Heterogeneous Mean First-Passage Time Scaling in Fractal Media.

The mean first passage time (MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.

Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study.

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of O(N), where N is the system size. Beyond the threshold, they are completely lost. Since the introduction of the Hopfield model, the theory of neural networks has been further developed toward realistic neural networks using analog neurons, spiking neurons, etc. Nevertheless, those advances are based on fully connected networks, which are inconsistent with recent experimental discovery that the number of connections of each neuron seems to be heterogeneous, following a heavy-tailed distribution. Motivated by this observation, we consider the Hopfield model on scale-free networks and obtain a different pattern of associative memory retrieval from that obtained on the fully connected network: the storage capacity becomes tremendously enhanced but with some error in the memory retrieval, which appears as the heterogeneity of the connections is increased. Moreover, the error rates are also obtained on several real neural networks and are indeed similar to that on scale-free model networks.

Extended finite-size scaling of synchronized coupled oscillators.

We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with nonidentical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of phase synchronization. In particular, we extend finite-size scaling (FSS) in the steady state to dynamics, determine critical exponents, and find the critical coupling strength. The dynamic scaling approach enables us to measure not only the FSS exponent associated with the correlation volume in finite systems but also thermodynamic critical exponents. Based on the extended FSS theory, we also discuss how the sampling of natural frequencies and thermal noise affect dynamic scaling, which is numerically confirmed.

Microscopic modelling circadian and bursty pattern of human activities.

Recent studies for a wide range of human activities such as email communication, Web browsing, and library visiting, have revealed the bursty nature of human activities. The distribution of inter-event times (IETs) between two consecutive human activities exhibits a heavy-tailed decay behavior and the oscillating pattern with a one-day period, reflective of the circadian pattern of human life. Even though a priority-based queueing model was successful as a basic model for understanding the heavy-tailed behavior, it ignored important ingredients, such as the diversity of individual activities and the circadian pattern of human life. Here, we collect a large scale of dataset which contains individuals' time stamps when articles are posted on blog posts, and based on which we construct a theoretical model which can take into account of both ignored ingredients. Once we identify active and inactive time intervals of individuals and remove the inactive time interval, thereby constructing an ad hoc continuous time domain. Therein, the priority-based queueing model is applied by adjusting the arrival and the execution rates of tasks by comparing them with the activity data of individuals. Then, the obtained results are transferred back to the real-time domain, which produces the oscillating and heavy-tailed IET distribution. This microscopic model enables us to develop theoretical understanding towards more empirical results.

Distinct universality classes of domain wall roughness in two-dimensional Pt/Co/Pt films.

We demonstrate here that the current-driven domain wall (DW) in two dimensions forms a "facet" roughness, distinctive to the conventional self-affine roughness induced by a magnetic field. Despite the different universality classes of these roughnesses, both the current- and field-driven DW speed follow the same creep law only with opposite angular dependences. Such angular dependences result in a stable facet angle, from which a single DW image can unambiguously quantify the spin-transfer torque efficiency, an essential parameter in DW-mediated nanodevices.

Thermodynamic selection of steric zipper patterns in the amyloid cross-beta spine.

At the core of amyloid fibrils is the cross-beta spine, a long tape of beta-sheets formed by the constituent proteins. Recent high-resolution x-ray studies show that the unit of this filamentous structure is a beta-sheet bilayer with side chains within the bilayer forming a tightly interdigitating "steric zipper" interface. However, for a given peptide, different bilayer patterns are possible, and no quantitative explanation exists regarding which pattern is selected or under what condition there can be more than one pattern observed, exhibiting molecular polymorphism. We address the structural selection mechanism by performing molecular dynamics simulations to calculate the free energy of incorporating a peptide monomer into a beta-sheet bilayer. We test filaments formed by several types of peptides including GNNQQNY, NNQQ, VEALYL, KLVFFAE and STVIIE, and find that the patterns with the lowest binding free energy correspond to available atomistic structures with high accuracy. Molecular polymorphism, as exhibited by NNQQ, is likely because there are more than one most stable structures whose binding free energies differ by less than the thermal energy. Detailed analysis of individual energy terms reveals that these short peptides are not strained nor do they lose much conformational entropy upon incorporating into a beta-sheet bilayer. The selection of a bilayer pattern is determined mainly by the van der Waals and hydrophobic forces as a quantitative measure of shape complementarity among side chains between the beta-sheets. The requirement for self-complementary steric zipper formation supports that amyloid fibrils form more easily among similar or same sequences, and it also makes parallel beta-sheets generally preferred over anti-parallel ones. But the presence of charged side chains appears to kinetically drive anti-parallel beta-sheets to form at early stages of assembly, after which the bilayer formation is likely driven by energetics.

