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Computational 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.Wed, 29 Jun 2016 07:16:56 GMThttp://hdl.handle.net/10261/1341892016-06-29T07:16:56ZComplex 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.Wed, 29 Jun 2016 07:07:09 GMThttp://hdl.handle.net/10261/1341872016-06-29T07:07:09ZComplex dynamics of delay-coupled lasers: fundamentals and applications
http://hdl.handle.net/10261/134184
Title: Complex dynamics of delay-coupled lasers: fundamentals and applications
Authors: Porte, Xavier
Abstract: he present thesis is devoted to the study of semiconductor lasers subject to delayed
optical feedback and coupling. The complex spectral and dynamical properties of these
systems have been investigated using state-of-the-art telecommunications detection technologies. With such tools, we have been able to experimentally characterize previously
unknown features in our delay-coupled systems. Along this work, both fundamental and
applied results are presented for the different experiments investigated.
The first part of the thesis is focusing on the system of the single delayed feedback
laser. The problem of feedback characterization is approached from a time scale perspective, relating the dynamical regimes to the characteristic frequencies of the delayed
feedback laser. We have empirically found that the ratios of these characteristic frequencies completely determine the dynamical behavior. This constitutes a model independent
approach that can be used, for example, to test the validity of numerical models that aim
at explaining the dynamical behavior of these lasers. Furthermore, the general extent of
our approach is validated by measuring various laser diodes with distinct characteristics.
Specific properties of the dynamics of the single laser with feedback system have also
been characterized by means of the intensity autocorrelation function. For this purpose,
the experimental autocorrelation is compared with the autocorrelation obtained from
a model of a stochastic linear oscillator with delay. The relation between the model
parameters and the experimental system parameters is analyzed and discussed together
with the limits of validity of this approach.
In the second part, systems with two delay-coupled lasers are studied. The phe-
nomenon of chaos synchronization is explored in two different configurations: a unidirectional coupling configuration where the delayed feedback laser signal is optically
coupled to a second laser, and a bidirectional scheme of two mutually coupled lasers
with self-feedback. In the first configuration, the relation between the consistency of
the dynamics and the synchronizability with the second laser is studied. In the latter
scheme, the robustness of the synchronized state is characterized against detuning in
parameters and noise.; The knowledge gained in the synchronization experiments is used to implement a classical public-channel secure-key exchange protocol in the bidirectional coupling scheme.This protocol is demonstrated experimentally, and its advantages and weaknesses are
analyzed.
Finally, we present a practical photonic implementation of a dynamical system experiencing two different delay times depending on the state of the system. The stationary
spectral characteristics of this experimental system are studied and the conditions for
the dynamics to occur in separated states are highlighted. We have also investigated
the real-time intensity and optical spectrum dynamics to demonstrate the existence and
properties of state-dependent delay dynamics. Qualitatively similar properties can be
found from a proper numerical model of this system.
Altogether, we have presented fundamental and applied aspects of semiconductor
lasers optically coupled with delay. The presented phenomenology is of immediate potential use for a variety of applications that range from photonics-based reservoir computing to chaos communications. In addition, the presented fundamental insights can
potentially be extended to other classes of dynamical systems.
Description: Tesi realitzada a l’Institut de Física Interdisciplinària i Sistemes Complexos (IFISC) i presentada a la Universitat de les Illes Balears (UIB).Wed, 29 Jun 2016 06:57:05 GMThttp://hdl.handle.net/10261/1341842016-06-29T06:57:05ZA complex network theory approach to oceanic and atmospheric transport phenomena
http://hdl.handle.net/10261/134183
Title: A complex network theory approach to oceanic and atmospheric transport phenomena
Authors: Ser-Giacomi, Enrico
Abstract: [EN] The last two decades have seen important advances in the Lagrangian description of
transport and mixing in fluid flows driven by concepts from dynamical systems theory,
and nowadays several approaches have been developed. Some of such techniques focus
on geometric objects - lines, surfaces - separating fluid regions with different properties
while others have focussed on computing stretching-like fields in the fluid domain,
such as different types of Lyapunov exponents or other Lagrangian descriptors. Finally,
there is a line of research focussing on the moving fluid regions themselves, the so-called
set-oriented methods.
