Interactive theorem provers: issues faced as a user and tackled as a developer

Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a machine is able to “understand” and process. The user perceives this gap in terms of missing features or inefficiencies. The developer tries to accommodate the user requests without increasing the already high complexity of these applications. We believe that satisfactory solutions can only come from a strong synergy between users and developers. We devoted most part of our PHD designing and developing the Matita interactive theorem prover. The software was born in the computer science department of the University of Bologna as the result of composing together all the technologies developed by the HELM team (to which we belong) for the MoWGLI project. The MoWGLI project aimed at giving accessibility through the web to the libraries of formalised mathematics of various interactive theorem provers, taking Coq as the main test case. The motivations for giving life to a new ITP are: • study the architecture of these tools, with the aim of understanding the source of their complexity • exploit such a knowledge to experiment new solutions that, for backward compatibility reasons, would be hard (if not impossible) to test on a widely used system like Coq. Matita is based on the Curry-Howard isomorphism, adopting the Calculus of Inductive Constructions (CIC) as its logical foundation. Proof objects are thus, at some extent, compatible with the ones produced with the Coq ITP, that is itself able to import and process the ones generated using Matita. Although the systems have a lot in common, they share no code at all, and even most of the algorithmic solutions are different. The thesis is composed of two parts where we respectively describe our experience as a user and a developer of interactive provers. In particular, the first part is based on two different formalisation experiences: • our internship in the Mathematical Components team (INRIA), that is formalising the finite group theory required to attack the Feit Thompson Theorem. To tackle this result, giving an effective classification of finite groups of odd order, the team adopts the SSReflect Coq extension, developed by Georges Gonthier for the proof of the four colours theorem. • our collaboration at the D.A.M.A. Project, whose goal is the formalisation of abstract measure theory in Matita leading to a constructive proof of Lebesgue’s Dominated Convergence Theorem. The most notable issues we faced, analysed in this part of the thesis, are the following: the difficulties arising when using “black box” automation in large formalisations; the impossibility for a user (especially a newcomer) to master the context of a library of already formalised results; the uncomfortable big step execution of proof commands historically adopted in ITPs; the difficult encoding of mathematical structures with a notion of inheritance in a type theory without subtyping like CIC. In the second part of the manuscript many of these issues will be analysed with the looking glasses of an ITP developer, describing the solutions we adopted in the implementation of Matita to solve these problems: integrated searching facilities to assist the user in handling large libraries of formalised results; a small step execution semantic for proof commands; a flexible implementation of coercive subtyping allowing multiple inheritance with shared substructures; automatic tactics, integrated with the searching facilities, that generates proof commands (and not only proof objects, usually kept hidden to the user) one of which specifically designed to be user driven.

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Sonno e funzioni cognitive: ruolo della microstruttura del sonno NREM

STUDY OBJECTIVE: Cyclic Alternating Pattern (CAP) is a fluctuation of the arousal level during NREM sleep and consists of the alternation between two phases: phase A (divided into three subtypes A1, A2, and A3) and phase B. A1 is thought to be generated by the frontal cortex and is characterized by the presence of K complexes or delta bursts; additionally, CAP A1 seems to have a role in the involvement of sleep slow wave activity in cognitive processing. Our hypothesis was that an overall CAP rate would have a negative influence on cognitive performance due to excessive fluctuation of the arousal level during NREM sleep. However, we also predicted that CAP A1 would be positively correlated with cognitive functions, especially those related to frontal lobe functioning. For this reason, the objective of our study was to correlate objective sleep parameters with cognitive behavioral measures in normal healthy adults. METHODS: 8 subjects (4 males; 4 females; mean age 27.75 years, range 2334) were recruited for this study. Two nocturnal polysomnography (night 2 and 3 = N2 and N3) were carried out after a night of adaptation. A series of neuropsychological tests were performed by the subjects in the morning and afternoon of the second day (D2am; D2pm) and in the morning of the third day (D3am). Raw scores from the neuropsychological tests were used as dependent variables in the statistical analysis of the results. RESULTS: We computed a series of partial correlations between sleep microstructure parameters (CAP, A1, A2 and A3 rate) and a number of indices of cognitive functioning. CAP rate was positively correlated with visuospatial working memory (Corsi block test), Trial Making Test Part A (planning and motor sequencing) and the retention of words from the Hopkins Verbal Learning Test (HVLT). Conversely, CAP was negatively correlated with visuospatial fluency (Ruff Figure Fluency Test). CAP A1 were correlated with many of the tests of neuropsychological functioning, such as verbal fluency (as measured by the COWAT), working memory (as measured by the Digit Span – Backward test), and both delay recall and retention of the words from the HVLT. The same parameters were found to be negatively correlated with CAP A2 subtypes. CAP 3 were negatively correlated with the Trial Making Test Parts A and B. DISCUSSION: To our knowledge this is the first study indicating a role of CAP A1 and A2 on behavioral cognitive performance of healthy adults. The results suggest that high rate of CAP A1 might be related to an improvement whereas high rate of CAP A2 to a decline of cognitive functions. Further studies need to be done to better determine the role of the overall CAP rate and CAP A3 on cognitive behavioral performances.

