156 research outputs found
Scaling theory of transport in complex networks
Transport is an important function in many network systems and understanding
its behavior on biological, social, and technological networks is crucial for a
wide range of applications. However, it is a property that is not
well-understood in these systems and this is probably due to the lack of a
general theoretical framework. Here, based on the finding that renormalization
can be applied to bio-networks, we develop a scaling theory of transport in
self-similar networks. We demonstrate the networks invariance under length
scale renormalization and we show that the problem of transport can be
characterized in terms of a set of critical exponents. The scaling theory
allows us to determine the influence of the modular structure on transport. We
also generalize our theory by presenting and verifying scaling arguments for
the dependence of transport on microscopic features, such as the degree of the
nodes and the distance between them. Using transport concepts such as diffusion
and resistance we exploit this invariance and we are able to explain, based on
the topology of the network, recent experimental results on the broad flow
distribution in metabolic networks.Comment: 8 pages, 6 figure
Metabolite essentiality elucidates robustness of Escherichia coli metabolism
Complex biological systems are very robust to genetic and environmental
changes at all levels of organization. Many biological functions of Escherichia
coli metabolism can be sustained against single-gene or even multiple-gene
mutations by using redundant or alternative pathways. Thus, only a limited
number of genes have been identified to be lethal to the cell. In this regard,
the reaction-centric gene deletion study has a limitation in understanding the
metabolic robustness. Here, we report the use of flux-sum, which is the
summation of all incoming or outgoing fluxes around a particular metabolite
under pseudo-steady state conditions, as a good conserved property for
elucidating such robustness of E. coli from the metabolite point of view. The
functional behavior, as well as the structural and evolutionary properties of
metabolites essential to the cell survival, was investigated by means of a
constraints-based flux analysis under perturbed conditions. The essential
metabolites are capable of maintaining a steady flux-sum even against severe
perturbation by actively redistributing the relevant fluxes. Disrupting the
flux-sum maintenance was found to suppress cell growth. This approach of
analyzing metabolite essentiality provides insight into cellular robustness and
concomitant fragility, which can be used for several applications, including
the development of new drugs for treating pathogens.Comment: Supplements available at
http://stat.kaist.ac.kr/publication/2007/PJKim_pnas_supplement.pd
Dynamics of a Josephson Array in a Resonant Cavity
We derive dynamical equations for a Josephson array coupled to a resonant
cavity by applying the Heisenberg equations of motion to a model Hamiltonian
described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B
{\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show
that, in the absence of an applied current and dissipation, our model reduces
to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371
(1997)] for coupled qubits, and that it corresponds to a capacitive coupling
between the array and the cavity mode. From extensive numerical solutions of
the model in one dimension, we find that the array locks into a coherent,
periodic state above a critical number of active junctions, that the
current-voltage characteristics of the array have self-induced resonant steps
(SIRS's), that when active junctions are synchronized on a SIRS, the
energy emitted into the resonant cavity is quadratic in , and that when a
fixed number of junctions is biased on a SIRS, the energy is linear in the
input power. All these results are in agreement with recent experiments. By
choosing the initial conditions carefully, we can drive the array into any of a
variety of different integer SIRS's. We tentatively identify terms in the
equations of motion which give rise to both the SIRS's and the coherence
threshold. We also find higher-order integer SIRS's and fractional SIRS's in
some simulations. We conclude that a resonant cavity can produce threshold
behavior and SIRS's even in a one-dimensional array with appropriate
experimental parameters, and that the experimental data, including the coherent
emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.
Walks on Apollonian networks
We carry out comparative studies of random walks on deterministic Apollonian
networks (DANs) and random Apollonian networks (RANs). We perform computer
simulations for the mean first passage time, the average return time, the
mean-square displacement, and the network coverage for unrestricted random
walk. The diffusions both on DANs and RANs are proved to be sublinear. The
search efficiency for walks with various strategies and the influence of the
topology of underlying networks on the dynamics of walks are discussed.
Contrary to one's intuition, it is shown that the self-avoiding random walk,
which has been verified as an optimal strategy for searching on scale-free and
small-world networks, is not the best strategy for the DAN in the thermodynamic
limit.Comment: 5 pages, 4 figure
Two-Component Genetic Switch as a Synthetic Module with Tunable Stability
Despite stochastic fluctuations, some genetic switches are able to retain their expression states through multiple cell divisions, providing epigenetic memory. We propose a novel rationale for tuning the functional stability of a simple synthetic gene switch through protein dimerization. Introducing an approximation scheme to access long-time stochastic dynamics of multiple-component gene circuits, we find that the spontaneous switching rate may exhibit greater than 8orders of magnitude variation. The manipulation of the circuit's biochemical properties offers a practical strategy for designing robust epigenetic memory with synthetic circuits.open101
Recursive graphs with small-world scale-free properties
We discuss a category of graphs, recursive clique trees, which have
small-world and scale-free properties and allow a fine tuning of the clustering
and the power-law exponent of their discrete degree distribution. We determine
relevant characteristics of those graphs: the diameter, degree distribution,
and clustering parameter. The graphs have also an interesting recursive
property, and generalize recent constructions with fixed degree distributions.Comment: 4 pages, 2 figure
Simple models of small world networks with directed links
We investigate the effect of directed short and long range connections in a
simple model of small world network. Our model is such that we can determine
many quantities of interest by an exact analytical method. We calculate the
function , defined as the number of sites affected up to time when a
naive spreading process starts in the network. As opposed to shortcuts, the
presence of un-favorable bonds has a negative effect on this quantity. Hence
the spreading process may not be able to affect all the network. We define and
calculate a quantity named the average size of accessible world in our model.
The interplay of shortcuts, and un-favorable bonds on the small world
properties is studied.Comment: 15 pages, 9 figures, published versio
Eigenstates of a Small Josephson Junction Coupled to a Resonant Cavity
We carry out a quantum-mechanical analysis of a small Josephson junction
coupled to a single-mode resonant cavity. We find that the eigenstates of the
combined junction-cavity system are strongly entangled only when the gate
voltage applied at one of the superconducting islands is tuned to certain
special values. One such value corresponds to the resonant absorption of a
single photon by Cooper pairs in the junction. Another special value
corresponds to a {\em two-photon} absorption process. Near the single-photon
resonant absorption, the system is accurately described by a simplified model
in which only the lowest two levels of the Josephson junction are retained in
the Hamiltonian matrix. We noticed that this approximation does not work very
well as the number of photons in the resonator increases. Our system shows also
the phenomenon of ``collapse and revival'' under suitable initial conditions,
and our full numerical solution agrees with the two level approximation result.Comment: 7 pages, and 6 figures. To be published in Phys. Rev.
Potts Model On Random Trees
We study the Potts model on locally tree-like random graphs of arbitrary
degree distribution. Using a population dynamics algorithm we numerically solve
the problem exactly. We confirm our results with simulations. Comparisons with
a previous approach are made, showing where its assumption of uniform local
fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure
Constrained spin dynamics description of random walks on hierarchical scale-free networks
We study a random walk problem on the hierarchical network which is a
scale-free network grown deterministically. The random walk problem is mapped
onto a dynamical Ising spin chain system in one dimension with a nonlocal spin
update rule, which allows an analytic approach. We show analytically that the
characteristic relaxation time scale grows algebraically with the total number
of nodes as . From a scaling argument, we also show the
power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim
t^{-\alpha}, which is the probability to find the Ising spins in the initial
state {\bfsigma} after time steps, with the state-dependent non-universal
exponent . It turns out that the power-law scaling behavior has its
origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure
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