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.

Catch and by-catch analyses of tropical tuna fishery in the Gulf of Guinea from 2010 to 2012.

Canned tuna is one of the most widespread and recognizable fish commodities in the world. Over all oceans 80% of the total tuna catches are caught by purse seine fishery and in tropical waters their target species are: yellowfin (Thunnus albacares), bigeye (Thunnus obesus) and skipjack (Katsuwonus pelamis). Even if this fishing gear is claimed to be very selective, there are high levels of by-catch especially when operating under Fish Aggregating Devices (FADs). The main problem is underestimation of by-catch data. In order to solve this problem the scientific community has developed many specific programs (e.g. Observe Program) to collect data about both target species and by-catch with observers onboard. The purposes of this study are to estimate the quantity and composition of target species and by-catch by tuna purse seiner fishery operating in tropical waters and to underline a possible seasonal variability in the by-catch ratio (tunas versus by-catch). Data were collected with the French scientific program ”Observe” on board of the French tuna purse seiner “Via Avenir” during a fishing trip in the Gulf of Guinea (C-E Atlantic) from August to September 2012. Furthermore some by-catch specimens have been sampled to obtain more information about size class composition. In order to achieve those purposes we have shared our data with the French Institute of Research for the Development (IRD), which has data collected by observers onboard in the same study area. Yellowfin tuna results to be the main specie caught in all trips considered (around 71% of the total catches) especially on free swimming schools (FSC) sets. Instead skipjack tuna is the main specie caught under FADs. Different percentages of by-catch with the two fishing modes are observed: the by-catch incidence is higher on FADs sets (96.5% of total by-catch) than on FSC sets (3.5%) and the main category of by-catch is little-tuna (73%). When pooling data for both fishing sets used in purse seine fishery the overall by-catch/catch ratio is 5%, a lower level than in other fishing gears like long-lining and trawling.

Large-scale coupled-cluster calculations

Coupled-cluster theory provides one of the most successful concepts in electronic-structure theory. This work covers the parallelization of coupled-cluster energies, gradients, and second derivatives and its application to selected large-scale chemical problems, beside the more practical aspects such as the publication and support of the quantum-chemistry package ACES II MAB and the design and development of a computational environment optimized for coupled-cluster calculations. The main objective of this thesis was to extend the range of applicability of coupled-cluster models to larger molecular systems and their properties and therefore to bring large-scale coupled-cluster calculations into day-to-day routine of computational chemistry. A straightforward strategy for the parallelization of CCSD and CCSD(T) energies, gradients, and second derivatives has been outlined and implemented for closed-shell and open-shell references. Starting from the highly efficient serial implementation of the ACES II MAB computer code an adaptation for affordable workstation clusters has been obtained by parallelizing the most time-consuming steps of the algorithms. Benchmark calculations for systems with up to 1300 basis functions and the presented applications show that the resulting algorithm for energies, gradients and second derivatives at the CCSD and CCSD(T) level of theory exhibits good scaling with the number of processors and substantially extends the range of applicability. Within the framework of the ’High accuracy Extrapolated Ab initio Thermochemistry’ (HEAT) protocols effects of increased basis-set size and higher excitations in the coupled- cluster expansion were investigated. The HEAT scheme was generalized for molecules containing second-row atoms in the case of vinyl chloride. This allowed the different experimental reported values to be discriminated. In the case of the benzene molecule it was shown that even for molecules of this size chemical accuracy can be achieved. Near-quantitative agreement with experiment (about 2 ppm deviation) for the prediction of fluorine-19 nuclear magnetic shielding constants can be achieved by employing the CCSD(T) model together with large basis sets at accurate equilibrium geometries if vibrational averaging and temperature corrections via second-order vibrational perturbation theory are considered. Applying a very similar level of theory for the calculation of the carbon-13 NMR chemical shifts of benzene resulted in quantitative agreement with experimental gas-phase data. The NMR chemical shift study for the bridgehead 1-adamantyl cation at the CCSD(T) level resolved earlier discrepancies of lower-level theoretical treatment. The equilibrium structure of diacetylene has been determined based on the combination of experimental rotational constants of thirteen isotopic species and zero-point vibrational corrections calculated at various quantum-chemical levels. These empirical equilibrium structures agree to within 0.1 pm irrespective of the theoretical level employed. High-level quantum-chemical calculations on the hyperfine structure parameters of the cyanopolyynes were found to be in excellent agreement with experiment. Finally, the theoretically most accurate determination of the molecular equilibrium structure of ferrocene to date is presented.

