2,074 research outputs found

### Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The
evolution of these hierarchical networks reduces to the Eden model and the
Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively.
We show that the distribution of the bond strengths (energies) is described by
the Fermi statistics. We discuss the relation of the present results with the
scale-free networks described by Bose statistics

### Percolation transition and distribution of connected components in generalized random network ensembles

In this work, we study the percolation transition and large deviation
properties of generalized canonical network ensembles. This new type of random
networks might have a very rich complex structure, including high heterogeneous
degree sequences, non-trivial community structure or specific spatial
dependence of the link probability for networks embedded in a metric space. We
find the cluster distribution of the networks in these ensembles by mapping the
problem to a fully connected Potts model with heterogeneous couplings. We show
that the nature of the Potts model phase transition, linked to the birth of a
giant component, has a crossover from second to first order when the number of
critical colors $q_c = 2$ in all the networks under study. These results shed
light on the properties of dynamical processes defined on these network
ensembles.Comment: 27 pages, 15 figure

### Multiband superconductors close to a 3D-2D electronic topological transition

Within the two-band model of superconductivity, we study the dependence of
the critical temperature Tc and of the isotope exponent alpha in the proximity
to an electronic topological transition (ETT). The ETT is associated with a
3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband
of the diborides. Our results agree with the observed dependence of Tc on Mg
content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be
interpreted as due to the proximity to a "shape resonance". Moreover we have
calculated a possible variation of the isotope effect on the superconducting
critical temperature by tuning the chemical potential.Comment: J. Supercond., to appea

### Quantum statistics in complex networks

In this work we discuss the symmetric construction of bosonic and fermionic
networks and we present a case of a network showing a mixed quantum statistics.
This model takes into account the different nature of nodes, described by a
random parameter that we call energy, and includes rewiring of the links. The
system described by the mixed statistics is an inhomogemeous system formed by
two class of nodes. In fact there is a threshold energy $\epsilon_s$ such that
nodes with lower energy $(\epsilon<\epsilon_s)$ increase their connectivity
while nodes with higher energy $(\epsilon>\epsilon_s)$ decrease their
connectivity in time.Comment: 5 pages, 2 figure

### Weighted Multiplex Networks

One of the most important challenges in network science is to quantify the
information encoded in complex network structures. Disentangling randomness
from organizational principles is even more demanding when networks have a
multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that
can be linked in multiple interacting and co-evolving layers. In these
networks, relevant information might not be captured if the single layers were
analyzed separately. Here we demonstrate that such partial analysis of layers
fails to capture significant correlations between weights and topology of
complex multiplex networks. To this end, we study two weighted multiplex
co-authorship and citation networks involving the authors included in the
American Physical Society. We show that in these networks weights are strongly
correlated with multiplex structure, and provide empirical evidence in favor of
the advantage of studying weighted measures of multiplex networks, such as
multistrength and the inverse multiparticipation ratio. Finally, we introduce a
theoretical framework based on the entropy of multiplex ensembles to quantify
the information stored in multiplex networks that would remain undetected if
the single layers were analyzed in isolation.Comment: (22 pages, 10 figures

### Rare events and discontinuous percolation transitions

Percolation theory characterizing the robustness of a network has
applications ranging from biology, to epidemic spreading, and complex
infrastructures. Percolation theory, however, only concern the typical response
of a infinite network to random damage of its nodes while in real finite
networks, fluctuations are observable. Consequently for finite networks there
is an urgent need to evaluate the risk of collapse in response to rare
configurations of the initial damage. Here we build a large deviation theory of
percolation characterizing the response of a sparse network to rare events.
This general theory includes the second order phase transition observed
typically for random configurations of the initial damage but reveals also
discontinuous transitions corresponding to rare configurations of the initial
damage for which the size of the giant component is suppressed.Comment: (11 pages, 4 figures

### Effects of azimuth-symmetric acceptance cutoffs on the measured asymmetry in unpolarized Drell-Yan fixed target experiments

Fixed-target unpolarized Drell-Yan experiments often feature an acceptance
depending on the polar angle of the lepton tracks in the laboratory frame.
Typically leptons are detected in a defined angular range, with a dead zone in
the forward region. If the cutoffs imposed by the angular acceptance are
independent of the azimuth, at first sight they do not appear dangerous for a
measurement of the cos(2\phi)-asymmetry, relevant because of its association
with the violation of the Lam-Tung rule and with the Boer-Mulders function. On
the contrary, direct simulations show that up to 10 percent asymmetries are
produced by these cutoffs. These artificial asymmetries present qualitative
features that allow them to mimic the physical ones. They introduce some
model-dependence in the measurements of the cos(2\phi)-asymmetry, since a
precise reconstruction of the acceptance in the Collins-Soper frame requires a
Monte Carlo simulation, that in turn requires some detailed physical input to
generate event distributions. Although experiments in the eighties seem to have
been aware of this problem, the possibility of using the Boer-Mulders function
as an input parameter in the extraction of Transversity has much increased the
requirements of precision on this measurement. Our simulations show that the
safest approach to these measurements is a strong cutoff on the Collins-Soper
polar angle. This reduces statistics, but does not necessarily decrease the
precision in a measurement of the Boer-Mulders function.Comment: 13 pages, 14 figure

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