36,974 research outputs found
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 to . We performed Monte Carlo studies on the
overlap between "identical twins" raised in independent dynamical environments,
up to size . Our results suggest an overlap decaying with time as
with ; 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 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 of
face-centered cubic (FCC) crystal increases linearly. At low temperatures,
although plateaus at integer values, the crystal
behavior changes continuously with density. The previously ambiguous crossover
around 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
. 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 .Comment: 9 pages 4 figure
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