arXiv subjects

Deok-Sun Lee

Publications and source records attributed to Deok-Sun Lee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Degree distributions under general node removal: Power-law or Poisson?

Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resultant disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling, which is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including random removal and preferred or protective removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.

physics.soc-ph↗

arXiv2022

Stability and selective extinction in complex mutualistic networks

We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intra-group competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found to be identified by the signs of its non-zero components and those of its neighboring fixed points. Taking the annealed approximation, we derive the non-zero components to be formulated in terms of degrees and the rescaled interaction strengths, which lead us to find different stable fixed points depending on parameters, and we obtain the phase diagram. The selective extinction phase finds small-degree species extinct and effective interaction reduced, maintaining stability and hindering the onset of instability. The non-zero minimum species abundances from different empirical networks show data collapse when rescaled as predicted theoretically.

q-bio.PE↗

arXiv2021

Uncovering hidden dependency in weighted networks via information entropy

Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are opaque or hidden in numerous real systems. For instance, when a node in a network with limited interaction capacity spends its capacity to its neighboring nodes, the allocation of the total amount of interactions to them can be vastly diverse. Even if such potentially heterogeneous interactions epitomized by weighted networks are observable, as a result of the aforementioned ego-centric allocation of interactions, the relative importance or dependency between two interacting nodes can only be implicitly accessible. In this work, we precisely pinpoint such relative dependency by proposing the framework to discover hidden dependent relations extracted from weighted networks. For a given weighted network, we provide a systematic criterion to select the most essential interactions for individual nodes based on the concept of information entropy. The criterion is symbolized by assigning the effective number of neighbors or the effective out-degree to each node, and the resultant directed subnetwork decodes the hidden dependent relations by leaving only the most essential directed interactions. We apply our methodology to two time-stamped empirical network data, namely the international trade relations between nations in the world trade web (WTW) and the network of people in the historical record of Korea, Annals of the Joseon Dynasty (AJD). Based on the data analysis, we discover that the properties of mutual dependency encoded in the two systems are vastly different.

physics.soc-ph↗

arXiv2020

Skewness of local logarithmic exports

The distributions of trade values and relationships among countries and product categories reflect how countries select their trade partners and design export portfolios. Here we consider the exporter-importer network and the exporter-product network with directed links weighted by the logarithm of the corresponding export values each year from 1962 to 2018, and study how the weights of the outgoing links from each country are distributed. Such local logarithmic export distributions by destinations and products are found to follow approximately the Gaussian distribution across exporters and time, implying random assignment of export values on logarithmic scale. However, a non-zero skewness is identified, changing from positive to negative as exporters have more partner importers and more product categories in their portfolios. Seeking the origin, we analyze how local exports depend on the out-degree of exporter and the in-degrees of destinations/products and formulate their quantitative and measurable relation incorporating randomness, which uncovers the fundamental nature of the export strategies of individual countries.

physics.soc-ph↗

arXiv2020

Optimizing hospital distribution across districts for reducing tuberculosis fatalities

The spatial distributions of diverse facilities are often understood in terms of the optimization of the commute distance or the economic profit. Incorporating more general objective functions into such optimization framework may be useful, helping the policy decisions to meet various social and economic demands. As an example, we consider how hospitals should be distributed to minimize the total fatalities of tuberculosis (TB). The empirical data of Korea shows that the fatality rate of TB in a district decreases with the areal density of hospitals, implying their correlation and the possibility of reducing the nationwide fatalities by adjusting the hospital distribution across districts. Approximating the fatality rate by the probability of a patient not to visit a hospital in her/his residential district for the duration period of TB and evaluating the latter probability in the random-walk framework, we obtain the fatality rate as an exponential function of the hospital density with a characteristic constant related to each district's effective lattice constant estimable empirically. This leads us to the optimal hospital distribution which finds the hospital density in a district to be a logarithmic function of the rescaled patient density. The total fatalities is reduced by 13\% with this optimum. The current hospital density deviates from the optimized one in different manners from district to district, which is analyzed in the proposed model framework. The assumptions and limitations of our study are also discussed.

physics.soc-ph↗

arXiv2019

Giant component in a configuration-model power-law graph with a variable number of links

