Noisy Oncology: applications of bounded noise transitions in modelling tumor growth

I tumori macroscopici e microscopici, dopo la loro prima fase di crescita, sono composti da un numero medio elevato di cellule. Così, in assenza di perturbazioni esterne, la loro crescita e i punti di equilibrio possono essere descritti da equazioni differenziali. Tuttavia, il tumore interagisce fortemente col macroambiente che lo circonda e di conseguenza una descrizione del tutto deterministica risulta a volte inappropriata. In questo caso si può considerare l'interazione con fluttuazioni statistiche, causate da disturbi esterni, utilizzando le equazioni differenziali stocastiche (SDE). Questo è vero in modo particolare quando si cerca di modellizzare tumori altamente immunogenici che interagiscono con il sistema immunitario, in quanto la complessità di questa interazione risulta in fenomeni di multistabilità. Così, il rumore può provocare disturbi e indurre transizioni di stato (Noise-Induced-Transitions). E' importante notare che una NIT può avere implicazioni profonde sulla vita di un paziente, dal momento che una transizione da uno stato di equilibrio piccolo, nelle dimensioni del tumore, ad uno stato di equilibrio macroscopico, nella maggior parte dei casi significa il passaggio dalla vita alla morte. Generalmente l'approccio standard è quello di modellizzare le fluttuazioni stocastiche dei parametri per mezzo di rumore gaussiano bianco o colorato. In alcuni casi però questa procedura è altamente inadeguata, a causa della illimitatezza intrinseca dei rumori gaussiani che può portare a gravi incongruenze biologiche: pertanto devono essere utilizzati dei rumori "limitati", che, tuttavia, sono molto meno studiati di quelli gaussiani. Inoltre, l'insorgenza di NIT dipende dal tipo di rumore scelto, che rivela un nuovo livello di complessità in biologia. Lo scopo di questa tesi è quello di studiare le applicazioni di due tipi diversi di "rumori limitati" nelle transizioni indotte in due casi: interazione tra tumore e sistema immunitario e chemioterapia dei tumori. Nel primo caso, abbiamo anche introdotto un nuovo modello matematico di terapia, che estende, in modo nuovo, il noto modello di Norton-Simon.

Effective procedure for the optimization of the linear controller in an industrial drive for a nonlinear mechanism

Il progetto di tesi è incentrato sull’ottimizzazione del procedimento di taratura dei regolatori lineari degli anelli di controllo di posizione e velocità presenti negli azionamenti usati industrialmente su macchine automatiche, specialmente quando il carico è ad inerzia variabile in dipendenza dalla posizione, dunque non lineare, come ad esempio un quadrilatero articolato. Il lavoro è stato svolto in collaborazione con l’azienda G.D S.p.A. ed il meccanismo di prova è realmente utilizzato nelle macchine automatiche per il packaging di sigarette. L’ottimizzazione si basa sulla simulazione in ambiente Matlab/Simulink dell’intero sistema di controllo, cioè comprensivo del modello Simulink degli anelli di controllo del drive, inclusa la dinamica elettrica del motore, e del modello Simscape del meccanismo, perciò una prima necessaria fase del lavoro è stata la validazione di tali modelli affinché fossero sufficientemente fedeli al comportamento reale. Il secondo passo è stato fornire una prima taratura di tentativo che fungesse da punto di partenza per l’algoritmo di ottimizzazione, abbiamo fatto ciò linearizzando il modello meccanico con l’inerzia minima e utilizzando il metodo delle formule di inversione per determinare i parametri di controllo. Già questa taratura, seppur conservativa, ha portato ad un miglioramento delle performance del sistema rispetto alla taratura empirica comunemente fatta in ambito industriale. Infine, abbiamo lanciato l’algoritmo di ottimizzazione definendo opportunamente la funzione di costo, ed il risultato è stato decisamente positivo, portando ad un miglioramento medio del massimo errore di inseguimento di circa il 25%, ma anche oltre il 30% in alcuni casi.