The application of a new psychotherapeutic strategy for enhancing eudaimonic well-being in children with mood and anxiety disorders

The aim of the dissertation was to test the feasibility of a new psychotherapeutic protocol for treating children and adolescents with mood and anxiety disorders: Child-Well-Being Therapy (CWBT). It originates from adult Well-Being Therapy protocol (WBT) and represents a conceptual innovation for treating affective disorders. WBT is based on the multidimensional model of well-being postulated by Ryff (eudaimonic perspective), in sequential combination with cognitive-behavioral therapy (CBT). Results showed that eudaimonic well-being was impaired in children with affective disorders in comparison with matched healthy students. A first open investigation aimed at exploring the feasibility of a 8-session CWBT protocol in a group of children with emotional and behavioural disorders has been implemented. Data showed how CWBT resulted associated to symptoms reduction, together with the decrease of externalizing problems, maintained at 1-year follow-up. CWBT triggered also an improvement in psychological well-being as well as an increasing flourishing trajectory over time. Subsequently, a modified and extended version of CWBT (12-sessions) has been developed and then tested in a controlled study with 34 patients (8 to 16 years) affected by mood and anxiety disorders. They were consecutively randomized into 3 different groups: CWBT, CBT, 6-month waiting list (WL). Both treatments resulted effective in decreasing distress and in improving well-being. Moreover, CWBT was associated with higher improvement in anxiety and showed a greater recovery rate (83%) than CBT (54%). Both groups maintained beneficial effects and CWBT group displayed a lower level of distress as well as a higher positive trend in well-being scores over time. Findings need to be interpret with caution, because of study limitations, however important clinical implications emerged. Further investigations should determine whether the sequential integration of well-being and symptom-oriented strategies could play an important role in children and adolescents’ psychotherapeutic options, fostering a successful adaptation to adversities during the growth process.

The relationship between eating behavior and psychological distress among overweight and obese people: is there a role for mindfulness?

This research based on 3 indipendent studies, sought to explore the nature of the relationship between overweight/obesity, eating behaviors and psychological distress; the construct of Mindful eating trough the validation of the Italian adaptation of the Mindful Eating Questionnaire (MEQ); the role of mindfulnessand mindful eating as respectively potential mediator and moderator between overeating behavior (binge eating and emotional overeating) and negative outcomes (psychological distress, body dissatisfaction). All the samples were divided in normal weight, overweight and obese according to BMI categories. STUDY1: In a sample of 691 subjects (69.6% female, mean aged 39.26 years) was found that BMI was not associated with psychological distress, whereas binge eating increases the psychopathological level. BMI and male gender represent negative predictors of psychological distress, but certain types of overeating (i.e., NES/grazing, overeating during or out of meals, and guilt/restraint) result as positive predictors.. STUDY 2 : A sample of 1067 subjects (61.4% female, mean aged 34 years) was analized. The Italian MEQ resulted in a 26-item 4-factor model measuring Disinhibition, Awareness, Distraction, and Emotional response. Internal consistency and test-retest reliability were acceptable MEQ correlated positively with mindfulness (FMI) and it was associated with sociodemographic variables, BMI, meditation. type of exercise and diet. STUDY 3, based on a sample of 502 subjects (68.8% female, mean aged 39.42 years) showed that MEQ and FMI negatively correlated with BES, EOQ, SCL-90-R, and BIAQ. Obese people showed lower level of mindful eating and higher levels of binge eating, emotional overeating, and body dissatisfaction, compared to the other groups Mindfulness resulted to partially mediates the relationship between a) binge eating and psychological distress, b) emotional overeating and psychological distress, c) binge eating and mental well-being, d) emotional overeating and menal well-being. Mindful eating was a moderator only in the relationship between emotional overeating and body dissatisfaction.