We generalize an algorithm used widely in the configuration model such that power-law degree sequences with the degree exponent $λ$ and the number of links per node $K$ controllable independently may be generated. It yields the degree distribution in a different form from that of the static model or under random removal of links while sharing the same $λ$ and $K$. With this generalized power-law degree distribution, the critical point $K_c$ for the appearance of the giant component remains zero not only for $λ\leq 3$ but also for $3<λ<λ_l \simeq 3.81$. This is contrasted with $K_c=0$ only for $λ\leq 3$ in the static model and under random link removal. The critical exponents and the cluster-size distribution for $λ<λ_l$ are also different from known results. By analyzing the moments and the generating function of the degree distribution and comparison with those of other models, we show that the asymptotic behavior and the degree exponent may not be the only properties of the degree distribution relevant to the critical phenomena but that its whole functional form can be relevant. These results can be useful in designing and assessing the structure and robustness of networked systems.

physics.soc-ph↗

arXiv2019

Engel's law in the commodity composition of exports

Different shares of distinct commodity sectors in production, trade, and consumption illustrate how resources and capital are allocated and invested. Economic progress has been claimed to change the share distribution in a universal manner as exemplified by the Engel's law for the household expenditure and the shift from primary to manufacturing and service sector in the three sector model. Searching for large-scale quantitative evidence of such correlation, we analyze the gross-domestic product (GDP) and international trade data based on the standard international trade classification (SITC) in the period 1962 to 2000. Three categories, among ten in the SITC, are found to have their export shares significantly correlated with the GDP over countries and time; The machinery category has positive and food and crude materials have negative correlations. The export shares of commodity categories of a country are related to its GDP by a power-law with the exponents characterizing the GDP-elasticity of their export shares. The distance between two countries in terms of their export portfolios is measured to identify several clusters of countries sharing similar portfolios in 1962 and 2000. We show that the countries whose GDP is increased significantly in the period are likely to transit to the clusters displaying large share of the machinery category.

q-fin.GN↗

arXiv2019

Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time

For a reliable prediction of an epidemic or information spreading pattern in complex systems, well-defined measures are essential. In the susceptible-infected model on heterogeneous networks, the cluster of infected nodes in the intermediate-time regime exhibits too large fluctuation in size to use its mean size as a representative value. The cluster size follows quite a broad distribution, which is shown to be derived from the variation of the cluster size with the time when a hub node was first infected. On the contrary, the distribution of the time taken to infect a given number of nodes is well concentrated at its mean, suggesting the mean infection time is a better measure. We show that the mean infection time can be evaluated by using the scaling behaviors of the boundary area of the infected cluster and use it to find a non-exponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks. Such slow spreading originates in only small-degree nodes left susceptible, while most hub nodes are already infected in the early exponential-spreading stage. Our results offer a way to detour around large statistical fluctuations and quantify reliably the temporal pattern of spread under structural heterogeneity.

physics.soc-ph↗

arXiv2019

Competition-induced increase of species abundance in mutualistic networks

Nutrients from a flowering plant are shared by its pollinators, giving rise to competition in the latter. Such exploitative competition of pollinators can limit their abundance and affect the global organization of the mutualistic partnership in the plant-pollinator mutualistic community. Here we investigate the effects of the exploitative competition between pollinators on the structure and the species abundance of the mutualistic networks which evolve by changing mutualistic partnership towards higher abundance of species. Simulations show different emergent network characteristics between plants and animals; hub plants connected to many pollinators are very rare while a few super-hub pollinators appear with the exploitative competition included, in contrast to equally many hubs of both types without the exploitative competition. More interestingly, the abundance of plant species increases with increasing the exploitative competition strength. We analyze the inverse of the generalized interaction matrix in the weak-interaction limit to identify the leading structural factors relevant to the species abundance, which are shown to be instrumental in optimizing the network structure to increase the mutualistic benefit and lower the cost of exploitative competition.

q-bio.PE↗

arXiv2016

The Eigenmode Analysis of Human Motion

Rapid advances in modern communication technology are enabling the accumulation of large-scale, high-resolution observational data of spatiotemporal movements of humans. Classification and prediction of human mobility based on the analysis of such data carry great potential in applications such as urban planning as well as being of theoretical interest. A robust theoretical framework is therefore required to study and properly understand human motion. Here we perform the eigenmode analysis of human motion data gathered from mobile communication records, which allows us to explore the scaling properties and characteristics of human motion.

physics.soc-ph↗

arXiv2014

Evolution of regulatory networks towards adaptability and stability in a changing environment

Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which evolve by selectively rewiring links towards enhancing adaptability to a changing environment and stability against dynamical perturbations. We find that sparse and heterogeneous connectivity patterns emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks. The characteristic scaling behavior of stability reflects the balance between robustness and flexibility. The scaling of fluctuation in the perturbation spread shows a dynamic crossover, which is analyzed by investigating separately the stochasticity of internal dynamics and the network structures different depending on the evolution pathways. Our study delineates how the ambivalent pressure of evolution shapes biological networks, which can be helpful for studying general complex systems interacting with environments.

