Su Do Yi

Network robustness of multiplex networks with interlayer degree correlations.

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address various notions of the network robustness relevant to multiplex networks, such as the resilience of ordinary and mutual connectivity under random or targeted node removals, as well as the biconnectivity. We found that correlated coupling can affect the structural robustness of multiplex networks in diverse fashion. For example, for maximally correlated duplex networks, all pairs of nodes in the giant component are connected via at least two independent paths and network structure is highly resilient to random failure. In contrast, anticorrelated duplex networks are on one hand robust against targeted attack on high-degree nodes, but on the other hand they can be vulnerable to random failure.

Percolation properties of growing networks under an Achlioptas process

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with probability δ, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying δ and the critical point δc = 0.5149(1) is determined from the power-law behavior of the order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the δc. Using the finite-size scaling analysis, we get and , which implies β ≈ 1/2 and . The Fisher exponent τ = 2.24(1) for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.

Theory of fads: traveling-wave solution of evolutionary dynamics in a one-dimensional trait space.

We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and mutation on a mean-field level. We argue that this dynamics can be expressed as a variant of the Fisher equation with high-order correction terms. The equation has a traveling-wave solution, and the phase-space method shows how the wave shape depends on the correction. We compare this solution with empirical time-series data of given names in Quebec, treating it as a descriptive model for the observed patterns. Our model explains the reason that many names exhibit a similar pattern of the rise and fall as time goes by. At the same time, we have found that their dissimilarities are also statistically significant.

Allometric exponent and randomness

An allometric height-mass exponent gives an approximative power-law relation hMi / H between the average mass hMi and the height H for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age interval. The body mass index is often used for practical purposes when characterizing humans and it is based on the allometric exponent = 2. It is shown here that the actual value of is to a large extent determined by the degree of correlation between mass and height within the sample studied: no correlation between mass and height means = 0, whereas if there was a precise relation between mass and height such that all individuals had the same shape and density then = 3. The connection is demonstrated by showing that the value of can be obtained directly from three numbers characterizing the spreads of the relevant random Gaussian statistical distributions: the spread of the height and mass distributions together with the spread of the mass distribution for the average height. Possible implications for allometric relations, in general, are discussed.

Force correlations in molecular and stochastic dynamics

Abstract A molecular gas system in three dimensions is numerically studied by the energy conserving molecular dynamics (MD). The autocorrelation functions for the velocity and the force are computed and the friction coefficient is estimated. From the comparison with the stochastic dynamics (SD) of a Brownian particle, it is shown that the force correlation function in MD is different from the delta-function force correlation in SD in short time scale. However, as the measurement time scale is increased further, the ensemble equivalence between the microcanonical MD and the canonical SD is restored. We also discuss the practical implication of the result.

Diffusion on a heptagonal lattice

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence the displacement of a classical random walker increases linearly in time. The diffusion of a quantum particle put on the heptagonal lattice is also studied in the framework of the tight-binding model Hamiltonian, and we again find the linear diffusion like the classical random walk. A comparison with diffusion on complex networks is also made.

Human bipedalism and body-mass index

Body-mass index, abbreviated as BMI and given by M/H2 with the mass M and the height H, has been widely used as a useful proxy to measure a general health status of a human individual. We generalise BMI in the form of M/Hp and pursue to answer the question of the value of p for populations of animal species including human. We compare values of p for several different datasets for human populations with the ones obtained for other animal populations of fish, whales, and land mammals. All animal populations but humans analyzed in our work are shown to have p ≈ 3 unanimously. In contrast, human populations are different: As young infants grow to become toddlers and keep growing, the sudden change of p is observed at about one year after birth. Infants younger than one year old exhibit significantly larger value of p than two, while children between one and five years old show p ≈ 2, sharply different from other animal species. The observation implies the importance of the upright posture of human individuals. We also propose a simple mechanical model for a human body and suggest that standing and walking upright should put a clear division between bipedal human (p ≈ 2) and other animals (p ≈ 3).

Particle in a box with a time-dependentδ-functionpotential

In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schrodinger equation with a time-dependent

Quantum Monte Carlo study of the transverse-field quantum Ising modelon infinite-dimensional structures

\delta

Phase transition in a coevolving network of conformist and contrarian voters

-function potential. It is a natural generalization of the particle in a box, a canonical example of quantum mechanics, and we present analytic and numerical investigations on this problem. After deriving an exact Volterra-type integral equation, composed of an infinite sum of modes, we show that approximate formulas with the lowest-frequency modes correctly capture the qualitative behavior of the wave function. If we take into account hundreds of modes, our numerical calculation shows that the quantum adiabatic theorem actually gives a very good approximation even if the barrier height diverges within finite time, as long as it is sufficiently longer than the characteristic time scale of the particle. In particular, if the barrier is slowly inserted at an asymmetric position, the particle is localized by the insertion itself, in accordance with a prediction of the adiabatic theorem. On the other hand, when the barrier is inserted quickly, the wave function becomes rugged after the insertion because of the energy transfer to the particle. Regardless of the position of the barrier, the fast insertion leaves the particle unlocalized so that we can obtain meaningful information by a which-side measurement. Our numerical procedure provides a precise way to calculate the wave function throughout the process, from which one can estimate the amount of this information for an arbitrary insertion protocol.