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.

Changes in tumor stiffness for early prediction of tumor response to sorafenib: a proof-of-concept study with elastosonography in an animal model of Hepatocellular Carcinoma (HCC)

Background and aims: Sorafenib is the reference therapy for advanced Hepatocellular Carcinoma (HCC). No method exists to predict in the very early period subsequent individual response. Starting from the clinical experience in humans that subcutaneous metastases may rapidly change consistency under sorafenib and that elastosonography a new ultrasound based technique allows assessment of tissue stiffness, we investigated the role of elastonography in the very early prediction of tumor response to sorafenib in a HCC animal model. Methods: HCC (Huh7 cells) subcutaneous xenografting in mice was utilized. Mice were randomized to vehicle or treatment with sorafenib when tumor size was 5-10 mm. Elastosonography (Mylab 70XVG, Esaote, Genova, Italy) of the whole tumor mass on a sagittal plane with a 10 MHz linear transducer was performed at different time points from treatment start (day 0, +2, +4, +7 and +14) until mice were sacrified (day +14), with the operator blind to treatment. In order to overcome variability in absolute elasticity measurement when assessing changes over time, values were expressed in arbitrary units as relative stiffness of the tumor tissue in comparison to the stiffness of a standard reference stand-off pad lying on the skin over the tumor. Results: Sor-treated mice showed a smaller tumor size increase at day +14 in comparison to vehicle-treated (tumor volume increase +192.76% vs +747.56%, p=0.06). Among Sor-treated tumors, 6 mice showed a better response to treatment than the other 4 (increase in volume +177% vs +553%, p=0.011). At day +2, median tumor elasticity increased in Sor-treated group (+6.69%, range –30.17-+58.51%), while decreased in the vehicle group (-3.19%, range –53.32-+37.94%) leading to a significant difference in absolute values (p=0.034). From this time point onward, elasticity decreased in both groups, with similar speed over time, not being statistically different anymore. In Sor-treated mice all 6 best responders at day 14 showed an increase in elasticity at day +2 (ranging from +3.30% to +58.51%) in comparison to baseline, whereas 3 of the 4 poorer responders showed a decrease. Interestingly, these 3 tumours showed elasticity values higher than responder tumours at day 0. Conclusions: Elastosonography appears a promising non-invasive new technique for the early prediction of HCC tumor response to sorafenib. Indeed, we proved that responder tumours are characterized by an early increase in elasticity. The possibility to distinguish a priori between responders and non responders based on the higher elasticity of the latter needs to be validated in ad-hoc experiments as well as a confirmation of our results in humans is warranted.

Background minimization issues for next generation hard X-ray focusing telescopes

The hard X-ray band (10 - 100 keV) has been only observed so far by collimated and coded aperture mask instruments, with a sensitivity and an angular resolution lower than two orders of magnitude as respects the current X-ray focusing telescopes operating below 10 - 15 keV. The technological advance in X-ray mirrors and detection systems is now able to extend the X-ray focusing technique to the hard X-ray domain, filling the gap in terms of observational performances and providing a totally new deep view on some of the most energetic phenomena of the Universe. In order to reach a sensitivity of 1 muCrab in the 10 - 40 keV energy range, a great care in the background minimization is required, a common issue for all the hard X-ray focusing telescopes. In the present PhD thesis, a comprehensive analysis of the space radiation environment, the payload design and the resulting prompt X-ray background level is presented, with the aim of driving the feasibility study of the shielding system and assessing the scientific requirements of the future hard X-ray missions. A Geant4 based multi-mission background simulator, BoGEMMS, is developed to be applied to any high energy mission for which the shielding and instruments performances are required. It allows to interactively create a virtual model of the telescope and expose it to the space radiation environment, tracking the particles along their path and filtering the simulated background counts as a real observation in space. Its flexibility is exploited to evaluate the background spectra of the Simbol-X and NHXM mission, as well as the soft proton scattering by the X-ray optics and the selection of the best shielding configuration. Altough the Simbol-X and NHXM missions are the case studies of the background analysis, the obtained results can be generalized to any future hard X-ray telescope. For this reason, a simplified, ideal payload model is also used to select the major sources of background in LEO. All the results are original contributions to the assessment studies of the cited missions, as part of the background groups activities.

