13,163 research outputs found
Scale-free networks with tunable degree distribution exponents
We propose and study a model of scale-free growing networks that gives a
degree distribution dominated by a power-law behavior with a model-dependent,
hence tunable, exponent. The model represents a hybrid of the growing networks
based on popularity-driven and fitness-driven preferential attachments. As the
network grows, a newly added node establishes new links to existing nodes
with a probability based on popularity of the existing nodes and a
probability based on fitness of the existing nodes. An explicit form of
the degree distribution is derived within a mean field approach. For
reasonably large , , where the
function is dominated by the behavior of for small
values of and becomes -independent as , and is a
model-dependent exponent. The degree distribution and the exponent
are found to be in good agreement with results obtained by extensive numerical
simulations.Comment: 12 pages, 2 figures, submitted to PR
Scaling Behaviour of Developing and Decaying Networks
We find that a wide class of developing and decaying networks has scaling
properties similar to those that were recently observed by Barab\'{a}si and
Albert in the particular case of growing networks. The networks considered here
evolve according to the following rules: (i) Each instant a new site is added,
the probability of its connection to old sites is proportional to their
connectivities. (ii) In addition, (a) new links between some old sites appear
with probability proportional to the product of their connectivities or (b)
some links between old sites are removed with equal probability.Comment: 7 pages (revtex
Signature Characters for A_2 and B_2
The signatures of the inner product matrices on a Lie algebra's highest
weight representation are encoded in the representation's signature character.
We show that the signature characters of a finite-dimensional Lie algebra's
highest weight representations obey simple difference equations that have a
unique solution once appropriate boundary conditions are imposed. We use these
results to derive the signature characters of all and highest
weight representations. Our results extend, and explain, signature patterns
analogous to those observed by Friedan, Qiu and Shenker in the Virasoro
algebra's representation theory.Comment: 22 p
Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods
We analyze the synchronization dynamics of phase oscillators far from the
synchronization manifold, including the onset of synchronization on scale-free
networks with low and high clustering coefficients. We use normal coordinates
and corresponding time-averaged velocities derived from the Laplacian matrix,
which reflects the network's topology. In terms of these coordinates,
synchronization manifests itself as a contraction of the dynamics onto
progressively lower-dimensional submanifolds of phase space spanned by
Laplacian eigenvectors with lower eigenvalues. Differences between high and low
clustering networks can be correlated with features of the Laplacian spectrum.
For example, the inhibition of full synchoronization at high clustering is
associated with a group of low-lying modes that fail to lock even at strong
coupling, while the advanced partial synchronizationat low coupling noted
elsewhere is associated with high-eigenvalue modes.Comment: Revised version: References added, introduction rewritten, additional
minor changes for clarit
Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
We generalize the Barab\'{a}si--Albert's model of growing networks accounting
for initial properties of sites and find exactly the distribution of
connectivities of the network and the averaged connectivity
of a site in the instant (one site is added per unit of
time). At long times at and
at , where the exponent
varies from 2 to depending on the initial attractiveness of sites. We
show that the relation between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur
Random matrix analysis of complex networks
We study complex networks under random matrix theory (RMT) framework. Using
nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the
eigenvalues of adjacency matrix of various model networks, namely, random,
scale-free and small-world networks. These distributions follow Gaussian
orthogonal ensemble statistic of RMT. To probe long-range correlations in the
eigenvalues we study spectral rigidity via statistic of RMT as well.
It follows RMT prediction of linear behavior in semi-logarithmic scale with
slope being . Random and scale-free networks follow RMT
prediction for very large scale. Small-world network follows it for
sufficiently large scale, but much less than the random and scale-free
networks.Comment: accepted in Phys. Rev. E (replaced with the final version
Theory of Networked Minority Games based on Strategy Pattern Dynamics
We formulate a theory of agent-based models in which agents compete to be in
a winning group. The agents may be part of a network or not, and the winning
group may be a minority group or not. The novel feature of the present
formalism is its focus on the dynamical pattern of strategy rankings, and its
careful treatment of the strategy ties which arise during the system's temporal
evolution. We apply it to the Minority Game (MG) with connected populations.
Expressions for the mean success rate among the agents and for the mean success
rate for agents with neighbors are derived. We also use the theory to
estimate the value of connectivity above which the Binary-Agent-Resource
system with high resource level goes into the high-connectivity state.Comment: 24 pages, 3 figures, submitted to PR
The Number of Incipient Spanning Clusters in Two-Dimensional Percolation
Using methods of conformal field theory, we conjecture an exact form for the
probability that n distinct clusters span a large rectangle or open cylinder of
aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison
with existing numerical results include
High-Q-factor Al [subscript 2]O[subscript 3] micro-trench cavities integrated with silicon nitride waveguides on silicon
We report on the design and performance of high-Q integrated optical micro-trench cavities on silicon. The microcavities are co-integrated with silicon nitride bus waveguides and fabricated using wafer-scale silicon-photonics-compatible processing steps. The amorphous aluminum oxide resonator material is deposited via sputtering in a single straightforward post-processing step. We examine the theoretical and experimental optical properties of the aluminum oxide micro-trench cavities for different bend radii, film thicknesses and near-infrared wavelengths and demonstrate experimental Q factors of > 10[superscript 6]. We propose that this high-Q micro-trench cavity design can be applied to incorporate a wide variety of novel microcavity materials, including rare-earth-doped films for microlasers, into wafer-scale silicon photonics platforms
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