3,673 research outputs found
Maximum Power Efficiency and Criticality in Random Boolean Networks
Random Boolean networks are models of disordered causal systems that can
occur in cells and the biosphere. These are open thermodynamic systems
exhibiting a flow of energy that is dissipated at a finite rate. Life does work
to acquire more energy, then uses the available energy it has gained to perform
more work. It is plausible that natural selection has optimized many biological
systems for power efficiency: useful power generated per unit fuel. In this
letter we begin to investigate these questions for random Boolean networks
using Landauer's erasure principle, which defines a minimum entropy cost for
bit erasure. We show that critical Boolean networks maximize available power
efficiency, which requires that the system have a finite displacement from
equilibrium. Our initial results may extend to more realistic models for cells
and ecosystems.Comment: 4 pages RevTeX, 1 figure in .eps format. Comments welcome, v2: minor
clarifications added, conclusions unchanged. v3: paper rewritten to clarify
it; conclusions unchange
The Omega Dependence of the Evolution of xi(r)
The evolution of the two-point correlation function, xi(r,z), and the
pairwise velocity dispersion, sigma(r,z), for both the matter and halo
population, in three different cosmological models:
(Omega_M,Omega_Lambda)=(1,0), (0.2,0) and (0.2,0.8) are described. If the
evolution of xi is parameterized by xi(r,z)=(1+z)^{-(3+eps)}xi(r,0), where
xi(r,0)=(r/r_0)^{-gamma}, then eps(mass) ranges from 1.04 +/- 0.09 for (1,0) to
0.18 +/- 0.12 for (0.2,0), as measured by the evolution of at 1 Mpc (from z ~ 5
to the present epoch). For halos, eps depends on their mean overdensity. Halos
with a mean overdensity of about 2000 were used to compute the halo two-point
correlation function tested with two different group finding algorithms: the
friends of friends and the spherical overdensity algorithm. It is certainly
believed that the rate of growth of this xihh will give a good estimate of the
evolution of the galaxy two-point correlation function, at least from z ~ 1 to
the present epoch. The values we get for eps(halos) range from 1.54 for (1,0)
to -0.36 for (0.2,0), as measured by the evolution of xi(halos) from z ~ 1.0 to
the present epoch. These values could be used to constrain the cosmological
scenario. The evolution of the pairwise velocity dispersion for the mass and
halo distribution is measured and compared with the evolution predicted by the
Cosmic Virial Theorem (CVT). According to the CVT, sigma(r,z)^2 ~ G Q rho(z)
r^2 xi(r,z) or sigma proportional to (1+z)^{-eps/2}. The values of eps measured
from our simulated velocities differ from those given by the evolution of xi
and the CVT, keeping gamma and Q constant: eps(CVT) = 1.78 +/- 0.13 for (1,0)
or 1.40 +/- 0.28 for (0.2,0).Comment: Accepted for publication in the ApJ. Also available at
http://manaslu.astro.utoronto.ca/~carlberg/cnoc/xiev/xi_evo.ps.g
Teleportation, Braid Group and Temperley--Lieb Algebra
We explore algebraic and topological structures underlying the quantum
teleportation phenomena by applying the braid group and Temperley--Lieb
algebra. We realize the braid teleportation configuration, teleportation
swapping and virtual braid representation in the standard description of the
teleportation. We devise diagrammatic rules for quantum circuits involving
maximally entangled states and apply them to three sorts of descriptions of the
teleportation: the transfer operator, quantum measurements and characteristic
equations, and further propose the Temperley--Lieb algebra under local unitary
transformations to be a mathematical structure underlying the teleportation. We
compare our diagrammatical approach with two known recipes to the quantum
information flow: the teleportation topology and strongly compact closed
category, in order to explain our diagrammatic rules to be a natural
diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version
of the preprint, quant-ph/0601050, which includes details of calculation,
more topics such as topological diagrammatical operations and entanglement
swapping, and calls the Temperley--Lieb category for the collection of all
the Temperley--Lieb algebra with physical operations like local unitary
transformation
Quantifying the complexity of random Boolean networks
We study two measures of the complexity of heterogeneous extended systems,
taking random Boolean networks as prototypical cases. A measure defined by
Shalizi et al. for cellular automata, based on a criterion for optimal
statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)],
does not distinguish between the spatial inhomogeneity of the ordered phase and
the dynamical inhomogeneity of the disordered phase. A modification in which
complexities of individual nodes are calculated yields vanishing complexity
values for networks in the ordered and critical regimes and for highly
disordered networks, peaking somewhere in the disordered regime. Individual