q-bio.MN↗

arXiv2014

Lattice Model for Spontaneous Imbibition in Porous Media: The Role of Effective Tension and Universality Class

Recently anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nano-porous medium, were reported: the mean height and the width of the propagating front increase with time $t$ both proportional to $t^{1/2}$. Here we propose a simple lattice imbibition model and elucidate quantitatively how the correlation range of the hydrostatic pressure and the disorder strength of the pore radii affect the scaling properties of the imbibition front. We introduce an effective tension of liquid across neighboring pores, which depends on the aspect ratio of each pore, and show that it leads to a dynamical crossover: both the mean height and the roughness grow faster in the presence of tension in the intermediate-time regime but eventually saturate in the long-time regime. The universality class of the long-time behavior is discussed by examining the associated scaling exponents and their relation to directed percolation.

cond-mat.stat-mech↗

arXiv2012

Interspecific competition underlying mutualistic networks

The architecture of bipartite networks linking two classes of constituents is affected by the interactions within each class. For the bipartite networks representing the mutualistic relationship between pollinating animals and plants, it has been known that their degree distributions are broad but often deviate from power-law form, more significantly for plants than animals. Here we consider a model for the evolution of the mutualistic networks and find that their topology is strongly dependent on the asymmetry and non-linearity of the preferential selection of mutualistic partners. Real-world mutualistic networks analyzed in the framework of the model show that a new animal species determines its partners not only by their attractiveness but also as a result of the competition with pre-existing animals, which leads to the stretched-exponential degree distributions of plant species.

q-bio.PE↗

arXiv2012

Scaling of nestedness in complex networks

Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the nodes linked to the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of species in ecological communities exhibit such nestedness, which is known to support the network robustness. Despite such importance, quantitative characteristics of nestedness is little understood. Here we take graph-theoretic approach to derive the scaling properties of nestedness in various model networks. Our results show how the heterogeneous connectivity patterns enhance nestedness. Also we find that the nestedness of bipartite networks depend sensitively on the fraction of different types of nodes, causing nestedness to scale differently for nodes of different types.

physics.soc-ph↗

arXiv2008

Broad edge of chaos in strongly heterogeneous Boolean networks

The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form $P_d(k)\sim k^{-γ}$ with $2<γ<3$, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite $N$ with decreasing $γ$. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.

cond-mat.stat-mech↗

arXiv2006

Comparative study of the transcriptional regulatory networks of E. coli and yeast: Structural characteristics leading to marginal dynamic stability

Dynamical properties of the transcriptional regulatory network of {\it Escherichia coli} and {\it Saccharomyces cerevisiae} are studied within the framework of random Boolean functions. The dynamical response of these networks to a single point mutation is characterized by the number of mutated elements as a function of time and the distribution of the relaxation time to a new stationary state, which turn out to be different in both networks. Comparison with the behavior of randomized networks reveals relevant structural characteristics other than the mean connectivity, namely the organization of circuits and the functional form of the in-degree distribution. The abundance of single-element circuits in {\it E. coli} and the power-law in-degree distribution of {\it S. cerevisiae} shift their dynamics towards marginal stability overcoming the restrictions imposed by their mean connectivities, which is argued to be related to the simultaneous presence of robustness and adaptivity in living organisms.

q-bio.MN↗

arXiv2006

Universal fluctuation of the average height in the early-time regime of the one-dimensional Kardar-Parisi-Zhang-type growth

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the early-time regime, $t\ll N^{3/2}$ with $t$ time and $N$ the system size, from the known characteristic function in the stationary state ($t\gg N^{3/2}$) of the single-step model derivable from a Bethe Ansatz solution, and thereby find the scaling properties of the cumulants and the large deviation function in the early-time regime. These results, combined with the scaling analysis of the KPZ equation, imply the existence of the universal scaling functions for the cumulants and an universal large deviation function. The analytic predictions are supported by the simulation results for two different models.

cond-mat.stat-mech↗

arXiv2006

Maximum flow and topological structure of complex networks

The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$ and $t$. The average of $q$ over all node pairs with smaller degree $k_{\rm min}$ is $ _{k_{\rm min}} \simeq c k_{\rm min}$ for large $k_{\rm min}$ with $c$ a constant implying that the statistics of $q$ is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and $q$ can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient $c$. The applicability of our results to real world networks is tested for the Internet at the autonomous system level.

cond-mat.stat-mech↗