168 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
Worldwide spreading of economic crisis
We model the spreading of a crisis by constructing a global economic network
and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a
variable probability of infection. The probability of infection depends on the
strength of economic relations between the pair of countries, and the strength
of the target country. It is expected that a crisis which originates in a large
country, such as the USA, has the potential to spread globally, like the recent
crisis. Surprisingly we show that also countries with much lower GDP, such as
Belgium, are able to initiate a global crisis. Using the {\it k}-shell
decomposition method to quantify the spreading power (of a node), we obtain a
measure of ``centrality'' as a spreader of each country in the economic
network. We thus rank the different countries according to the shell they
belong to, and find the 12 most central countries. These countries are the most
likely to spread a crisis globally. Of these 12 only six are large economies,
while the other six are medium/small ones, a result that could not have been
otherwise anticipated. Furthermore, we use our model to predict the crisis
spreading potential of countries belonging to different shells according to the
crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia
Modularity map of the network of human cell differentiation
Cell differentiation in multicellular organisms is a complex process whose
mechanism can be understood by a reductionist approach, in which the individual
processes that control the generation of different cell types are identified.
Alternatively, a large scale approach in search of different organizational
features of the growth stages promises to reveal its modular global structure
with the goal of discovering previously unknown relations between cell types.
Here we sort and analyze a large set of scattered data to construct the network
of human cell differentiation (NHCD) based on cell types (nodes) and
differentiation steps (links) from the fertilized egg to a crying baby. We
discover a dynamical law of critical branching, which reveals a fractal
regularity in the modular organization of the network, and allows us to observe
the network at different scales. The emerging picture clearly identifies
clusters of cell types following a hierarchical organization, ranging from
sub-modules to super-modules of specialized tissues and organs on varying
scales. This discovery will allow one to treat the development of a particular
cell function in the context of the complex network of human development as a
whole. Our results point to an integrated large-scale view of the network of
cell types systematically revealing ties between previously unrelated domains
in organ functions.Comment: 32 pages, 7 figure
Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study
Anisotropic disordered system are studied in this work within the random
barrier model. In such systems the transition probabilities in different
directions have different probability density functions. The
frequency-dependent conductivity at low temperatures is obtained using an
effective medium approximation. It is shown that the isotropic universal
ac-conduction law, , is recovered if properly scaled
conductivity () and frequency () variables are used.Comment: 5 pages, no figures, final form (with corrected equations
Spectral statistics of random geometric graphs
We use random matrix theory to study the spectrum of random geometric graphs,
a fundamental model of spatial networks. Considering ensembles of random
geometric graphs we look at short range correlations in the level spacings of
the spectrum via the nearest neighbour and next nearest neighbour spacing
distribution and long range correlations via the spectral rigidity Delta_3
statistic. These correlations in the level spacings give information about
localisation of eigenvectors, level of community structure and the level of
randomness within the networks. We find a parameter dependent transition
between Poisson and Gaussian orthogonal ensemble statistics. That is the
spectral statistics of spatial random geometric graphs fits the universality of
random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert
and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio
Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks
In the reaction-diffusion process on random scale-free
(SF) networks with the degree exponent , the particle density decays
with time in a power law with an exponent when initial densities of
each species are the same. The exponent is for and for . Here, we examine the reaction
process on fractal SF networks, finding that even for . This slowly decaying behavior originates from the segregation effect:
Fractal SF networks contain local hubs, which are repulsive to each other.
Those hubs attract particles and accelerate the reaction, and then create
domains containing the same species of particles. It follows that the reaction
takes place at the non-hub boundaries between those domains and thus the
particle density decays slowly. Since many real SF networks are fractal, the
segregation effect has to be taken into account in the reaction kinetics among
heterogeneous particles.Comment: 4 pages, 6 figure
Explosive Percolation in the Human Protein Homology Network
We study the explosive character of the percolation transition in a
real-world network. We show that the emergence of a spanning cluster in the
Human Protein Homology Network (H-PHN) exhibits similar features to an
Achlioptas-type process and is markedly different from regular random
percolation. The underlying mechanism of this transition can be described by
slow-growing clusters that remain isolated until the later stages of the
process, when the addition of a small number of links leads to the rapid
interconnection of these modules into a giant cluster. Our results indicate
that the evolutionary-based process that shapes the topology of the H-PHN
through duplication-divergence events may occur in sudden steps, similarly to
what is seen in first-order phase transitions.Comment: 13 pages, 6 figure
Temperature dependence of the charge carrier mobility in gated quasi-one-dimensional systems
The many-body Monte Carlo method is used to evaluate the frequency dependent
conductivity and the average mobility of a system of hopping charges,
electronic or ionic on a one-dimensional chain or channel of finite length. Two
cases are considered: the chain is connected to electrodes and in the other
case the chain is confined giving zero dc conduction. The concentration of
charge is varied using a gate electrode. At low temperatures and with the
presence of an injection barrier, the mobility is an oscillatory function of
density. This is due to the phenomenon of charge density pinning. Mobility
changes occur due to the co-operative pinning and unpinning of the
distribution. At high temperatures, we find that the electron-electron
interaction reduces the mobility monotonically with density, but perhaps not as
much as one might intuitively expect because the path summation favour the
in-phase contributions to the mobility, i.e. the sequential paths in which the
carriers have to wait for the one in front to exit and so on. The carrier
interactions produce a frequency dependent mobility which is of the same order
as the change in the dc mobility with density, i.e. it is a comparably weak
effect. However, when combined with an injection barrier or intrinsic disorder,
the interactions reduce the free volume and amplify disorder by making it
non-local and this can explain the too early onset of frequency dependence in
the conductivity of some high mobility quasi-one-dimensional organic materials.Comment: 9 pages, 8 figures, to be published in Physical Review
Diffusion with random distribution of static traps
The random walk problem is studied in two and three dimensions in the
presence of a random distribution of static traps. An efficient Monte Carlo
method, based on a mapping onto a polymer model, is used to measure the
survival probability P(c,t) as a function of the trap concentration c and the
time t. Theoretical arguments are presented, based on earlier work of Donsker
and Varadhan and of Rosenstock, why in two dimensions one expects a data
collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda
t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects
a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of
t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both
data collapses show a clear crossover from the early-time Rosenstock behavior
to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure
Order statistics of the trapping problem
When a large number N of independent diffusing particles are placed upon a
site of a d-dimensional Euclidean lattice randomly occupied by a concentration
c of traps, what is the m-th moment of the time t_{j,N} elapsed
until the first j are trapped? An exact answer is given in terms of the
probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j
particles is trapped by time t. The Rosenstock approximation is used to
evaluate Phi_M(t), and it is found that for a large range of trap
concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as
x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant
and two corrective terms) is given for for the one-dimensional
lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
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