arXiv subjects

James P. Gleeson

Publications and source records attributed to James P. Gleeson.

64 records · Page 4Linked to original sources

arXiv2011

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k_i. In this paper we identify a binary mixture of heterogeneous k-core which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erdos-Renyi networks and 2d square lattices.

cond-mat.dis-nn↗

arXiv2011

High-accuracy approximation of binary-state dynamics on networks

Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories are shown to result from seeking approximate solutions of the master equations. Applications to the calculation of SIS epidemic thresholds and critical points of non-equilibrium spin models are also demonstrated.

physics.soc-ph↗

arXiv2011

Cascades on a class of clustered random networks

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced in [M.E.J. Newman, Phys. Rev. Lett. 103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion which determines whether increasing the level of clustering will increase, or decrease, the expected cascade size. Applications, examples of which are provided, include site percolation, bond percolation, and Watts' threshold model; in all cases analytical results give excellent agreement with numerical simulations.

physics.soc-ph↗

arXiv2010

How clustering affects the bond percolation threshold in complex networks

The question of how clustering (non-zero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modelling highly-clustered networks are employed here to analytically study the bond percolation threshold. In comparison to the threshold in an unclustered network with the same degree distribution and correlation structure, the presence of triangles in these model networks is shown to lead to a larger bond percolation threshold (i.e. clustering \emph{increases} the epidemic threshold or \emph{decreases} resilience of the network to random edge deletion).

cond-mat.stat-mech↗

arXiv2010

The unreasonable effectiveness of tree-based theory for networks with clustering

We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance $\ell$ is sufficiently small - i.e., as long as it is close to the value of $\ell$ in a random network with negligible clustering and the same degree-degree correlations. We confirm this hypothesis numerically using real-world networks from various domains and on several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks provided that the networks are "sufficiently small" worlds.

cond-mat.dis-nn↗

arXiv2009

Bond percolation on a class of clustered random networks

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be prescribed, and theoretical results match well to numerical simulations on both synthetic and real-world networks.

cond-mat.stat-mech↗

arXiv2009

Analytical results for bond percolation and k-core sizes on clustered networks

An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a generalization of Trapman's [P. Trapman, Theor. Pop. Biol. {\bf 71}, 160 (2007)] model of cliques embedded in tree-like random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly-wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a non-zero percolation (epidemic) threshold.

cond-mat.stat-mech↗

arXiv2008

Transport in randomly-fluctuating spatially-periodic potentials

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical aimulations show two distinct parameter regimes, corresponding to free-running near-deterministic particles, and particles which are trapped in local minima of the potential with intermittent escape flights. Perturbation and asymptotic methods are developed to understand the drift velocity and diffusion coefficient in each parameter regime.

cond-mat.stat-mech↗

arXiv2005

An analytical approach to sorting in periodic potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

cond-mat.soft↗

arXiv2003

Motion in random fields - an application to stock market data

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-scale field show characteristics similar to those found in empirical studies of stock market data. Specifically, short-term returns have a non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying correlation function. The correlation function of the absolute value of returns decays as a power-law, and the returns distribution converges towards Gaussian over long times. Some important characteristics of empirical data are not, however, reproduced by the model, notably the scaling of tails of the cumulative distribution function of returns.

cond-mat.stat-mech↗