Aerobic biodegradation of chlorinated solvents and plastics in batch and continuous-flow bioreactors: process development, and identification of suitable chemical pre-Treatments

The purpose of the first part of the research activity was to develop an aerobic cometabolic process in packed bed reactors (PBR) to treat real groundwater contaminated by trichloroethylene (TCE) and 1,1,2,2-tetrachloroethane (TeCA). In an initial screening conducted in batch bioreactors, different groundwater samples from 5 wells of the contaminated site were fed with 5 growth substrates. The work led to the selection of butane as the best growth substrate, and to the development and characterization from the site’s indigenous biomass of a suspended-cell consortium capable to degrade TCE with a 90 % mineralization of the organic chlorine. A kinetic study conducted in batch and continuous flow PBRs and led to the identification of the best carrier. A kinetic study of butane and TCE biodegradation indicated that the attached-cell consortium is characterized by a lower TCE specific degredation rates and by a lower level of mutual butane-TCE inhibition. A 31 L bioreactor was designed and set up for upscaling the experiment. The second part of the research focused on the biodegradation of 4 polymers, with and with-out chemical pre-treatments: linear low density polyethylene (LLDPE), polyethylene (PP), polystyrene (PS) and polyvinyl chloride (PVC). Initially, the 4 polymers were subjected to different chemical pre-treatments: ozonation and UV/ozonation, in gaseous and aqueous phase. It was found that, for LLDPE and PP, the coupling UV and ozone in gas phase is the most effective way to oxidize the polymers and to generate carbonyl groups on the polymer surface. In further tests, the effect of chemical pretreatment on polyner biodegrability was studied. Gas-phase ozonated and virgin polymers were incubated aerobically with: (a) a pure strain, (b) a mixed culture of bacteria; and (c) a fungal culture, together with saccharose as a co-substrate.

Reduced endurance of the cervical flexor muscles in patients with concurrent temporomandibular disorders and neck disability

Subjects with temporomandibular disorders (TMDs) have been found to have clinical signs and symptoms of cervical dysfunction. Although many studies have investigated the relationship between the cervical spine and TMD, no study has evaluated the endurance capacity of the cervical muscles in patients with TMD. Thus the objective of this study was to determine whether patients with TMD had a reduced endurance of the cervical flexor muscles at any level of muscular contraction when compared with healthy subjects. One hundred and forty-nine participants provided data for this study (49 subjects were healthy, 54 had myogenous TMD, and 46 had mixed TMD). There was a significant difference in holding time at 25% MVC between subjects with mixed TMD when compared to subjects with myogenous TMD and healthy subjects. This implies that subjects with mixed TMD had less endurance capacity at a lower level of contraction (25% MVC) than healthy subjects and subjects with myogenous TMD. No significant associations between neck disability, jaw disability, clinical variables and neck flexor endurance test were found.

Habitat-specific demography and source-sink dynamics in a population of Siberian jays

P>1. There are a number of models describing population structure, many of which have the capacity to incorporate spatial habitat effects. One such model is the source-sink model, that describes a system where some habitats have a natality that is higher than mortality (source) and others have a mortality that exceeds natality (sink). A source can be maintained in the absence of migration, whereas a sink will go extinct. 2. However, the interaction between population dynamics and habitat quality is complex, and concerns have been raised about the validity of published empirical studies addressing source-sink dynamics. In particular, some of these studies fail to provide data on survival, a significant component in disentangling a sink from a low quality source. Moreover, failing to account for a density-dependent increase in mortality, or decrease in fecundity, can result in a territory being falsely assigned as a sink, when in fact, this density-dependent suppression only decreases the population size to a lower level, hence indicating a 'pseudo-sink'. 3. In this study, we investigate a long-term data set for key components of territory-specific demography (mortality and reproduction) and their relationship to habitat characteristics in the territorial, group-living Siberian jay (Perisoreus infaustus). We also assess territory-specific population growth rates (r), to test whether spatial population dynamics are consistent with the ideas of source-sink dynamics. 4. Although average mortality did not differ between sexes, habitat-specific mortality did. Female mortality was higher in older forests, a pattern not observed in males. Male mortality only increased with an increasing amount of open areas. Moreover, reproductive success was higher further away from human settlement, indicating a strong effect of human-associated nest predators. 5. Averaged over all years, 76% of the territories were sources. These territories generally consisted of less open areas, and were located further away from human settlement. 6. The source-sink model provides a tool for modelling demography in distinct habitat patches of different quality, which can aid in identifying key habitats within the landscape, and thus, reduce the risk of implementing unsound management decisions.

