334 research outputs found
Uniform random generation of large acyclic digraphs
Directed acyclic graphs are the basic representation of the structure
underlying Bayesian networks, which represent multivariate probability
distributions. In many practical applications, such as the reverse engineering
of gene regulatory networks, not only the estimation of model parameters but
the reconstruction of the structure itself is of great interest. As well as for
the assessment of different structure learning algorithms in simulation
studies, a uniform sample from the space of directed acyclic graphs is required
to evaluate the prevalence of certain structural features. Here we analyse how
to sample acyclic digraphs uniformly at random through recursive enumeration,
an approach previously thought too computationally involved. Based on
complexity considerations, we discuss in particular how the enumeration
directly provides an exact method, which avoids the convergence issues of the
alternative Markov chain methods and is actually computationally much faster.
The limiting behaviour of the distribution of acyclic digraphs then allows us
to sample arbitrarily large graphs. Building on the ideas of recursive
enumeration based sampling we also introduce a novel hybrid Markov chain with
much faster convergence than current alternatives while still being easy to
adapt to various restrictions. Finally we discuss how to include such
restrictions in the combinatorial enumeration and the new hybrid Markov chain
method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
Development of an approximate method for quantum optical models and their pseudo-Hermicity
An approximate method is suggested to obtain analytical expressions for the
eigenvalues and eigenfunctions of the some quantum optical models. The method
is based on the Lie-type transformation of the Hamiltonians. In a particular
case it is demonstrated that Jahn-Teller Hamiltonian can
easily be solved within the framework of the suggested approximation. The
method presented here is conceptually simple and can easily be extended to the
other quantum optical models. We also show that for a purely imaginary coupling
the Hamiltonian becomes non-Hermitian but -symmetric. Possible generalization of this approach is outlined.Comment: Paper prepared fo the "3rd International Workshop on Pseudo-Hermitian
Hamiltonians in Quantum Physics" June 2005 Istanbul. To be published in
Czechoslovak Journal of Physic
Short-range repulsion and isospin dependence in the KN system
The short-range properties of the KN interaction are studied within the
meson-exchange model of the Juelich group. Specifically, dynamical explanations
for the phenomenological short-range repulsion, required in this model for
achieving agreement with the empirical KN data, are explored. Evidence is found
that contributions from the exchange of a heavy scalar-isovector meson
(a_0(980)) as well as from genuine quark-gluon exchange processes are needed.
Taking both mechanisms into account a satisfactory description of the KN phase
shifts can be obtained without resorting to phenomenological pieces.Comment: 26 pages, 5 figure
Universality in percolation of arbitrary Uncorrelated Nested Subgraphs
The study of percolation in so-called {\em nested subgraphs} implies a
generalization of the concept of percolation since the results are not linked
to specific graph process. Here the behavior of such graphs at criticallity is
studied for the case where the nesting operation is performed in an
uncorrelated way. Specifically, I provide an analyitic derivation for the
percolation inequality showing that the cluster size distribution under a
generalized process of uncorrelated nesting at criticality follows a power law
with universal exponent . The relevance of the result comes from
the wide variety of processes responsible for the emergence of the giant
component that fall within the category of nesting operations, whose outcome is
a family of nested subgraphs.Comment: 5 pages, no figures. Mistakes found in early manuscript have been
remove
On the topological classification of binary trees using the Horton-Strahler index
The Horton-Strahler (HS) index has been shown to
be relevant to a number of physical (such at diffusion limited aggregation)
geological (river networks), biological (pulmonary arteries, blood vessels,
various species of trees) and computational (use of registers) applications.
Here we revisit the enumeration problem of the HS index on the rooted,
unlabeled, plane binary set of trees, and enumerate the same index on the
ambilateral set of rooted, plane binary set of trees of leaves. The
ambilateral set is a set of trees whose elements cannot be obtained from each
other via an arbitrary number of reflections with respect to vertical axes
passing through any of the nodes on the tree. For the unlabeled set we give an
alternate derivation to the existing exact solution. Extending this technique
for the ambilateral set, which is described by an infinite series of non-linear
functional equations, we are able to give a double-exponentially converging
approximant to the generating functions in a neighborhood of their convergence
circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos
correcte
Generating correlated networks from uncorrelated ones
In this paper we consider a transformation which converts uncorrelated
networks to correlated ones(here by correlation we mean that coordination
numbers of two neighbors are not independent). We show that this
transformation, which converts edges to nodes and connects them according to a
deterministic rule, nearly preserves the degree distribution of the network and
significantly increases the clustering coefficient. This transformation also
enables us to relate percolation properties of the two networks.Comment: 14 pages, 6 figures, Revtex
Kaon-Nucleon Scattering Amplitudes and Z-Enhancements from Quark Born Diagrams
We derive closed form kaon-nucleon scattering amplitudes using the ``quark
Born diagram" formalism, which describes the scattering as a single interaction
(here the OGE spin-spin term) followed by quark line rearrangement. The low
energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with
experiment given conventional quark model parameters. For Gev
however the I=1 elastic phase shift is larger than predicted by Gaussian
wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent
low energy KN potentials for S-wave scattering are also derived. Finally we
consider OGE forces in the related channels K, KN and K,
and determine which have attractive interactions and might therefore exhibit
strong threshold enhancements or ``Z-molecule" meson-baryon bound states.
We find that the minimum-spin, minimum-isospin channels and two additional
K channels are most conducive to the formation of bound states.
Related interesting topics for future experimental and theoretical studies of
KN interactions are also discussed.Comment: 34 pages, figures available from the authors, revte
The spread of epidemic disease on networks
The study of social networks, and in particular the spread of disease on
networks, has attracted considerable recent attention in the physics community.
In this paper, we show that a large class of standard epidemiological models,
the so-called susceptible/infective/removed (SIR) models can be solved exactly
on a wide variety of networks. In addition to the standard but unrealistic case
of fixed infectiveness time and fixed and uncorrelated probability of
transmission between all pairs of individuals, we solve cases in which times
and probabilities are non-uniform and correlated. We also consider one simple
case of an epidemic in a structured population, that of a sexually transmitted
disease in a population divided into men and women. We confirm the correctness
of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure
Correlations in Scale-Free Networks: Tomography and Percolation
We discuss three related models of scale-free networks with the same degree
distribution but different correlation properties. Starting from the
Barabasi-Albert construction based on growth and preferential attachment we
discuss two other networks emerging when randomizing it with respect to links
or nodes. We point out that the Barabasi-Albert model displays dissortative
behavior with respect to the nodes' degrees, while the node-randomized network
shows assortative mixing. These kinds of correlations are visualized by
discussig the shell structure of the networks around their arbitrary node. In
spite of different correlation behavior, all three constructions exhibit
similar percolation properties.Comment: 6 pages, 2 figures; added reference
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