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Construction and analysis of subdivision schemes from a linear algebra perspective.
Get PDFSubdivision schemes are efficient tools for generating smooth curves and surfaces as limit of an iterative algorithm based on simple refinement rules starting from few control points defining a polyline or a mesh. Aim of this thesis is to give a complete framework regarding the tools used for the analysis of subdivision schemes and to exploit them to construct new subdivision schemes. We focus our attention on some linear algebra structures that allow to give an exhaustive characterization on the analysis of convergence and smoothness of the limit curves and surfaces produced. Moreover, we propose general sufficient conditions to check the convergence of non-stationary subdivision schemes on arbitrary manifold topology meshes, exploiting the eigenproperties of a block-circulant matrix. These linear algebra tools are fundamental for the construction and analysis of subdivision schemes on arbitrary manifold topology meshes. The use of this kind of meshes is extremely important: regular meshes do not allow us to design the complex models used in computer aided design as well as in biomedical imaging segmentation. Moreover, non-stationary subdivision schemes allow us to design particular shapes such as ellipsoids and tori, thanks to their capability of generating exponential polynomials. In the univariate setting, to work out necessary and sufficient conditions for the Cr continuity of a subdivision scheme, we should exploit the joint spectral radius of a set of matrices
Single- and multi-population kinetic models for vehicular traffic reproducing fundamental diagrams and with low computational complexity.
Get PDFIn this work, we focus on kinetic theory of vehicular traffic. We introduce (Boltzmann and Fokker-Planck) models having the following properties: they are amenable for computations and analytical investigations, but at the same time they are able to characterize and to explain the features of experimental diagrams.
The scattering observed in experimental data is reproduced by a multi-population model. We propose a new interpretation of the dispersion of data since it can be attributed to the heterogeneous composition of the flow. In fact, the scattering is obtained by treating traffic as a mixture of vehicles with different physical and kinematic characteristics.
The multi-population model is built as generalization of a new single-population model for which the analytical expression of the steady state can be computed explicitly. This is possible thanks to the particular choice of the microscopic interactions. These models are able to catch the macroscopic properties of the flow at equilibrium, as the phase transition, the capacity drop and the scattering of data.
The proposed models are endowed with a robust mathematical structure. We study the mathematical properties which induce the structure of diagrams, the well posedness with the existence and uniqueness proof of the solution of the kinetic equations.
A further result of this thesis is the analysis of the effects of the microscopic interactions on the macroscopic dynamics. This purely multiscale issue which is tackled by an asymptotic study of the model in the Fokker-Planck limit
Low temperature theoretical and numerical study of structural glasses.
Get PDFLe proprietà termiche e dielettriche dei vetri alle basse temperature (1K) sono generalmente attribuite all’esistenza dei sistemi di tunneling in potenziali a doppia buca asimmetrica del landscape di energia potenziale. Attraverso un’estensione del modello teorico che descrive la fenomenologia dei vetri alle basse temperature e assumendo un nuovo tipo di sistema di tunneling, costituito da un potenziale a tre buche, abbiamo spiegato dei recenti dati sperimentali in presenza di campo magnetico. I fit ottenuti con il modello teorico per la magnetizzazione sono in accordo con i dati sperimentali.
Inoltre i calcoli effettuati con un modello esteso sino a quattro buche di potenziale hanno mostrato che il modello più semplice in grado di spiegare le anomalie dei dati sperimentali nei vetri reali è proprio quello a tre buche.
Le estensive simulazioni numeriche condotte presso il Laboratorio dell’Università di Montpellier hanno permesso di far luce sulla natura dei sistemi di tunneling. Il nuovo metodo EIS che abbiamo implementato è stato preliminarmente validato at-
traverso simulazioni di un cristallo FCC di tipo Lennard-Jones. Nel seguito la stessa procedura è stata applicata ad un modello di vetro, la miscela binaria Lennard-Jones. Le configurazioni analizzate, a bassissime temperature (ottenute con la tecnica del parallel tempering) mostrano l’esistenza di “valli” interne nel bacino dei minimi del landscape di energia potenziale. Le geometrie trovate sembrerebbero essere legate ai sistemi di tunneling, dunque tale risultato può essere considerato in linea di principio come una prima evidenza di tali sistemi nelle simulazioni numeriche
A multi-scale study of fibrin gels formation: from the early phases to the final network.