Rehabilitation Engineering in Parkinson's disease

Impairment of postural control is a common consequence of Parkinson's disease (PD) that becomes more and more critical with the progression of the disease, in spite of the available medications. Postural instability is one of the most disabling features of PD and induces difficulties with postural transitions, initiation of movements, gait disorders, inability to live independently at home, and is the major cause of falls. Falls are frequent (with over 38% falling each year) and may induce adverse consequences like soft tissue injuries, hip fractures, and immobility due to fear of falling. As the disease progresses, both postural instability and fear of falling worsen, which leads patients with PD to become increasingly immobilized. The main aims of this dissertation are to: 1) detect and assess, in a quantitative way, impairments of postural control in PD subjects, investigate the central mechanisms that control such motor performance, and how these mechanism are affected by levodopa; 2) develop and validate a protocol, using wearable inertial sensors, to measure postural sway and postural transitions prior to step initiation; 3) find quantitative measures sensitive to impairments of postural control in early stages of PD and quantitative biomarkers of disease progression; and 4) test the feasibility and effects of a recently-developed audio-biofeedback system in maintaining balance in subjects with PD. In the first set of studies, we showed how PD reduces functional limits of stability as well as the magnitude and velocity of postural preparation during voluntary, forward and backward leaning while standing. Levodopa improves the limits of stability but not the postural strategies used to achieve the leaning. Further, we found a strong relationship between backward voluntary limits of stability and size of automatic postural response to backward perturbations in control subjects and in PD subjects ON medication. Such relation might suggest that the central nervous system presets postural response parameters based on perceived maximum limits and this presetting is absent in PD patients OFF medication but restored with levodopa replacement. Furthermore, we investigated how the size of preparatory postural adjustments (APAs) prior to step initiation depend on initial stance width. We found that patients with PD did not scale up the size of their APA with stance width as much as control subjects so they had much more difficulty initiating a step from a wide stance than from a narrow stance. This results supports the hypothesis that subjects with PD maintain a narrow stance as a compensation for their inability to sufficiently increase the size of their lateral APA to allow speedy step initiation in wide stance. In the second set of studies, we demonstrated that it is possible to use wearable accelerometers to quantify postural performance during quiet stance and step initiation balance tasks in healthy subjects. We used a model to predict center of pressure displacements associated with accelerations at the upper and lower back and thigh. This approach allows the measurement of balance control without the use of a force platform outside the laboratory environment. We used wearable accelerometers on a population of early, untreated PD patients, and found that postural control in stance and postural preparation prior to a step are impaired early in the disease when the typical balance and gait intiation symptoms are not yet clearly manifested. These novel results suggest that technological measures of postural control can be more sensitive than clinical measures. Furthermore, we assessed spontaneous sway and step initiation longitudinally across 1 year in patients with early, untreated PD. We found that changes in trunk sway, and especially movement smoothness, measured as Jerk, could be used as an objective measure of PD and its progression. In the third set of studies, we studied the feasibility of adapting an existing audio-biofeedback device to improve balance control in patients with PD. Preliminary results showed that PD subjects found the system easy-to-use and helpful, and they were able to correctly follow the audio information when available. Audiobiofeedback improved the properties of trunk sway during quiet stance. Our results have many implications for i) the understanding the central mechanisms that control postural motor performance, and how these mechanisms are affected by levodopa; ii) the design of innovative protocols for measuring and remote monitoring of motor performance in the elderly or subjects with PD; and iii) the development of technologies for improving balance, mobility, and consequently quality of life in patients with balance disorders, such as PD patients with augmented biofeedback paradigms.

Controllo dell'atto di prensione: coinvolgimento dell'area V6A nell'orientamento del polso

