Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.

From "wet biology" to statistical analysis of structural features with bioinformatics tools

Many new Escherichia coli outer membrane proteins have recently been identified by proteomics techniques. However, poorly expressed proteins and proteins expressed only under certain conditions may escape detection when wild-type cells are grown under standard conditions. Here, we have taken a complementary approach where candidate outer membrane proteins have been identified by bioinformatics prediction, cloned and overexpressed, and finally localized by cell fractionation experiments. Out of eight predicted outer membrane proteins, we have confirmed the outer membrane localization for five—YftM, YaiO, YfaZ, CsgF, and YliI—and also provide preliminary data indicating that a sixth—YfaL—may be an outer membrane autotransporter.

Statistical methods for biomedical signal analysis and processing

Statistical modelling and statistical learning theory are two powerful analytical frameworks for analyzing signals and developing efficient processing and classification algorithms. In this thesis, these frameworks are applied for modelling and processing biomedical signals in two different contexts: ultrasound medical imaging systems and primate neural activity analysis and modelling. In the context of ultrasound medical imaging, two main applications are explored: deconvolution of signals measured from a ultrasonic transducer and automatic image segmentation and classification of prostate ultrasound scans. In the former application a stochastic model of the radio frequency signal measured from a ultrasonic transducer is derived. This model is then employed for developing in a statistical framework a regularized deconvolution procedure, for enhancing signal resolution. In the latter application, different statistical models are used to characterize images of prostate tissues, extracting different features. These features are then uses to segment the images in region of interests by means of an automatic procedure based on a statistical model of the extracted features. Finally, machine learning techniques are used for automatic classification of the different region of interests. In the context of neural activity signals, an example of bio-inspired dynamical network was developed to help in studies of motor-related processes in the brain of primate monkeys. The presented model aims to mimic the abstract functionality of a cell population in 7a parietal region of primate monkeys, during the execution of learned behavioural tasks.

Microfluidic device and interfacial transport: application to biomolecules and nanostructures

The aim of my dissertation is to provide new knowledge and applications of microfluidics in a variety of problems, from materials science, devices, and biomedicine, where the control on the fluid dynamics and the local concentration of the solutions containing the relevant molecules (either materials, precursors, or biomolecules) is crucial. The control of interfacial phenomena occurring in solutions at dierent length scales is compelling in nanotechnology for devising new sensors, molecular electronics devices, memories. Microfluidic devices were fabricated and integrated with organic electronics devices. The transduction involves the species in the solution which infills the transistor channel and confined by the microfluidic device. This device measures what happens on the surface, at few nanometers from the semiconductor channel. Soft-lithography was adopted to fabricate platinum electrodes, starting from platinum carbonyl precursor. I proposed a simple method to assemble these nanostructures in periodic arrays of microstripes, and form conductive electrodes with characteristic dimension of 600 nm. The conductivity of these sub-microwires is compared with the values reported in literature and bulk platinum. The process is suitable for fabricating thin conductive patterns for electronic devices or electrochemical cells, where the periodicity of the conductive pattern is comparable with the diusion length of the molecules in solution. The ordering induced among artificial nanostructures is of particular interest in science. I show that large building blocks, like carbon nanotubes or core-shell nanoparticles, can be ordered and self-organised on a surface in patterns due to capillary forces. The eective probability of inducing order with microfluidic flow is modeled with finite element calculation on the real geometry of the microcapillaries, in soft-lithographic process. The oligomerization of A40 peptide in microconfined environment represents a new investigation of the extensively studied peptide aggregation. The added value of the approach I devised is the precise control on the local concentration of peptides together with the possibility to mimick cellular crowding. Four populations of oligomers where distinguished, with diameters ranging from 15 to 200 nm. These aggregates could not be addresses separately in fluorescence. The statistical analysis on the atomic force microscopy images together with a model of growth reveal new insights on the kinetics of amyloidogenesis as well as allows me to identify the minimum stable nucleus size. This is an important result owing to its implications in the understanding and early diagnosis and therapy of the Alzheimer’s disease

Development of a new galaxy classification technique and its application to the zCOSMOS survey

