123 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
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.
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.
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
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
Resonant-Cavity-Induced Phase Locking and Voltage Steps in a Josephson Array
We describe a simple dynamical model for an underdamped Josephson junction
array coupled to a resonant cavity. From numerical solutions of the model in
one dimension, we find that (i) current-voltage characteristics of the array
have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling
strength, the array locks into a coherent, periodic state above a critical
number of active Josephson junctions, and (iii) when active junctions are
synchronized on an SIRS, the energy emitted into the resonant cavity is
quadratic with . All three features are in agreement with a recent
experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com
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
Global organization of metabolic fluxes in the bacterium, Escherichia coli
Cellular metabolism, the integrated interconversion of thousands of metabolic
substrates through enzyme-catalyzed biochemical reactions, is the most
investigated complex intercellular web of molecular interactions. While the
topological organization of individual reactions into metabolic networks is
increasingly well understood, the principles governing their global functional
utilization under different growth conditions pose many open questions. We
implement a flux balance analysis of the E. coli MG1655 metabolism, finding
that the network utilization is highly uneven: while most metabolic reactions
have small fluxes, the metabolism's activity is dominated by several reactions
with very high fluxes. E. coli responds to changes in growth conditions by
reorganizing the rates of selected fluxes predominantly within this high flux
backbone. The identified behavior likely represents a universal feature of
metabolic activity in all cells, with potential implications to metabolic
engineering.Comment: 15 pages 4 figure
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