On the other hand many real-world systems can be studied by using the Network
paradigm and in the last years Network Theory approaches have been successfully used
for geophysical systems in the context of climate networks in which the connections
among the different locations represent statistical relationships between climatic time
series from these locations, inferred from correlations and other statistical methods.
In this thesis we propose a new paradigm linking the network formalism with transport
and mixing phenomena in geophysical flows.
We analyze directly the network describing the material fluid flow among different
locations, which we call flow network. Among other characteristics this network is
directed, weighted, spatially embedded and time-dependent. We illustrate the general
ideas with an exemplary network derived from a realistic simulation of the surface
flow in the Mediterranean sea. We use network-theory tools to analyze them and gain
insights into transport processes from a general point of view. We quantitatively relate
dispersion and mixing characteristics, classically quantified by Lyapunov exponents,
to the degree of the network nodes. A family of network entropies is defined from
the network adjacency matrix, and related to the statistics of stretching in the fluid, in
particular to the Lyapunov exponent field. We use a network community detection
algorithm, Infomap, to partition the network into coherent regions, i.e. areas internally
well mixed, but with little fluid interchange between them.
We find interesting applications of this approach to marine biology of the Mediterranean
Sea. Oceanic dispersal and connectivity have been identified indeed as crucial factors for
structuring marine populations and designing Marine Protected Areas (MPAs). Larvae
of different pelagic durations and seasons could be modeled as passive tracers advected
in a simulated oceanic surface flow from which a flow network is constructed. By ap-
plying the Infomap algorithm we extract hydrodynamical provinces from the network
that result to be delimited by frontiers which match multi-scale oceanographic features.
By examining the repeated occurrence of such boundaries, we identify the spatial scales
and geographic structures that would control larval dispersal across the entire seascape.
Based on these hydrodynamical units, we study novel connectivity metrics for existing MPAs.; We also define node-by-node proxies measuring local larval retention and
exchange. From the analysis of such measures we confirm that retention processes
are favored along the coastlines while they are weak in the open ocean due to specific
oceanographic conditions. Although these proxies were often studied separately in the
literature, we demonstrated that they are inter-related under certain conditions and that
their integrated analysis leads to a better understanding of metapopulation dynamics,
informing both genetic and demographic connectivities.
We also consider paths in weighted and directed temporal networks, introducing tools
to compute sets of paths of high probability. We quantify the relative importance of the
most probable path between two nodes with respect to the whole set of paths, and to a
subset of highly probable paths which incorporate most of the connection probability.
These concepts are used to provide alternative definitions of betweenness centrality.
We apply these tools to the temporal flow network describing surface currents in the
Mediterranean sea. Despite the full transport dynamics is described by a very large
number of paths we find that, for realistic time scales, only a very small subset of high
probability paths (or even a single most probable one) is enough to characterize global
connectivity properties of the network.
Finally we apply the same analysis to the atmospheric blocking of eastern Europe and
western Russia in summer 2010. We compute the most probable paths followed by
fluid particles which reveal the Omega-block skeleton of the event. A hierarchy of sets
of highly probable paths is introduced to describe transport pathways when the most
probable path alone is not representative enough. These sets of paths have the shape of
narrow coherent tubes flowing close to the most probable one. Thus, as for the case of
Mediterranean Sea, even when the most probable path is not very significant in terms
of its probability, it still identifies the geometry of the transport pathways
Description: Doctoral thesis 2015. Doctoral Program of Physics (Universitat de les Illes Balears).Wed, 29 Jun 2016 06:45:05 GMThttp://hdl.handle.net/10261/1341832016-06-29T06:45:05Z