1,765 research outputs found
Complex Network Analysis of State Spaces for Random Boolean Networks
We apply complex network analysis to the state spaces of random Boolean
networks (RBNs). An RBN contains Boolean elements each with inputs. A
directed state space network (SSN) is constructed by linking each dynamical
state, represented as a node, to its temporal successor. We study the
heterogeneity of an SSN at both local and global scales, as well as
sample-to-sample fluctuations within an ensemble of SSNs. We use in-degrees of
nodes as a local topological measure, and the path diversity [Phys. Rev. Lett.
98, 198701 (2007)] of an SSN as a global topological measure. RBNs with exhibit non-trivial fluctuations at both local and global scales,
while K=2 exhibits the largest sample-to-sample, possibly non-self-averaging,
fluctuations. We interpret the observed ``multi scale'' fluctuations in the
SSNs as indicative of the criticality and complexity of K=2 RBNs. ``Garden of
Eden'' (GoE) states are nodes on an SSN that have in-degree zero. While
in-degrees of non-GoE nodes for SSNs can assume any integer value between
0 and , for K=1 all the non-GoE nodes in an SSN have the same in-degree
which is always a power of two
Dry and wet interfaces: Influence of solvent particles on molecular recognition
We present a coarse-grained lattice model to study the influence of water on
the recognition process of two rigid proteins. The basic model is formulated in
terms of the hydrophobic effect. We then investigate several modifications of
our basic model showing that the selectivity of the recognition process can be
enhanced by considering the explicit influence of single solvent particles.
When the number of cavities at the interface of a protein-protein complex is
fixed as an intrinsic geometric constraint, there typically exists a
characteristic fraction that should be filled with water molecules such that
the selectivity exhibits a maximum. In addition the optimum fraction depends on
the hydrophobicity of the interface so that one has to distinguish between dry
and wet interfaces.Comment: 11 pages, 7 figure
Gauge Theories with a Layered Phase
We study abelian gauge theories with anisotropic couplings in
dimensions. A layered phase is present, in the absence as well as in the
presence of fermions. A line of second order transitions separates the layered
from the Coulomb phase, if .Comment: 17 pages+9 figures (in LATeX and PostScript in a uuencoded,
compressed tar file appended at the end of the LATeX file) , CPT-94/P.303
Noncompact sigma-models: Large N expansion and thermodynamic limit
Noncompact SO(1,N) sigma-models are studied in terms of their large N
expansion in a lattice formulation in dimensions d \geq 2. Explicit results for
the spin and current two-point functions as well as for the Binder cumulant are
presented to next to leading order on a finite lattice. The dynamically
generated gap is negative and serves as a coupling-dependent infrared regulator
which vanishes in the limit of infinite lattice size. The cancellation of
infrared divergences in invariant correlation functions in this limit is
nontrivial and is in d=2 demonstrated by explicit computation for the above
quantities. For the Binder cumulant the thermodynamic limit is finite and is
given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that
the remainder is small or zero. The potential implications for ``criticality''
and ``triviality'' of the theories in the SO(1,N) invariant sector are
discussed.Comment: 46 pages, 2 figure
Random sampling vs. exact enumeration of attractors in random Boolean networks
We clarify the effect different sampling methods and weighting schemes have
on the statistics of attractors in ensembles of random Boolean networks (RBNs).
We directly measure cycle lengths of attractors and sizes of basins of
attraction in RBNs using exact enumeration of the state space. In general, the
distribution of attractor lengths differs markedly from that obtained by
randomly choosing an initial state and following the dynamics to reach an
attractor. Our results indicate that the former distribution decays as a
power-law with exponent 1 for all connectivities in the infinite system
size limit. In contrast, the latter distribution decays as a power law only for
K=2. This is because the mean basin size grows linearly with the attractor
cycle length for , and is statistically independent of the cycle length
for K=2. We also find that the histograms of basin sizes are strongly peaked at
integer multiples of powers of two for
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
On the Tail of the Overlap Probability Distribution in the Sherrington--Kirkpatrick Model
We investigate the large deviation behavior of the overlap probability
density in the Sherrington--Kirkpatrick model from several analytical
perspectives. First we analyze the spin glass phase using the coupled replica
scheme. Here generically
, and we compute the first correction to the expansion of \A
in powers of . We study also the case, where is know
exactly. Finally we study the paramagnetic phase, where exact results valid for
all 's are obtained. The overall agreement between the various points of
view is very satisfactory. Data from large scale numerical simulations show
that the predicted behavior can be detected already on moderate lattice sizes.Comment: 18 pages including ps figure
Leveraging Sport Mega-Events: New Model or Convenient Justification?
A range of recent studies have shown that the social and economic impacts of mega-events are often disappointing. This has stimulated interest in the notion of leveraging; an approach which views mega-events as a resource which can be levered to achieve outcomes which would not have happened automatically by staging an event. This paper aims to advance understanding about leveraging – by exploring the rationale for this approach and by identifying different types of leveraging and their relative merits. The work critically explores whether mega-event leveraging represents a new approach or whether it simply provides a convenient justification for expensive and controversial mega-event projects. The paper aims to enhance conceptual understanding, rather than to explore a specific case empirically; but a series of examples are used for illustrative purposes. These are drawn from projects adopted in association with the London 2012 Olympic and Paralympic Games
Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
We study temperature chaos in a two-dimensional Ising spin glass with random
quenched bimodal couplings, by an exact computation of the partition functions
on large systems. We study two temperature correlators from the total free
energy and from the domain wall free energy: in the second case we detect a
chaotic behavior. We determine and discuss the chaos exponent and the fractal
dimension of the domain walls.Comment: 5 pages, 6 postscript figures; added reference
New Universality Classes for Two-Dimensional -Models
We argue that the two-dimensional -invariant lattice -model
with mixed isovector/isotensor action has a one-parameter family of nontrivial
continuum limits, only one of which is the continuum -model constructed
by conventional perturbation theory. We test the proposed scenario with a
high-precision Monte Carlo simulation for on lattices up to , using a Wolff-type embedding algorithm. [CPU time 7 years IBM
RS-6000/320H] The finite-size-scaling data confirm the existence of the
predicted new family of continuum limits. In particular, the and
-vector models do not lie in the same universality class.Comment: 10 pages (includes 2 figures), 211176 bytes Postscript,
NYU-TH-93/07/03, IFUP-TH 34/9
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