Design of experiment in drug development: optimal allocations in multi-arm clinical trials and design space for multi-step processes

In this thesis, we deal with the design of experiments in the drug development process, focusing on the design of clinical trials for treatment comparisons (Part I) and the design of preclinical laboratory experiments for proteins development and manufacturing (Part II). In Part I we propose a multi-purpose design methodology for sequential clinical trials. We derived optimal allocations of patients to treatments for testing the efficacy of several experimental groups by also taking into account ethical considerations. We first consider exponential responses for survival trials and we then present a unified framework for heteroscedastic experimental groups that encompasses the general ANOVA set-up. The very good performance of the suggested optimal allocations, in terms of both inferential and ethical characteristics, are illustrated analytically and through several numerical examples, also performing comparisons with other designs proposed in the literature. Part II concerns the planning of experiments for processes composed of multiple steps in the context of preclinical drug development and manufacturing. Following the Quality by Design paradigm, the objective of the multi-step design strategy is the definition of the manufacturing design space of the whole process and, as we consider the interactions among the subsequent steps, our proposal ensures the quality and the safety of the final product, by enabling more flexibility and process robustness in the manufacturing.

Many-Core Architectures: Hardware-Software Optimization and Modeling Techniques

During the last few decades an unprecedented technological growth has been at the center of the embedded systems design paramount, with Moore’s Law being the leading factor of this trend. Today in fact an ever increasing number of cores can be integrated on the same die, marking the transition from state-of-the-art multi-core chips to the new many-core design paradigm. Despite the extraordinarily high computing power, the complexity of many-core chips opens the door to several challenges. As a result of the increased silicon density of modern Systems-on-a-Chip (SoC), the design space exploration needed to find the best design has exploded and hardware designers are in fact facing the problem of a huge design space. Virtual Platforms have always been used to enable hardware-software co-design, but today they are facing with the huge complexity of both hardware and software systems. In this thesis two different research works on Virtual Platforms are presented: the first one is intended for the hardware developer, to easily allow complex cycle accurate simulations of many-core SoCs. The second work exploits the parallel computing power of off-the-shelf General Purpose Graphics Processing Units (GPGPUs), with the goal of an increased simulation speed. The term Virtualization can be used in the context of many-core systems not only to refer to the aforementioned hardware emulation tools (Virtual Platforms), but also for two other main purposes: 1) to help the programmer to achieve the maximum possible performance of an application, by hiding the complexity of the underlying hardware. 2) to efficiently exploit the high parallel hardware of many-core chips in environments with multiple active Virtual Machines. This thesis is focused on virtualization techniques with the goal to mitigate, and overtake when possible, some of the challenges introduced by the many-core design paradigm.

Methodologies for Synthesizable Programmable Devices based on Multi-Stage Switching Networks

Nowadays the rise of non-recurring engineering (NRE) costs associated with complexity is becoming a major factor in SoC design, limiting both scaling opportunities and the flexibility advantages offered by the integration of complex computational units. The introduction of embedded programmable elements can represent an appealing solution, able both to guarantee the desired flexibility and upgradabilty and to widen the SoC market. In particular embedded FPGA (eFPGA) cores can provide bit-level optimization for those applications which benefits from synthesis, paying on the other side in terms of performance penalties and area overhead with respect to standard cell ASIC implementations. In this scenario this thesis proposes a design methodology for a synthesizable programmable device designed to be embedded in a SoC. A soft-core embedded FPGA (eFPGA) is hence presented and analyzed in terms of the opportunities given by a fully synthesizable approach, following an implementation flow based on Standard-Cell methodology. A key point of the proposed eFPGA template is that it adopts a Multi-Stage Switching Network (MSSN) as the foundation of the programmable interconnects, since it can be efficiently synthesized and optimized through a standard cell based implementation flow, ensuring at the same time an intrinsic congestion-free network topology. The evaluation of the flexibility potentialities of the eFPGA has been performed using different technology libraries (STMicroelectronics CMOS 65nm and BCD9s 0.11μm) through a design space exploration in terms of area-speed-leakage tradeoffs, enabled by the full synthesizability of the template. Since the most relevant disadvantage of the adopted soft approach, compared to a hardcore, is represented by a performance overhead increase, the eFPGA analysis has been made targeting small area budgets. The generation of the configuration bitstream has been obtained thanks to the implementation of a custom CAD flow environment, and has allowed functional verification and performance evaluation through an application-aware analysis.

