The assessment of change in rural landscape and the analysis of the driving forces. Proposal of a spatial model for the rural built environment

The presented study carried out an analysis on rural landscape changes. In particular the study focuses on the understanding of driving forces acting on the rural built environment using a statistical spatial model implemented through GIS techniques. It is well known that the study of landscape changes is essential for a conscious decision making in land planning. From a bibliography review results a general lack of studies dealing with the modeling of rural built environment and hence a theoretical modelling approach for such purpose is needed. The advancement in technology and modernity in building construction and agriculture have gradually changed the rural built environment. In addition, the phenomenon of urbanization of a determined the construction of new volumes that occurred beside abandoned or derelict rural buildings. Consequently there are two types of transformation dynamics affecting mainly the rural built environment that can be observed: the conversion of rural buildings and the increasing of building numbers. It is the specific aim of the presented study to propose a methodology for the development of a spatial model that allows the identification of driving forces that acted on the behaviours of the building allocation. In fact one of the most concerning dynamic nowadays is related to an irrational expansion of buildings sprawl across landscape. The proposed methodology is composed by some conceptual steps that cover different aspects related to the development of a spatial model: the selection of a response variable that better describe the phenomenon under study, the identification of possible driving forces, the sampling methodology concerning the collection of data, the most suitable algorithm to be adopted in relation to statistical theory and method used, the calibration process and evaluation of the model. A different combination of factors in various parts of the territory generated favourable or less favourable conditions for the building allocation and the existence of buildings represents the evidence of such optimum. Conversely the absence of buildings expresses a combination of agents which is not suitable for building allocation. Presence or absence of buildings can be adopted as indicators of such driving conditions, since they represent the expression of the action of driving forces in the land suitability sorting process. The existence of correlation between site selection and hypothetical driving forces, evaluated by means of modeling techniques, provides an evidence of which driving forces are involved in the allocation dynamic and an insight on their level of influence into the process. GIS software by means of spatial analysis tools allows to associate the concept of presence and absence with point futures generating a point process. Presence or absence of buildings at some site locations represent the expression of these driving factors interaction. In case of presences, points represent locations of real existing buildings, conversely absences represent locations were buildings are not existent and so they are generated by a stochastic mechanism. Possible driving forces are selected and the existence of a causal relationship with building allocations is assessed through a spatial model. The adoption of empirical statistical models provides a mechanism for the explanatory variable analysis and for the identification of key driving variables behind the site selection process for new building allocation. The model developed by following the methodology is applied to a case study to test the validity of the methodology. In particular the study area for the testing of the methodology is represented by the New District of Imola characterized by a prevailing agricultural production vocation and were transformation dynamic intensively occurred. The development of the model involved the identification of predictive variables (related to geomorphologic, socio-economic, structural and infrastructural systems of landscape) capable of representing the driving forces responsible for landscape changes.. The calibration of the model is carried out referring to spatial data regarding the periurban and rural area of the study area within the 1975-2005 time period by means of Generalised linear model. The resulting output from the model fit is continuous grid surface where cells assume values ranged from 0 to 1 of probability of building occurrences along the rural and periurban area of the study area. Hence the response variable assesses the changes in the rural built environment occurred in such time interval and is correlated to the selected explanatory variables by means of a generalized linear model using logistic regression. Comparing the probability map obtained from the model to the actual rural building distribution in 2005, the interpretation capability of the model can be evaluated. The proposed model can be also applied to the interpretation of trends which occurred in other study areas, and also referring to different time intervals, depending on the availability of data. The use of suitable data in terms of time, information, and spatial resolution and the costs related to data acquisition, pre-processing, and survey are among the most critical aspects of model implementation. Future in-depth studies can focus on using the proposed model to predict short/medium-range future scenarios for the rural built environment distribution in the study area. In order to predict future scenarios it is necessary to assume that the driving forces do not change and that their levels of influence within the model are not far from those assessed for the time interval used for the calibration.

