Ultrasound entropy may be a new non-invasive measure of pre-clinical vascular damage in young hypertensive patients

Background: The identification of pre-clinical microvascular damage in hypertension by non-invasive techniques has proved frustrating for clinicians. This proof of concept study investigated whether entropy, a novel summary measure for characterizing blood velocity waveforms, is altered in participants with hypertension and may therefore be useful in risk stratification.

Methods: Doppler ultrasound waveforms were obtained from the carotid and retrobulbar circulation in 42 participants with uncomplicated grade 1 hypertension (mean systolic/diastolic blood pressure (BP) 142/92 mmHg), and 26 healthy controls (mean systolic/diastolic BP 116/69 mmHg). Mean wavelet entropy was derived from flow-velocity data and compared with traditional haemodynamic measures of microvascular function, namely the resistive and pulsatility indices.

Results: Entropy, was significantly higher in control participants in the central retinal artery (CRA) (differential mean 0.11 (standard error 0.05 cms(-1)), CI 0.009 to 0.219, p 0.017) and ophthalmic artery (0.12 (0.05), CI 0.004 to 0.215, p 0.04). In comparison, the resistive index (0.12 (0.05), CI 0.005 to 0.226, p 0.029) and pulsatility index (0.96 (0.38), CI 0.19 to 1.72, p 0.015) showed significant differences between groups in the CRA alone. Regression analysis indicated that entropy was significantly influenced by age and systolic blood pressure (r values 0.4-0.6). None of the measures were significantly altered in the larger conduit vessel.

Conclusion: This is the first application of entropy to human blood velocity waveform analysis and shows that this new technique has the ability to discriminate health from early hypertensive disease, thereby promoting the early identification of cardiovascular disease in a young hypertensive population.

Microneedles: an innovative platform for gene delivery

The advent of microneedle (MN) technology has provided a revolutionary platform for the delivery of therapeutic agents, particularly in the field of gene therapy. For over 20 years, the area of gene therapy has undergone intense innovation and progression which has seen advancement of the technology from an experimental concept to a widely acknowledged strategy for the treatment and prevention of numerous disease states. However, the true potential of gene therapy has yet to be achieved due to limitations in formulation and delivery technologies beyond parenteral injection of the DNA. Microneedle-mediated delivery provides a unique platform for the delivery of DNA therapeutics clinically. It provides a means to overcome the skin barriers to gene delivery and deposit the DNA directly into the dermal layers, a key site for delivery of therapeutics to treat a wide range of skin and cutaneous diseases. Additionally, the skin is a tissue rich in immune sentinels, an ideal target for the delivery of a DNA vaccine directly to the desired target cell populations. This review details the advancement of MN-mediated DNA delivery from proof-of-concept to the delivery of DNA encoding clinically relevant proteins and antigens and examines the key considerations for the improvement of the technology and progress into a clinically applicable delivery system.

Sporting Justice: An Arbitrator's Perspective

Drawing on my experience of a number of sports dispute resolution tribunals in the UK and Ireland (such as Sports Resolutions UK; Just Sport Ireland; the Football Association of Ireland’s Disciplinary Panel and the Gaelic Athletic Association’s Dispute Resolution Authority) I intend to use this paper to review the legal arguments typically made in sports-related arbitrations. These points of interest can be summarised as a series of three questions: the fairness question; the liability question; the penalty question.

In answer to the fairness question, the aim is to give a brief outline on best practice in establishing a "fair" sports disciplinary tribunal. The answer, I believe, is always twofold in nature: first, and to paraphrase Lord Steyn in R v Secretary of State For The Home Department, Ex Parte Daly [2001] UKHL 26 at [28] "in law, context is everything" – translated into the present matter, this means that in sports disciplinary cases, the more serious the charges against the individual (in terms of reputational damage, economic impact and/or length of sanction); the more tightly wrapped the procedural safeguards surrounding any subsequent disciplinary hearing must be. A fair disciplinary system will be discussed in the context of the principles laid down in Article 8 of the World Anti-Doping Code which, in effect, acts as sport’s Article 6 of the ECHR on a right to a fair trial.