Interconnection systems for highly integrated computation devices

The sustained demand for faster,more powerful chips has beenmet by the availability of chip manufacturing processes allowing for the integration of increasing numbers of computation units onto a single die. The resulting outcome, especially in the embedded domain, has often been called SYSTEM-ON-CHIP (SOC) or MULTI-PROCESSOR SYSTEM-ON-CHIP (MPSOC). MPSoC design brings to the foreground a large number of challenges, one of the most prominent of which is the design of the chip interconnection. With a number of on-chip blocks presently ranging in the tens, and quickly approaching the hundreds, the novel issue of how to best provide on-chip communication resources is clearly felt. NETWORKS-ON-CHIPS (NOCS) are the most comprehensive and scalable answer to this design concern. By bringing large-scale networking concepts to the on-chip domain, they guarantee a structured answer to present and future communication requirements. The point-to-point connection and packet switching paradigms they involve are also of great help in minimizing wiring overhead and physical routing issues. However, as with any technology of recent inception, NoC design is still an evolving discipline. Several main areas of interest require deep investigation for NoCs to become viable solutions: • The design of the NoC architecture needs to strike the best tradeoff among performance, features and the tight area and power constraints of the on-chip domain. • Simulation and verification infrastructure must be put in place to explore, validate and optimize the NoC performance. • NoCs offer a huge design space, thanks to their extreme customizability in terms of topology and architectural parameters. Design tools are needed to prune this space and pick the best solutions. • Even more so given their global, distributed nature, it is essential to evaluate the physical implementation of NoCs to evaluate their suitability for next-generation designs and their area and power costs. This dissertation focuses on all of the above points, by describing a NoC architectural implementation called ×pipes; a NoC simulation environment within a cycle-accurate MPSoC emulator called MPARM; a NoC design flow consisting of a front-end tool for optimal NoC instantiation, called SunFloor, and a set of back-end facilities for the study of NoC physical implementations. This dissertation proves the viability of NoCs for current and upcoming designs, by outlining their advantages (alongwith a fewtradeoffs) and by providing a full NoC implementation framework. It also presents some examples of additional extensions of NoCs, allowing e.g. for increased fault tolerance, and outlines where NoCsmay find further application scenarios, such as in stacked chips.

Multi Processor Systems On Chip with Configurable Hardware Acceleration

The evolution of the electronics embedded applications forces electronics systems designers to match their ever increasing requirements. This evolution pushes the computational power of digital signal processing systems, as well as the energy required to accomplish the computations, due to the increasing mobility of such applications. Current approaches used to match these requirements relies on the adoption of application specific signal processors. Such kind of devices exploits powerful accelerators, which are able to match both performance and energy requirements. On the other hand, the too high specificity of such accelerators often results in a lack of flexibility which affects non-recurrent engineering costs, time to market, and market volumes too. The state of the art mainly proposes two solutions to overcome these issues with the ambition of delivering reasonable performance and energy efficiency: reconfigurable computing and multi-processors computing. All of these solutions benefits from the post-fabrication programmability, that definitively results in an increased flexibility. Nevertheless, the gap between these approaches and dedicated hardware is still too high for many application domains, especially when targeting the mobile world. In this scenario, flexible and energy efficient acceleration can be achieved by merging these two computational paradigms, in order to address all the above introduced constraints. This thesis focuses on the exploration of the design and application spectrum of reconfigurable computing, exploited as application specific accelerators for multi-processors systems on chip. More specifically, it introduces a reconfigurable digital signal processor featuring a heterogeneous set of reconfigurable engines, and a homogeneous multi-core system, exploiting three different flavours of reconfigurable and mask-programmable technologies as implementation platform for applications specific accelerators. In this work, the various trade-offs concerning the utilization multi-core platforms and the different configuration technologies are explored, characterizing the design space of the proposed approach in terms of programmability, performance, energy efficiency and manufacturing costs.

Dinamica dell’intrusione salina nella costa ravennate: aspetti idrogeochimici ed evoluzione attesa

