to other complex phenotypes in identifying topological features that play an important role in disease pathobiology.

q-bio.MN↗

arXiv2023

Impact of noise on the instability of spiral waves in stochastic 2D mathematical models of human atrial fibrillation

Sustained spiral waves, also known as rotors, are pivotal mechanisms in persistent atrial fibrillation (AF). Stochasticity is inevitable in nonlinear biological systems such as the heart; however, it is unclear how noise affects the instability of spiral waves in human AF. This study presents a stochastic two-dimensional mathematical model of human AF and explores how Gaussian white noise affects the instability of spiral waves. In homogeneous tissue models, Gaussian white noise may lead to spiral-wave meandering and wavefront break-up. As the noise intensity increases, the spatial dispersion of phase singularity (PS) points increases. This finding indicates the potential AF-protective effects of cardiac system stochasticity by destabilizing the rotors. By contrast, Gaussian white noise is unlikely to affect the spiral-wave instability in the presence of localized scar or fibrosis regions. The PS points are located at the boundary or inside the scar/fibrosis regions. Localized scar or fibrosis may play a pivotal role in stabilizing spiral waves regardless of the presence of noise. This study suggests that fibrosis and scars are essential for stabilizing the rotors in stochastic mathematical models of AF. Further patient-derived realistic modeling studies are required to confirm the role of scar/fibrosis in AF pathophysiology.

physics.bio-ph↗

arXiv2022

Energy landscape analysis of cardiac fibrillation wave dynamics using pairwise maximum entropy model

Cardiac fibrillation is characterized by chaotic and disintegrated spiral wave dynamics patterns, whereas sinus rhythm shows synchronized excitation patterns. To determine functional correlations among cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the 2D numerical simulation data of human atrial fibrillation. We then constructed an energy landscape and estimated a hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. The MEM could describe the wave dynamics of sinus rhythm, single stable rotor, and single rotor with wavebreak (both accuracy and reliability>0.9), but not the multiple random wavelet case. The energy landscapes exhibited unique profiles of local minima and energy barriers, characterizing the spatiotemporal patterns of cardiac fibrillation dynamics. The pairwise MEM-based energy landscape analysis provides reliable explanations of complex nonlinear dynamics of cardiac fibrillation, which might be determined by the presence of a 'driver' such as a sinus node or rotor.

q-bio.TO↗