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 structure differences 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.
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.
To characterize the outcomes of initial and repeated office-based probing as a primary treatment for congenital nasolacrimal duct obstruction (CNLDO) in children.
The medical records of patients who ...underwent nasolacrimal duct office-based probing for CNLDO between March 2004 and January 2008 were reviewed retrospectively. Nasolacrimal duct probing was performed on 244 eyes from 229 consecutive patients with CNLDO. Patients who were refractory to the first probing underwent a second probing 4 to 8 weeks later.
Based on exclusion criteria, 244 eyes from 229 patients (117 males and 112 females), aged 6 to 71 months (mean, 12.4 ± 8.36) were included. The success rate of the initial probing was 80% (196 of 244) for all patients, 82% (111 of 136) in the 6 to 12 month age group, 79% (64 of 81) in the 13 to 18 months age group, and 78% (21 of 27) among individuals older than 19 months (p = 0.868, Pearson chi-square test). The success rate of the second probing was 61% (25 of 41) for all patients, 74% (17 of 23) in the 6 to 12 months age group, 58% (7 of 12) in the 13 to 18 months age group, and 17% (1 of 6) among individuals older than 19 months (p = 0.043, Fisher's exact test).
While the success rate of initial nasolacrimal duct probing is not affected by age, the rate of success rate with a second probing was significantly lower in patients older than 19 months. Based on the results, authors recommend further surgical interventions, such as silicone tube intubation or balloon dacryocystoplasty, instead of repeated office probing for patients older than 19 months, if an initial office probing has failed.
A 4-year-old boy visited the hospital with exotropia after brain hemorrhage caused by trauma. He had undergone decompressive craniectomy and cranioplasty 18 months prior to presentation at our ...hospital. An alternate prism cover test showed more than 50 prism diopters (PD) of left exotropia when he was fixing with the right eye and 30 PD of right exotropia when he was fixing with the left eye at near and far distance. On the Hirschberg test, 60 PD of left exotropia was noted in the primary position. Brain computerized tomography imaging performed 18 months prior showed hypodense changes in the right middle cerebral artery and anterior cerebral artery territories. Subfalcian herniation was also noted secondary to swelling of the right hemisphere. The patient underwent a left lateral rectus muscle recession of 7.0 mm and a left medial rectus muscle resection of 3.5 mm. Three weeks after the surgery, the Hirschberg test showed orthotropia. On alternate prism cover testing, 8 PD of left exotropia and 8 PD of right esotropia were noted at distance. We report a patient who developed dissociated horizontal deviation after right subfalcian subdural hemorrhage caused by trauma.
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.
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.
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.
Recently, anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nanoporous 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.
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), in which we incorporate 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 optimum minimizing exit time {\tau} . We substantiate this finding by using mean-field theory on annealed uniform hypergraphs with N nodes, for which {\tau} scales as A ln N, where the prefactor 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.
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.
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