Following on from the above, in the 60 or so sports arbitrations that I have heard, there are two further points of interest. First, the claim before the arbitral panel will often be framed in an argument that, for various reasons of substantive and procedural irregularity, the sanction imposed on the appellant should be quashed ("the liability"). Second, and in alternative, that the sanction imposed was wholly disproportionate ("the penalty").

The liability issue usually breaks down into two further questions. First, what is the nature of the legal duty upon a sports body in exercising its disciplinary remit? Second, to what extent does a de novo hearing on appeal cure any apparent defects in a hearing of first instance? The first issue often results in an arbitral panel debating the contra preferentum approach to the interpretation of a contested rule i.e., the sports body’s rules in question are so ambiguous that they should be interpreted in a manner to the detriment of the rule maker and in favour of the appellant. On the second matter, it now appears to be a general principle of sports law, administrative law and even human rights law that even if a violation of the principles of natural justice takes place at the first instance stage of a disciplinary process, they may be cured on de novo appeal. Authority for this approach can be found at the Court of Arbitration for Sport and in particular in CAS 2009/A/1920 FK Pobeda, Aleksandar Zabrcanec, Nikolce Zdraveski v UEFA at para 87.

The question on proportionality asks what, aside from precedent found within the decisions of the sports body in question, are the general legal principles against which a sanction by a sports disciplinary body can be benchmarked in order to ascertain whether it is disproportionate in length or even irrational in nature?

On the matter of (dis)proportionality of sanction, the debate is usually guided by the authority in Bradley v the Jockey Club [2004] EWHC 2164 (QB) and affirmed at [2005] EWCA Civ 1056. The Bradley principles on proportionality of sports-specific sanctions, recently cited with approval at the Court of Arbitration for Sport, will be examined in this presentation.

Finally, an interesting application of many of the above principles (and others such as the appropriate standard of proof in sports disciplinary procedures) can be made to recent match-fixing or corruption related hearings held by the British Horse Racing Authority, the integrity units of snooker and tennis, and at the Court of Arbitration for Sport.

Sorting out mix-ups. The provenance of tissue sections may be confirmed by PCR using microsatellite markers

Standard identification systems usually ensure that biopsy material is correctly associated with a given patient. Sometimes, as when a tumor is unexpectedly found, the provenance (proof of origin) of a tissue sample may be questioned; the tissue may have been mislabelled or contaminated with tissue from another patient. Techniques used to confirm tissue provenance include comparing either tissue markers of gender or ABO blood groups; however, these methods have weak confirmatory power. Recently, the use of DNA-based polymerase chain reaction (PCR) techniques has been reported. Paired, formalin-fixed, paraffin-embedded, 10 microns tissue sections were selected from 17 patients, 8 of whom had carcinoma, either by dividing a biopsy section, using sequential biopsies, or sequential biopsy and autopsy tissue. The resulting 36 samples were coded before analysis. In two additional cases, 1-mm fragments of tumor from one patient were included in the tissue block of benign tissue from another patient, the tumor fragments were identified on hematoxylin-and-eosin-stained sections, separately scraped off the glass slide, and analyzed. Tissue from two clinical cases, one of suspected mislabelling and one with a suspected carry-over of malignant tissue were also investigated. Short tandem repeat sequences (STR) or microsatellites, are 2-5 base pair repeats that vary in their repeat number between individuals. This variation (polymorphism) can be assessed using a PCR. A panel of markers of 3 STRs; ACPP, INT 2, and CYP 19 (on chromosomes 3, 11, and 15, respectively) were used. DNA was isolated from the samples after xylene deparaffinization and proteinase digestion, and was then amplified in a radioactive PCR using primers selected to give a product size ranging from 136-178 bases. Amplified products were electrophoresed on denaturing polyacrylamide gels, dried, and autoradiographed. DNA segments were successfully extracted from all samples but one, which was fixed in Bouin's fluid. By comparing allele sizes from the panel, all tissue pairs (other than the Bouin's pair) were successfully matched, the 1-mm tumor fragments were correctly assigned, and the two clinical problems were solved. STRs are highly informative and robust markers, well suited to PCR of small portions of tissue sections, and are an effective method to confirm the provenance of benign and malignant biopsy and autopsy material.