Il ruolo delle idee e del loro cambiamento nei processi di policy making universitario nel mondo anglosassone dagli anni ottanta ad oggi. I casi di Inghilterra e Nuova Zelanda in prospettiva comparata

THE TITLE OF MY THESIS IS THE ROLE OF THE IDEAS AND THEIR CHANGE IN HIGHER EDUCATION POLICY-MAKING PROCESSES FROM THE EIGHTIES TO PRESENT-DAY: THE CASES OF ENGLAND AND NEW ZEALAND IN COMPARATIVE PERSPECTIVE UNDER A THEORETICAL POINT OF VIEW, THE AIM OF MY WORK IS TO CARRY OUT A RESEARCH MODELLED ON THE CONSTRUCTIVIST THEORY. IT FOCUSES ON THE ANALYSIS OF THE IMPACT OF IDEAS ON THE PROCESSES OF POLICY MAKING BY MEANS OF EPISTEMIC COMMUNITIES, THINK TANKS AND VARIOUS SOCIOECONOMIC CONTEXTS THAT MAY HAVE PLAYED A KEY ROLE IN THE CONSTRUCTION OF THE DIFFERENT PATHS. FROM MY POINT OF VIEW IDEAS CONSTITUTE A PRIORITY RESEARCH FIELD WHICH IS WORTH ANALYSING SINCE THEIR ROLE IN POLICY MAKING PROCESSES HAS BEEN TRADITIONALLY RATHER UNEXPLORED. IN THIS CONTEXT AND WITH THE AIM OF DEVELOPING A RESEARCH STRAND BASED ON THE ROLE OF IDEAS, I INTEND TO CARRY ON MY STUDY UNDER THE PERSPECTIVE OF CHANGE. DEPENDING ON THE DATA AND INFORMATION THAT I COLLECTED I EVALUATED THE WEIGHT OF EACH OF THESE VARIABLES AND MAYBE OTHERS SUCH AS THE INSTITUTIONS AND THE INDIVIDUAL INTERESTS, WHICH MAY HAVE INFLUENCED THE FORMATION OF THE POLICY MAKING PROCESSES. UNDER THIS LIGHT, I PLANNED TO ADOPT THE QUALITATIVE METHODOLOGY OF RESEARCH WHICH I BELIEVE TO BE VERY EFFECTIVE AGAINST THE MORE DIFFICULT AND POSSIBLY REDUCTIVE APPLICATION OF QUANTITIVE DATA SETS. I RECKON THEREFORE THAT THE MOST APPROPRIATE TOOLS FOR INFORMATION PROCESSING INCLUDE CONTENT ANALYSIS, AND IN-DEPTH INTERVIEWS TO PERSONALITIES OF THE POLITICAL PANORAMA (ÉLITE OR NOT) WHO HAVE PARTICIPATED IN THE PROCESS OF HIGHER EDUCATION REFORM FROM THE EIGHTIES TO PRESENT-DAY. THE TWO CASES TAKEN INTO CONSIDERATION SURELY SET AN EXAMPLE OF RADICAL REFORM PROCESSES WHICH HAVE OCCURRED IN QUITE DIFFERENT CONTEXTS DETERMINED BY THE SOCIOECONOMIC CHARACTERISTICS AND THE TRAITS OF THE ÉLITE. IN NEW ZEALAND THE DESCRIBED PROCESS HAS TAKEN PLACE WITH A STEADY PACE AND A GOOD GRADE OF CONSEQUANTIALITY, IN LINE WTH THE REFORMS IN OTHER STATE DIVISIONS DRIVEN BY THE IDEAS OF THE NEW PUBLIC MANAGEMENT. CONTRARILY IN ENGLAND THE REFORMATIVE ACTION OF MARGARET THATCHER HAS ACQUIRED A VERY RADICAL CONNOTATION AS IT HAS BROUGHT INTO THE AMBIT OF HIGHER EDUCATION POLICY CONCEPTS LIKE EFFICIENCY, EXCELLENCE, RATIONALIZATION THAT WOULD CONTRAST WITH THE GENERALISTIC AND MASS-ORIENTED IDEAS THAT WERE FASHIONABLE DURING THE SEVENTIES. THE MISSION I INTEND TO ACCOMPLISH THORUGHOUT MY RESEARCH IS TO INVESTIGATE AND ANALYSE INTO MORE DEPTH THE DIFFERENCES THAT SEEM TO EMERGE FROM TWO CONTEXTS WHICH MOST OF THE LITERATURE REGARDS AS A SINGLE MODEL: THE ANGLO-SAXON MODEL. UNDER THIS LIGHT, THE DENSE ANALYSIS OF POLICY PROCESSES ALLOWED TO BRING OUT BOTH THE CONTROVERSIAL AND CONTRASTING ASPECTS OF THE TWO REALITIES COMPARED, AND THE ROLE AND WEIGHT OF VARIABLES SUCH AS IDEAS (MAIN VARIABLE), INSTITUTIONAL SETTINGS AND INDIVIDUAL INTERESTS ACTING IN EACH CONTEXT. THE CASES I MEAN TO ATTEND PRESENT PECULIAR ASPECTS WORTH DEVELOPING AN IN-DEPTH ANALYSIS, AN OUTLINE OF WHICH WILL BE PROVIDED