5,854 research outputs found
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
Diassociative algebras and Milnor's invariants for tangles
We extend Milnor's mu-invariants of link homotopy to ordered (classical or
virtual) tangles. Simple combinatorial formulas for mu-invariants are given in
terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves
corresponds to axioms of Loday's diassociative algebra. The relation of tangles
to diassociative algebras is formulated in terms of a morphism of corresponding
operads.Comment: 17 pages, many figures; v2: several typos correcte
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
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
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
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
On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions
NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N
Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To
each NK-Kauffman network it is possible to assign a unique Boolean function on
N variables through the function \Psi: {\cal L}^N_K \to \Lambda_N. The
probability {\cal P}_K that \Psi (f) = \Psi (f'), when f' is obtained through f
by a change of one of its K-Boolean functions (b_K: \IZ_2^K \to \IZ_2), and/or
connections; is calculated. The leading term of the asymptotic expansion of
{\cal P}_K, for N \gg 1, turns out to depend on: the probability to extract the
tautology and contradiction Boolean functions, and in the average value of the
distribution of probability of the Boolean functions; the other terms decay as
{\cal O} (1 / N). In order to accomplish this, a classification of the Boolean
functions in terms of what I have called their irreducible degree of
connectivity is established. The mathematical findings are discussed in the
biological context where, \Psi is used to model the genotype-phenotype map.Comment: 17 pages, 1 figure, Accepted in Journal of Mathematical Physic
The dynamics of critical Kauffman networks under asynchronous stochastic update
We show that the mean number of attractors in a critical Boolean network
under asynchronous stochastic update grows like a power law and that the mean
size of the attractors increases as a stretched exponential with the system
size. This is in strong contrast to the synchronous case, where the number of
attractors grows faster than any power law.Comment: submitted to PR
Survey for Galaxies Associated with z~3 Damped Lyman alpha Systems I: Spectroscopic Calibration of u'BVRI Photometric Selection
We present a survey for z~3 Lyman break galaxies (LBGs) associated with
damped Lyman alpha systems (DLAs) with the primary purpose of determining the
DLA-LBG cross-correlation. This paper describes the acquisition and analysis of
imaging and spectroscopic data of 9 quasar fields having 11 known z~3 DLAs
covering an area of 465 arcmin^2. Using deep u'BVRI images, 796 LBG candidates
to an apparent R_AB magnitude of 25.5 were photometrically selected from 17,343
sources detected in the field. Spectroscopic observations of 529 LBG candidates
using Keck LRIS yielded 339 redshifts. We have conservatively identified 211
z>2 objects with =3.02+/-0.32. We discuss our method of z~3 LBG
identification and present a model of the u'BVRI photometric selection
function. We use the 339 spectra to evaluate our u'BVRI z~3 Lyman break
photometric selection technique.Comment: 26 pages, 6 tables, 11 figures, accepted for publication in Ap
Annealing schedule from population dynamics
We introduce a dynamical annealing schedule for population-based optimization
algorithms with mutation. On the basis of a statistical mechanics formulation
of the population dynamics, the mutation rate adapts to a value maximizing
expected rewards at each time step. Thereby, the mutation rate is eliminated as
a free parameter from the algorithm.Comment: 6 pages RevTeX, 4 figures PostScript; to be published in Phys. Rev.
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