265 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
Growth-rate-dependent dynamics of a bacterial genetic oscillator
Gene networks exhibiting oscillatory dynamics are widespread in biology. The
minimal regulatory designs giving rise to oscillations have been implemented
synthetically and studied by mathematical modeling. However, most of the
available analyses generally neglect the coupling of regulatory circuits with
the cellular "chassis" in which the circuits are embedded. For example, the
intracellular macromolecular composition of fast-growing bacteria changes with
growth rate. As a consequence, important parameters of gene expression, such as
ribosome concentration or cell volume, are growth-rate dependent, ultimately
coupling the dynamics of genetic circuits with cell physiology. This work
addresses the effects of growth rate on the dynamics of a paradigmatic example
of genetic oscillator, the repressilator. Making use of empirical growth-rate
dependences of parameters in bacteria, we show that the repressilator dynamics
can switch between oscillations and convergence to a fixed point depending on
the cellular state of growth, and thus on the nutrients it is fed. The physical
support of the circuit (type of plasmid or gene positions on the chromosome)
also plays an important role in determining the oscillation stability and the
growth-rate dependence of period and amplitude. This analysis has potential
application in the field of synthetic biology, and suggests that the coupling
between endogenous genetic oscillators and cell physiology can have substantial
consequences for their functionality.Comment: 14 pages, 9 figures (revised version, accepted for publication
Gene silencing and large-scale domain structure of the E. coli genome
The H-NS chromosome-organizing protein in E. coli can stabilize genomic DNA
loops, and form oligomeric structures connected to repression of gene
expression. Motivated by the link between chromosome organization, protein
binding and gene expression, we analyzed publicly available genomic data sets
of various origins, from genome-wide protein binding profiles to evolutionary
information, exploring the connections between chromosomal organization,
genesilencing, pseudo-gene localization and horizontal gene transfer. We report
the existence of transcriptionally silent contiguous areas corresponding to
large regions of H-NS protein binding along the genome, their position
indicates a possible relationship with the known large-scale features of
chromosome organization
Soft bounds on diffusion produce skewed distributions and Gompertz growth
Constraints can affect dramatically the behavior of diffusion processes.
Recently, we analyzed a natural and a technological system and reported that
they perform diffusion-like discrete steps displaying a peculiar constraint,
whereby the increments of the diffusing variable are subject to
configuration-dependent bounds. This work explores theoretically some of the
revealing landmarks of such phenomenology, termed "soft bound". At long times,
the system reaches a steady state irreversibly (i.e., violating detailed
balance), characterized by a skewed "shoulder" in the density distribution, and
by a net local probability flux, which has entropic origin. The largest point
in the support of the distribution follows a saturating dynamics, expressed by
the Gompertz law, in line with empirical observations. Finally, we propose a
generic allometric scaling for the origin of soft bounds. These findings shed
light on the impact on a system of such "scaling" constraint and on its
possible generating mechanisms.Comment: 9 pages, 6 color figure
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
Dicke simulators with emergent collective quantum computational abilities
Using an approach inspired from Spin Glasses, we show that the multimode
disordered Dicke model is equivalent to a quantum Hopfield network. We propose
variational ground states for the system at zero temperature, which we
conjecture to be exact in the thermodynamic limit. These ground states contain
the information on the disordered qubit-photon couplings. These results lead to
two intriguing physical implications. First, once the qubit-photon couplings
can be engineered, it should be possible to build scalable pattern-storing
systems whose dynamics is governed by quantum laws. Second, we argue with an
example how such Dicke quantum simulators might be used as a solver of "hard"
combinatorial optimization problems.Comment: 5+2 pages, 2 figures. revisited in the exposition and supplementary
added. Comments are welcom
Isotropic-Nematic transition of long thin hard spherocylinders confined in a quasi-two-dimensional planar geometry
We present computer simulations of long thin hard spherocylinders in a narrow
planar slit. We observe a transition from the isotropic to a nematic phase with
quasi-long-range orientational order upon increasing the density. This phase
transition is intrinsically two dimensional and of the Kosterlitz-Thouless
type. The effective two-dimensional density at which this transition occurs
increases with plate separation. We qualitatively compare some of our results
with experiments where microtubules are confined in a thin slit, which gave the
original inspiration for this work.Comment: 8 pages, 10 figure
Counting the learnable functions of structured data
Cover's function counting theorem is a milestone in the theory of artificial
neural networks. It provides an answer to the fundamental question of
determining how many binary assignments (dichotomies) of points in
dimensions can be linearly realized. Regrettably, it has proved hard to extend
the same approach to more advanced problems than the classification of points.
In particular, an emerging necessity is to find methods to deal with structured
data, and specifically with non-pointlike patterns. A prominent case is that of
invariant recognition, whereby identification of a stimulus is insensitive to
irrelevant transformations on the inputs (such as rotations or changes in
perspective in an image). An object is therefore represented by an extended
perceptual manifold, consisting of inputs that are classified similarly. Here,
we develop a function counting theory for structured data of this kind, by
extending Cover's combinatorial technique, and we derive analytical expressions
for the average number of dichotomies of generically correlated sets of
patterns. As an application, we obtain a closed formula for the capacity of a
binary classifier trained to distinguish general polytopes of any dimension.
These results may help extend our theoretical understanding of generalization,
feature extraction, and invariant object recognition by neural networks
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