1,739 research outputs found
Comment on "Regularizing capacity of metabolic networks"
In a recent paper, Marr, Muller-Linow and Hutt [Phys. Rev. E 75, 041917
(2007)] investigate an artificial dynamic system on metabolic networks. They
find a less complex time evolution of this dynamic system in real networks,
compared to networks of reference models. The authors argue that this suggests
that metabolic network structure is a major factor behind the stability of
biochemical steady states. We reanalyze the same kind of data using a dynamic
system modeling actual reaction kinetics. The conclusions about stability, from
our analysis, are inconsistent with those of Marr et al. We argue that this
issue calls for a more detailed type of modeling
Majority-vote model on hyperbolic lattices
We study the critical properties of a non-equilibrium statistical model, the
majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices
have the special feature that they only can be embedded in negatively curved
surfaces. We find, by using Monte Carlo simulations and finite-size analysis,
that the critical exponents , and are different
from those of the majority-vote model on regular lattices with periodic
boundary condition, which belongs to the same universality class as the
equilibrium Ising model. The exponents are also from those of the Ising model
on a hyperbolic lattice. We argue that the disagreement is caused by the
effective dimensionality of the hyperbolic lattices. By comparative studies, we
find that the critical exponents of the majority-vote model on hyperbolic
lattices satisfy the hyperscaling relation
, where is an
effective dimension of the lattice. We also investigate the effect of boundary
nodes on the ordering process of the model.Comment: 8 pages, 9 figure
Local interaction scale controls the existence of a non-trivial optimal critical mass in opinion spreading
We study a model of opinion formation where the collective decision of group
is said to happen if the fraction of agents having the most common opinion
exceeds a threshold value, a \textit{critical mass}. We find that there exists
a unique, non-trivial critical mass giving the most efficient convergence to
consensus. In addition, we observe that for small critical masses, the
characteristic time scale for the relaxation to consensus splits into two. The
shorter time scale corresponds to a direct relaxation and the longer can be
explained by the existence of intermediate, metastable states similar to those
found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)].
This longer time-scale is dependent on the precise condition for
consensus---with a modification of the condition it can go away.Comment: 4 pages, 6 figure
Discrete concavity and the half-plane property
Murota et al. have recently developed a theory of discrete convex analysis
which concerns M-convex functions on jump systems. We introduce here a family
of M-concave functions arising naturally from polynomials (over a field of
generalized Puiseux series) with prescribed non-vanishing properties. This
family contains several of the most studied M-concave functions in the
literature. In the language of tropical geometry we study the tropicalization
of the space of polynomials with the half-plane property, and show that it is
strictly contained in the space of M-concave functions. We also provide a short
proof of Speyer's hive theorem which he used to give a new proof of Horn's
conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected
A Ronkin type function for coamoebas
The Ronkin function plays a fundamental role in the theory of amoebas. We introduce an analogue of the Ronkin function in the setting of coamoebas. It turns out to be closely related to a certain toric arrangement known as the shell of the coamoeba and we use our Ronkin type function to obtain some properties of it
A Ronkin type function for coamoebas
The Ronkin function plays a fundamental role in the theory of amoebas. We introduce an analogue of the Ronkin function in the setting of coamoebas. It turns out to be closely related to a certain toric arrangement known as the shell of the coamoeba and we use our Ronkin type function to obtain some properties of it
Spatiotemporal Stochastic Resonance in Fully Frustrated Josephson Ladders
We consider a Josephson-junction ladder in an external magnetic field with
half flux quantum per plaquette. When driven by external currents, periodic in
time and staggered in space, such a fully frustrated system is found to display
spatiotemporal stochastic resonance under the influence of thermal noise. Such
resonance behavior is investigated both numerically and analytically, which
reveals significant effects of anisotropy and yields rich physics.Comment: 8 pages in two columns, 8 figures, to appear in Phys. Rev.
Nonequilibrium phase transition in the coevolution of networks and opinions
Models of the convergence of opinion in social systems have been the subject
of a considerable amount of recent attention in the physics literature. These
models divide into two classes, those in which individuals form their beliefs
based on the opinions of their neighbors in a social network of personal
acquaintances, and those in which, conversely, network connections form between
individuals of similar beliefs. While both of these processes can give rise to
realistic levels of agreement between acquaintances, practical experience
suggests that opinion formation in the real world is not a result of one
process or the other, but a combination of the two. Here we present a simple
model of this combination, with a single parameter controlling the balance of
the two processes. We find that the model undergoes a continuous phase
transition as this parameter is varied, from a regime in which opinions are
arbitrarily diverse to one in which most individuals hold the same opinion. We
characterize the static and dynamical properties of this transition
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