Nell’ambito del progetto multidisciplinare “Coastal Salt Water Intrusion”, che si propone di indagare “l’Intrusione salina nella costa ravennate con i conseguenti impatti territoriali-ambientali, connessi al previsto innalzamento del livello marino per cause climatiche e di subsidenza”, si inserisce il presente studio con l’obiettivo di fornire una caratterizzazione idrogeochimica delle acque di falda e superficiali e un modello geochimico generale sui processi di salinizzazione o desalinizzazione in atto nella falda freatica costiera della costa ravennate. E’ stato fatto un confronto fra tre metodiche di estrazione del complesso di scambio della matrice solida dell’acquifero che utilizzano rispettivamente acetato di ammonio, cloruro di bario e argento-tiourea. Sono stati posizionati 5 transetti perpendicolari alla linea di costa per un totale di 44 punti di campionamento con due campagne di prelievi, al termine della primavera e al termine dell’estate. La caratterizzazione dei processi di mixing e scambio ionico con la matrice solida dell’acquifero è avvenuta mediante analisi dei cationi ed anioni fondamentali, determinazione della CEC sulla matrice solida dell’acquifero, modellizzazione mixing/scambio ionico, modellizzazione della composizione teorica della frazione scambiabile in funzione della composizione acqua all’equilibrio e interpolazione geostatistica dei dati raccolti e costruzione di mappe geochimiche (curve di iso-concentrazione). La metodologia di estrazione che utilizza il bario-cloruro è risultata la più affidabile. Le acque prelevate dalla falda superficiale evidenziano miscelazione in varie proporzioni acqua marina/acqua dolce, scambi ionici per interazione acqua/sedimento, dissoluzione di CaSO4.2H2O. I processi di salinizzazione e/o addolcimento mostrano una significativa variabilità nello spazio (variabilità legata alla distanza dalla costa, al profilo topografico e alla distribuzione dei corpi sabbiosi litoranei) e nel tempo (variabilità legata alla piovosità e alla gestione delle acque superficiali e del sottosuolo). La complessa variabilità spazio-temporale dei processi in atto nella falda superficiale non consente di evidenziare una complessiva prevalenza di fenomeni di salinizzazione rispetto a quelli di addolcimento.

Parallel Architectures for Many-Core Systems-On-Chip in Deep Sub-Micron Technology

Despite the several issues faced in the past, the evolutionary trend of silicon has kept its constant pace. Today an ever increasing number of cores is integrated onto the same die. Unfortunately, the extraordinary performance achievable by the many-core paradigm is limited by several factors. Memory bandwidth limitation, combined with inefficient synchronization mechanisms, can severely overcome the potential computation capabilities. Moreover, the huge HW/SW design space requires accurate and flexible tools to perform architectural explorations and validation of design choices. In this thesis we focus on the aforementioned aspects: a flexible and accurate Virtual Platform has been developed, targeting a reference many-core architecture. Such tool has been used to perform architectural explorations, focusing on instruction caching architecture and hybrid HW/SW synchronization mechanism. Beside architectural implications, another issue of embedded systems is considered: energy efficiency. Near Threshold Computing is a key research area in the Ultra-Low-Power domain, as it promises a tenfold improvement in energy efficiency compared to super-threshold operation and it mitigates thermal bottlenecks. The physical implications of modern deep sub-micron technology are severely limiting performance and reliability of modern designs. Reliability becomes a major obstacle when operating in NTC, especially memory operation becomes unreliable and can compromise system correctness. In the present work a novel hybrid memory architecture is devised to overcome reliability issues and at the same time improve energy efficiency by means of aggressive voltage scaling when allowed by workload requirements. Variability is another great drawback of near-threshold operation. The greatly increased sensitivity to threshold voltage variations in today a major concern for electronic devices. We introduce a variation-tolerant extension of the baseline many-core architecture. By means of micro-architectural knobs and a lightweight runtime control unit, the baseline architecture becomes dynamically tolerant to variations.

An architecture for network acceleration as a service in the cloud continuum

The pervasive availability of connected devices in any industrial and societal sector is pushing for an evolution of the well-established cloud computing model. The emerging paradigm of the cloud continuum embraces this decentralization trend and envisions virtualized computing resources physically located between traditional datacenters and data sources. By totally or partially executing closer to the network edge, applications can have quicker reactions to events, thus enabling advanced forms of automation and intelligence. However, these applications also induce new data-intensive workloads with low-latency constraints that require the adoption of specialized resources, such as high-performance communication options (e.g., RDMA, DPDK, XDP, etc.). Unfortunately, cloud providers still struggle to integrate these options into their infrastructures. That risks undermining the principle of generality that underlies the cloud computing scale economy by forcing developers to tailor their code to low-level APIs, non-standard programming models, and static execution environments. This thesis proposes a novel system architecture to empower cloud platforms across the whole cloud continuum with Network Acceleration as a Service (NAaaS). To provide commodity yet efficient access to acceleration, this architecture defines a layer of agnostic high-performance I/O APIs, exposed to applications and clearly separated from the heterogeneous protocols, interfaces, and hardware devices that implement it. A novel system component embodies this decoupling by offering a set of agnostic OS features to applications: memory management for zero-copy transfers, asynchronous I/O processing, and efficient packet scheduling. This thesis also explores the design space of the possible implementations of this architecture by proposing two reference middleware systems and by adopting them to support interactive use cases in the cloud continuum: a serverless platform and an Industry 4.0 scenario. A detailed discussion and a thorough performance evaluation demonstrate that the proposed architecture is suitable to enable the easy-to-use, flexible integration of modern network acceleration into next-generation cloud platforms.