Local probing of ferroelectric and ferroelastic switching through stress-mediated piezoelectric spectroscopy

Strain effects have a significant role in mediating classic ferroelectric behavior such as polarization switching and domain wall dynamics. These effects are of critical relevance if the ferroelectric order parameter is coupled to strain and is therefore, also ferroelastic. Here, switching spectroscopy piezoresponse force microscopy (SS-PFM) is combined with control of applied tip pressure to exert direct control over the ferroelastic and ferroelectric switching events, a modality otherwise unattainable in traditional PFM. As a proof of concept, stress-mediated SS-PFM is applied toward the study of polarization switching events in a lead zirconate titanate thin film, with a composition near the morphotropic phase boundary with co-existing rhombohedral and tetragonal phases. Under increasing applied pressure, shape modification of local hysteresis loops is observed, consistent with a reduction in the ferroelastic domain variants under increased pressure. These experimental results are further validated by phase field simulations. The technique can be expanded to explore more complex electromechanical responses under applied local pressure, such as probing ferroelectric and ferroelastic piezoelectric nonlinearity as a function of applied pressure, and electro-chemo-mechanical response through electrochemical strain microscopy.

Biocontrol agents promote growth of potato pathogens, depending on environmental conditions

There is a pressing need to understand and optimize biological control so as to avoid over-reliance on the synthetic chemical pesticides that can damage environmental and human health. This study focused on interactions between a novel biocontrol-strain, Bacillus sp. JC12GB43, and potato-pathogenic Phytophthora and Fusarium species. In assays carried out in vitro and on the potato tuber, the bacterium was capable of near-complete inhibition of pathogens. This Bacillus was sufficiently xerotolerant (water activity limit for growth = 0.928) to out-perform Phytophthora infestans (~0.960) and challenge Fusarium coeruleum (~0.847) and Fusarium sambucinum (~0.860) towards the lower limits of their growth windows. Under some conditions, however, strain JC12GB43 stimulated proliferation of the pathogens: for instance, Fusarium coeruleum growth-rate was increased under chaotropic conditions in vitro (132 mM urea) by >100% and on tubers (2-M glycerol) by up to 570%. Culture-based assays involving macromolecule-stabilizing (kosmotropic) compatible solutes provided proof-of-principle that the Bacillus may provide kosmotropic metabolites to the plant pathogen under conditions that destabilize macromolecular systems of the fungal cell. Whilst unprecedented, this finding is consistent with earlier reports that fungi can utilize metabolites derived from bacterial cells. Unless the antimicrobial activities of candidate biocontrol strains are assayed over a full range of field-relevant parameters, biocontrol agents may promote plant pathogen infections and thereby reduce crop yields. These findings indicate that biocontrol activity, therefore, ought to be regarded as a mode-of-behaviour (dependent on prevailing conditions) rather than an inherent property of a bacterial strain.

Weak and strong disjunction in possibilistic ASP

Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.

Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

The Richardson–Lucy algorithm is one of the most important in image deconvolution. However, a drawback is its slow convergence. A significant acceleration was obtained using the technique proposed by Biggs and Andrews (BA), which is implemented in the deconvlucy function of the image processing MATLAB toolbox. The BA method was developed heuristically with no proof of convergence. In this paper, we introduce the heavy-ball (H-B) method for Poisson data optimization and extend it to a scaled H-B method, which includes the BA method as a special case. The method has a proof of the convergence rateof O(K^2), where k is the number of iterations. We demonstrate the superior convergence performance, by a speedup factor off ive, of the scaled H-B method on both synthetic and real 3D images.

