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.

The dynamics of ultra-thin polymer films in different confinements studied by resonance enhanced dynamic light scattering

Die Kontroverse über den Glasübergang im Nanometerbereich, z. B. die Glas¬über¬gangs-temperatur Tg von dünnen Polymerfilmen, ist nicht vollständig abgeschlossen. Das dynamische Verhalten auf der Nanoskala ist stark von den einschränkenden Bedingungen abhängig, die auf die Probe wirken. Dünne Polymerfilme sind ideale Systeme um die Dynamik von Polymerketten unter der Einwirkung von Randbedingungen zu untersuchen, wie ich sie in dieser Arbeit variiert habe, um Einblick in dieses Problem zu erhalten.rnrnResonanzverstärkte dynamische Lichtstreuung ist eine Methode, frei von z.B. Fluoreszenzmarkern, die genutzt werden kann um in dünnen Polymerfilmen dynamische Phänomene

Finite element modeling of flow/compression-induced deformation of alginate scaffolds for bone tissue engineering

Trauma or degenerative diseases such as osteonecrosis may determine bone loss whose recover is promised by a "tissue engineering“ approach. This strategy involves the use of stem cells, grown onboard of adequate biocompatible/bioreabsorbable hosting templates (usually defined as scaffolds) and cultured in specific dynamic environments afforded by differentiation-inducing actuators (usually defined as bioreactors) to produce implantable tissue constructs. The purpose of this thesis is to evaluate, by finite element modeling of flow/compression-induced deformation, alginate scaffolds intended for bone tissue engineering. This work was conducted at the Biomechanics Laboratory of the Institute of Biomedical and Neural Engineering of the Reykjavik University of Iceland. In this respect, Comsol Multiphysics 5.1 simulations were carried out to approximate the loads over alginate 3D matrices under perfusion, compression and perfusion+compression, when varyingalginate pore size and flow/compression regimen. The results of the simulations show that the shear forces in the matrix of the scaffold increase coherently with the increase in flow and load, and decrease with the increase of the pore size. Flow and load rates suggested for proper osteogenic cell differentiation are reported.

On Certain Applications of the Khukhro-Makarenko Theorem

Some recent results of Khukhro and Makarenko on the existence of characteristic X-subgroups of finite index in a group G, for certain varieties X, are used to obtain generalisations of some well-known results in the literature pertaining to groups G, in which all proper subgroups satisfy some condition or other related to the property 'soluble-by-finite'. In addition, a partial generalisation is obtained for the aforementioned results on the existence of characteristic subgroups.

Investigating the Effects of Various Crowd Characteristics on the Dynamic Properties of an Occupied Structure

One of the challenges for structural engineers during design is considering how the structure will respond to crowd-induced dynamic loading. It has been shown that human occupants of a structure do not simply add mass to the system when considering the overall dynamic response of the system, but interact with it and may induce changes of the dynamic properties from those of the empty structure. This study presents an investigation into the human-structure interaction based on several crowd characteristics and their effect on the dynamic properties of an empty structure. The dynamic properties including frequency, damping, and mode shapes were estimated for a single test structure by means of experimental modal analysis techniques. The same techniques were utilized to estimate the dynamic properties when the test structure was occupied by a crowd with different combinations of size, posture, and distribution. The goal of this study is to isolate the occupant characteristics in order to determine the significance of each to be considered when designing new structures to avoid crowd serviceability issues. The results are presented and summarized based on the level of influence of each characteristic. The posture that produces the most significant effects based on the scope of this research is standing with bent knees with a maximum decrease in frequency of the first mode of the empty structure by 32 percent atthe highest mass ratio. The associated damping also increased 36 times the damping of the empty structure. In addition to the analysis of the experimental data, finite element models and a two degree-of-freedom model were created. These models were used to gain an understanding of the test structure, model a crowd as an equivalent mass, and also to develop a single degree-of-freedom (SDOF) model to best represent a crowd of occupants based on the experimental results. The SDOF models created had an averagefrequency of 5.0 Hz, within the range presented in existing biomechanics research, and combined SDOF systems of the test structure and crowd were able to reproduce the frequency and damping ratios associated with experimental tests. Results of this study confirmed the existence of human-structure interaction andthe inability to simply model a crowd as only additional mass. The two degree-offreedom model determined was able to predict the change in natural frequency and damping ratio for a structure occupied by multiple group sizes in a single posture. These results and model are the preliminary steps in the development of an appropriate methodfor modeling a crowd in combination with a more complex FE model of the empty structure.