A comprehensive study on robotic manipulation of deformable linear objects

There are many deformable objects such as papers, clothes, ropes in a person’s living space. To have a robot working in automating the daily tasks it is important that the robot works with these deformable objects. Manipulation of deformable objects is a challenging task for robots because these objects have an infinite-dimensional configuration space and are expensive to model, making real-time monitoring, planning and control difficult. It forms a particularly important field of robotics with relevant applications in different sectors such as medicine, food handling, manufacturing, and household chores. In this report, there is a clear review of the approaches used and are currently in use along with future developments to achieve this task. My research is more focused on the last 10 years, where I have systematically reviewed many articles to have a clear understanding of developments in this field. The main contribution is to show the whole landscape of this concept and provide a broad view of how it has evolved. I also explained my research methodology by following my analysis from the past to the present along with my thoughts for the future.

Shear behavior of reinforced concrete slabs under concentrated load: an investigation through Sequentially Linear Analysis

ABSTRACT (italiano) Con crescente attenzione riguardo al problema della sicurezza di ponti e viadotti esistenti nei Paesi Bassi, lo scopo della presente tesi è quello di studiare, mediante la modellazione con Elementi Finiti ed il continuo confronto con risultati sperimentali, la risposta in esercizio di elementi che compongono infrastrutture del genere, ovvero lastre in calcestruzzo armato sollecitate da carichi concentrati. Tali elementi sono caratterizzati da un comportamento ed una crisi per taglio, la cui modellazione è, da un punto di vista computazionale, una sfida piuttosto ardua, a causa del loro comportamento fragile combinato a vari effetti tridimensionali. La tesi è incentrata sull'utilizzo della Sequentially Linear Analysis (SLA), un metodo di soluzione agli Elementi Finiti alternativo rispetto ai classici approcci incrementali e iterativi. Il vantaggio della SLA è quello di evitare i ben noti problemi di convergenza tipici delle analisi non lineari, specificando direttamente l'incremento di danno sull'elemento finito, attraverso la riduzione di rigidezze e resistenze nel particolare elemento finito, invece dell'incremento di carico o di spostamento. Il confronto tra i risultati di due prove di laboratorio su lastre in calcestruzzo armato e quelli della SLA ha dimostrato in entrambi i casi la robustezza del metodo, in termini di accuratezza dei diagrammi carico-spostamento, di distribuzione di tensioni e deformazioni e di rappresentazione del quadro fessurativo e dei meccanismi di crisi per taglio. Diverse variazioni dei più importanti parametri del modello sono state eseguite, evidenziando la forte incidenza sulle soluzioni dell'energia di frattura e del modello scelto per la riduzione del modulo elastico trasversale. Infine è stato effettuato un paragone tra la SLA ed il metodo non lineare di Newton-Raphson, il quale mostra la maggiore affidabilità della SLA nella valutazione di carichi e spostamenti ultimi insieme ad una significativa riduzione dei tempi computazionali. ABSTRACT (english) With increasing attention to the assessment of safety in existing dutch bridges and viaducts, the aim of the present thesis is to study, through the Finite Element modeling method and the continuous comparison with experimental results, the real response of elements that compose these infrastructures, i.e. reinforced concrete slabs subjected to concentrated loads. These elements are characterized by shear behavior and crisis, whose modeling is, from a computational point of view, a hard challenge, due to their brittle behavior combined with various 3D effects. The thesis is focused on the use of Sequentially Linear Analysis (SLA), an alternative solution technique to classical non linear Finite Element analyses that are based on incremental and iterative approaches. The advantage of SLA is to avoid the well-known convergence problems of non linear analyses by directly specifying a damage increment, in terms of a reduction of stiffness and strength in the particular finite element, instead of a load or displacement increment. The comparison between the results of two laboratory tests on reinforced concrete slabs and those obtained by SLA has shown in both the cases the robustness of the method, in terms of accuracy of load-displacements diagrams, of the distribution of stress and strain and of the representation of the cracking pattern and of the shear failure mechanisms. Different variations of the most important parameters have been performed, pointing out the strong incidence on the solutions of the fracture energy and of the chosen shear retention model. At last a confrontation between SLA and the non linear Newton-Raphson method has been executed, showing the better reliability of the SLA in the evaluation of the ultimate loads and displacements, together with a significant reduction of computational times.