IN THIS ABSTRACT. ENGLAND THE CONSERVATIVE GOVERNMENT, SINCE 1981, INTRODUCED RADICAL CHANGES IN THE SECTOR OF HIGHER EDUCATION: FIRST CUTTING DOWN ON STATE FUNDINGS AND THEN WITH THE CREATION OF AN INSTITUTION FOR THE PLANNING AND LEADERSHIP OF THE POLYTECHNICS (NON-UNIVERSITY SECTOR). AFTERWARDS THE SCHOOL REFORM BY MARGARET THATCHER IN 1988 RAISED TO A GREAT STIR ALL OVER EUROPE DUE TO BOTH ITS CONSIDERABLE INNOVATIVE IMPRINT AND THE STRONG ATTACK AGAINST THE PEDAGOGY OF THE ‘ACTIVE’ SCHOOLING AND PROGRESSIVE EDUCATION, UNTIL THEN RECOGNIZED AS A MERIT OF THE BRITISH PUBLIC SCHOOL. IN THE AMBIT OF UNIVERSITY EDUCATION THIS REFORM, TOGETHER WITH SIMILAR MEASURES BROUGHT IN DURING 1992, PUT INTO PRACTICE THE CONSERVATIVE PRINCIPLES THROUGH A SERIES OF ACTIONS THAT INCLUDED: THE SUPPRESSION OF THE IRREMOVABILITY PRINCIPLE FOR UNIVERSITY TEACHERS; THE INTRODUCTION OF STUDENT LOANS FOR LOW-INCOME STUDENTS AND THE CANCELLATION OF THE CLEAR DISTINCTION BETWEEN UNIVERSITIES AND POLYTECHNICS. THE POLICIES OF THE LABOUR MAJORITY OF MR BLAIR DID NOT QUITE DIVERGE FROM THE CONSERVATIVES’ POSITION. IN 2003 BLAIR’S CABINET RISKED TO BECOME A MINORITY RIGHT ON THE OCCASION OF AN IMPORTANT UNIVERSITY REFORM PROPOSAL. THIS PROPOSAL WOULD FORESEE THE AUTONOMY FOR THE UNIVERSITIES TO RAISE UP TO 3.000 POUNDS THE ENROLMENT FEES FOR STUDENTS (WHILE FORMERLY THE CEILING WAS 1.125 POUNDS). BLAIR HAD TO FACE INTERNAL OPPOSITION WITHIN HIS OWN PARTY IN RELATION TO A MEASURE THAT, ACCORDING TO THE 150 MPS PROMOTERS OF AN ADVERSE MOTION, HAD NOT BEEN INCLUDED IN THE ELECTORAL PROGRAMME AND WOULD RISK CREATING INCOME-BASED DISCRIMINATION AMONG STUDENTS. AS A MATTER OF FACT THE BILL FOCUSED ON THE INTRODUCTION OF VERY LOW-INTEREST STUDENT LOANS TO BE SETTLED ONLY WHEN THE STUDENT WOULD HAVE FOUND A REMUNERATED OCCUPATION (A SYSTEM ALREADY PROVIDED FOR BY THE AUSTRALIAN LEGISLATION). NEW ZEALAND CONTRARILY TO MANY OTHER COUNTRIES, NEW ZEALAND HAS ADOPTED A VERY WIDE VISION OF THE TERTIARY EDUCATION. IT INCLUDES IN FACT THE FULL EDUCATIONAL PROGRAMME THAT IS INTERNATIONALLY RECOGNIZED AS THE POST-SECONDARY EDUCATION. SHOULD WE SPOTLIGHT A PECULIARITY OF THE NEW ZEALAND TERTIARY EDUCATION POLICY THEN IT WOULD BE ‘CHANGE’. LOOKING AT THE REFORM HISTORY RELATED TO THE TERTIARY EDUCATION SYSTEM, WE CAN CLEARLY IDENTIFY FOUR ‘SUB-PERIODS’ FROM THE EIGHTIES TO PRESENT-DAY: 1. BEFORE THE 80S’: AN ELITARIAN SYSTEM CHARACTERIZED BY LOW PARTICIPATION RATES. 2. BETWEEN MID AND LATE 80S’: A TREND TOWARDS THE ENLARGEMENT OF PARTICIPATION ASSOCIATED TO A GREATER COMPETITION. 3. 1990-1999: A FUTHER STEP TOWARDS A COMPETITIVE MODEL BASED ON THE MARKET-ORIENTED SYSTEM. 4. FROM 2000 TO TODAY: A CONTINUOUS EVOLUTION TOWARDS A MORE COMPETITIVE MODEL BASED ON THE MARKET-ORIENTED SYSTEM TOGETHER WITH A GROWING ATTENTION TO STATE CONTROL FOR SOCIAL AND ECONOMIC DEVELOPMENT OF THE NATION. AT PRESENT THE GOVERNMENT OF NEW ZEALAND OPERATES TO STRENGHTHEN THIS PROCESS, PRIMARILY IN RELATION TO THE ROLE OF TERTIARY EDUCATION AS A STEADY FACTOR OF NATIONAL WALFARE, WHERE PROFESSIONAL DEVELOPMENT CONTRIBUTES ACTIVELY TO THE GROWTH OF THE NATIONAL ECONOMIC SYSTEM5. THE CASES OF ENGLAND AND NEW ZEALAND ARE THE FOCUS OF AN IN-DEPTH INVESTIGATION THAT