Early changes in biochemical markers of bone formation during teriparatide therapy correlate with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis

Summary Changes of the bone formation marker PINP correlated positively with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis (GIO) who received 18-month treatment with teriparatide, but not with risedronate. These results support the use of PINP as a surrogate marker of bone strength in GIO patients treated with teriparatide. Introduction To investigate the correlations between biochemical markers of bone turnover and vertebral strength estimated by finite element analysis (FEA) in men with GIO. Methods A total of 92 men with GIO were included in an 18-month, randomized, open-label trial of teriparatide (20 μg/day, n = 45) and risedronate (35 mg/week, n = 47). High-resolution quantitative computed tomography images of the 12th thoracic vertebra obtained at baseline, 6 and 18 months were converted into digital nonlinear FE models and subjected to anterior bending, axial compression and torsion. Stiffness and strength were computed for each model and loading mode. Serum biochemical markers of bone formation (amino-terminal-propeptide of type I collagen [PINP]) and bone resorption (type I collagen cross-linked C-telopeptide degradation fragments [CTx]) were measured at baseline, 3 months, 6 months and 18 months. A mixed-model of repeated measures analysed changes from baseline and between-group differences. Spearman correlations assessed the relationship between changes from baseline of bone markers with FEA variables. Results PINP and CTx levels increased in the teriparatide group and decreased in the risedronate group. FEA-derived parameters increased in both groups, but were significantly higher at 18 months in the teriparatide group. Significant positive correlations were found between changes from baseline of PINP at 3, 6 and 18 months with changes in FE strength in the teriparatide-treated group, but not in the risedronate group. Conclusions Positive correlations between changes in a biochemical marker of bone formation and improvement of biomechanical properties support the use of PINP as a surrogate marker of bone strength in teriparatide-treated GIO patients.

Comparative effects of Teriparatide and Risedronate in glucocorticoid‐induced osteoporosis in men: 18‐month results of the EuroGIOPs trial

Data on treatment of glucocorticoid-induced osteoporosis (GIO) in men are scarce. We performed a randomized, open-label trial in men who have taken glucocorticoids (GC) for ≥3 months, and had an areal bone mineral density (aBMD) T-score ≤ –1.5 standard deviations. Subjects received 20 μg/d teriparatide (n = 45) or 35 mg/week risedronate (n = 47) for 18 months. Primary objective was to compare lumbar spine (L1–L3) BMD measured by quantitative computed tomography (QCT). Secondary outcomes included BMD and microstructure measured by high-resolution QCT (HRQCT) at the 12th thoracic vertebra, biomechanical effects for axial compression, anterior bending, and axial torsion evaluated by finite element (FE) analysis from HRQCT data, aBMD by dual X-ray absorptiometry, biochemical markers, and safety. Computed tomography scans were performed at 0, 6, and 18 months. A mixed model repeated measures analysis was performed to compare changes from baseline between groups. Mean age was 56.3 years. Median GC dose and duration were 8.8 mg/d and 6.4 years, respectively; 39.1% of subjects had a prevalent fracture, and 32.6% received prior bisphosphonate treatment. At 18 months, trabecular BMD had significantly increased for both treatments, with significantly greater increases with teriparatide (16.3% versus 3.8%; p = 0.004). HRQCT trabecular and cortical variables significantly increased for both treatments with significantly larger improvements for teriparatide for integral and trabecular BMD and bone surface to volume ratio (BS/BV) as a microstructural measure. Vertebral strength increases at 18 months were significant in both groups (teriparatide: 26.0% to 34.0%; risedronate: 4.2% to 6.7%), with significantly higher increases in the teriparatide group for all loading modes (0.005 < p < 0.015). Adverse events were similar between groups. None of the patients on teriparatide but five (10.6%) on risedronate developed new clinical fractures (p = 0.056). In conclusion, in this 18-month trial in men with GIO, teriparatide showed larger improvements in spinal BMD, microstructure, and FE-derived strength than risedronate.

Individual group efficacy beliefs and performance motivation: A mediational approach

Introduction: According to the theoretical model of Cranach, Ochsenbein, and Valach (1986) understanding group actions needs consideration of aspects at both the group level and the level of individual members. For example individual action units constituting group actions are motivated at the individual level while potentially being affected by characteristics of the group. Theoretically, group efficacy beliefs could be a part of this motivational process as they are an individual’s cognitive contents about group-level abilities to perform well in a specific task. Positive relations between group level efficacy-beliefs and group performance have been reported and Bandura and Locke (2003) argue that this relationship is being mediated by motivational processes and goal setting. The aims of this study were a) to examine the effects of group characteristics on individual performance motivation and b) to test if those are mediated by individual group efficacy beliefs. Methods: Forty-seven students (M=22.83 years, SD=2.83, 34% women) of the university of Berne participated in this scenario based experiment. Data were collected on two collection points. Subjects were provided information about fictive team members with whom they had to perform a group triathlon. Three values (low, medium, high) of the other team members’ abilities to perform in their parts of the triathlon (swimming and biking respectively) were combined in a 3x3 full factorial design (Anderson, 1982) yielding nine groups. Subjects were asked how confident they were that the teams would perform well in the task (individual group efficacy beliefs), and to provide information about their motivation to perform at their best in the respective group contexts (performance motivation). Multilevel modeling (Mplus) was used to estimate the effects of the factors swim and bike, and the context-varying covariate individual group efficacy beliefs on performance motivation. Further analyses were undertaken to test if the effects of group contexts on performance motivation are mediated by individual group efficacy beliefs. Results: Significant effects were reported for both the group characteristics (βswim = 7.86; βbike = 8.57; both p < .001) and the individual group efficacy beliefs (βigeb; .40, p < .001) on performance motivation. The subsequent mediation model indicated that the effects of group characteristics on performance motivation were partly mediated by the individual group efficacy beliefs of the subjects with significant mediation effects for both factors swim and bike. Discussion/Conclusion: The results of the study provide further support for the motivational character of efficacy beliefs and point out a mechanism by which team characteristics influence performance relevant factors at the level of individual team members. The study indicates that high team abilities lead to augmented performance motivation, adding a psychological advantage to teams already high on task relevant abilities. Future investigations will be aiming at possibilities to keep individual performance motivation high in groups with low task relevant abilities. One possibility could be the formulation of individual task goals. References: Anderson, N. H. (1982). Methods of information integration theory. New York: Academic Press. Bandura, A. & Locke, E. A. (2003). Negative self-efficacy and goal effects revisited. Journal of Applied Psychology, 88, 87-99. Cranach, M. von, Ochsenbein, G. & Valach, L. (1986). The group as a self-active system: Outline of a theory of group action. European Journal of Social Psychology, 16, 193-229.

Modelización y simulación numérica de sistemas geotérmicos planos

En el presente proyecto se estudiará la conveniencia de utilizar simulación numérica para evaluar, diseñar y mejorar el diseño de instalaciones geotérmicas planas. Para ello, se modelizará el conjunto de terreno y sistema geotérmico mediante el acoplamiento de un modelo tridimensional (terreno) y un modelo unidimensional, formado por la red de tubería geotérmica, que estará dispuesta en un plano cuya orientación dependerá de las aplicaciones. Para la simulación numérica se utilizará un software de análisis y resolución por elementos finitos tipo comercial. Finalmente, se definirán unos parámetros geométricos de diseño y, teniendo en cuenta las propiedades térmicas de cada material, se realizarán estudios paramétricos para determinar la influencia de cada grupo de parámetros. Ello requerirá la realización de cientos de simulaciones numéricas que permitirán optimizar el rendimiento de sistemas geotérmicos planos tanto horizontales (soleras), como verticales (muros pantalla). ABSTRACT In this project it is going to be studied the convenience of numerical simulation as to evaluate, design and improve the design of geothermal planar installations. With this purpose, the terrain and the geothermal system will be modeled by coupling a three-dimensional model (terrain) and a one-dimensional model formed by the geothermal piping network disposed in a plane with an orientation which will depend on the applications. For the numerical simulation commercial software of analyzing and resolving by finite elements will be used. Finally, geometric design parameters will be defined, and taking into account the thermal properties of each material, parametric studies will be performed to determine the influence of each group of parameters. This will require the completion of hundreds of numerical simulations which will enhance the performance of both horizontal (slabs) and vertical (diaphragm walls) geothermal systems.

The development of a wind tunnel DAQ system by using Labview tools

This paper presents the experimental three-year learning activity developed by a group of teachers in a wind tunnel facility. The authors, leading a team of students, carried out a project consisting of the design, assembly and testing of a wind tunnel. The project included all stages of the process from its initial specifications to its final quality flow assessments, going through the calculation of each element, and the building of the whole wind tunnel. The group of (final year) students was responsible for the whole wind tunnel project as a part of their bachelor degree project. The paper focuses on the development of wind tunnel data acquisition software. This automatic tool is essential to improve the automation of the data acquisition of the wind tunnel facility systems, in particular for a 6DOF multi-axis force/torque sensor. This work can be considered as a typical example of real engineering practice: a set of specifications that has to be modified due to the constraints imposed throughout the project, in order to obtain the final result

A public key cryptosystem based on block upper triangular matrices

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while maintaining the key size. We also propose a key exchange protocol that guarantees that both parties share a secret element of this group and a digital signature scheme that provides data authenticity and integrity.

The individual within the group: Balancing the need to belong with the need to be different

Many theorists have wrestled with the notion of how people balance their need to be included in social groups with their need to be different and distinctive. This question is particularly salient to researchers from the social identify perspective, who have traditionally viewed individual differentiation within groups as being inimical to group identification. In this article we present a number of strategies that people can use to balance their need to belong and their need to be different, without violating social identity principles. First, drawing from optimal distinctiveness theory, we discuss 4 ways in which the need for belonging and the need to be different can be resolved by maximizing group distinctiveness. We then discuss 4 ways in which it is possible to achieve individual differentiation within a group at the same time demonstrating group identification. These strategies are discussed and integrated with reference to recent empirical research and to the social identity perspective.

Evaluation of the effectiveness of enrichment for a group of captive squirrel monkeys (Saimiri sciureus) using time-lapse recording and instantaneous scan sampling

One aim of providing enrichment to captive animals is to promote the expression of behavioural patterns similar to their wild conspecifics. We evaluated the effectiveness of four types of simple feeding enrichment, using surveillance cameras to record the behaviour of 11 captive squirrel monkeys housed in a single enclosure at Alma Park Zoo in Brisbane, Australia. The enrichment involved differences in presentation (whole/chopped) and distribution (localised/scattered) of fruit and vegetables that were part of the normal diet of these animals. Distinguishing between individual squirrel monkeys was not possible from the videos, so Instantaneous Scan Sampling was used to record the numbers of animals performing particular behaviours every 15 minutes over the 24 hour period as well as every 5 minutes for the hour following provision of enrichment. This provided an estimation of the percentage of time spent by the group in various activities. As a result of the enrichment, the activity budget of the group more closely approximated that of wild squirrel monkeys. However on a number of occasions where the enrichment required the squirrel monkeys to work to obtain their food (whole fruit and vegetables), a number of individuals became aggressive towards the zookeepers. This result highlights the variation in responses of individual animals towards enrichment and indicates that in enclosures with large numbers of animals, the response of each individual should be evaluated in addition to the overall benefit of the enrichment for the group. Furthermore, this variation also suggests that it may be beneficial to provide the animals with choices of enrichment as opposed to providing single forms of enrichment that may only be effective for a proportion of the animals in the enclosure, and may even result in undesirable responses from some individuals.

Changes in social identity when joining a new group: The role of individual-level and group-level adaptation processes

While classic intergroup theories have specified the processes explaining situational shifts in social identification, the processes whereby social identities change more profoundly and become integrated within the self have to be proposed. To this aim, the present studies investigate the processes by which group members integrate a new social identity as they are joining a new group. Combining a social identity approach and stress and coping models, this research tests if social factors (i.e., needs satisfied by fellow group members, social support), have an impact on the adaptation strategies group members use to deal with the novelty of the situation and to fit into their new group (seeking information & adopting group norms vs. disengaging). These strategies, in turn, should predict changes in level of identification with the new social group over time, as well as enhanced psychological adjustment. These associations are tested among university students over the course of their first academic year (Study 1), and among online gamers joining a newly established online community (Study 2). Path analyses provide support for the hypothesised associations. The results are discussed in light of recent theoretical developments pertaining to intraindividual changes in social identities and their integration in the self.

Finite-size effects in on-line learning of multilayer neural networks

We complement recent advances in thermodynamic limit analyses of mean on-line gradient descent learning dynamics in multi-layer networks by calculating fluctuations possessed by finite dimensional systems. Fluctuations from the mean dynamics are largest at the onset of specialisation as student hidden unit weight vectors begin to imitate specific teacher vectors, increasing with the degree of symmetry of the initial conditions. In light of this, we include a term to stimulate asymmetry in the learning process, which typically also leads to a significant decrease in training time.