Prehension in an act of coordinated reaching and grasping. The reaching component is concerned with bringing the hand to object to be grasped (transport phase); the grasping component refers to the shaping of the hand according to the object features (grasping phase) (Jeannerod, 1981). Reaching and grasping involve different muscles, proximal and distal muscles respectively, and are controlled by different parietofrontal circuit (Jeannerod et al., 1995): a medial circuit, involving area of superior parietal lobule and dorsal premotor area 6 (PMd) (dorsomedial visual stream), is mainly concerned with reaching; a lateral circuit, involving the inferior parietal lobule and ventral premotor area 6 (PMv) (dorsolateral visual stream), with grasping. Area V6A is located in the caudalmost part of the superior parietal lobule, so it belongs to the dorsomedial visual stream; it contains neurons sensitive to visual stimuli (Galletti et al. 1993, 1996, 1999) as well as cells sensitive to the direction of gaze (Galletti et al. 1995) and cells showing saccade-related activity (Nakamura et al. 1999; Kutz et al. 2003). Area V6A contains also arm-reaching neurons likely involved in the control of the direction of the arm during movements towards objects in the peripersonal space (Galletti et al. 1997; Fattori et al. 2001). The present results confirm this finding and demonstrate that during the reach-to-grasp the V6A neurons are also modulated by the orientation of the wrist. Experiments were approved by the Bioethical Committee of the University of Bologna and were performed in accordance with National laws on care and use of laboratory animals and with the European Communities Council Directive of 24th November 1986 (86/609/EEC), recently revised by the Council of Europe guidelines (Appendix A of Convention ETS 123). Experiments were performed in two awake Macaca fascicularis. Each monkey was trained to sit in a primate chair with the head restrained to perform reaching and grasping arm movements in complete darkness while gazing a small fixation point. The object to be grasped was a handle that could have different orientation. We recorded neural activity from 163 neurons of the anterior parietal sulcus; 116/163 (71%) neurons were modulated by the reach-to-grasp task during the execution of the forward movements toward the target (epoch MOV), 111/163 (68%) during the pulling of the handle (epoch HOLD) and 102/163 during the execution of backward movements (epoch M2) (t_test, p ≤ 0.05). About the 45% of the tested cells turned out to be sensitive to the orientation of the handle (one way ANOVA, p ≤ 0.05). To study how the distal components of the movement, such as the hand preshaping during the reaching of the handle, could influence the neuronal discharge, we compared the neuronal activity during the reaching movements towards the same spatial location in reach-to-point and reach-to-grasp tasks. Both tasks required proximal arm movements; only the reach-to-grasp task required distal movements to orient the wrist and to shape the hand to grasp the handle. The 56% of V6A cells showed significant differences in the neural discharge (one way ANOVA, p ≤ 0.05) between the reach-to-point and the reach-to-grasp tasks during MOV, 54% during HOLD and 52% during M2. These data show that reaching and grasping are processed by the same population of neurons, providing evidence that the coordination of reaching and grasping takes place much earlier than previously thought, i.e., in the parieto-occipital cortex. The data here reported are in agreement with results of lesions to the medial posterior parietal cortex in both monkeys and humans, and with recent imaging data in humans, all of them indicating a functional coupling in the control of reaching and grasping by the medial parietofrontal circuit.

Costrutti ed Applicazioni di Programmazione Generica in Linguaggi Object-Oriented

Generic programming is likely to become a new challenge for a critical mass of developers. Therefore, it is crucial to refine the support for generic programming in mainstream Object-Oriented languages — both at the design and at the implementation level — as well as to suggest novel ways to exploit the additional degree of expressiveness made available by genericity. This study is meant to provide a contribution towards bringing Java genericity to a more mature stage with respect to mainstream programming practice, by increasing the effectiveness of its implementation, and by revealing its full expressive power in real world scenario. With respect to the current research setting, the main contribution of the thesis is twofold. First, we propose a revised implementation for Java generics that greatly increases the expressiveness of the Java platform by adding reification support for generic types. Secondly, we show how Java genericity can be leveraged in a real world case-study in the context of the multi-paradigm language integration. Several approaches have been proposed in order to overcome the lack of reification of generic types in the Java programming language. Existing approaches tackle the problem of reification of generic types by defining new translation techniques which would allow for a runtime representation of generics and wildcards. Unfortunately most approaches suffer from several problems: heterogeneous translations are known to be problematic when considering reification of generic methods and wildcards. On the other hand, more sophisticated techniques requiring changes in the Java runtime, supports reified generics through a true language extension (where clauses) so that backward compatibility is compromised. In this thesis we develop a sophisticated type-passing technique for addressing the problem of reification of generic types in the Java programming language; this approach — first pioneered by the so called EGO translator — is here turned into a full-blown solution which reifies generic types inside the Java Virtual Machine (JVM) itself, thus overcoming both performance penalties and compatibility issues of the original EGO translator. Java-Prolog integration Integrating Object-Oriented and declarative programming has been the subject of several researches and corresponding technologies. Such proposals come in two flavours, either attempting at joining the two paradigms, or simply providing an interface library for accessing Prolog declarative features from a mainstream Object-Oriented languages such as Java. Both solutions have however drawbacks: in the case of hybrid languages featuring both Object-Oriented and logic traits, such resulting language is typically too complex, thus making mainstream application development an harder task; in the case of library-based integration approaches there is no true language integration, and some “boilerplate code” has to be implemented to fix the paradigm mismatch. In this thesis we develop a framework called PatJ which promotes seamless exploitation of Prolog programming in Java. A sophisticated usage of generics/wildcards allows to define a precise mapping between Object-Oriented and declarative features. PatJ defines a hierarchy of classes where the bidirectional semantics of Prolog terms is modelled directly at the level of the Java generic type-system.