The purpose of this Thesis is to develop a robust and powerful method to classify galaxies from large surveys, in order to establish and confirm the connections between the principal observational parameters of the galaxies (spectral features, colours, morphological indices), and help unveil the evolution of these parameters from $z \sim 1$ to the local Universe. Within the framework of zCOSMOS-bright survey, and making use of its large database of objects ($\sim 10\,000$ galaxies in the redshift range $0 < z \lesssim 1.2$) and its great reliability in redshift and spectral properties determinations, first we adopt and extend the \emph{classification cube method}, as developed by Mignoli et al. (2009), to exploit the bimodal properties of galaxies (spectral, photometric and morphologic) separately, and then combining together these three subclassifications. We use this classification method as a test for a newly devised statistical classification, based on Principal Component Analysis and Unsupervised Fuzzy Partition clustering method (PCA+UFP), which is able to define the galaxy population exploiting their natural global bimodality, considering simultaneously up to 8 different properties. The PCA+UFP analysis is a very powerful and robust tool to probe the nature and the evolution of galaxies in a survey. It allows to define with less uncertainties the classification of galaxies, adding the flexibility to be adapted to different parameters: being a fuzzy classification it avoids the problems due to a hard classification, such as the classification cube presented in the first part of the article. The PCA+UFP method can be easily applied to different datasets: it does not rely on the nature of the data and for this reason it can be successfully employed with others observables (magnitudes, colours) or derived properties (masses, luminosities, SFRs, etc.). The agreement between the two classification cluster definitions is very high. ``Early'' and ``late'' type galaxies are well defined by the spectral, photometric and morphological properties, both considering them in a separate way and then combining the classifications (classification cube) and treating them as a whole (PCA+UFP cluster analysis). Differences arise in the definition of outliers: the classification cube is much more sensitive to single measurement errors or misclassifications in one property than the PCA+UFP cluster analysis, in which errors are ``averaged out'' during the process. This method allowed us to behold the \emph{downsizing} effect taking place in the PC spaces: the migration between the blue cloud towards the red clump happens at higher redshifts for galaxies of larger mass. The determination of $M_{\mathrm{cross}}$ the transition mass is in significant agreement with others values in literature.

Statistical methods for analysis and processing of medical ultrasound: applications to segmentation and restoration

In this thesis two major topics inherent with medical ultrasound images are addressed: deconvolution and segmentation. In the first case a deconvolution algorithm is described allowing statistically consistent maximum a posteriori estimates of the tissue reflectivity to be restored. These estimates are proven to provide a reliable source of information for achieving an accurate characterization of biological tissues through the ultrasound echo. The second topic involves the definition of a semi automatic algorithm for myocardium segmentation in 2D echocardiographic images. The results show that the proposed method can reduce inter- and intra observer variability in myocardial contours delineation and is feasible and accurate even on clinical data.

Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Statistical Physics and Modeling of Human Mobility

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Application of innovative methods of source apportionment in air contamination assessment

In this work, new tools in atmospheric pollutant sampling and analysis were applied in order to go deeper in source apportionment study. The project was developed mainly by the study of atmospheric emission sources in a suburban area influenced by a municipal solid waste incinerator (MSWI), a medium-sized coastal tourist town and a motorway. Two main research lines were followed. For what concerns the first line, the potentiality of the use of PM samplers coupled with a wind select sensor was assessed. Results showed that they may be a valid support in source apportionment studies. However, meteorological and territorial conditions could strongly affect the results. Moreover, new markers were investigated, particularly focusing on the processes of biomass burning. OC revealed a good biomass combustion process indicator, as well as all determined organic compounds. Among metals, lead and aluminium are well related to the biomass combustion. Surprisingly PM was not enriched of potassium during bonfire event. The second research line consists on the application of Positive Matrix factorization (PMF), a new statistical tool in data analysis. This new technique was applied to datasets which refer to different time resolution data. PMF application to atmospheric deposition fluxes identified six main sources affecting the area. The incinerator’s relative contribution seemed to be negligible. PMF analysis was then applied to PM2.5 collected with samplers coupled with a wind select sensor. The higher number of determined environmental indicators allowed to obtain more detailed results on the sources affecting the area. Vehicular traffic revealed the source of greatest concern for the study area. Also in this case, incinerator’s relative contribution seemed to be negligible. Finally, the application of PMF analysis to hourly aerosol data demonstrated that the higher the temporal resolution of the data was, the more the source profiles were close to the real one.

A new method for the estimation of the reverberation time from measured room impulse responses with application to Italian opera houses

The Schroeder's backward integration method is the most used method to extract the decay curve of an acoustic impulse response and to calculate the reverberation time from this curve. In the literature the limits and the possible improvements of this method are widely discussed. In this work a new method is proposed for the evaluation of the energy decay curve. The new method has been implemented in a Matlab toolbox. Its performance has been tested versus the most accredited literature method. The values of EDT and reverberation time extracted from the energy decay curves calculated with both methods have been compared in terms of the values themselves and in terms of their statistical representativeness. The main case study consists of nine Italian historical theatres in which acoustical measurements were performed. The comparison of the two extraction methods has also been applied to a critical case, i.e. the structural impulse responses of some building elements. The comparison underlines that both methods return a comparable value of the T30. Decreasing the range of evaluation, they reveal increasing differences; in particular, the main differences are in the first part of the decay, where the EDT is evaluated. This is a consequence of the fact that the new method returns a “locally" defined energy decay curve, whereas the Schroeder's method accumulates energy from the tail to the beginning of the impulse response. Another characteristic of the new method for the energy decay extraction curve is its independence on the background noise estimation. Finally, a statistical analysis is performed on the T30 and EDT values calculated from the impulse responses measurements in the Italian historical theatres. The aim of this evaluation is to know whether a subset of measurements could be considered representative for a complete characterization of these opera houses.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks