11 resultados para Bayesian hierarchical linear model

em AMS Tesi di Dottorato - Alm@DL - Università di Bologna


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Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software. Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.

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The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

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A new methodology is being devised for ensemble ocean forecasting using distributions of the surface wind field derived from a Bayesian Hierarchical Model (BHM). The ocean members are forced with samples from the posterior distribution of the wind during the assimilation of satellite and in-situ ocean data. The initial condition perturbations are then consistent with the best available knowledge of the ocean state at the beginning of the forecast and amplify the ocean response to uncertainty only in the forcing. The ECMWF Ensemble Prediction System (EPS) surface winds are also used to generate a reference ocean ensemble to evaluate the performance of the BHM method that proves to be eective in concentrating the forecast uncertainty at the ocean meso-scale. An height month experiment of weekly BHM ensemble forecasts was performed in the framework of the operational Mediterranean Forecasting System. The statistical properties of the ensemble are compared with model errors throughout the seasonal cycle proving the existence of a strong relationship between forecast uncertainties due to atmospheric forcing and the seasonal cycle.

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

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This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

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In Performance-Based Earthquake Engineering (PBEE), evaluating the seismic performance (or seismic risk) of a structure at a designed site has gained major attention, especially in the past decade. One of the objectives in PBEE is to quantify the seismic reliability of a structure (due to the future random earthquakes) at a site. For that purpose, Probabilistic Seismic Demand Analysis (PSDA) is utilized as a tool to estimate the Mean Annual Frequency (MAF) of exceeding a specified value of a structural Engineering Demand Parameter (EDP). This dissertation focuses mainly on applying an average of a certain number of spectral acceleration ordinates in a certain interval of periods, Sa,avg (T1,…,Tn), as scalar ground motion Intensity Measure (IM) when assessing the seismic performance of inelastic structures. Since the interval of periods where computing Sa,avg is related to the more or less influence of higher vibration modes on the inelastic response, it is appropriate to speak about improved IMs. The results using these improved IMs are compared with a conventional elastic-based scalar IMs (e.g., pseudo spectral acceleration, Sa ( T(¹)), or peak ground acceleration, PGA) and the advanced inelastic-based scalar IM (i.e., inelastic spectral displacement, Sdi). The advantages of applying improved IMs are: (i ) "computability" of the seismic hazard according to traditional Probabilistic Seismic Hazard Analysis (PSHA), because ground motion prediction models are already available for Sa (Ti), and hence it is possibile to employ existing models to assess hazard in terms of Sa,avg, and (ii ) "efficiency" or smaller variability of structural response, which was minimized to assess the optimal range to compute Sa,avg. More work is needed to assess also "sufficiency" and "scaling robustness" desirable properties, which are disregarded in this dissertation. However, for ordinary records (i.e., with no pulse like effects), using the improved IMs is found to be more accurate than using the elastic- and inelastic-based IMs. For structural demands that are dominated by the first mode of vibration, using Sa,avg can be negligible relative to the conventionally-used Sa (T(¹)) and the advanced Sdi. For structural demands with sign.cant higher-mode contribution, an improved scalar IM that incorporates higher modes needs to be utilized. In order to fully understand the influence of the IM on the seismis risk, a simplified closed-form expression for the probability of exceeding a limit state capacity was chosen as a reliability measure under seismic excitations and implemented for Reinforced Concrete (RC) frame structures. This closed-form expression is partuclarly useful for seismic assessment and design of structures, taking into account the uncertainty in the generic variables, structural "demand" and "capacity" as well as the uncertainty in seismic excitations. The assumed framework employs nonlinear Incremental Dynamic Analysis (IDA) procedures in order to estimate variability in the response of the structure (demand) to seismic excitations, conditioned to IM. The estimation of the seismic risk using the simplified closed-form expression is affected by IM, because the final seismic risk is not constant, but with the same order of magnitude. Possible reasons concern the non-linear model assumed, or the insufficiency of the selected IM. Since it is impossibile to state what is the "real" probability of exceeding a limit state looking the total risk, the only way is represented by the optimization of the desirable properties of an IM.

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Leaf rust caused by Puccinia triticina is a serious disease of durum wheat (Triticum durum) worldwide. However, genetic and molecular mapping studies aimed at characterizing leaf rust resistance genes in durum wheat have been only recently undertaken. The Italian durum wheat cv. Creso shows a high level of resistance to P. triticina that has been considered durable and that appears to be due to a combination of a single dominant gene and one or more additional factors conferring partial resistance. In this study, the genetic basis of leaf rust resistance carried by Creso was investigated using 176 recombinant inbred lines (RILs) from the cross between the cv. Colosseo (C, leaf rust resistance donor) and Lloyd (L, susceptible parent). Colosseo is a cv. directly related to Creso with the leaf rust resistance phenotype inherited from Creso, and was considered as resistance donor because of its better adaptation to local (Emilia Romagna, Italy) cultivation environment. RILs have been artificially inoculated with a mixture of 16 Italian P. triticina isolates that were characterized for virulence to seedlings of 22 common wheat cv. Thatcher isolines each carrying a different leaf rust resistance gene, and for molecular genotypes at 15 simple sequence repeat (SSR) loci, in order to determine their specialization with regard to the host species. The characterization of the leaf rust isolates was conducted at the Cereal Disease Laboratory of the University of Minnesota (St. Paul, USA) (Chapter 2). A genetic linkage map was constructed using segregation data from the population of 176 RILs from the cross CL. A total of 662 loci, including 162 simple sequence repeats (SSRs) and 500 Diversity Arrays Technology markers (DArTs), were analyzed by means of the package EasyMap 0.1. The integrated SSR-DArT linkage map consisted of 554 loci (162 SSR and 392 DArT markers) grouped into 19 linkage blocks with an average marker density of 5.7 cM/marker. The final map spanned a total of 2022 cM, which correspond to a tetraploid genome (AABB) coverage of ca. 77% (Chapter 3). The RIL population was phenotyped for their resistance to leaf rust under artificial inoculation in 2006; the percentage of infected leaf area (LRS, leaf rust susceptibility) was evaluated at three stages through the disease developmental cycle and the area under disease progress curve (AUDPC) was then calculated. The response at the seedling stage (infection type, IT) was also investigated. QTL analysis was carried out by means of the Composite Interval Mapping method based on a selection of markers from the CL map. A major QTL (QLr.ubo-7B.2) for leaf rust resistance controlling both the seedling and the adult plant response, was mapped on the distal region of chromosome arm 7BL (deletion bin 7BL10-0.78-1.00), in a gene-dense region known to carry several genes/QTLs for resistance to rusts and other major cereal fungal diseases in wheat and barley. QLr.ubo-7B.2 was identified within a supporting interval of ca. 5 cM tightly associated with three SSR markers (Xbarc340.2, Xgwm146 e Xgwm344.2), and showed an R2 and an LOD peak value for the AUDPC equal to 72.9% an 44.5, respectively. Three additional minor QTLs were also detected (QLr.ubo-7B.1 on chr. 7BS; QLr.ubo-2A on chr. 2AL and QLr.ubo-3A on chr. 3AS) (Chapter 4). The presence of the major QTL (QLr.ubo-7B.2) was validated by a linkage disequilibrium (LD)-based test using field data from two different plant materials: i) a set of 62 advanced lines from multiple crosses involving Creso and his directly related resistance derivates Colosseo and Plinio, and ii) a panel of 164 elite durum wheat accessions representative of the major durum breeding program of the Mediterranean basin. Lines and accessions were phenotyped for leaf rust resistance under artificial inoculation in two different field trials carried out at Argelato (BO, Italy) in 2006 and 2007; the durum elite accessions were also evaluated in two additional field experiments in Obregon (Messico; 2007 and 2008) and in a green-house experiment (seedling resistance) at the Cereal Disease Laboratory (St. Paul, USA, 2008). The molecular characterization involved 14 SSR markers mapping on the 7BL chromosome region found to harbour the major QTL. Association analysis was then performed with a mixed-linear-model approach. Results confirmed the presence of a major QTL for leaf rust resistance, both at adult plant and at seedling stage, located between markers Xbarc340.2, Xgwm146 and Xgwm344.2, in an interval that coincides with the supporting interval (LOD-2) of QLr.ubo-7B.2 as resulted from the RIL QTL analysis. (Chapter 5). The identification and mapping of the major QTL associated to the durable leaf rust resistance carried by Creso, together with the identification of the associated SSR markers, will enhance the selection efficiency in durum wheat breeding programs (MAS, Marker Assisted Selection) and will accelerate the release of cvs. with durable resistance through marker-assisted pyramiding of the tagged resistance genes/QTLs most effective against wheat fungal pathogens.