Behaviour-time budget and functional habitat use of a free-ranging European badger (Meles meles)

Background: The European badger (Melesmeles) is involved in the maintenance of bovine tuberculosis infection and onward spread to cattle. However, little is known about how transmission occurs. One possible route could be through direct contact between infected badgers and cattle. It is also possible that indirect contact between cattle and infected badger excretory products such as faeces or urine may occur either on pasture or within and around farm buildings. A better understanding of behaviour patterns in wild badgers may help to develop biosecurity measures to minimise direct and indirect contact between badgers and cattle. However, monitoring the behaviour of free-ranging badgers can be logistically challenging and labour intensive due to their nocturnal and semi-fossorial nature.We trialled a GPS and tri-axial accelerometer-equipped collar on a free-ranging badger to assess its potential value to elucidate behaviour-time budgets and functional habitat use. Results: During the recording period between 16:00 and 08:00 on a single night, resting was the most commonly identified behaviour (67.4%) followed by walking (20.9%), snuffling (9.5%) and trotting (2.3%).When examining accelerometer data associated with each GPS fix and habitat type (occurring 2 min 30 s before and after), walking was themost common behaviour in woodland (40.3%) and arable habitats (53.8%), while snuffling was themost common behaviour in pasture (61.9%). Several nocturnal resting periods were also observed. The total distance travelled was 2.28 km. Conclusions: In the present report, we demonstrate proof of principle in the application of a combined GPS and accelerometer device to collect detailed quantitative data on wild badger behaviour. Behaviour-time budgets allow us to investigate how badgers allocate energy to different activities and how thismight change with disease status. Such information could be useful in the development of measures to reduce opportunities for onward transmission of bovine tuberculosis from badgers to cattle.

Improving E-Assessment Systems With A focus On Adaptive Feedback And Marking

Institutions involved in the provision of tertiary education across Europe are feeling the pinch. European universities, and other higher education (HE) institutions, must operate in a climate where the pressure of government spending cuts (Garben, 2012) is in stark juxtaposition to the EU’s strategy to drive forward and maintain a growth of student numbers in the sector (eurostat, 2015).

In order to remain competitive, universities and HE institutions are making ever-greater use of electronic assessment (E-Assessment) systems (Chatzigavriil et all, 2015; Ferrell, 2012). These systems are attractive primarily because they offer a cost-effect and scalable approach for assessment. In addition to scalability, they also offer reliability, consistency and impartiality; furthermore, from the perspective of a student they are most popular because they can offer instant feedback (Walet, 2012).

There are disadvantages, though.

First, feedback is often returned to a student immediately on competition of their assessment. While it is possible to disable the instant feedback option (this is often the case during an end of semester exam period when assessment scores must be can be ratified before release), however, this option tends to be a global ‘all on’ or ‘all off’ configuration option which is controlled centrally rather than configurable on a per-assessment basis.

If a formative in-term assessment is to be taken by multiple groups of
students, each at different times, this restriction means that answers to each question will be disclosed to the first group of students undertaking the assessment. As soon as the answers are released “into the wild” the academic integrity of the assessment is lost for subsequent student groups.

Second, the style of feedback provided to a student for each question is often limited to a simple ‘correct’ or ‘incorrect’ indicator. While this type of feedback has its place, it often does not provide a student with enough insight to improve their understanding of a topic that they did not answer correctly.

Most E-Assessment systems boast a wide range of question types including Multiple Choice, Multiple Response, Free Text Entry/Text Matching and Numerical questions. The design of these types of questions is often quite restrictive and formulaic, which has a knock-on effect on the quality of feedback that can be provided in each case.

Multiple Choice Questions (MCQs) are most prevalent as they are the most prescriptive and therefore most the straightforward to mark consistently. They are also the most amenable question types, which allow easy provision of meaningful, relevant feedback to each possible outcome chosen.
Text matching questions tend to be more problematic due to their free text entry nature. Common misspellings or case-sensitivity errors can often be accounted for by the software but they are by no means fool proof, as it is very difficult to predict in advance the range of possible variations on an answer that would be considered worthy of marks by a manual marker of a paper based equivalent of the same question.

Numerical questions are similarly restricted. An answer can be checked for accuracy or whether it is within a certain range of the correct answer, but unless it is a special purpose-built mathematical E-Assessment system the system is unlikely to have computational capability and so cannot, for example, account for “method marks” which are commonly awarded in paper-based marking.

From a pedagogical perspective, the importance of providing useful formative feedback to students at a point in their learning when they can benefit from the feedback and put it to use must not be understated (Grieve et all, 2015; Ferrell, 2012).