Design and implementation of a novel multi-constellation FPGA-based dual frequency GNSS receiver for space applications

The PhD activity described in the document is part of the Microsatellite and Microsystem Laboratory of the II Faculty of Engineering, University of Bologna. The main objective is the design and development of a GNSS receiver for the orbit determination of microsatellites in low earth orbit. The development starts from the electronic design and goes up to the implementation of the navigation algorithms, covering all the aspects that are involved in this type of applications. The use of GPS receivers for orbit determination is a consolidated application used in many space missions, but the development of the new GNSS system within few years, such as the European Galileo, the Chinese COMPASS and the Russian modernized GLONASS, proposes new challenges and offers new opportunities to increase the orbit determination performances. The evaluation of improvements coming from the new systems together with the implementation of a receiver that is compatible with at least one of the new systems, are the main activities of the PhD. The activities can be divided in three section: receiver requirements definition and prototype implementation, design and analysis of the GNSS signal tracking algorithms, and design and analysis of the navigation algorithms. The receiver prototype is based on a Virtex FPGA by Xilinx, and includes a PowerPC processor. The architecture follows the software defined radio paradigm, so most of signal processing is performed in software while only what is strictly necessary is done in hardware. The tracking algorithms are implemented as a combination of Phase Locked Loop and Frequency Locked Loop for the carrier, and Delay Locked Loop with variable bandwidth for the code. The navigation algorithm is based on the extended Kalman filter and includes an accurate LEO orbit model.

Hardware/Software Design of Dynamic Real-Time Schedulers for Embedded Multiprocessor Systems

The new generation of multicore processors opens new perspectives for the design of embedded systems. Multiprocessing, however, poses new challenges to the scheduling of real-time applications, in which the ever-increasing computational demands are constantly flanked by the need of meeting critical time constraints. Many research works have contributed to this field introducing new advanced scheduling algorithms. However, despite many of these works have solidly demonstrated their effectiveness, the actual support for multiprocessor real-time scheduling offered by current operating systems is still very limited. This dissertation deals with implementative aspects of real-time schedulers in modern embedded multiprocessor systems. The first contribution is represented by an open-source scheduling framework, which is capable of realizing complex multiprocessor scheduling policies, such as G-EDF, on conventional operating systems exploiting only their native scheduler from user-space. A set of experimental evaluations compare the proposed solution to other research projects that pursue the same goals by means of kernel modifications, highlighting comparable scheduling performances. The principles that underpin the operation of the framework, originally designed for symmetric multiprocessors, have been further extended first to asymmetric ones, which are subjected to major restrictions such as the lack of support for task migrations, and later to re-programmable hardware architectures (FPGAs). In the latter case, this work introduces a scheduling accelerator, which offloads most of the scheduling operations to the hardware and exhibits extremely low scheduling jitter. The realization of a portable scheduling framework presented many interesting software challenges. One of these has been represented by timekeeping. In this regard, a further contribution is represented by a novel data structure, called addressable binary heap (ABH). Such ABH, which is conceptually a pointer-based implementation of a binary heap, shows very interesting average and worst-case performances when addressing the problem of tick-less timekeeping of high-resolution timers.

Engineering Complex Computational Ecosystems

Self-organising pervasive ecosystems of devices are set to become a major vehicle for delivering infrastructure and end-user services. The inherent complexity of such systems poses new challenges to those who want to dominate it by applying the principles of engineering. The recent growth in number and distribution of devices with decent computational and communicational abilities, that suddenly accelerated with the massive diffusion of smartphones and tablets, is delivering a world with a much higher density of devices in space. Also, communication technologies seem to be focussing on short-range device-to-device (P2P) interactions, with technologies such as Bluetooth and Near-Field Communication gaining greater adoption. Locality and situatedness become key to providing the best possible experience to users, and the classic model of a centralised, enormously powerful server gathering and processing data becomes less and less efficient with device density. Accomplishing complex global tasks without a centralised controller responsible of aggregating data, however, is a challenging task. In particular, there is a local-to-global issue that makes the application of engineering principles challenging at least: designing device-local programs that, through interaction, guarantee a certain global service level. In this thesis, we first analyse the state of the art in coordination systems, then motivate the work by describing the main issues of pre-existing tools and practices and identifying the improvements that would benefit the design of such complex software ecosystems. The contribution can be divided in three main branches. First, we introduce a novel simulation toolchain for pervasive ecosystems, designed for allowing good expressiveness still retaining high performance. Second, we leverage existing coordination models and patterns in order to create new spatial structures. Third, we introduce a novel language, based on the existing ``Field Calculus'' and integrated with the aforementioned toolchain, designed to be usable for practical aggregate programming.