Sustained oscillations in extended genetic oscillatory systems.

Various dynamic cellular behaviors have been successfully modeled in terms of elementary circuitries showing particular characteristics such as negative feedback loops for sustained oscillations. Given, however, the increasing evidences indicating that cellular components do not function in isolation but form a complex interwoven network, it is still unclear to what extent the conclusions drawn from the elementary circuit analogy hold for systems that are highly interacting with surrounding environments. In this article, we consider a specific example of genetic oscillator systems, the so-called repressilator, as a starting point toward a systematic investigation into the dynamic consequences of the extension through interlocking of elementary biological circuits. From in silico analyses with both continuous and Boolean dynamics approaches to the four-node extension of the repressilator, we found that 1), the capability of sustained oscillation depends on the topology of extended systems; and 2), the stability of oscillation under the extension also depends on the coupling topology. We then deduce two empirical rules favoring the sustained oscillations, termed the coherent coupling and the homogeneous regulation. These simple rules will help us prioritize candidate patterns of network wiring, guiding both the experimental investigations for further physiological verification and the synthetic designs for bioengineering.

Atomistic simulation approach to a continuum description of self-assembled beta-sheet filaments.

We investigated the supramolecular structure and continuum mechanical properties of a beta-sheet nanofiber comprised of a self-assembling peptide ac-[RARADADA]2-am using computer simulations. The supramolecular structure was determined by constructing candidate filaments with dimensions compatible with those observed in atomic force microscopy and selecting the most stable ones after running molecular dynamics simulations on each of them. Four structures with different backbone hydrogen-bonding patterns were identified to be similarly stable. We then quantified the continuum mechanical properties of these identified structures by running three independent simulations: thermal motion analysis, normal mode analysis, and steered molecular dynamics. Within the range of deformations investigated, the filament showed linear elasticity in transverse directions with an estimated persistence length of 1.2-4.8 microm. Although side-chain interactions govern the propensity and energetics of filament self-assembly, we found that backbone hydrogen-bonding interactions are the primary determinant of filament elasticity, as demonstrated by its effective thickness, which is smaller than that estimated by atomic force microscopy or from the molecular geometry, as well as by the similar bending stiffness of a model filament without charged side chains. The generality of our approach suggests that it should be applicable to developing continuum elastic ribbon models of other beta-sheet filaments and amyloid fibrils.

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 intuition might suggest that the reactions with larger fluxes are more likely to be lethal under the blockade of its catalysing 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 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.

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 between ness centrality displays a power-law distribution with an exponent eta, which is robust, and use it to classify the scale-free networks. We have observed two universality classes with eta approximately equal 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 coauthorship 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.

Harmonic forcing of an extended oscillatory system: homogeneous and periodic solutions.

In this paper we study the effect of external harmonic forcing on a one-dimensional oscillatory system described by the complex Ginzburg-Landau equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous state with no spatial structure is observed. The state becomes unstable to a spatially periodic "stripe" state via a supercritical bifurcation as the forcing amplitude decreases. An approximate phase equation is derived, and an analytic solution for the stripe state is obtained, through which the asymmetric behavior of the stability border of the state is explained. The phase equation, in particular the analytic solution, is found to be very useful in understanding the stability borders of the homogeneous and stripe states of the forced CGLE.