Numerical Analysis and Redesign of a High Speed Linear Cascade Wind Tunnel for Aircraft Gas Turbine Engines Testing

Linear cascade testing serves a fundamental role in the research, development, and design of turbomachines as it is a simple yet very effective way to compute the performance of a generic blade geometry. These kinds of experiments are usually carried out in specialized wind tunnel facilities. This thesis deals with the numerical characterization and subsequent partial redesign of the S-1/C Continuous High Speed Wind Tunnel of the Von Karman Institute for Fluid Dynamics. The current facility is powered by a 13-stage axial compressor that is not powerful enough to balance the energy loss experienced when testing low turning airfoils. In order to address this issue a performance assessment of the wind tunnel was performed under several flow regimes via numerical simulations. After that, a redesign proposal aimed at reducing the pressure loss was investigated. This consists of a linear cascade of turning blades to be placed downstream of the test section and designed specifically for the type of linear cascade being tested. An automatic design procedure was created taking as input parameters those measured at the outlet of the cascade. The parametrization method employed Bézier curves to produce an airfoil geometry that could be imported into a CAD software so that a cascade could be designed. The proposal was simulated via CFD analysis and proved to be effective in reducing pressure losses up to 41%. The same tool developed in this thesis could be adopted to design similar apparatuses and could also be optimized and specialized for the design of turbomachines components.

Seismic mitigation of existing masonry structures by means of added damping and stiffness

In this work seismic upgrading of existing masonry structures by means of hysteretic ADAS dampers is treated. ADAS are installed on external concrete walls, which are built parallel to the building, and then linked to the building's slab by means of steel rod connection system. In order to assess the effectiveness of the intervention, a parametric study considering variation of damper main features has been conducted. To this aim, the concepts of equivalent linear system (ELS) or equivalent viscous damping are deepen. Simplified equivalent linear model results are then checked respect results of the yielding structures. Two alternative displacement based methods for damper design are herein proposed. Both methods have been validated through non linear time history analyses with spectrum compatible accelerograms. Finally ADAS arrangement for the non conventional implementation is proposed.

Origin of cold gas and dust in massive elliptical galaxies

The recent availability of multi-wavelength data revealed the presence of large reservoirs of warm and cold gas and dust in the innermost regions of the majority of massive elliptical galaxies. To prove an internal origin of cold and warm gas, the investigation of the spatially distributed cooling process which occurs because of non-linear density perturbations and subsequent thermal instabilities is of crucial importance. The first goal of this work of thesis is to investigate the internal origin of warm and cold phases. Numerical simulations are the powerful tool of analysis. The way in which a spatially distributed cooling process originates has been examined and the off-centre amount of gas mass which cools when different and differently characterized AGN feedback mechanisms operate has been quantified. This thesis demonstrates that the aforementioned non-linear density perturbations originate and develop from AGN feedback mechanisms in a natural fashion. An internal origin of the warm phase from the once hot gas is shown to be possible. Computed velocity dispersions of ionized and hot gas are similar. The cold gas as well can originate from the cooling process: indeed, it has been estimated that the surrounding stellar radiation, which is one of the most feasible sources of ionization of the warm gas, does not manage to keep ionized all the gas at 10^4 K. Therefore, cooled gas does undergo a further cooling which can lead the warm phase to lower temperatures. However, the gas which has cooled from the hot phase is expected to be dustless; nonetheless, a large fraction of early type galaxies has detectable dust in their cores, both concentrated in filamentary and disky structures and spread over larger regions. Therefore a regularly rotating disk of cold and dusty gas has been included in the simulations. A new quantitative investigation of the spatially distributed cooling process has therefore been essential: the contribution of the included amount of dust which is embedded in the cold gas does have a role in promoting and enhancing the cooling. The fate of dust which was at first embedded in cold gas has been investigated. The role of AGN feedback mechanisms in dragging (if able) cold and dusty gas from the core of massive ellipticals up to large radii has been studied.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

Tomographic 3D reconstruction through linear inversion for breast microwave imaging

In the present thesis we address the problem of detecting and localizing a small spherical target with characteristic electrical properties inside a volume of cylindrical shape, representing female breast, with MWI. One of the main works of this project is to properly extend the existing linear inversion algorithm from planar slice to volume reconstruction; results obtained, under the same conditions and experimental setup are reported for the two different approaches. Preliminar comparison and performance analysis of the reconstruction algorithms is performed via numerical simulations in a software-created environment: a single dipole antenna is used for illuminating the virtual breast phantom from different positions and, for each position, the corresponding scattered field value is registered. Collected data are then exploited in order to reconstruct the investigation domain, along with the scatterer position, in the form of image called pseudospectrum. During this process the tumor is modeled as a dielectric sphere of small radius and, for electromagnetic scattering purposes, it's treated as a point-like source. To improve the performance of reconstruction technique, we repeat the acquisition for a number of frequencies in a given range: the different pseudospectra, reconstructed from single frequency data, are incoherently combined with MUltiple SIgnal Classification (MUSIC) method which returns an overall enhanced image. We exploit multi-frequency approach to test the performance of 3D linear inversion reconstruction algorithm while varying the source position inside the phantom and the height of antenna plane. Analysis results and reconstructed images are then reported. Finally, we perform 3D reconstruction from experimental data gathered with the acquisition system in the microwave laboratory at DIFA, University of Bologna for a recently developed breast-phantom prototype; obtained pseudospectrum and performance analysis for the real model are reported.