No full textFibrin gel polymerization, key element of blood coagulation, produces the network inside which platelets and other blood components are trapped, forming the hemostatic plug that stops bleeding. As fully biocompatible materials with extraordinary mechanical properties, fibrin gels are ideal substrates for many biotechnological applications.
By studying the early phases of polymerization, using simultaneous Small Angle X-ray Scattering and Wide Angle Light Scattering, we defined a new polymerization model in which single-bonded "Y Ladder" polymers rapidly elongate before undergoing a delayed transition to the traditional double-stranded fibrils.
Completely formed fibrin gel appears as a fractal collection of straight fibers, almost monodisperse in diameter and connected together at nodal points with a branching order 3-4. Taking into account these features, we implemented a simple iterative algorithm able to generate in silico gels. The resulting 3D network resembles real fibrin gels and can be sketched as an assembly of densely packed fractal blobs. Using this model we refined the analytical expression of the form factor which is capable of accurately fitting the Light Scattering data, giving the gels' structural parameters.
By globally fitting Low Angle Elastic Light Scattering data with the refined form factor and Turbidimetry data with a function obtained by angularly integrating the scattering form factor, all the parameters characterizing the gel can be robustly recovered.
Finally we have also developed a 2D method for the determination of the gel pore size that analyze thin stacks of randomly sampled thresholded 3D confocal images
Lager e Gulag. Riflessioni sulla società concentrazionaria.
Get PDFLager e Gulag. Riflessioni sulla società concentrazionaria is about Nazi and Soviet Concentration Camps. It tries to show that this subject is still relevant, not only because Concentration Camp as an institution has never disappeared, but also because what happened in Germany and Russia in the first part of the XX century concerns Contemporary Age, so every human being today and in the future: that's why Lager e Gulag intends to be more than a descriptive monograph about the most impressive tragedy of the history. We could say that this work investigates a representative set of factors involved in the matter of totalitarian camps, from a philosophical, anthropological and theological perspective. It is divided in two parts: the first one deals with Concentration Camps in general (chapter I) and Nazi and Soviet Camps in particular (chapters II and III), seen as spaces where time, bodies and minds are brutally controlled by the authorities in order to dominate prisoners. The second one deals with disciplines and topics strictly connected with life and thinking inside Concentration Camps: biopolitics (chapter IV), behaviours (chapter V), faith (chapter VI); the quest for God after Auschwitz and Kolyma, the problem of evil and human nature (chapter VII). This Ph.D. thesis is therefore an attempt to focus on two different forms of the same “world apart”
Equivalence relations and operators on ordered algebraic structures with difference.
Get PDFThis work concerns algebraic models of fuzzy and many-valued propositional logics, in particular Boolean Algebras, Heyting algebras, GBL-algebras and their dual structures, and partial algebras.
The central idea is the representation of complex structures through simpler structures and equivalence relations on them: in order to achieve this, a structure is often considered under two points of view, as total algebra and partial algebra. The equivalence relations which allow the representation are congruences of partial algebras.
The first chapter introduces D-posets, the partial algebraic structures used for this representation, which generalize Boolean algebras and MV-algebras.
The second chapter is a study of congruences on D-posets and the structure of the quotients, in particular for congruences induced by some kinds of idempotent operators, here called S-operators. The case of Boolean algebras and MV-algebras is studied more in detail.
The third chapter introduces GBL-algebras and their dual, and shows how the interplay of an S-operator with a closure operator gives rise to a dual GBL-algebra. Other results about the representation of finite GBL-algebras and GBL*algebras (GBL-algebras with monoidal sum), part of two papers previously published, are summarized and put in relation with the other results of this work
Molecular characterization of nosocomial infections: an Italian (KPC-producing Klebsiella pneumoniae) and a Spanish (Clostridium difficile ribotype 027) experience
Get PDFDuring the last decade, Clostridium difficile and Klebsiella pneumoniae represented two of the most emblematic cause of nosocomial outbreaks, especially following the spread of epidemic variants, able to produce virulent factors and to present higher resistance against several antimicrobial classes.