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Introduction: Nocturnal frontal lobe epilepsy (NFLE) is a distinct syndrome of partial epilepsy whose clinical features comprise a spectrum of paroxysmal motor manifestations of variable duration and complexity, arising from sleep. Cardiovascular changes during NFLE seizures have previously been observed, however the extent of these modifications and their relationship with seizure onset has not been analyzed in detail. Objective: Aim of present study is to evaluate NFLE seizure related changes in heart rate (HR) and in sympathetic/parasympathetic balance through wavelet analysis of HR variability (HRV). Methods: We evaluated the whole night digitally recorded video-polysomnography (VPSG) of 9 patients diagnosed with NFLE with no history of cardiac disorders and normal cardiac examinations. Events with features of NFLE seizures were selected independently by three examiners and included in the study only if a consensus was reached. Heart rate was evaluated by measuring the interval between two consecutive R-waves of QRS complexes (RRi). RRi series were digitally calculated for a period of 20 minutes, including the seizures and resampled at 10 Hz using cubic spline interpolation. A multiresolution analysis was performed (Daubechies-16 form), and the squared level specific amplitude coefficients were summed across appropriate decomposition levels in order to compute total band powers in bands of interest (LF: 0.039062 - 0.156248, HF: 0.156248 - 0.624992). A general linear model was then applied to estimate changes in RRi, LF and HF powers during three different period (Basal) (30 sec, at least 30 sec before seizure onset, during which no movements occurred and autonomic conditions resulted stationary); pre-seizure period (preSP) (10 sec preceding seizure onset) and seizure period (SP) corresponding to the clinical manifestations. For one of the patients (patient 9) three seizures associated with ictal asystole were recorded, hence he was treated separately. Results: Group analysis performed on 8 patients (41 seizures) showed that RRi remained unchanged during the preSP, while a significant tachycardia was observed in the SP. A significant increase in the LF component was instead observed during both the preSP and the SP (p<0.001) while HF component decreased only in the SP (p<0.001). For patient 9 during the preSP and in the first part of SP a significant tachycardia was observed associated with an increased sympathetic activity (increased LF absolute values and LF%). In the second part of the SP a progressive decrease in HR that gradually exceeded basal values occurred before IA. Bradycardia was associated with an increase in parasympathetic activity (increased HF absolute values and HF%) contrasted by a further increase in LF until the occurrence of IA. Conclusions: These data suggest that changes in autonomic balance toward a sympathetic prevalence always preceded clinical seizure onset in NFLE, even when HR changes were not yet evident, confirming that wavelet analysis is a sensitive technique to detect sudden variations of autonomic balance occurring during transient phenomena. Finally we demonstrated that epileptic asystole is associated with a parasympathetic hypertonus counteracted by a marked sympathetic activation.

