5,445 research outputs found
Teleportation Topology
We discuss the structure of teleportation. By associating matrices to the
preparation and measurement states, we show that for a unitary transformation M
there is a full teleportation procedure for obtaining M|S> from a given state
|S>. The key to this construction is a diagrammatic intepretation of matrix
multiplication that applies equally well to a topological composition of a
maximum and a minimum that underlies the structure of the teleportation. This
paper is a preliminary report on joint work with H. Carteret and S. Lomonaco.Comment: LaTeX document, 16 pages, 8 figures, Talk delivered at the Xth
International Conference on Quantum Optics, Minsk, Belaru
Phase transition in a class of non-linear random networks
We discuss the complex dynamics of a non-linear random networks model, as a
function of the connectivity k between the elements of the network. We show
that this class of networks exhibit an order-chaos phase transition for a
critical connectivity k = 2. Also, we show that both, pairwise correlation and
complexity measures are maximized in dynamically critical networks. These
results are in good agreement with the previously reported studies on random
Boolean networks and random threshold networks, and show once again that
critical networks provide an optimal coordination of diverse behavior.Comment: 9 pages, 3 figures, revised versio
The computational complexity of Kauffman nets and the P versus NP problem
Complexity theory as practiced by physicists and computational complexity
theory as practiced by computer scientists both characterize how difficult it
is to solve complex problems. Here it is shown that the parameters of a
specific model can be adjusted so that the problem of finding its global energy
minimum is extremely sensitive to small changes in the problem statement. This
result has implications not only for studies of the physics of random systems
but may also lead to new strategies for resolving the well-known P versus NP
question in computational complexity theory.Comment: 4 pages, no figure
On the number of attractors in random Boolean networks
The evaluation of the number of attractors in Kauffman networks by Samuelsson
and Troein is generalized to critical networks with one input per node and to
networks with two inputs per node and different probability distributions for
update functions. A connection is made between the terms occurring in the
calculation and between the more graphic concepts of frozen, nonfrozen and
relevant nodes, and relevant components. Based on this understanding, a
phenomenological argument is given that reproduces the dependence of the
attractor numbers on system size.Comment: 6 page
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page
The phase transition in random catalytic sets
The notion of (auto) catalytic networks has become a cornerstone in
understanding the possibility of a sudden dramatic increase of diversity in
biological evolution as well as in the evolution of social and economical
systems. Here we study catalytic random networks with respect to the final
outcome diversity of products. We show that an analytical treatment of this
longstanding problem is possible by mapping the problem onto a set of
non-linear recurrence equations. The solution of these equations show a crucial
dependence of the final number of products on the initial number of products
and the density of catalytic production rules. For a fixed density of rules we
can demonstrate the existence of a phase transition from a practically
unpopulated regime to a fully populated and diverse one. The order parameter is
the number of final products. We are able to further understand the origin of
this phase transition as a crossover from one set of solutions from a quadratic
equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction
Robustness of Transcriptional Regulation in Yeast-like Model Boolean Networks
We investigate the dynamical properties of the transcriptional regulation of
gene expression in the yeast Saccharomyces Cerevisiae within the framework of a
synchronously and deterministically updated Boolean network model. By means of
a dynamically determinant subnetwork, we explore the robustness of
transcriptional regulation as a function of the type of Boolean functions used
in the model that mimic the influence of regulating agents on the transcription
level of a gene. We compare the results obtained for the actual yeast network
with those from two different model networks, one with similar in-degree
distribution as the yeast and random otherwise, and another due to Balcan et
al., where the global topology of the yeast network is reproduced faithfully.
We, surprisingly, find that the first set of model networks better reproduce
the results found with the actual yeast network, even though the Balcan et al.
model networks are structurally more similar to that of yeast.Comment: 7 pages, 4 figures, To appear in Int. J. Bifurcation and Chaos, typos
were corrected and 2 references were adde
Production of a Higgs pseudoscalar plus two jets in hadronic collisions
We consider the production of a Higgs pseudoscalar accompanied by two jets in
hadronic collisions. We work in the limit that the top quark is much heavier
than the Higgs pseudoscalar and use an effective Lagrangian for the
interactions of gluons with the pseudoscalar. We compute the amplitudes
involving: 1) four gluons and the pseudoscalar, 2) two quarks, two gluons and
the pseudoscalar and 3) four quarks and the pseudoscalar. We find that the
pseudoscalar amplitudes are nearly identical to those for the scalar case, the
only differences being the overall size and the relative signs between terms.
We present numerical cross sections for proton-proton collisions with
center-of-mass energy 14 TeV.Comment: 12 pages, LaTeX, 4 Postscript figures, submitted to Phys. Rev.
Self-organized Networks of Competing Boolean Agents
A model of Boolean agents competing in a market is presented where each agent
bases his action on information obtained from a small group of other agents.
The agents play a competitive game that rewards those in the minority. After a
long time interval, the poorest player's strategy is changed randomly, and the
process is repeated. Eventually the network evolves to a stationary but
intermittent state where random mutation of the worst strategy can change the
behavior of the entire network, often causing a switch in the dynamics between
attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure
added. To appear in PR
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