Development and performance assessment of a Plasma Focus electron beam generator for Intra-Operative Radiation Therapy

The Plasma Focus is a device designed to generate a plasma sheet between two coaxial electrodes by means of a high voltage difference. The plasma is then driven to collapse into a “pinch”, where thermonuclear conditions prevail. During the “pinch phase” charged particles are emitted, with two main components: an ion beam peaked forward and an electron beam directed backward. The electron beam emitted backward by Plasma Focus devices is being investigated as a radiation source for medical applications, using it to produce x-rays by interaction with appropriate targets (through bremsstrahlung and characteristic emission). A dedicated Plasma Focus device, named PFMA-3 (Plasma Focus for Medical Applications number 3), has been designed, put in operation and tested by the research groups of the Universities of Bologna and Ferrara. The very high dose rate (several gray per discharge, in less than 1 µs) is a peculiarity of this device that has to be investigated, as it might modify the relative biological effectiveness (RBE). Aim of this Ph.D. project was to investigate the main physical properties of the low-energy x-ray beams produced by a Plasma Focus device and their potential medical applications to IORT treatments. It was necessary to develop the optimal geometrical configuration; to evaluate the x-rays produced and their dose deposited; to estimate the energy electron spectrum produced in the “pinch phase”; to study an optimal target for the conversion of the x-rays; to conduct simulations to study the physics involved; and in order to evaluate the radio-biological features of the beam, cell holders had to be developed for both irradiations and cell growth conditions.

Analyzing convergence of Agricultural and Rural Areas in the Enlarged EU: The case of Hungary

The fall of the Berlin Wall opened the way for a reform path – the transition process – which accompanied ten former Socialist countries in Central and South Eastern Europe to knock at the EU doors. By the way, at the time of the EU membership several economic and structural weaknesses remained. A tendency towards convergence between the new Member States (NMS) and the EU average income level emerged, together with a spread of inequality at the sub-regional level, mainly driven by the backwardness of the agricultural and rural areas. Several progresses were made in evaluating the policies for rural areas, but a shared definition of rurality is still missing. Numerous indicators were calculated for assessing the effectiveness of the Common Agricultural Policy and Rural Development Policy. Previous analysis on the Central and Eastern European countries found that the characteristics of the most backward areas were insufficiently addressed by the policies enacted; the low data availability and accountability at a sub-regional level, and the deficiencies in institutional planning and implementation represented an obstacle for targeting policies and payments. The next pages aim at providing a basis for understanding the connections between the peculiarities of the transition process, the current development performance of NMS and the EU role, with particular attention to the agricultural and rural areas. Applying a mixed methodological approach (multivariate statistics, non-parametric methods, spatial econometrics), this study contributes to the identification of rural areas and to the analysis of the changes occurred during the EU membership in Hungary, assessing the effect of CAP introduction and its contribution to the convergence of the Hungarian agricultural and rural. The author believes that more targeted – and therefore efficient – policies for agricultural and rural areas require a deeper knowledge of their structural and dynamic characteristics.

Travi in parete sottile con deformabilità a taglio e distorsione di sezione: formulazione teorica, modellazione numerica e applicazioni

Il presente lavoro di tesi ha riguardato una riformulazione teorica, una modellazione numerica e una serie di applicazioni della Generalized Beam Theory per lo studio dei profili in parete sottile con particolare riguardo ai profili in acciaio formati a freddo. In particolare, in questo lavoro è proposta una riscrittura della cinematica GBT che introduce in una forma originale la deformabilità a taglio della sezione. Tale formulazione consente di conservare il formato della GBT classica e introducendo uno spostamento di warping variabile lungo lo spessore della generica parete della sezione trasversale, garantisce perfetta coerenza tra la componente flessionale e tagliante della trave. E' mostrato, come tale riscrittura consente in maniera agevole di ricondursi alle teorie classiche di trave, anche deformabili a taglio. Inoltre, in tale contesto, è stata messa a punto una procedura di ricostruzione dello sforzo tridimensionale in grado ricostruire la parte reattiva delle componenti di tensioni dovuta al vincolamento interno proprio di un modello a cinematica ridotta. Sulla base di tali strumenti, è stato quindi proposto un approccio progettuale dedicato ai profili in classe 4, definito ESA (Embedded Stability Analysis), in grado di svolgere le verifiche coerentemente con quanto prescritto dalle normative vigenti. Viene infine presentata una procedura numerica per la progettazione di sistemi di copertura formati a freddo. Tale procedura permette di effettuare in pochi semplici passi il progetto dell'arcareccio e dei dettagli costruttivi relativi alla copertura.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.

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

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

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.