The rapid identification of dangerous pathogens circulating in nosocomial environment has been made possible by the contribution of molecular methods in support to the classical diagnostic techniques.
The principal objective of this work is to highlight the effectiveness of different molecular typing techniques in the characterization of nosocomial infections, evidencing the genetic relatedness among isolates and the transmission routes of strains involved in epidemic events.
In the first part of the work (Chapter one), the analysis of the principal molecular and phenotypic features of clinical isolates of KPC-producing K. pneumoniae collected in a 27-months period at Ospedale di Circolo e Fondazione Macchi (Varese, Italy) is reported.
Of the 16 isolates analyzed, 7 were involved in an outbreak occurred the Intensive Care Unit (ICU). We investigated the presence of genes involved in carbapenemases resistance (i.e. blaKPC, blaIMP, blaNDM, blaVIM, and blaOXA), the expression of genes for virulence factors (pili/fimbriae, capsular antigen, hypermucousviscosity protein, and siderophores), and mutations leading to colistin resistance.
We also made a phylogenetic analysis adding all the 16 genomes to 319 genomes that represent the global diversity of K. pneumoniae strains.
We found that all isolates analyzed belong to clonal complex CG258. This finding is not surprising, considering previous reports that showed the worldwide diffusion and high prevalence of this clonal group among carbapenem-resistant K. pneumoniae strains. Interestingly, three of the four previously identified groups of Italian isolates of CG258 were found circulating in the hospital, suggesting that several entrance events of the clones may occur over the study period.
About resistance genes, we showed that all 16 genomes express blaKPC genes and none of them had other known carbapenem-resistance genes. Interestingly, 10 of the sixteen isolates, which were colistin-resistance, presented IS5-like transposons in mgrB gene, conferring resistance to this drug.
The second part of the work (Chapter two) aimed to identify and characterize all the clinical isolates of Clostridium difficile ribotype 027 (here, briefly CD027) collected during a 20-months period in the Hospital General Universitario Gregorio Marañon (Madrid, Spain).
The main objective was to characterize the epidemiological links among the CD027 clinical isolates and to defining their transmission routes. To better understand the epidemiological relationships between the strains, all cases identified since January 2014 were added to the analyses. Besides, presence of genetic markers (i.e. mutation in gyrA gene) characterizing the evolution and spread of specific epidemic lineages of CD027 was investigated.
During a 20-months period (January 2014-August 2015), 132 first episodes of C. difficile ribotype 027 has been detected, distinguishing 9 different subtypes (MLVA-types), organized in 5 different clonal complexes (CC) and 4 unique MLVA-patterns. Specifically, one of the five clonal groups (named MLVA-type 1) was responsible of an outbreak which involved 111 patients, and quickly spread in the hospital from October 2014. MLVA typing analysis showed the close genetic relationship of all the strains, suggesting the evolution from a common ancestor. All CD027 isolates carried a specific mutation in gyrA genes, indicating the presence of high transmissible clones belonging to CD027 lineages, but this do not provide more information on their dissemination course.
Moreover, the clonal complexes showed different capacity of spread, which was evidenced by the dissemination of the only CC of MLVA-type 1 leading to the epidemic event.
For this reason, the second objective of Chapter two aimed to evaluate the possible correlation between the transmissibility of the analyzed CD027 clinical isolates and the ability to sporulate. An in vitro protocol has been performed for the evaluation of sporulation rate of epidemic CD027 strain comparing them with those of the ribotype 001, with the objective of determining whether the increased transmissibility of CD027 is due to the greater ability to release endospores into the environment. Comparison between strains belonging to the same ribotype was performed, to evaluate the possible association between sporulation rate and transmissibility.