STARTS FROM AN ANALYSIS OF THE POLICIES OF EACH NATION AND DEVELOP INTO A COMPARATIVE STUDY. AT THIS POINT I ATTEMPT TO DRAW SOME PRELIMINARY IMPRESSIONS ON THE FACTS ESSENTIALLY DECRIBED ABOVE. THE UNIVERSITY POLICIES IN ENGLAND AND NEW ZEALAND HAVE BOTH UNDERGONE A SIGNIFICANT REFORMATORY PROCESS SINCE THE EARLY EIGHTIES; IN BOTH CONTEXTS THE IMPORTANCE OF IDEAS THAT CONSTITUTED THE BASE OF POLITICS UNTIL 1980 WAS QUITE RELEVANT. GENERALLY SPEAKING, IN BOTH CASES THE PRE-REFORM POLICIES WERE INSPIRED BY EGALITARIANISM AND EXPANSION OF THE STUDENT POPULATION WHILE THOSE BROUGHT IN BY THE REFORM WOULD PURSUE EFFICIENCY, QUALITY AND COMPETITIVENESS. UNDOUBTEDLY, IN LINE WITH THIS GENERAL TENDENCY THAT REFLECTS THE HYPOTHESIS PROPOSED, THE TWO UNIVERSITY SYSTEMS PRESENT SEVERAL DIFFERENCES. THE UNIVERSITY SYSTEM IN NEW ZEALAND PROCEEDED STEADILY TOWARDS THE IMPLEMENTATION OF A MANAGERIAL CONCEPTION OF TERTIARY EDUCATION, ESPECIALLY FROM 1996 ONWARDS, IN ACCORDANCE WITH THE REFORMATORY PROCESS OF THE WHOLE PUBLIC SECTOR. IN THE UNITED KINGDOM, AS IN THE REST OF EUROPE, THE NEW APPROACH TO UNIVERSITY POLICY-MAKING HAD TO CONFRONT A DEEP-ROOTED TRADITION OF PROGRESSIVE EDUCATION AND THE IDEA OF EDUCATION EXPANSION THAT IN FACT DOMINATED UNTIL THE EIGHTIES. FROM THIS VIEW POINT THE GOVERNING ACTION OF MARGARET THATCHER GAVE RISE TO A RADICAL CHANGE THAT REVOLUTIONIZED THE OBJECTIVES AND KEY VALUES OF THE WHOLE EDUCATIONAL SYSTEM, IN PARTICULAR IN THE HIGHER EDUCATION SECTOR. IDEAS AS EFFICIENCY, EXCELLENCE AND CONTROL OF THE PERFORMANCE BECAME DECISIVE. THE LABOUR CABINETS OF BLAIR DEVELOPED IN THE WAKE OF CONSERVATIVE REFORMS. THIS APPEARS TO BE A FOCAL POINT OF THIS STUDY THAT OBSERVES HOW ALSO IN NEW ZEALAND THE REFORMING PROCESS OCCURRED TRANSVERSELY DURING PROGRESSIVE AND CONSERVATIVE ADMINISTRATIONS. THE PRELIMINARY IMPRESSION IS THEREFORE THAT IDEAS DEEPLY MARK THE REFORMATIVE PROCESSES: THE AIM OF MY RESEARCH IS TO VERIFY TO WHICH EXTENT THIS STATEMENT IS TRUE. IN ORDER TO BUILD A COMPREHENSIVE ANALYLIS, FURTHER SIGNIFICANT FACTORS WILL HAVE TO BE INVESTIGATED: THE WAY IDEAS ARE PERCEIVED AND IMPLEMENTED BY THE DIFFERENT POLITICAL ELITES; HOW THE VARIOUS SOCIOECONOMIC CONTEXTS INFLUENCE THE REFORMATIVE PROCESS; HOW THE INSTITUTIONAL STRUCTURES CONDITION THE POLICY-MAKING PROCESSES; WHETHER INDIVIDUAL INTERESTS PLAY A ROLE AND, IF YES, TO WHICH EXTENT.

Multilevel Analysis in Household Survey: An Application to Health Condition Data

The aim of this thesis is to apply multilevel regression model in context of household surveys. Hierarchical structure in this type of data is characterized by many small groups. In last years comparative and multilevel analysis in the field of perceived health have grown in size. The purpose of this thesis is to develop a multilevel analysis with three level of hierarchy for Physical Component Summary outcome to: evaluate magnitude of within and between variance at each level (individual, household and municipality); explore which covariates affect on perceived physical health at each level; compare model-based and design-based approach in order to establish informativeness of sampling design; estimate a quantile regression for hierarchical data. The target