Efficient and Accurate Characterization of the Bergman Cyclization for an Expanded Substructure of Esperamicin A1

Incorporation of enediynes into anticancer drugs remains an intriguing yet elusive strategy for the design of therapeutically active agents. Density functional theory was used to locate reactants, products, and transition states along the Bergman cyclization pathways connecting enediynes to reactive para-biradicals. Sum method correction to low-level calculations confirmed B3LYP/6-31G(d,p) as the method of choice in investigating enediynes. Herein described as MI:Sum, calculated reaction enthalpies differed from experiment by an average of 2.1 kcal·mol−1 (mean unsigned error). A combination of strain energy released across the reaction coordinate and the critical intramolecular distance between reacting diynes explains reactivity differences. Where experimental and calculated barrier heights are in disagreement, higher level multireference treatment of the enediynes confirms lower level estimates. Previous work concerning the chemically reactive fragment of esperamcin, MTC, is expanded to our model system MTC2.

Psychosocial outcome in patients at clinical high risk of psychosis: a prospective follow-up

Purpose In patients at clinical high risk (CHR) of psychosis, transition to psychosis has been the focus of recent studies. Their broader outcome has received less attention. We studied psychosocial state and outcome in CHR patients. Methods In the European Prediction of Psychosis Study, 244 young help-seeking CHR patients were assessed with the Strauss and Carpenter Prognostic Scale (SCPS) at baseline, and 149 (61.1 %) of them were assessed for the second time at the 18-month follow-up. The followed patients were classified into poor and good outcome groups. Results Female gender, ever-married/cohabitating relationship, and good working/studying situation were associated with good baseline SCPS scores. During follow-up, patients’ SCPS scores improved significantly. Good follow-up SCPS scores were predicted by higher level of education, good working/studying status at baseline, and white ethnicity. One-third of the followed CHR patients had poor global outcome. Poor working/studying situation and lower level of education were associated with poor global outcome. Transition to psychosis was associated with baseline, but not with follow-up SCPS scores or with global outcome. Conclusion The majority of CHR patients experience good short-term recovery, but one-third have poor psychosocial outcome. Good working situation is the major indicator of good outcome, while low level of education and non-white ethnicity seem to be associated with poor outcome. Transition to psychosis has little effect on psychosocial outcome in CHR patients. In treating CHR patients, clinicians should focus their attention on a broader outcome, and not only on preventing transition to psychosis.

A global ”imaging” view on systems approaches in immunology

The immune system exhibits an enormous complexity. High throughput methods such as the "-omic'' technologies generate vast amounts of data that facilitate dissection of immunological processes at ever finer resolution. Using high-resolution data-driven systems analysis, causal relationships between complex molecular processes and particular immunological phenotypes can be constructed. However, processes in tissues, organs, and the organism itself (so-called higher level processes) also control and regulate the molecular (lower level) processes. Reverse systems engineering approaches, which focus on the examination of the structure, dynamics and control of the immune system, can help to understand the construction principles of the immune system. Such integrative mechanistic models can properly describe, explain, and predict the behavior of the immune system in health and disease by combining both higher and lower level processes. Moving from molecular and cellular levels to a multiscale systems understanding requires the development of methodologies that integrate data from different biological levels into multiscale mechanistic models. In particular, 3D imaging techniques and 4D modeling of the spatiotemporal dynamics of immune processes within lymphoid tissues are central for such integrative approaches. Both dynamic and global organ imaging technologies will be instrumental in facilitating comprehensive multiscale systems immunology analyses as discussed in this review.