Crystal phases and glassy dynamics in monodisperse hard ellipsoids

We have performed Monte Carlo and molecular dynamics simulations of suspensions of monodisperse, hard ellipsoids of revolution. Hard-particle models play a key role in statistical mechanics. They are conceptually and computationally simple, and they offer insight into systems in which particle shape is important, including atomic, molecular, colloidal, and granular systems. In the high density phase diagram of prolate hard ellipsoids we have found a new crystal, which is more stable than the stretched FCC structure proposed previously . The new phase, SM2, has a simple monoclinic unit cell containing a basis of two ellipsoids with unequal orientations. The angle of inclination is very soft for length-to-width (aspect) ratio l/w=3, while the other angles are not. A symmetric state of the unit cell exists, related to the densest-known packings of ellipsoids; it is not always the stable one. Our results remove the stretched FCC structure for aspect ratio l/w=3 from the phase diagram of hard, uni-axial ellipsoids. We provide evidence that this holds between aspect ratios 3 and 6, and possibly beyond. Finally, ellipsoids in SM2 at l/w=1.55 exhibit end-over-end flipping, warranting studies of the cross-over to where this dynamics is not possible. Secondly, we studied the dynamics of nearly spherical ellipsoids. In equilibrium, they show a first-order transition from an isotropic phase to a rotator phase, where positions are crystalline but orientations are free. When over-compressing the isotropic phase into the rotator regime, we observed super-Arrhenius slowing down of diffusion and relaxation, and signatures of the cage effect. These features of glassy dynamics are sufficiently strong that asymptotic scaling laws of the Mode-Coupling Theory of the glass transition (MCT) could be tested, and were found to apply. We found strong coupling of positional and orientational degrees of freedom, leading to a common value for the MCT glass-transition volume fraction. Flipping modes were not slowed down significantly. We demonstrated that the results are independent of simulation method, as predicted by MCT. Further, we determined that even intra-cage motion is cooperative. We confirmed the presence of dynamical heterogeneities associated with the cage effect. The transit between cages was seen to occur on short time scales, compared to the time spent in cages; but the transit was shown not to involve displacements distinguishable in character from intra-cage motion. The presence of glassy dynamics was predicted by molecular MCT (MMCT). However, as MMCT disregards crystallization, a test by simulation was required. Glassy dynamics is unusual in monodisperse systems. Crystallization typically intervenes unless polydispersity, network-forming bonds or other asymmetries are introduced. We argue that particle anisometry acts as a sufficient source of disorder to prevent crystallization. This sheds new light on the question of which ingredients are required for glass formation.

Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

Proof theory of quantified modal logics

We introduce labelled sequent calculi for indexed modal logics. We prove that the structural rules of weakening and contraction are height-preserving admissible, that all rules are invertible, and that cut is admissible. Then we prove that each calculus introduced is sound and complete with respect to the appropriate class of transition frames.

Hard x-ray photoelectron spectroscopy of bulk and thin films of Heusler compounds

