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K. -I. Goh

Publications and source records attributed to K. -I. Goh.

At least 55 records · Page 3Linked to original sources
arXiv2006

Lethality and synthetic lethality in the genome-wide metabolic network of Escherichia coli

Recent genomic analyses on the cellular metabolic network show that reaction flux across enzymes are diverse and exhibit power-law behavior in its distribution. While one may guess that the reactions with larger fluxes are more likely to be lethal under the blockade of its catalyzing gene products or gene knockouts, we find, by in silico flux analysis, that the lethality rarely has correlations with the flux level owing to the widespread backup pathways innate in the genome-wide metabolism of \textit{Escherichia coli}. Lethal reactions, of which the deletion generates cascading failure of following reactions up to the biomass reaction, are identified in terms of the Boolean network scheme as well as the flux balance analysis. The avalanche size of a reaction, defined as the number of subsequently blocked reactions after its removal, turns out to be a useful measure of lethality. As a means to elucidate phenotypic robustness to a single deletion, we investigate synthetic lethality in reaction level, where simultaneous deletion of a pair of nonlethal reactions leads to the failure of the biomass reaction. Synthetic lethals identified via flux balance and Boolean scheme are consistently shown to act in parallel pathways, working in such a way that the backup machinery is compromised.

q-bio.MN↗
arXiv2006

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.

cond-mat.stat-mech↗
arXiv2006

Robustness of the avalanche dynamics in data packet transport on scale-free networks

We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter $a$ as well as which vertex triggers it. We find that there exists a critical value $a_c$ at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3, and is close in value to that of the distribution of the diameter changes by single vertex removal.

cond-mat.stat-mech↗
arXiv2006

Load distribution in weighted complex networks

We study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex. The optimal path, along which the total cost is minimum, crucially depend on the cost distribution function $p_c(c)$. In the strong disorder limit, where $p_c(c)\sim c^{-1}$, the load distribution follows a power law both in the Erdős-Rényi (ER) random graphs and in the scale-free (SF) networks, and its characteristics are determined by the structure of the minimum spanning tree. The distribution of loads at vertices with a given vertex degree also follows the SF nature similar to the whole load distribution, implying that the global transport property is not correlated to the local structural information. Finally, we measure the effect of disorder by the correlation coefficient between vertex degree and load, finding that it is larger for ER networks than for SF networks.

cond-mat.stat-mech↗
arXiv2006

Nonlocal evolution of weighted scale-free networks

We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the network is determined nonlocally, this approach can explain the generic nonlinear scaling between the strength and the degree of a node. We demonstrate by a simple model that the strength-driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule, generating the power-law behaviors in degree and in strength simultaneously.

cond-mat.stat-mech↗
arXiv2006

Intrinsic degree-correlations in static model of scale-free networks

We calculate the mean neighboring degree function $\bar k_{\rm{nn}}(k)$ and the mean clustering function $C(k)$ of vertices with degree $k$ as a function of $k$ in finite scale-free random networks through the static model. While both are independent of $k$ when the degree exponent $γ\geq 3$, they show the crossover behavior for $2 < γ< 3$ from $k$-independent behavior for small $k$ to $k$-dependent behavior for large $k$. The $k$-dependent behavior is analytically derived. Such a behavior arises from the prevention of self-loops and multiple edges between each pair of vertices. The analytic results are confirmed by numerical simulations. We also compare our results with those obtained from a growing network model, finding that they behave differently from each other.

cond-mat.stat-mech↗
arXiv2005

Reply to Comment on "The origin of bursts and heavy tails in human dynamics"

Understanding human dynamics is of major scientific and practical importance and can be increasingly addressed in a quantitative fashion thanks to electronic records capturing various human activity patterns. The authors of Ref. [1] revisit the datasets studied in Ref. [2], making four technical observations. Some of the observations of Ref. [1] are based on the authors' unfamiliarity with the details of the data collection process and have little relevance to the findings of Ref. [2] and others are resolved in quantitative fashion by other authors [3].