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This work presents exact algorithms for the Resource Allocation and Cyclic Scheduling Problems (RA&CSPs). Cyclic Scheduling Problems arise in a number of application areas, such as in hoist scheduling, mass production, compiler design (implementing scheduling loops on parallel architectures), software pipelining, and in embedded system design. The RA&CS problem concerns time and resource assignment to a set of activities, to be indefinitely repeated, subject to precedence and resource capacity constraints. In this work we present two constraint programming frameworks facing two different types of cyclic problems. In first instance, we consider the disjunctive RA&CSP, where the allocation problem considers unary resources. Instances are described through the Synchronous Data-flow (SDF) Model of Computation. The key problem of finding a maximum-throughput allocation and scheduling of Synchronous Data-Flow graphs onto a multi-core architecture is NP-hard and has been traditionally solved by means of heuristic (incomplete) algorithms. We propose an exact (complete) algorithm for the computation of a maximum-throughput mapping of applications specified as SDFG onto multi-core architectures. Results show that the approach can handle realistic instances in terms of size and complexity. Next, we tackle the Cyclic Resource-Constrained Scheduling Problem (i.e. CRCSP). We propose a Constraint Programming approach based on modular arithmetic: in particular, we introduce a modular precedence constraint and a global cumulative constraint along with their filtering algorithms. Many traditional approaches to cyclic scheduling operate by fixing the period value and then solving a linear problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model and tackles the problem as a whole: the period value is inferred from the scheduling decisions. The proposed approaches have been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances achieving good results on practical size problem.

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L’Inserimento Eterofamigliare Supportato di Adulti (IESA) sofferenti di disturbi psichici consiste nell’accogliere persone in cura presso i servizi psichiatrici territoriali, nel proprio domicilio, integrandole nelle proprie relazioni famigliari. Obiettivo è migliorare la qualità di vita dell’utente e favorirne l’integrazione nella comunità. Obiettivo. Valutare gli esiti dello IESA, con un disegno di ricerca longitudinale, considerando: psicopatologia, benessere psicologico, funzionamento sociale e familiare. Metodologia. 40 soggetti: 20 pazienti e 20 ospitanti. La valutazione clinica è stata effettuata all’inizio della convivenza e al follow-up di 1, 3, 6 e 12 mesi. Strumenti utilizzati: BPRS, VGF, PWB, SQ, FAD. Analisi statistica: Modello Lineare Generale (GLM) con l’Analisi della Varianza per prove ripetute e calcolo dell’effect-size. Risultati. 15 pazienti maschi e 5 femmine, 17 italiani. 11 soddisfano i criteri diagnostici (DSM-IV-TR) per schizofrenia e disturbi psicotici, 5 per i disturbi dell’umore e 4 per i disturbi di personalità. Dopo l’inserimento 3 sono stati i ricoveri e 4 le visite psichiatriche urgenti. 8 pazienti modificano/diminuiscono la terapia e 3 la sospendono. Aumenta il benessere psicologico (PWB); diminuiscono i sintomi psicopatologici (BPRS ed SQ) e migliora il funzionamento globale (VFG). Il gruppo dei famigliari composto da 11 uomini e 9 donne, 19 di nazionalità italiana; con età media di 55 anni. 8 sono coniugati, 6 celibi/nubili, 4 divorziati e 2 vedovi. 9 hanno figli, 11 lavorano e 8 sono pensionati. Nei famigliari aumenta il benessere psicologico (PWB), migliora il funzionamento famigliare (FAD) e la valutazione del funzionamento globale (VGF) rimane costante nel tempo. Discussioni e conclusioni. Il progetto IESA sembra migliorare la psicopatologia, con una diminuzione dei comportamenti maladattativi e un aumento delle capacità relazionali dell’ospite favorendone l’integrazione. Inoltre, lo IESA sembra diminuire i costi della cronicità psichiatrica: diminuzione degli accessi al Pronto Soccorso, delle visite psichiatriche urgenti e delle giornate di ricovero.

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This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.