X-ray photoemission spectroscopy (XPS) is one of the most universal and powerful tools for investigation of chemical states and electronic structures of materials. The application of hard x-rays increases the inelastic mean free path of the emitted electrons within the solid and thus makes hard x-ray photoelectron spectroscopy (HAXPES) a bulk sensitive probe for solid state research and especially a very effective nondestructive technique to study buried layers.rnThis thesis focuses on the investigation of multilayer structures, used in magnetic tunnel junctions (MTJs), by a number of techniques applying HAXPES. MTJs are the most important components of novel nanoscale devices employed in spintronics. rnThe investigation and deep understanding of the mechanisms responsible for the high performance of such devices and properties of employed magnetic materials that are, in turn, defined by their electronic structure becomes feasible applying HAXPES. Thus the process of B diffusion in CoFeB-based MTJs was investigated with respect to the annealing temperature and its influence on the changes in the electronic structure of CoFeB electrodes that clarify the behaviour and huge TMR ratio values obtained in such devices. These results are presented in chapter 6. The results of investigation of the changes in the valence states of buried off-stoichiometric Co2MnSi electrodes were investigated with respect to the Mn content α and its influence on the observed TMR ratio are described in chapter 7.rnrnMagnetoelectronic properties such as exchange splitting in ferromagnetic materials as well as the macroscopic magnetic ordering can be studied by magnetic circular dichroism in photoemission (MCDAD). It is characterized by the appearance of an asymmetry in the photoemission spectra taken either from the magnetized sample with the reversal of the photon helicity or by reversal of magnetization direction of the sample when the photon helicity direction is fixed. Though recently it has been widely applied for the characterization of surfaces using low energy photons, the bulk properties have stayed inaccessible. Therefore in this work this method was integrated to HAXPES to provide an access to exploration of magnetic phenomena in the buried layers of the complex multilayer structures. Chapter 8 contains the results of the MCDAD measurements employing hard x-rays for exploration of magnetic properties of the common CoFe-based band-ferromagnets as well as half-metallic ferromagnet Co2FeAl-based MTJs.rnrnInasmuch as the magnetoresistive characteristics in spintronic devices are fully defined by the electron spins of ferromagnetic materials their direct measurements always attracted much attention but up to date have been limited by the surface sensitivity of the developed techniques. Chapter 9 presents the results on the successfully performed spin-resolved HAXPES experiment using a spin polarimeter of the SPLEED-type on a buried Co2FeAl0.5Si0.5 magnetic layer. The measurements prove that a spin polarization of about 50 % is retained during the transmission of the photoelectrons emitted from the Fe 2p3/2 state through a 3-nm-thick oxide capping layer.rn

Individualisierte Krebstherapie : präklinischer „proof of concept“ einer mutationsspezifischen Immuntherapie

