39 research outputs found
Shortest paths and load scaling in scale-free trees
The average node-to-node distance of scale-free graphs depends
logarithmically on N, the number of nodes, while the probability distribution
function (pdf) of the distances may take various forms. Here we analyze these
by considering mean-field arguments and by mapping the m=1 case of the
Barabasi-Albert model into a tree with a depth-dependent branching ratio. This
shows the origins of the average distance scaling and allows a demonstration of
why the distribution approaches a Gaussian in the limit of N large. The load
(betweenness), the number of shortest distance paths passing through any node,
is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende
The number of matchings in random graphs
We study matchings on sparse random graphs by means of the cavity method. We
first show how the method reproduces several known results about maximum and
perfect matchings in regular and Erdos-Renyi random graphs. Our main new result
is the computation of the entropy, i.e. the leading order of the logarithm of
the number of solutions, of matchings with a given size. We derive both an
algorithm to compute this entropy for an arbitrary graph with a girth that
diverges in the large size limit, and an analytic result for the entropy in
regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical
Mechanic
Tag-Aware Recommender Systems: A State-of-the-art Survey
In the past decade, Social Tagging Systems have attracted increasing
attention from both physical and computer science communities. Besides the
underlying structure and dynamics of tagging systems, many efforts have been
addressed to unify tagging information to reveal user behaviors and
preferences, extract the latent semantic relations among items, make
recommendations, and so on. Specifically, this article summarizes recent
progress about tag-aware recommender systems, emphasizing on the contributions
from three mainstream perspectives and approaches: network-based methods,
tensor-based methods, and the topic-based methods. Finally, we outline some
other tag-related works and future challenges of tag-aware recommendation
algorithms.Comment: 19 pages, 3 figure
Quadrupole deformations of neutron-drip-line nuclei studied within the Skyrme Hartree-Fock-Bogolyubov approach
We introduce a local-scaling point transformation to allow for modifying the
asymptotic properties of the deformed three-dimensional Cartesian harmonic
oscillator wave functions. The resulting single-particle bases are very well
suited for solving the Hartree-Fock-Bogoliubov equations for deformed drip-line
nuclei. We then present results of self-consistent calculations performed for
the Mg isotopes and for light nuclei located near the two-neutron drip line.
The results suggest that for all even-even elements with =10--18 the most
weakly-bound nucleus has an oblate ground-state shape.Comment: 20 pages, 7 figure
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for
the efficient truncation of the Hilbert space of low-dimensional strongly
correlated quantum systems based on a rather general decimation prescription.
This algorithm has achieved unprecedented precision in the description of
one-dimensional quantum systems. It has therefore quickly acquired the status
of method of choice for numerical studies of one-dimensional quantum systems.
Its applications to the calculation of static, dynamic and thermodynamic
quantities in such systems are reviewed. The potential of DMRG applications in
the fields of two-dimensional quantum systems, quantum chemistry,
three-dimensional small grains, nuclear physics, equilibrium and
non-equilibrium statistical physics, and time-dependent phenomena is discussed.
This review also considers the theoretical foundations of the method, examining
its relationship to matrix-product states and the quantum information content
of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the
January 2005 issu
Continuum effects for the mean-field and pairing properties of weakly bound nuclei
Continuum effects in the weakly bound nuclei close to the drip-line are
investigated using the analytically soluble Poschl-Teller-Ginocchio potential.
Pairing correlations are studied within the Hartree-Fock-Bogoliubov method. We
show that both resonant and non-resonant continuum phase space is active in
creating the pairing field. The influence of positive-energy phase space is
quantified in terms of localizations of states within the nuclear volume.Comment: 27 RevTeX pages, 12 EPS figures included, submitted to Physical
Review