Castration of lambs: a welfare comparison of different castration techniques in lambs over 10 weeks of age

Seventy male lambs over 10 weeks of age were castrated using Burdizzo, rubber rings, or surgery to assess the acute and long-term effects of castration. All castrations were performed under local anaesthesia. The surgically castrated lambs were additionally sedated with xylazine and the sedation reversed with tolazoline. The frequency of abnormal postures and immediate behavioural responses indicated that surgically castrated lambs were most distressed; the lambs castrated using Burdizzo and rubber rings were not dissimilar to those of the control group. Between 1.5 and 9h after castration, signs of pain and distress were at a lower level in lambs anaesthetised with bupivacaine compared with those treated with lidocaine. Due to the markedly faster wound healing, Burdizzo castration seemed to be preferable (fewer signs of long-term pain) when compared to the rubber ring technique. It was concluded that local anaesthesia with bupivacaine, followed by the Burdizzo method is the preferable technique for the castration of lambs older than 10 weeks of age.

Genetic Variation and Population Structure in Native Americans

We examined genetic diversity and population structure in the American landmass using 678 autosomal microsatellite markers genotyped in 422 individuals representing 24 Native American populations sampled from North, Central, and South America. These data were analyzed jointly with similar data available in 54 other indigenous populations worldwide, including an additional five Native American groups. The Native American populations have lower genetic diversity and greater differentiation than populations from other continental regions. We observe gradients both of decreasing genetic diversity as a function of geographic distance from the Bering Strait and of decreasing genetic similarity to Siberians-signals of the southward dispersal of human populations from the northwestern tip of the Americas. We also observe evidence of: (1) a higher level of diversity and lower level of population structure in western South America compared to eastern South America, (2) a relative lack of differentiation between Mesoamerican and Andean populations, (3) a scenario in which coastal routes were easier for migrating peoples to traverse in comparison with inland routes, and (4) a partial agreement on a local scale between genetic similarity and the linguistic classification of populations. These findings offer new insights into the process of population dispersal and differentiation during the peopling of the Americas.

TRPC1 is regulated by caveolin-1 and is involved in oxidized LDL-induced apoptosis of vascular smooth muscle cells

Oxidized low-density lipoprotein (oxLDL) induced-apoptosis of vascular cells may participate in plaque instability and rupture. We have previously shown that vascular smooth muscle cells (VSMC) stably expressing caveolin-1 were more susceptible to oxLDL-induced apoptosis than VSMC expressing lower level of caveolin-1, and this was correlated with enhanced Ca(2+) entry and pro-apoptotic events. In this study we aimed to identify the molecular events involved in oxLDL-induced Ca(2+) influx and their regulation by the structural protein caveolin-1. In VSMC, transient receptor potential canonical-1 (TRPC1) silencing by ARN interference, prevents the Ca(2+) influx and reduces the toxicity induced by oxLDL. Moreover, caveolin-1 silencing induces concomitant decrease of TRPC1 expression and reduces oxLDL-induced-apoptosis of VSMC. OxLDL enhanced the cell surface expression of TRPC1, as shown by biotinylation of cell surface proteins, and induced TRPC1 translocation into caveolar compartment, as assessed by subcellular fractionation. OxLDL-induced TRPC1 translocation was dependent on actin cytoskeleton and associated with a dramatic rise of 7-ketocholesterol (a major oxysterol in oxLDL) into caveolar membranes, whereas the caveolar content of cholesterol was unchanged. Altogether, the reported results show that TRPC1 channels play a role in Ca(2+) influx and Ca(2+) homeostasis deregulation that mediate apoptosis induced by oxLDL. These data also shed new light on the role of caveolin-1 and caveolar compartment as important regulators of TRPC1 trafficking to the plasma membrane and apoptotic processes that play a major role in atherosclerosis.

Composing New Abstractions From Object Fragments

As object-oriented languages are extended with novel modularization mechanisms, better underlying models are required to implement these high-level features. This paper describes CELL, a language model that builds on delegation-based chains of object fragments. Composition of groups of cells is used: 1) to represent objects, 2) to realize various forms of method lookup, and 3) to keep track of method references. A running prototype of CELL is provided and used to realize the basic kernel of a Smalltalk system. The paper shows, using several examples, how higher-level features such as traits can be supported by the lower-level model.