In this work, we propose a number of software-based solutions, which will overcome the limitations and inflexibilities of existing E-Assessment systems.

Guided post-acceleration of laser-driven ions by a miniature modular structure

All-optical approaches to particle acceleration are currently attracting a significant research effort internationally. Although characterized by exceptional transverse and longitudinal emittance, laser-driven ion beams currently have limitations in terms of peak ion energy, bandwidth of the energy spectrum and beam divergence. Here we introduce the concept of a versatile, miniature linear accelerating module, which, by employing laser-excited electromagnetic pulses directed along a helical path surrounding the laser-accelerated ion beams, addresses these shortcomings simultaneously. In a proof-of-principle experiment on a university-scale system, we demonstrate post-acceleration of laser-driven protons from a flat foil at a rate of 0.5 GeVm^-1, already beyond what can be sustained by conventional accelerator technologies, with dynamic beam collimation and energy selection. These results open up new opportunities for the development of extremely compact and cost-effective ion accelerators for both established and innovative applications.

Lattice-based Encryption Over Standard Lattices in Hardware

Lattice-based cryptography has gained credence recently as a replacement for current public-key cryptosystems, due to its quantum-resilience, versatility, and relatively low key sizes. To date, encryption based on the learning with errors (LWE) problem has only been investigated from an ideal lattice standpoint, due to its computation and size efficiencies. However, a thorough investigation of standard lattices in practice has yet to be considered. Standard lattices may be preferred to ideal lattices due to their stronger security assumptions and less restrictive parameter selection process. In this paper, an area-optimised hardware architecture of a standard lattice-based cryptographic scheme is proposed. The design is implemented on a FPGA and it is found that both encryption and decryption fit comfortably on a Spartan-6 FPGA. This is the first hardware architecture for standard lattice-based cryptography reported in the literature to date, and thus is a benchmark for future implementations.
Additionally, a revised discrete Gaussian sampler is proposed which is the fastest of its type to date, and also is the first to investigate the cost savings of implementing with lamda_2-bits of precision. Performance results are promising in comparison to the hardware designs of the equivalent ring-LWE scheme, which in addition to providing a stronger security proof; generate 1272 encryptions per second and 4395 decryptions per second.

Network signatures based on gene pair expression ratios improve classification and the analysis of muscle-invasive urothelial cancer

Urothelial cancer (UC) is highly recurrent and can progress from non-invasive (NMIUC) to a more aggressive muscle-invasive (MIUC) subtype that invades the muscle tissue layer of the bladder. We present a proof of principle study that network-based features of gene pairs can be used to improve classifier performance and the functional analysis of urothelial cancer gene expression data. In the first step of our procedure each individual sample of a UC gene expression dataset is inflated by gene pair expression ratios that are defined based on a given network structure. In the second step an elastic net feature selection procedure for network-based signatures is applied to discriminate between NMIUC and MIUC samples. We performed a repeated random subsampling cross validation in three independent datasets. The network signatures were characterized by a functional enrichment analysis and studied for the enrichment of known cancer genes. We observed that the network-based gene signatures from meta collections of proteinprotein interaction (PPI) databases such as CPDB and the PPI databases HPRD and BioGrid improved the classification performance compared to single gene based signatures. The network based signatures that were derived from PPI databases showed a prominent enrichment of cancer genes (e.g., TP53, TRIM27 and HNRNPA2Bl). We provide a novel integrative approach for large-scale gene expression analysis for the identification and development of novel diagnostical targets in bladder cancer. Further, our method allowed to link cancer gene associations to network-based expression signatures that are not observed in gene-based expression signatures.