Rheological Characterization of Bitumen and Asphalt including the effect of Added-recycled Material

This thesis evaluates the rheological behaviour of asphalt mixtures and the corresponding extracted binders from the mixtures containing different amounts of Reclaimed Asphalt (RA). Generally, the use of RA is limited to certain amounts. The study materials are Stone Mastic Asphalts including a control sample with 0% RA, and other samples with RA rates of 30%, 60% and 100%. Another set of studied mixtures are Asphalt Concretes (AC) types with again a control mix having 0% RA rate and the other mixtures designs containing 30%, 60% and 90% of reclaimed asphalt which also contain additives. In addition to the bitumen samples extracted from asphalt mixes, there are bitumen samples directly extracted from the original RA. To characterize the viscoelastic behaviour of the binders, Dynamic Shear Rheometer (DSR) tests were conducted on bitumen specimens. The resulting influence of the RA content in the bituminous binders are illustrated through master curves, black diagrams and Cole-Cole plots with regressing these experimental data by the application of the analogical 2S2P1D and the analytical CA model. The advantage of the CA model is in its limited number of parameters and thus is a simple model to use. The 2S2P1D model is an analogical rheological model for the prediction of the linear viscoelastic properties of both asphalt binders and mixtures. In order to study the influence of RA on mixtures, the Indirect Tensile Test (ITT) has been conducted. The master curves of different mixture samples are evaluated by regressing the test data points to a sigmoidal function and subsequently by comparing the master curves, the influence of RA materials is studied. The thesis also focusses on the applicability and also differences of CA model and 2S2P1D model for bitumen samples and the sigmoid function for the mixtures and presents the influence of the RA rate on the investigated model parameters.

Evaluation of confidence-driven cost aggregation strategies

In this thesis I describe eight new stereo matching algorithms that perform the cost-aggregation step using a guided filter with a confidence map as guidance image, and share the structure of a linear stereo matching algorithm. The results of the execution of the proposed algorithms on four pictures from the Middlebury dataset are shown as well. Finally, based on these results, a ranking of the proposed algorithms is presented.

Magnetic field in the outskirts of PSZ2 G096.88+24.18 from depolarization analysis of radio relics

Radio relics are one of the different types of diffuse radio sources present in a fraction of galaxy clusters. They are characterized by elongated arc-like shapes, with sizes that range between 0.5 and 2 Mpc, and highly polarized emission (up to ∼60%) at GHz frequencies The linearly polarized radiation of relics, moving through a magnetized plasma which is the ICM, is affected by the rotation of the linear polarization vector. This effect, known as “Faraday rotation”, can cause depolarization. The study of this effect allows us to constrain the magnetic field projected along the line of sight. The aim of this thesis work is to constrain the magnetic field intensity and distribution in the periphery of the cluster PSZ2 G096.88+24.18: this cluster hosts a pair of radio relics that can be used for polarization analysis. To analyse the polarization properties of the relics in PSZ2 G096.88+24.18 radio relics we used new Jansky Very Large Array (VLA) observations together with archival observations. The polarization study has been performed using the Rotation Measure Synthesis technique, which allows us to recover polarization, minimizing the bandwidth depolarization. Thanks to this technique, we recovered more polarization from the southern relic (with respect to provious works), We studied also the depolarization trend with the resolution for the southern relic, and found that the polarization fraction decreases with the beamsize. Finally, we have produced simulated magnetic fields models, varying the auto-correlation lengths of the magnetic field, in order to reproduce the observed depolarization trend in the southern relic. Comparing our observational results and model predictions, we were able to constrain the scales over which the turbulent magnetic field varies within the cluster. We conclude that the depolarization observed in the southern relic is likely due to external depolarization caused by the magnetized ICM distribution within the cluster.