15,452 research outputs found
Quantum entanglement with acousto-optic modulators: 2-photon beatings and Bell experiments with moving beamsplitters
We present an experiment testing quantum correlations with frequency shifted
photons. We test Bell inequality with 2-photon interferometry where we replace
the beamsplitters by acousto-optic modulators, which are equivalent to moving
beamsplitters. We measure the 2-photon beatings induced by the frequency
shifts, and we propose a cryptographic scheme in relation. Finally, setting the
experiment in a relativistic configuration, we demonstrate that the quantum
correlations are not only independent of the distance but also of the time
ordering between the two single-photon measurements.Comment: 14 pages, 16 figure
Time series irreversibility: a visibility graph approach
We propose a method to measure real-valued time series irreversibility which
combines two differ- ent tools: the horizontal visibility algorithm and the
Kullback-Leibler divergence. This method maps a time series to a directed
network according to a geometric criterion. The degree of irreversibility of
the series is then estimated by the Kullback-Leibler divergence (i.e. the
distinguishability) between the in and out degree distributions of the
associated graph. The method is computationally effi- cient, does not require
any ad hoc symbolization process, and naturally takes into account multiple
scales. We find that the method correctly distinguishes between reversible and
irreversible station- ary time series, including analytical and numerical
studies of its performance for: (i) reversible stochastic processes
(uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic
pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii)
reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv)
dissipative chaotic maps in the presence of noise. Two alternative graph
functionals, the degree and the degree-degree distributions, can be used as the
Kullback-Leibler divergence argument. The former is simpler and more intuitive
and can be used as a benchmark, but in the case of an irreversible process with
null net current, the degree-degree distribution has to be considered to
identifiy the irreversible nature of the series.Comment: submitted for publicatio
Horizontal Visibility graphs generated by type-I intermittency
The type-I intermittency route to (or out of) chaos is investigated within
the Horizontal Visibility graph theory. For that purpose, we address the
trajectories generated by unimodal maps close to an inverse tangent bifurcation
and construct, according to the Horizontal Visibility algorithm, their
associated graphs. We show how the alternation of laminar episodes and chaotic
bursts has a fingerprint in the resulting graph structure. Accordingly, we
derive a phenomenological theory that predicts quantitative values of several
network parameters. In particular, we predict that the characteristic power law
scaling of the mean length of laminar trend sizes is fully inherited in the
variance of the graph degree distribution, in good agreement with the numerics.
We also report numerical evidence on how the characteristic power-law scaling
of the Lyapunov exponent as a function of the distance to the tangent
bifurcation is inherited in the graph by an analogous scaling of the block
entropy over the degree distribution. Furthermore, we are able to recast the
full set of HV graphs generated by intermittent dynamics into a renormalization
group framework, where the fixed points of its graph-theoretical RG flow
account for the different types of dynamics. We also establish that the
nontrivial fixed point of this flow coincides with the tangency condition and
that the corresponding invariant graph exhibit extremal entropic properties.Comment: 8 figure
Risks of Friendships on Social Networks
In this paper, we explore the risks of friends in social networks caused by
their friendship patterns, by using real life social network data and starting
from a previously defined risk model. Particularly, we observe that risks of
friendships can be mined by analyzing users' attitude towards friends of
friends. This allows us to give new insights into friendship and risk dynamics
on social networks.Comment: 10 pages, 8 figures, 3 tables. To Appear in the 2012 IEEE
International Conference on Data Mining (ICDM
Feigenbaum graphs: a complex network perspective of chaos
The recently formulated theory of horizontal visibility graphs transforms
time series into graphs and allows the possibility of studying dynamical
systems through the characterization of their associated networks. This method
leads to a natural graph-theoretical description of nonlinear systems with
qualities in the spirit of symbolic dynamics. We support our claim via the case
study of the period-doubling and band-splitting attractor cascades that
characterize unimodal maps. We provide a universal analytical description of
this classic scenario in terms of the horizontal visibility graphs associated
with the dynamics within the attractors, that we call Feigenbaum graphs,
independent of map nonlinearity or other particulars. We derive exact results
for their degree distribution and related quantities, recast them in the
context of the renormalization group and find that its fixed points coincide
with those of network entropy optimization. Furthermore, we show that the
network entropy mimics the Lyapunov exponent of the map independently of its
sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Experimental Entanglement of Temporal Orders
The study of causal relations has recently been applied to the quantum realm,
leading to the discovery that not all quantum processes have a definite causal
structure. While such processes have previously been experimentally
demonstrated, these demonstrations relied on the assumption that quantum theory
can be applied to causal structures and laboratory operations. Here, we present
the first demonstration of entangled temporal orders beyond the quantum
formalism. We do so by proving the incompatibility of our experimental outcomes
with a class of generalized probabilistic theories which satisfy the
assumptions of locality and definite temporal orders. To this end, we derive
physical constraints (in the form of a Bell-like inequality) on experimental
outcomes within such a class of theories. We then experimentally invalidate
these theories by violating the inequality, thus providing an experimental
proof, outside the quantum formalism, that nature is incompatible with the
assumption that the temporal order between events is definite locally.Comment: 20 pages, 8 figures. Thoroughly revised manuscript. Updated
theory-independent proofs including new experimental dat
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