DSpace Community:
http://hdl.handle.net/10261/2855
2016-07-23T11:24:33ZPercolation-based precursors of transitions in extended systems
http://hdl.handle.net/10261/134805
Title: Percolation-based precursors of transitions in extended systems
Authors: Víctor Rodríguez-Méndez, Víctor M. Eguíluz, Emilio Hernández-García, José J. Ramasco
Abstract: Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining warnings of an approaching transition well in advance remains an elusive task. Here we show that a functional network, constructed from spatial correlations of the system’s time series, experiences a percolation transition way before the actual system reaches a bifurcation point due to the collective phenomena leading to the global change. Concepts from percolation theory are then used to introduce early warning precursors that anticipate the system’s tipping point. We illustrate the generality and versatility of our percolation-based framework with model systems experiencing different types of bifurcations and with Sea Surface Temperature time series associated to El Niño phenomenon.2016-07-14T13:14:59ZPercolation-based precursors of transitions in extended systems
http://hdl.handle.net/10261/134659
Title: Percolation-based precursors of transitions in extended systems
Authors: Rodríguez-Méndez, Víctor; Eguíluz, Víctor M.; Hernández-García, Emilio; Ramasco, José J.
Abstract: Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining warnings of an approaching transition well in advance remains an elusive task. Here we show that a functional network, constructed from spatial correlations of the system’s time series, experiences a percolation transition way before the actual system reaches a bifurcation point due to the collective phenomena leading to the global change. Concepts from percolation theory are then used to introduce early warning precursors that anticipate the system’s tipping point. We illustrate the generality and versatility
of our percolation-based framework with model systems experiencing different types of bifurcations and with Sea Surface Temperature time series associated to El Niño phenomenon.2016-07-11T10:05:06ZComputational Properties of Delay-Coupled Systems
http://hdl.handle.net/10261/134189
Title: Computational Properties of Delay-Coupled Systems
Authors: Escalona-Morán, M.
Abstract: In this research work we study the computational properties of delay-coupled
systems. In particular, we use a machine learning technique known as
reservoir
computing. In machine learning, a computer
learns
to solve different tasks using
examples and without knowing explicitly their solution.
For the study of the computational properties, a numerical toolbox, written
in Python, was developed. This toolbox allows a fast implementation of the
different scenarios described in this thesis.
Using a reservoir computer, we studied several computational properties, focusing on its kernel quality, its ability to separate different input samples and
the intrinsic memory capacity. This intrinsic memory is related to the delayed-
feedback of the reservoir.
We used a delay-coupled system as reservoir to study its computational ability
in three different kinds of tasks: system’s modeling, time-series prediction and
classification tasks.
The system’s modeling task was performed using the Nonlinear Autoregressive
Moving Average (of ten steps), NARMA10. The NARMA10 model creates autoregressive time series from a set of normally distributed random sequences.
The reservoir computer learns how to emulate the system using only the sequence of random numbers and the autoregressive time series, but without
knowing the equations of the NARMA10. The results of our approach are
equivalent to those published by other authors and show the computational
power of our method.
For the time-series prediction tasks, we used three kinds of time series: a model
that gives the variations in temperature of the sea surface that provoke El Niño
phenomenon, the Lorenz system and the dynamics of a chaotic laser. Different
scenarios were explored depending on the nature of the time series. For the
prediction of the variation in temperature of the sea surface, we perform estimations of one, three and six months in advance. The error was measured as the Normalized Root Mean Square Error (NRMSE). For the different prediction
horizons, we obtained errors of 2%, 8% and 24%, respectively.
The classification tasks were carried out for a Spoken Digit Recognition (SDR)
task and a real-world biomedical task. The SDR
was used to illustrate different scenarios of a machine learning problem. The biomedical task consists
on the automatic classification of heartbeats with cardiac arrhythmias. We use
the MIT-BIH Arrhythmia database, a widely used database in cardiology. For
comparison purposes, we followed the guidelines of the Association for the Advancement of Medical Instrumentation for the evaluation of arrhythmia-detector
algorithms. We used a biostatistical learning process named logistic regression
that allowed to compute the probability that a heartbeat belongs to a particular
class.; This is in contrast to the commonly used linear regression. The results
obtained in this work show the versatility and efficiency of our implemented
reservoir computer. Our results are equivalent and show improvement over
other reported results on this problem under similar conditions and using the
same database.
To enhance the computational ability of our delay-coupled system, we included
a multivariate scheme that allows the consideration of different variables of a
system. We evaluated the influence of this multivariate scenario using a time-
series prediction and the classification of heartbeat tasks. The results show
improvement in the performance of the reservoir computer in comparison with
the same tasks in the univariate case.