population are the Italian residents aged 18 years and older. Our study shows a high degree of homogeneity within level 1 units belonging from the same group, with an intraclass correlation of 27% in a level-2 null model. Almost all variance is explained by level 1 covariates. In fact, in our model the explanatory variables having more impact on the outcome are disability, unable to work, age and chronic diseases (18 pathologies). An additional analysis are performed by using novel procedure of analysis :"Linear Quantile Mixed Model", named "Multilevel Linear Quantile Regression", estimate. This give us the possibility to describe more generally the conditional distribution of the response through the estimation of its quantiles, while accounting for the dependence among the observations. This has represented a great advantage of our models with respect to classic multilevel regression. The median regression with random effects reveals to be more efficient than the mean regression in representation of the outcome central tendency. A more detailed analysis of the conditional distribution of the response on other quantiles highlighted a differential effect of some covariate along the distribution.

Modeling the spatial dynamics of economic models

The advances that have been characterizing spatial econometrics in recent years are mostly theoretical and have not found an extensive empirical application yet. In this work we aim at supplying a review of the main tools of spatial econometrics and to show an empirical application for one of the most recently introduced estimators. Despite the numerous alternatives that the econometric theory provides for the treatment of spatial (and spatiotemporal) data, empirical analyses are still limited by the lack of availability of the correspondent routines in statistical and econometric software. Spatiotemporal modeling represents one of the most recent developments in spatial econometric theory and the finite sample properties of the estimators that have been proposed are currently being tested in the literature. We provide a comparison between some estimators (a quasi-maximum likelihood, QML, estimator and some GMM-type estimators) for a fixed effects dynamic panel data model under certain conditions, by means of a Monte Carlo simulation analysis. We focus on different settings, which are characterized either by fully stable or quasi-unit root series. We also investigate the extent of the bias that is caused by a non-spatial estimation of a model when the data are characterized by different degrees of spatial dependence. Finally, we provide an empirical application of a QML estimator for a time-space dynamic model which includes a temporal, a spatial and a spatiotemporal lag of the dependent variable. This is done by choosing a relevant and prolific field of analysis, in which spatial econometrics has only found limited space so far, in order to explore the value-added of considering the spatial dimension of the data. In particular, we study the determinants of cropland value in Midwestern U.S.A. in the years 1971-2009, by taking the present value model (PVM) as the theoretical framework of analysis.

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.