We found that CD027 strains possessed higher capacity (p=0.005) to produce spores respect to isolates belonging to CD001 but surprisingly their germination ability was significantly lower (p=0.0008) compared to that of CD001, leading to reflect on the adaptability of this pathogen to the environment and the complexity of the mechanisms regulating pathogenic capacity.
Once characterized the rapid spread of an outbreak due to a particular CD027 clone (MLVA-type 1), a further aim was to highlight the possible differences between the efficiency of sporulation and germination of strains belonging to the same ribotype but with different transmission characteristics, underlying the possible association between the ability of sporulation and the strain transmissibility.
Moreover, analysis showed non-significant strain-to-strain variability between C. difficile isolates belonging to the ribotype 027; in particular, comparison was conducted between highly transmissible MLVA-type 1 isolates and the other MLVA-types, showing that neither in sporulation rate (p value =0.72) nor in germination rate (p value=0.24) significant differences exist.
Our findings suggest that further studies preferably by analysis of the transcriptome must be performed to clarify the features involved in CD027 pathogenicity.
This work shows how is possible, by application of molecular typing, to identify pathogens responsible for epidemic situations and to determine the presence of virulence factors o drug resistance genes associated with pathogenicity of strains. Besides it is possible to obtain useful and additional information as the genetic relationships between analyzed strains and their transmission route.
In conclusion, it is showed that active surveillance and characterization of circulating strains at local and national level is crucial to prevent the spread of more virulent variants, with benefits for the patient and the health system
Angular resolution improvement of slumped thin glass optics for x-ray telescopes.
Get PDFCurrent X-ray telescopes such as Chandra and XMM were designed and built to privilege the angular resolution or the collecting area respectively, but using two different manufacturing techniques, and these two key aspects could not be optimised at the same time. The result is that the high-redshift X-ray Universe is still too unresolved to provide us with the understanding of the time evolution of the universe as we see it nowadays. Now the ATHENA mission, approved for the L2 slot in the Cosmic Vision program, is required to have an effective area of 2 m2 at 1 keV and an angular resolution better than 5 arcsec Half-Energy Width (HEW). At this regard, in addition to the baseline solution based on Silicon Pore Optics (SPO), thin glass foils are considered a viable alternative. Slumped glass foils are also considered as substrates for X-ray optics being developed in other projects; for example, the X-ray Surveyor mission being developed at SAO/CfA in USA, and the AXYOM project being developed in Italy. They both foresee the use of piezo-electric actuators to correct the shape errors of the mirrors.
The Brera Astronomical Observatory (INAF-OAB, Merate - Italy) has been working, from 2009 till 2013, under ESA contract aimed to develop in Europe a Slumped Glass Optics (SGO) technology, alternative to the one based on silicon pores, and based on the slumping of thin glass foils, in parallel to the work being carried out at NASA/GSFC and other institutes. The INAFOAB innovation is the use of pressure in the hot slumping process to replicate the mould figure.
This technology is coupled with an integration process able to damp low frequency errors. My Ph.D. activity, carried out at the INAF-OAB, is devoted to the advancement in the hot slumping technology assisted by pressure, for the production of glass mirrors for future X-ray telescopes. As a preliminary work, I have developed a new method to precisely characterise the mid frequency errors of the glass foils. An existing model, developed by Jimenez-Garate in 2003 to account for the relaxation of ripples in the slumped glass foil when in contact with the slumping mould, was modified to include the application of pressure, and the model was compared to the experimental results. The pressure was found to be essential, also from the the theory viewpoint, to reduce mid-frequency errors in the profile of slumped glass foils, which crucially degrade the performances of the optics. As for the slumping process, I have introduced a new glass material (Corning Eagle XG) combined with the Schott Zerodur K20, already chosen at earlier times as slumping mould material for its anti-sticking properties. I have developed cleaning protocols, used different thermal cycles and different pressures conditions, and reconditioned the pressure control system. I have also optimised the mould height with experiments based on Finite Element Analysis, and reduced the thermal gradients inside the mould and the glass foils.
