Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.Comment: 13 pages, 2 figure

Percolation in the Sherrington-Kirkpatrick Spin Glass

We present extended versions and give detailed proofs of results concerning percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The proofs involve comparison inequalities between SK multireplica bond occupation variables and the independent variables of standard Erdos-Renyi random graphs.Comment: 18 page

Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state ("nature") vs. the realization of the stochastic dynamics ("nurture") in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from $T=\infty$ to $T=0$. We performed Monte Carlo studies on the overlap between "identical twins" raised in independent dynamical environments, up to size $L=500$. Our results suggest an overlap decaying with time as $t^{-\theta_h}$ with $\theta_h = 0.22 \pm 0.02$; the same exponent holds for a quench to low but nonzero temperature. This "heritability exponent" may equal the persistence exponent for the 2D Ising ferromagnet, but the two differ more generally.Comment: 5 pages, 3 figures; new version includes results for nonzero temperatur

3 tera-basepairs as a fundamental limit for robust DNA replication

10 p.-2 tab.In order to maintain functional robustness and species integrity, organisms must ensure high fidelity of the genome duplication process. This is particularly true during early development, where cell division is often occurring both rapidly and coherently. By studying the extreme limits of suppressing DNA replication failure due to double fork stall errors, we uncover a fundamental constant that describes a trade-off between genome size and architectural complexity of the developing organism. This constant has the approximate value N_U ≈ 3×10^12 basepairs, and depends only on two highly conserved molecular properties of DNA biology. We show that our theory is successful in interpreting a diverse range of data across the Eukaryota.MAM, LA and TJN acknowledge prior support from the Scottish Universities Life Sciences Alliance. JJB acknowledges support from Cancer Research UK (grant C303/A14301) and the Wellcome Trust (grant WT096598MA). TJN acknowledges prior support from the National Institutes of Health (Physical Sciences in Oncology Centers, U54 CA143682).Peer reviewe

Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method

Implementation of the tridiagonal reduction method for real eigenvalue extraction in structural vibration and buckling problems is described. The basic concepts underlying the method are summarized and special features, such as the computation of error bounds and default modes of operation are discussed. In addition, the new user information and error messages and optional diagnostic output relating to the tridiagonal reduction method are presented. Some numerical results and initial experiences relating to usage in the NASTRAN environment are provided, including comparisons with other existing NASTRAN eigenvalue methods

Characterizing the structure of small-world networks

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN

[N]pT Monte Carlo Simulations of the Cluster-Crystal-Forming Penetrable Sphere Model

Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded isothermal-isobaric $[N]pT$ ensemble that surmounts this problem by allowing both particle number and lattice spacing to fluctuate. We apply the method with a Monte Carlo simulation scheme to solve the phase diagram of a prototypical cluster-crystal former, the penetrable sphere model (PSM), and compare the results with earlier theoretical predictions. At high temperatures and densities, the equilibrium occupancy $n_{\mathrm{c}}^{\mathrm{eq}}$ of face-centered cubic (FCC) crystal increases linearly. At low temperatures, although $n_{\mathrm{c}}^{\mathrm{eq}}$ plateaus at integer values, the crystal behavior changes continuously with density. The previously ambiguous crossover around $T\sim0.1$ is resolved

Liquid-liquid transition in supercooled silicon determined by first-principles simulation

First principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below $T_c\approx 1232K$. The low density phase is nearly tetra-coordinated, with a pseudogap at the Fermi surface, while the high density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below $T_c$.Comment: 9 pages 4 figure