Da nicht-synonyme tumorspezifische Punktmutationen nur in malignen Geweben vorkommen und das veränderte Proteinprodukt vom Immunsystem als „fremd“ erkannt werden kann, stellen diese einen bisher ungenutzten Pool von Zielstrukturen für die Immuntherapie dar. Menschliche Tumore können individuell bis zu tausenden nicht-synonymer Punktmutationen in ihrem Genom tragen, welche nicht der zentralen Immuntoleranz unterliegen. Ziel der vorliegenden Arbeit war die Hypothese zu untersuchen, dass das Immunsystem in der Lage sein sollte, mutierte Epitope auf Tumorzellen zu erkennen und zu klären, ob auf dieser Basis eine wirksame mRNA (RNA) basierte anti-tumorale Vakzinierung etabliert werden kann. Hierzu wurde von Ugur Sahin und Kollegen, das gesamte Genom des murinen B16-F10 Melanoms sequenziert und bioinformatisch analysiert. Im Rahmen der NGS Sequenzierung wurden mehr als 500 nicht-synonyme Punktmutationen identifiziert, von welchen 50 Mutationen selektiert und durch Sanger Sequenzierung validiert wurden. rnNach der Etablierung des immunologischen Testsysteme war eine Hauptfragestellung dieser Arbeit, die selektierten nicht-synonyme Punktmutationen in einem in vivo Ansatz systematisch auf Antigenität zu testen. Für diese Studien wurden mutierte Sequenzen in einer Länge von 27 Aminosäuren genutzt, in denen die mutierte Aminosäure zentral positioniert war. Durch die Länge der Peptide können prinzipiell alle möglichen MHC Klasse-I und -II Epitope abgedeckt werden, welche die Mutation enthalten. Eine Grundidee des Projektes Ansatzes ist es, einen auf in vitro transkribierter RNA basierten oligotopen Impfstoff zu entwickeln. Daher wurden die Impfungen naiver Mäuse sowohl mit langen Peptiden, als auch in einem unabhängigen Ansatz mit peptidkodierender RNA durchgeführt. Die Immunphänotypisierung der Impfstoff induzierten T-Zellen zeigte, dass insgesamt 16 der 50 (32%) mutierten Sequenzen eine T-Zellreaktivität induzierten. rnDie Verwendung der vorhergesagten Epitope in therapeutischen Vakzinierungsstudien bestätigten die Hypothese das mutierte Neo-Epitope potente Zielstrukturen einer anti-tumoralen Impftherapie darstellen können. So wurde in therapeutischen Tumorstudien gezeigt, dass auf Basis von RNA 9 von 12 bestätigten Epitopen einen anti-tumoralen Effekt zeigte.rnÜberaschenderweise wurde bei einem MHC Klasse-II restringierten mutiertem Epitop (Mut-30) sowohl in einem subkutanen, als auch in einem unabhängigen therapeutischen Lungenmetastasen Modell ein starker anti-tumoraler Effekt auf B16-F10 beobachtet, der dieses Epitop als neues immundominantes Epitop für das B16-F10 Melanom etabliert. Um den immunologischen Mechanismus hinter diesem Effekt näher zu untersuchen wurde in verschieden Experimenten die Rolle von CD4+, CD8+ sowie NK-Zellen zu verschieden Zeitpunkten der Tumorentwicklung untersucht. Die Analyse des Tumorgewebes ergab, eine signifikante erhöhte Frequenz von NK-Zellen in den mit Mut-30 RNA vakzinierten Tieren. Das NK Zellen in der frühen Phase der Therapie eine entscheidende Rolle spielen wurde anhand von Depletionsstudien bestätigt. Daran anschließend wurde gezeigt, dass im fortgeschrittenen Tumorstadium die NK Zellen keinen weiteren relevanten Beitrag zum anti-tumoralen Effekt der RNA Vakzinierung leisten, sondern die Vakzine induzierte adaptive Immunantwort. Durch die Isolierung von Lymphozyten aus dem Tumorgewebe und deren Einsatz als Effektorzellen im IFN-γ ELISPOT wurde nachgewiesen, dass Mut-30 spezifische T-Zellen das Tumorgewebe infiltrieren und dort u.a. IFN-γ sekretieren. Dass diese spezifische IFN-γ Ausschüttung für den beobachteten antitumoralen Effekt eine zentrale Rolle einnimmt wurde unter der Verwendung von IFN-γ -/- K.O. Mäusen bestätigt.rnDas Konzept der individuellen RNA basierten mutationsspezifischen Vakzine sieht vor, nicht nur mit einem mutations-spezifischen Epitop, sondern mit mehreren RNA-kodierten Mutationen Patienten zu impfen um der Entstehung von „escape“-Mutanten entgegenzuwirken. Da es nur Erfahrung mit der Herstellung und Verabreichung von Monotop-RNA gab, also RNA die für ein Epitop kodiert, war eine wichtige Fragestellungen, inwieweit Oligotope, welche die mutierten Sequenzen sequentiell durch Linker verbunden als Fusionsprotein kodieren, Immunantworten induzieren können. Hierzu wurden Pentatope mit variierender Position des einzelnen Epitopes hinsichtlich ihrer in vivo induzierten T-Zellreaktivitäten charakterisiert. Die Experimente zeigten, dass es möglich ist, unabhängig von der Position im Pentatop eine Immunantwort gegen ein Epitop zu induzieren. Des weiteren wurde beobachtet, dass die induzierten T-Zellfrequenzen nach Pentatop Vakzinierung im Vergleich zur Nutzung von Monotopen signifikant gesteigert werden kann.rnZusammenfassend wurde im Rahmen der vorliegenden Arbeit präklinisch erstmalig nachgewiesen, dass nicht-synonyme Mutationen eine numerisch relevante Quelle von Zielstrukturen für die anti-tumorale Immuntherapie darstellen. Überraschenderweise zeigte sich eine dominante Induktion MHC-II restringierter Immunantworten, welche partiell in der Lage waren massive Tumorabstoßungsreaktionen zu induzieren. Im Sinne einer Translation der gewonnenen Erkenntnisse wurde ein RNA basiertes Oligotop-Format etabliert, welches Eingang in die klinische Testung des Konzeptes fand.rn

Studio e sviluppo di un'infrastruttura di supporto alla schedulazione di hard/soft real-time tasks in ambiente QNX.

La tesi tratta lo studio del sistema QNX e dello sviluppo di un simulatore di task hard/soft real-time, tramite uso di un meta-scheduler. Al termine dello sviluppo vengono valutate le prestazioni del sistema operativo QNX Neutrino.

