6,650 research outputs found
Random Networks Tossing Biased Coins
In statistical mechanical investigations on complex networks, it is useful to
employ random graphs ensembles as null models, to compare with experimental
realizations. Motivated by transcription networks, we present here a simple way
to generate an ensemble of random directed graphs with, asymptotically,
scale-free outdegree and compact indegree. Entries in each row of the adjacency
matrix are set to be zero or one according to the toss of a biased coin, with a
chosen probability distribution for the biases. This defines a quick and simple
algorithm, which yields good results already for graphs of size n ~ 100.
Perhaps more importantly, many of the relevant observables are accessible
analytically, improving upon previous estimates for similar graphs
Exchangeable Random Networks
We introduce and study a class of exchangeable random graph ensembles. They
can be used as statistical null models for empirical networks, and as a tool
for theoretical investigations. We provide general theorems that carachterize
the degree distribution of the ensemble graphs, together with some features
that are important for applications, such as subgraph distributions and kernel
of the adjacency matrix. These results are used to compare to other models of
simple and complex networks. A particular case of directed networks with
power-law out--degree is studied in more detail, as an example of the
flexibility of the model in applications.Comment: to appear on "Internet Mathematics
A Model for the Self-Organization of Microtubules Driven by Molecular Motors
We propose a two-dimensional model for the organization of stabilized
microtubules driven by molecular motors in an unconfined geometry. In this
model two kinds of dynamics are competing. The first one is purely diffusive,
with an interaction between the rotational degrees of freedom, the second one
is a local drive, dependent on microtubule polarity. As a result, there is a
configuration dependent driving field. Applying a molecular field
approximation, we are able to derive continuum equations. A study on the
solutions shows nonequilibrium steady states. The presence and stability of
such self-organized states are investigated in terms of entropy production.
Numerical simulations confirm analytical results.Comment: 23 pages, 10 figures, LaTeX, ep
Folding and cytoplasm viscoelasticity contribute jointly to chromosome dynamics
The chromosome is a key player of cell physiology, and its dynamics provides
valuable information about its physical organization. In both prokaryotes and
eukaryotes, the short-time motion of chromosomal loci has been described as a
Rouse model in a simple or viscoelastic medium. However, little emphasis has
been put on the role played by the folded organization of chromosomes on the
local dynamics. Clearly, stress-propagation, and thus dynamics, must be
affected by such organization, but a theory allowing to extract such
information from data, e.g.\ of two-point correlations, is lacking. Here, we
describe a theoretical framework able to answer this general polymer dynamics
question, and we provide a general scaling analysis of the stress-propagation
time between two loci at a given arclength distance along the chromosomal
coordinate. The results suggest a precise way to detect folding information
from the dynamical coupling of chromosome segments. Additionally, we realize
this framework in a specific theoretical model of a polymer with variable-range
interactions in a viscoelastic medium characterized by a tunable scaling
exponent, where we derive analytical estimates of the correlation functions.Comment: 14 pages including supplementary material
Functional models for large-scale gene regulation networks: realism and fiction
High-throughput experiments are shedding light on the topology of large
regulatory networks and at the same time their functional states, namely the
states of activation of the nodes (for example transcript or protein levels) in
different conditions, times, environments. We now possess a certain amount of
information about these two levels of description, stored in libraries,
databases and ontologies. A current challenge is to bridge the gap between
topology and function, i.e. developing quantitative models aimed at
characterizing the expression patterns of large sets of genes. However,
approaches that work well for small networks become impossible to master at
large scales, mainly because parameters proliferate. In this review we discuss
the state of the art of large-scale functional network models, addressing the
issue of what can be considered as realistic and what the main limitations may
be. We also show some directions for future work, trying to set the goals that
future models should try to achieve. Finally, we will emphasize the possible
benefits in the understanding of biological mechanisms underlying complex
multifactorial diseases, and in the development of novel strategies for the
description and the treatment of such pathologies.Comment: to appear on Mol. BioSyst. 200
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