Automatic code generation: from process algebraic architectural descriptions to multithreaded java programs

Process algebraic architectural description languages provide a formal means for modeling software systems and assessing their properties. In order to bridge the gap between system modeling and system im- plementation, in this thesis an approach is proposed for automatically generating multithreaded object-oriented code from process algebraic architectural descriptions, in a way that preserves – under certain assumptions – the properties proved at the architectural level. The approach is divided into three phases, which are illustrated by means of a running example based on an audio processing system. First, we develop an architecture-driven technique for thread coordination management, which is completely automated through a suitable package. Second, we address the translation of the algebraically-specified behavior of the individual software units into thread templates, which will have to be filled in by the software developer according to certain guidelines. Third, we discuss performance issues related to the suitability of synthesizing monitors rather than threads from software unit descriptions that satisfy specific constraints. In addition to the running example, we present two case studies about a video animation repainting system and the implementation of a leader election algorithm, in order to summarize the whole approach. The outcome of this thesis is the implementation of the proposed approach in a translator called PADL2Java and its integration in the architecture-centric verification tool TwoTowers.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.

Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

Crustal heterogeneities and complexities of fault processes

In this work we study the relation between crustal heterogeneities and complexities in fault processes. The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane. In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust. In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface. Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons

Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system. To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system. The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.