Nuovi elastomeri termoplastici "soft-hard" a base di pbs per applicazioni biomedicali

Nuovi elastomeri termoplastici "soft-hard" a base di PBS per applicazioni biomedicali

Proof of concept di una mano ad azionamento bilaterale per l'impiego nei settori della Robotica e della Protesica.

A partire dal concept ideato dall’ing. Emanuele Gruppioni, ricercatore presso il Centro Protesi stesso, l’obiettivo del lavoro è rappresentato dallo studio di fattibilità, dalla realizzazione e dalla messa in opera della suddetta mano, che presenta come caratteristica peculiare e innovativa un azionamento bilaterale che le consente di essere ambidestra. Questo azionamento è attuato da due cavi posti in ogni dito, che grazie all’azione dei motori inseriti nel palmo vengono riavvolti su delle pulegge consentendo la flessione delle dita in una direzione o nell’altra, in una struttura di mano nella quale non sono quindi individuabili a priori le tipiche ragioni palmare e dorsale. Questo tipo di azionamento in futuro potrebbe essere rielaborato nell’ottica di avere un’unica protesi di mano che possa essere utilizzata sia da pazienti destrimani sia mancini, o, in alternativa, di avere un dispositivo protesico che ampli le funzionalità di presa rispetto alla mano umana.

Pro-inflammatory biomarkers during experimental gingivitis in patients with type 1 diabetes mellitus: a proof-of-concept study

To compare gingival crevicular fluid (GCF) biomarker levels and microbial distribution in plaque biofilm (SP) samples for subjects with type 1 diabetes (T1DM) versus healthy subjects without diabetes during experimental gingivitis (EG).

The effect of different implant neck configurations on soft and hard tissue healing: a randomized-controlled clinical trial

Objective: To compare the soft and hard tissue healing and remodeling around tissue-level implants with different neck configurations after at least 1 year of functional loading. Material and methods: Eighteen patients with multiple missing teeth in the posterior area received two implants inserted in the same sextant. One test (T) implant with a 1.8 mm turned neck and one control (C) implant with a 2.8 mm turned neck were randomly assigned. All implants were placed transmucosally to the same sink depth of approximately 1.8 mm. Peri-apical radiographs were obtained using the paralleling technique and digitized. Two investigators blinded to the implant type-evaluated soft and hard tissue conditions at baseline, 6 months and 1 year after loading. Results: The mean crestal bone levels and soft tissue parameters were not significantly different between T and C implants at all time points. However, T implants displayed significantly less crestal bone loss than C implants after 1 year. Moreover, a frequency analysis revealed a higher percentage (50%) of T implants with crestal bone levels 1–2 mm below the implant shoulder compared with C implants (5.6%) 1 year after loading. Conclusion: Implants with a reduced height turned neck of 1.8 mm may, indeed, lower the crestal bone resorption and hence, may maintain higher crestal bone levels than do implants with a 2.8 mm turned neck, when sunk to the same depth. Moreover, several factors other than the vertical positioning of the moderately rough SLA surface may influence crestal bone levels after 1 year of function.

A smooth transition protocol for patients with multifocal motor neuropathy going from intravenous to subcutaneous immunoglobulin therapy: an open-label proof-of-concept study

Intravenous immunoglobulin (IVIG) is the first-line therapy for multifocal motor neuropathy (MMN). This open-label multi-centre study (NCT00701662) assessed the efficacy, safety, and convenience of subcutaneous immunoglobulin (SCIG) in patients with MMN over 6 months, as an alternative to IVIG. Eight MMN patients (42-66 years), on stable IVIG dosing, received weekly SCIG at doses equivalent to previous IVIG using a "smooth transition protocol". Primary efficacy endpoint was the change from baseline to week 24 in muscle strength. Disability, motor function, and health-related quality of life (HRQL) endpoints were also assessed. One patient deteriorated despite dose increase and was withdrawn. Muscle strength, disability, motor function, and health status were unchanged in all seven study completers who rated home treatment as extremely good. Four experienced 18 adverse events, of which only two were moderate. This study suggests that MMN patients with stable clinical course on regular IVIG can be switched to SCIG at the same monthly dose without deterioration and with a sustained overall improvement in HRQL.