nodes with high complexity are the ones that pass the most information from the
past to the future, a quantity that depends in a nontrivial way on both the
Boolean function of a given node and its location within the network.Comment: 8 pages, 4 figure
Scale-free networks are not robust under neutral evolution
Recently it has been shown that a large variety of different networks have
power-law (scale-free) distributions of connectivities. We investigate the
robustness of such a distribution in discrete threshold networks under neutral
evolution. The guiding principle for this is robustness in the resulting
phenotype. The numerical results show that a power-law distribution is not
stable under such an evolution, and the network approaches a homogeneous form
where the overall distribution of connectivities is given by a Poisson
distribution.Comment: Submitted for publicatio
Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks
Canalization of genetic regulatory networks has been argued to be favored by
evolutionary processes due to the stability that it can confer to phenotype
expression. We explore whether a significant amount of canalization and partial
canalization can arise in purely random networks in the absence of evolutionary
pressures. We use a mapping of the Boolean functions in the Kauffman N-K model
for genetic regulatory networks onto a k-dimensional Ising hypercube to show
that the functions can be divided into different classes strictly due to
geometrical constraints. The classes can be counted and their properties
determined using results from group theory and isomer chemistry. We demonstrate
that partially canalized functions completely dominate all possible Boolean
functions, particularly for higher k. This indicates that partial canalization
is extremely common, even in randomly chosen networks, and has implications for
how much information can be obtained in experiments on native state genetic
regulatory networks.Comment: 14 pages, 4 figures; version to appear in J. Phys.
A 20 Ghz Depolarization Experiment Using the ATS-6 Satellite
A depolarization experiment using the 20 GHz downlink from the ATS-6 satellite was described. The following subjects were covered: (1) an operational summary of the experiment, (2) a description of the equipment used with emphasis on improvements made to the signal processing receiver used with the ATS-5 satellite, (3) data on depolarization and attenuation in one snow storm and two rain storms at 45 deg elevation, (4) data on low angle propagation, (5) conclusions about depolarization on satellite paths, and (6) recommendations for the depolarization portion of the CTS experiment
Spacetime Embedding Diagrams for Black Holes
We show that the 1+1 dimensional reduction (i.e., the radial plane) of the
Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how
features of this spacetime can be seen from the embedding diagram. The purpose
of this work is educational: The associated embedding diagrams may be useful
for explaining aspects of black holes to students who are familiar with special
relativity, but not general relativity.Comment: 22 pages, 21 figures, RevTex. To be submitted to the American Journal
of Physics. Experts will wish only to skim appendix A and to look at the
pictures. Suggested Maple code is now compatible with MapleV4r
Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring
We study an evolutionary algorithm that locally adapts thresholds and wiring
in Random Threshold Networks, based on measurements of a dynamical order
parameter. A control parameter determines the probability of threshold
adaptations vs. link rewiring. For any , we find spontaneous symmetry
breaking into a new class of self-organized networks, characterized by a much
higher average connectivity than networks without threshold
adaptation (). While and evolved out-degree distributions
are independent from for , in-degree distributions become broader
when , approaching a power-law. In this limit, time scale separation
between threshold adaptions and rewiring also leads to strong correlations
between thresholds and in-degree. Finally, evidence is presented that networks
converge to self-organized criticality for large .Comment: 4 pages revtex, 6 figure
The Asymptotic Number of Attractors in the Random Map Model
The random map model is a deterministic dynamical system in a finite phase
space with n points. The map that establishes the dynamics of the system is
constructed by randomly choosing, for every point, another one as being its
image. We derive here explicit formulas for the statistical distribution of the
number of attractors in the system. As in related results, the number of
operations involved by our formulas increases exponentially with n; therefore,
they are not directly applicable to study the behavior of systems where n is
large. However, our formulas lend themselves to derive useful asymptotic
expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of
Physics A: Mathematical and Genera
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