Design, realization, and characterization of complex reaction networks in dynamic mechanically interlocked molecules

The experimental projects discussed in this thesis are all related to the field of artificial molecular machines, specifically to systems composed of pseudorotaxane and rotaxane architectures. The characterization of the peculiar properties of these mechano-molecules is frequently associated with the analysis and elucidation of complex reaction networks; this latter aspect represents the main focus and central thread tying my thesis work. In each chapter, a specific project is described as summarized below: the focus of the first chapter is the realization and characterization of a prototype model of a photoactivated molecular transporter based on a pseudorotaxane architecture; in the second chapter is reported the design, synthesis, and characterization of a [2]rotaxane endowed with a dibenzylammonium station and a novel photochromic unit that acts as a recognition site for a DB24C8 crown ether macrocycle; in the last chapter is described the synthesis and characterization of a [3]rotaxane in which the relative number of rings and stations can be changed on command.

Mechanical design and hybrid control strategies for overconstrained cable-driven parallel robots

Cable-driven parallel robots offer significant advantages in terms of workspace dimensions and payload capability. They are attractive for many industrial tasks to be performed on a large scale, such as handling and manufacturing, without a substantial increase in costs and mechanical complexity with respect to a small-scale application. However, since cables can only sustain tensile stresses, cable tensions must be kept within positive limits during the end-effector motion. This problem can be managed by overconstraining the end-effector and controlling cable tensions. Tension control is typically achieved by mounting a load sensor on all cables, and using specific control algorithms to avoid cable slackness or breakage while the end-effector is controlled in a desired position. These algorithms require multiple cascade control loops and they can be complex and computationally demanding. To simplify the control of overconstrained cable-driven parallel robots, this Thesis proposes suitable mechanical design and hybrid control strategies. It is shown how a convenient design of the cable guidance system allows kinematic modeling to be simplified, without introducing geometric approximations. This guidance system employs swiveling pulleys equipped with position and tension sensors and provides a parallelogram arrangement of cables. Furthermore, a hybrid force/position control in the robot joint space is adopted. According to this strategy, a particular set of cables is chosen to be tension-controlled, whereas the other cables are length-controlled. The force-controlled cables are selected based on the computation of a novel index called force-distribution sensitivity to cable-tension errors. This index aims to evaluate the maximum expected cable-tension error in the length-controlled cables if a unit tension error is committed in the force-controlled cables. In practice, the computation of the force-distribution sensitivity allows determining which cables are best to be force-controlled, to ensure the lowest error in the overall force distribution when a hybrid force/position joint-space strategy is used.

Navigation design and flight dynamics operations of the ArgoMoon cis-lunar CubeSat.

On November 16, 2022, the NASA’s Space Launch System (SLS) has been launched for the first time in the context of Artemis-1 mission where, together with the Orion Multi-Purpose Crew Vehicle, a set of 10 CubeSats have been delivered into a translunar trajectory. Among the small satellites deployed during Artemis-1 there is ArgoMoon, a 6U CubeSat built by the Italian company Argotec and coordinated by Italian Space Agency (ASI). The primary goal of ArgoMoon is to capture images of the Interim Cryogenic Propulsion Stage. The ArgoMoon trajectory has been designed as a highly elliptical geocentric orbit, with several encounters with the Moon. In order to successfully fly ArgoMoon along the designed cis-lunar trajectory, a ground-based navigation system has been developed exploiting the guidance techniques also used for regular deep space missions. The navigation process is subdivided into Orbit Determi- nation (OD) and a Flight Path Control (FPC), and it is designed to follow the reference trajectory, prevent impacts with the Earth and the Moon, intensively test the navigation techniques, and guarantee the spacecraft disposal at the end of the mission. The work done in this thesis has accomplished the navigation of ArgoMoon, covering all aspects of the project life, from pre-launch design and analysis to actual operations. Firstly, the designed navigation process and the pre-mission assessment of its performance will be presented. Then, the results of the ArgoMoon navigation operations performed after the launch in November 2022 will be described in detail by discussing the main encountered challenges and the adopted solutions. The results of the operations confirmed the robustness of the designed navigation which allowed to accurately estimate the trajectory of ArgoMoon despite a series of complex events.

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.