5,233 research outputs found
On the 1-loop calculations of softly broken fermion-torsion theory in curved space using the Stuckelberg procedure
The soft breaking of gauge or other symmetries is the typical Quantum Field
Theory phenomenon. In many cases one can apply the Stuckelberg procedure, which
means introducing some additional field (or fields) and restore the gauge
symmetry. The original softly broken theory corresponds to a particular choice
of the gauge fixing condition. In this paper we use this scheme for performing
quantum calculations for fermion-torsion theory, softly broken by the torsion
mass in arbitrary curved spacetime.Comment: Talk given at the 7th Alexander Friedmann International Seminar on
Gravitation and Cosmology, Joao Pessoa, Brazil, 29 Jun - 5 Jul 2008. 4 pages
and one figur
Boolean networks with robust and reliable trajectories
We construct and investigate Boolean networks that follow a given reliable
trajectory in state space, which is insensitive to fluctuations in the updating
schedule, and which is also robust against noise. Robustness is quantified as
the probability that the dynamics return to the reliable trajectory after a
perturbation of the state of a single node. In order to achieve high
robustness, we navigate through the space of possible update functions by using
an evolutionary algorithm. We constrain the networks to having the minimum
number of connections required to obtain the reliable trajectory. Surprisingly,
we find that robustness always reaches values close to 100 percent during the
evolutionary optimization process. The set of update functions can be evolved
such that it differs only slightly from that of networks that were not
optimized with respect to robustness. The state space of the optimized networks
is dominated by the basin of attraction of the reliable trajectory.Comment: 12 pages, 9 figure
Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks
We investigate the evolution of Boolean networks subject to a selective
pressure which favors robustness against noise, as a model of evolved genetic
regulatory systems. By mapping the evolutionary process into a statistical
ensemble and minimizing its associated free energy, we find the structural
properties which emerge as the selective pressure is increased and identify a
phase transition from a random topology to a "segregated core" structure, where
a smaller and more densely connected subset of the nodes is responsible for
most of the regulation in the network. This segregated structure is very
similar qualitatively to what is found in gene regulatory networks, where only
a much smaller subset of genes --- those responsible for transcription factors
--- is responsible for global regulation. We obtain the full phase diagram of
the evolutionary process as a function of selective pressure and the average
number of inputs per node. We compare the theoretical predictions with Monte
Carlo simulations of evolved networks and with empirical data for Saccharomyces
cerevisiae and Escherichia coli.Comment: 12 pages, 10 figure
Boolean networks with reliable dynamics
We investigated the properties of Boolean networks that follow a given
reliable trajectory in state space. A reliable trajectory is defined as a
sequence of states which is independent of the order in which the nodes are
updated. We explored numerically the topology, the update functions, and the
state space structure of these networks, which we constructed using a minimum
number of links and the simplest update functions. We found that the clustering
coefficient is larger than in random networks, and that the probability
distribution of three-node motifs is similar to that found in gene regulation
networks. Among the update functions, only a subset of all possible functions
occur, and they can be classified according to their probability. More
homogeneous functions occur more often, leading to a dominance of canalyzing
functions. Finally, we studied the entire state space of the networks. We
observed that with increasing systems size, fixed points become more dominant,
moving the networks close to the frozen phase.Comment: 11 Pages, 15 figure
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