Description: Tesis Doctoral presentada por Miguel Angel Escalona Morán para optar al título
de Doctor, en el Programa de Física del Departamento de Física de la Universitat
de les Illes Balears, realizada en el IFISC bajo la dirección de Claudio Mirasso,
catedrático de universidad y Miguel Cornelles Soriano, contratado postdoctoral
CAIB.2016-06-29T07:16:56ZComplex dynamics of photonic delay systems: a story of consistency and unpredictability
http://hdl.handle.net/10261/134187
Title: Complex dynamics of photonic delay systems: a story of consistency and unpredictability
Authors: Oliver, Neus
Abstract: The field of photonics is revolutionizing the current industry and society, analogously to
what electronics did during the 20th century. The uses of photonics seem endless and are not
restricted to advanced science. Some of its applications have already become mature tech-
nologies, and belong now to our everyday life: internet relies on optical fiber communications,
lasers are an integrated tool in medical surgery and industrial manufacturing, and the use of
light has facilitated the measurement techniques in metrology, among many others.
The rich phenomenology in photonics makes it an emerging field with open perspectives,
whose full capabilities are still to be exploited. Specifically, two of the promising areas for
photonics are information processing and secure optical communications. Complex phenom-
ena in photonics can serve as a backbone for both applications. This Thesis comprises the
study of the emerging complex behavior in concrete photonic systems: semiconductor laser
systems with delay. These simple systems can generate an interesting variety of dynamical
regimes, like deterministic chaos and, therefore, we use them to contribute to the above men-
tioned areas. More precisely, we address the consistency properties for bio-inspired photonic
information processing and the optical generation of random numbers, thereby telling a story
of consistency and unpredictability.; On consistency or how to perform reliably photonic information processing.
Our brain is a fast and efficient organ, capable of performing reliably tasks that for any com-
puter would be rather hard, such as face recognition. Inspired by our brain, technical systems
have been introduced to mimic information processing in neural networks. Understanding
how these systems process information can lead to faster, low-energy demanding computing.
A recent technique for photonic information processing is Reservoir Computing. In Reser-
voir Computing, a nonlinear system performs computationally hard tasks, like spoken digit
recognition. Its operation is based on providing a consistent nonlinear response with respect
to an input signal, exactly as neurons do: they respond reliably to electrical and chemical
signals when processing information.
Consistency, as the ability of the system to respond in a similar way to similar inputs,
is therefore a key-ingredient to be studied. Surprisingly, consistency in nature is not always
a given, and a system might change from a consistent response to an inconsistent one. The
mechanisms underlying consistency as well as its quantification are thus pertinent proper
questions. Semiconductor lasers with feedback represent an excellent platform for its inves-
tigation. We approach these aspects by designing three experiments to
investigate and characterize the consistency properties of semiconductor laser with del
ayed optical feedback and an optoelectronic system. The high quality of the experiments allo
w us to illustrate the occurrence of transitions between consistent and inconsistent respon
ses in the laser, and characterize their dependence on the drive signal. Thus, we utilize vario
us drive signals, both optical and electrical, and present different ways to quantify consis
tency, including correlations and a direct measure for the sub-Lyapunov exponent. Beyond phot
onics, consistency in driven systems is a fundamental and far-reaching concept, present
in nature and technology. Therefore, the fundamental properties and the developed method r
epresent valuable findings for further fundamental investigations and applications.; On unpredictability or how to implement an optical random number generator.
Random numbers (or random bits) are crucial for information
security, online-gaming, complex numerical simulations and cryptography. Their ubiqui
ty has led to the emergence of random number generators (RNGs) based on photonic componen
ts, given the intrinsic advantages of photonics: first, an optical RNG is easy to integr
ate into telecommunication systems; and second, a photonic approach to random number generation allows for high generation speeds of order of gigabits per second (Gbit/s),
a key demand of current random number generators. Although some optical approaches to
random bit generation had been successfully put forward, open questions still remain
ed: Is it possible to employ simpler schemes to generate random numbers? Are we using the RNG opti
mally or can its performance be enhanced? What is the maximum bit rate attainable wi
th a given RNG? Can we know it in advance? In this Thesis, we contribute significant
ly to answer these questions. We propose a strikingly simple experimental setup based on a si
ngle semiconductor laser with optical feedback, benefiting from the unpredictability and
randomness of the chaotic output of the laser. Nevertheless, chaotic dynamics is only a neces
sary but not a sufficient condition to obtain random numbers. We present guidelines on the i
nterplay between dynamics, acquisition procedures and post-processing, and predict t
he potential of any RNG by using Information Theory to estimate the maximum achievable bit r
ate. The relevance of this work relies not only on the high speed of the bit rate, up to 160Gbit/s,
but also on the understanding of the factors involved in the random bit generation process
to guarantee the optimal operation of any laser-based generator.
Description: Tesis presentada en el Departamento de Física de la Universitat de les Illes Balears.2016-06-29T07:07:09Z