The final result obtained in this research are slumped glass foils with angular resolution improved from the initial 7 arcsec to 2.2±0.3 arcsec in single reflection, as expected from metrology at 1 keV X-ray energy and 0.7 incidence angle, and computed by simulating a perfect integration.
This result has to be compared with 2 arcsec defined as the error budget allocated for the slumped glass foils. About 1 arcsec is due to replication of the mid-frequency errors in the slumping mould which, owing to the improved result in the slumping, are now a limiting factor in the quality of the slumped glass foils. From the roughness point of view, the contribution to the HEW is guaranteed to be less then 1 arcsec at 1 keV, with an rms improvement from 21 to 11 Å throughout my Ph.D.
Moreover, the last tests carried out proved that the roughness of the slumped glass foils can be further reduced to _ 7 Å, making the technology attractive also for higher X-ray energies and higher incidence angles.
The glass foils slumped during this Ph.D. have been used for the production of two SGO Proof Of Concept prototypes (POC) for the ATHENA mission: the POC#3, (with 2 glass foils assembled) is characterised by HEW value of 5.5 arcsec at 0.27 keV in the best portion of the module, as tested at the PANTER facility; the POC#4 (with 8 glass foils) has expected HEW of about 15 arcsec from metrological data, but the result in X-ray was much higher because of accidental problems during the integration. The next prototype, the POC#5 (with the best eight glass foils produced during my Ph.D. activity), will soon be integrated and tested in X-rays, to assess the improvement already proven by metrology and simulations. Some of the produced slumped glass foils have also been used for studies of active profile corrections with piezoelectric elements, both for the AXYOM project and X-ray Surveyor mission.
Alternative materials and techniques have been used in this research to further improve the result. To reduce the surface micro-roughness of the slumped glass foils, I have proven that the slumping technique with pressure application can also be suited in the indirect slumping, in which the optical surface of the glass is not in contact with the mould, thus preserving its initial surface smoothness. Moreover, the dip coating technique was studied to fill the micro-pores present on the surface of the glass foils slumped with the direct technique. Alternative materials for the slumping mould were tested, defining Si3N4 as a very promising candidate, owing to its higher rigidity with respect to Zerodur K20 and therefore preferable to avoid mould deformations with the slumping, as experienced with K20. The Gorilla glass (normally used for smartphones and tablets), was proven to preserve the surface quality of the glass foils, once slumped and chemically tempered to increase the mirror endurance against the vibrations experienced at launch.
Finally, I have also studied the scattering and the reflectivity properties of multilayer coatings for X-ray optics. I have upgraded an IDL code to simulate the roughness growth in the multilayer deposition process, extending the computations from periodic to the more general case of graded multilayers. I have also contributed to the X-ray measurements at the BEAR beamline of the Elettra synchrotron in Trieste, on multilayers deposited on glass, silicon and electroformed nickel, for the polarimetric LAMP projec
Tikhonov-type iterative regularization methods for ill-posed inverse problems: theoretical aspects and applications
Get PDFIll-posed inverse problems arise in many fields of science and engineering. The ill-conditioning and the big dimension make the task of numerically solving this kind of problems very challenging.
In this thesis we construct several algorithms for solving ill-posed inverse problems. Starting from the classical Tikhonov regularization method we develop iterative methods that enhance the performances of the originating method.
In order to ensure the accuracy of the constructed algorithms we insert a priori knowledge on the exact solution and empower the regularization term. By exploiting the structure of the problem we are also able to achieve fast computation even when the size of the problem becomes very big.
We construct algorithms that enforce constraint on the reconstruction, like nonnegativity or flux conservation and exploit enhanced version of the Euclidian norm using a regularization operator and different semi-norms, like the Total Variaton, for the regularization term.
For most of the proposed algorithms we provide efficient strategies for the choice of the regularization parameters, which, most of the times, rely on the knowledge of the norm of the noise that corrupts the data.
For each method we analyze the theoretical properties in the finite dimensional case or in the more general case of Hilbert spaces.
Numerical examples prove the good performances of the algorithms proposed in term of both accuracy and efficiency