physics.data-an↗
arXiv2005

Modeling bursts and heavy tails in human dynamics

Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human activity patterns the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. We discuss two queueing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution with exponent alpha=3/2. The second model imposes limitations on the queue length, resulting in alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics.

physics.soc-ph↗
arXiv2005

Extremal dynamics on complex networks: Analytic solutions

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold $x_c$ to be 1/( _f+1), where _f= / (= ) in the quenched (annealed) updating case, where is the n-th moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent γ<3 (γ> 3) for the quenched case in the thermodynamic limit. The theoretical value x_c fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, P_a(s) ~ s^{-3/2}.

cond-mat.stat-mech↗
arXiv2005

Evolution of the Protein Interaction Network of Budding Yeast: Role of the Protein Family Compatibility Constraint

Understanding of how protein interaction networks (PIN) of living organisms have evolved or are organized can be the first stepping stone in unveiling how life works on a fundamental ground. Here we introduce a hybrid network model composed of the yeast PIN and the protein family interaction network. The essential ingredient of the model includes the protein family identity and its robustness under evolution, as well as the three previously proposed ones: gene duplication, divergence, and mutation. We investigate diverse structural properties of our model with parameter values relevant to yeast, finding that the model successfully reproduces the empirical data.

q-bio.MN↗
arXiv2005

Graph theoretic analysis of protein interaction networks of eukaryotes

Thanks to recent progress in high-throughput experimental techniques, the datasets of large-scale protein interactions of prototypical multicellular species, the nematode worm Caenorhabditis elegans and the fruit fly Drosophila melanogaster, have been assayed. The datasets are obtained mainly by using the yeast hybrid method, which contains false-positive and false-negative simultaneously. Accordingly, while it is desirable to test such datasets through further wet experiments, here we invoke recent developed network theory to test such high throughput datasets in a simple way. Based on the fact that the key biological processes indispensable to maintaining life are universal across eukaryotic species, and the comparison of structural properties of the protein interaction networks (PINs) of the two species with those of the yeast PIN, we find that while the worm and the yeast PIN datasets exhibit similar structural properties, the current fly dataset, though most comprehensively screened ever, does not reflect generic structural properties correctly as it is. The modularity is suppressed and the connectivity correlation is lacking. Addition of interlogs to the current fly dataset increases the modularity and enhances the occurrence of triangular motifs as well. The connectivity correlation function of the fly, however, remains distinct under such interlogs addition, for which we present a possible scenario through an in silico modeling.

q-bio.MN↗
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↗
arXiv2003

Sandpile on Scale-Free Networks

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on scale-free (SF) networks, where threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent $τ$. Applying the theory of multiplicative branching process, we obtain the exponent $τ$ and the dynamic exponent $z$ as a function of the degree exponent $γ$ of SF networks as $τ=γ/(γ-1)$ and $z=(γ-1)/(γ-2)$ in the range $2 < γ< 3$ and the mean field values $τ=1.5$ and $z=2.0$ for $γ>3$, with a logarithmic correction at $γ=3$. The analytic solution supports our numerical simulation results. We also consider the case of uniform threshold, finding that the two exponents reduce to the mean field ones.

cond-mat.stat-mech↗
arXiv2003

Probabilistic prediction in scale-free networks: Diameter changes

In complex systems, responses to small perturbations are too diverse to predict how much they would be definitely, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of each node for various in silico and real world scale-free networks. We find that the diameter changes are indeed diverse and exhibit an algebraic decay with an exponent ζasymptotically. Interestingly, the exponent ζis robust as ζ\simeq 2.2(1) for most scale-free networks, insensitive to the degree exponents γas long as 2 < γ\le 3. However, there is another type with ζ\simeq 1.7(1) and its examples include the Internet and its related in silico model.

cond-mat.stat-mech↗
arXiv2002

Classification of scale-free networks

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent ηwhich is robust and use it to classify the scale-free networks. We have observed two universality classes with η\approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.

cond-mat.stat-mech↗