39 research outputs found
Models and average properties of scale-free directed networks
We extend the merging model for undirected networks by Kim et al. [Eur. Phys.
J. B 43, 369 (2004)] to directed networks and investigate the emerging
scale-free networks. Two versions of the directed merging model, friendly and
hostile merging, give rise to two distinct network types. We uncover that some
non-trivial features of these two network types resemble two levels of a
certain randomization/non-specificity in the link reshuffling during network
evolution. Furthermore the same features show up, respectively, in metabolic
networks and transcriptional networks. We introduce measures that single out
the distinguishing features between the two prototype networks, as well as
point out features which are beyond the prototypes.Comment: 7 pages, 8 figure
One Hub-One Process: A Tool Based View on Regulatory Network Topology
The relationship between the regulatory design and the functionality of
molecular networks is a key issue in biology. Modules and motifs have been
associated to various cellular processes, thereby providing anecdotal evidence
for performance based localization on molecular networks. To quantify
structure-function relationship we investigate similarities of proteins which
are close in the regulatory network of the yeast Saccharomyces Cerevisiae. We
find that the topology of the regulatory network show weak remnants of its
history of network reorganizations, but strong features of co-regulated
proteins associated to similar tasks. This suggests that local topological
features of regulatory networks, including broad degree distributions, emerge
as an implicit result of matching a number of needed processes to a finite
toolbox of proteins.Comment: 18 pages, 3 figures, 5 supplementary figure
Equilibrium strategy and population-size effects in lowest unique bid auctions
In lowest unique bid auctions, players bid for an item. The winner is
whoever places the \emph{lowest} bid, provided that it is also unique. We use a
grand canonical approach to derive an analytical expression for the equilibrium
distribution of strategies. We then study the properties of the solution as a
function of the mean number of players, and compare them with a large dataset
of internet auctions. The theory agrees with the data with striking accuracy
for small population size , while for larger a qualitatively different
distribution is observed. We interpret this result as the emergence of two
different regimes, one in which adaptation is feasible and one in which it is
not. Our results question the actual possibility of a large population to adapt
and find the optimal strategy when participating in a collective game.Comment: 6 pag. - 7 figs - added Supplementary Material. Changed affiliations.
Published versio
Replicator dynamics with turnover of players
We study adaptive dynamics in games where players abandon the population at a
given rate, and are replaced by naive players characterized by a prior
distribution over the admitted strategies. We demonstrate how such process
leads macroscopically to a variant of the replicator equation, with an
additional term accounting for player turnover. We study how Nash equilibria
and the dynamics of the system are modified by this additional term, for
prototypical examples such as the rock-scissor-paper game and different classes
of two-action games played between two distinct populations. We conclude by
showing how player turnover can account for non-trivial departures from Nash
equilibria observed in data from lowest unique bid auctions.Comment: 14 pages, 7 figure
Size dependent word frequencies and translational invariance of books
It is shown that a real novel shares many characteristic features with a null
model in which the words are randomly distributed throughout the text. Such a
common feature is a certain translational invariance of the text. Another is
that the functional form of the word-frequency distribution of a novel depends
on the length of the text in the same way as the null model. This means that an
approximate power-law tail ascribed to the data will have an exponent which
changes with the size of the text-section which is analyzed. A further
consequence is that a novel cannot be described by text-evolution models like
the Simon model. The size-transformation of a novel is found to be well
described by a specific Random Book Transformation. This size transformation in
addition enables a more precise determination of the functional form of the
word-frequency distribution. The implications of the results are discussed.Comment: 10 pages, 2 appendices (6 pages), 5 figure
Degree Landscapes in Scale-Free Networks
We generalize the degree-organizational view of real-world networks with
broad degree-distributions in a landscape analogue with mountains (high-degree
nodes) and valleys (low-degree nodes). For example, correlated degrees between
adjacent nodes corresponds to smooth landscapes (social networks), hierarchical
networks to one-mountain landscapes (the Internet), and degree-disassortative
networks without hierarchical features to rough landscapes with several
mountains. We also generate ridge landscapes to model networks organized under
constraints imposed by the space the networks are embedded in, associated to
spatial or, in molecular networks, to functional localization. To quantify the
topology, we here measure the widths of the mountains and the separation
between different mountains.Comment: 4 pages, 5 figure
Neutral theory of chemical reaction networks
To what extent do the characteristic features of a chemical reaction network
reflect its purpose and function? In general, one argues that correlations
between specific features and specific functions are key to understanding a
complex structure. However, specific features may sometimes be neutral and
uncorrelated with any system-specific purpose, function or causal chain. Such
neutral features are caused by chance and randomness. Here we compare two
classes of chemical networks: one that has been subjected to biological
evolution (the chemical reaction network of metabolism in living cells) and one
that has not (the atmospheric planetary chemical reaction networks). Their
degree distributions are shown to share the very same neutral
system-independent features. The shape of the broad distributions is to a large
extent controlled by a single parameter, the network size. From this
perspective, there is little difference between atmospheric and metabolic
networks; they are just different sizes of the same random assembling network.
In other words, the shape of the degree distribution is a neutral
characteristic feature and has no functional or evolutionary implications in
itself; it is not a matter of life and death.Comment: 13 pages, 8 figure
Symmetry-allowed phase transitions realized by the two-dimensional fully frustrated XY class
A 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new
groundstate in addition to the checkerboard groundstates of the standard 2D
FFXY model. The spin configuration of this additional groundstate is obtained.
Associated with this groundstate there are additional phase transitions. An
order parameter accounting for these new transitions is proposed. The
transitions associated with the new order parameter are suggested to be similar
to a 2D liquid-gas transition which implies Z_2-Ising like transitions. This
suggests that the class of 2D FFXY models belongs within a U(1) x Z_2 x
Z_2-designation of possible transitions, which implies that there are seven
different possible single and combined transitions. MC-simulations for the
generalized fully frustrated XY (GFFXY) model on a square lattice are used to
investigate which of these possibilities can be realized in practice: five of
the seven are encountered. Four critical points are deduced from the
MC-simulations, three consistent with central charge c=3/2 and one with c=1.
The implications for the standard 2D FFXY-model are discussed in particular
with respect to the long standing controversy concerning the characteristics of
its phase transitions.Comment: 8 pages, 8 figure