O livro no jardim-de-infância : um olhar sobre a obra de Luísa Ducla Soares

A literatura para a infância tem sido objecto de discussão, especialmente notocante ao seu estatuto no universo literário, sobretudo a partir dos anos 70 doséculo XX, vindo, assim, a desenvolver-se e a assumir uma crescente importância. Decorrente da evolução do conceito de criança, a literatura para ainfância foi assumindo um lugar proeminente na sua formação,nomeadamente, em idade pré-escolar. A seguir à família, o educador de infância afigura-se como outro dos principais mediadores no encontro dacriança com o livro, tendo, desde aí, uma função influente face à promoção dogosto pela leitura. No entanto, este profissional sente a necessidade de, desdea sua formação inicial, sever dotado de conhecimentos básicos que lhe permitam práticas mais ajustadas e que salvaguardem as necessidades einteresses de leitura das crianças. A presente dissertação tem como principal finalidade aferir a importânciaatribuída à literatura para a infância, com especial destaque na obra de Luísa Ducla Soares, em contexto de jardim-de-infância. Apesar do lugar incontestável desta autora e da sua obra no cânone daliteratura portuguesa para a infância, a crítica literária de que tem sido alvo é ainda exígua. Por essa razão também, procurámos, através de uma análisedas especificidades da sua escrita, da diversidade das temáticas inerentes àssuas histórias e da qualidade estética e literária das suas publicações, reflectirsobre as potencialidades das obras que nos apresenta a referida escritora, pelas quais tem merecido vários prémios e nomeações. ABSTRACT: Literature for early years has been subject of quarrel, especially regarding to itsstatute in the literature universe, mostly since the 70’s of the 20th century, andconsequently came to grow and to assume an increasing importance. As aresult of the evolution of the child concept, literature for early years wasassuming a prominent position in children education, specifically, in preschoolage. After family, the kindergarten teacher figures hisself/herself as another of themain intermediaries in introducingchild to books, having, since then, an influential role endorsing reading’s taste on children. However, this practitionerneeds, since his/her formative years, to be endowed with basic knowledge thatallows him/her more adjusted practices that look after reading’s necessities and interests of children’s interests. The present dissertation’s main purpose is to survey which importance hasliterature for infants, with a special focus on the work of Luísa Ducla Soares, inearly childhood education. Even though her books are unquestionable at ruling literature for infants inPortugal, there hasn’t been that much literary analysis about it. Therefore, welooked, through the particulars aspects of her writing, the diversity of themesthat are inherent to her stories and the artistic and literary value of her publications, to proof the quality of the work presented by the mentioned writer,on behalf of which the author has justified several awards and nominations.

O desenvolvimento do raciocínio dedutivo ao nível do ensino secundário : recurso a geometrias planas

Este trabalho, no âmbito da Didáctica da Matemática, foca-se no estudo de abordagens alternativas de ensino e aprendizagem da Geometria Euclidiana, no Ensino Secundário, no sentido de promover níveis estruturados do pensamento matemático. Em particular, as potencialidades do recurso a outros modelos de Geometria Plana (e.g. Geometria Hiperbólica, Geometria do Motorista de Táxi) em relação a este problema serão investigadas. A opção pelo Ensino Secundário deve-se ao facto de se tratar de um nível de ensino onde se regista uma elevada taxa de insucesso escolar (especialmente no 10º ano) e onde é notório o abismo existente, entre o ensino Secundário e Universitário, no âmbito do raciocínio lógico - dedutivo. O trabalho a desenvolver pretende aprofundar o estudo de questões ligadas à natureza do conhecimento envolvido que estarão na base de decisões, tais como: Quais os processos que vão ser ensinados? Que processos queremos que os alunos dominem? E, por outro lado, ter em conta que se pretende desenvolver capacidades de ordem superior, significando que o ensino da Matemática deve dirigir-se para níveis elevados de pensamento, tais como: resolução de problemas; comunicar matematicamente; raciocínio e demonstração. No currículo de matemática para o Ensino Básico e Secundário tem-se negligenciado a demonstração matemática, contribuindo para que exista uma desconformidade entre os graus de ensino, secundário e universitário. Muitas vezes as abordagens de ensino centram-se na verificação de resultados e desvalorizam a exploração e explicação (Villiers, 1998). Actualmente, assiste-se a uma tendência para retomar o raciocínio lógico - dedutivo. O principal objectivo desta investigação é analisar ambientes de aprendizagem em que os alunos sejam solicitados a resolver problemas de prova em contextos diversificados e, de uma forma mais geral promover o desenvolvimento do raciocínio dedutivo e uma visão mais alargada do conhecimento matemático. Em particular, a abordagem de problemas de prova num contexto de geometria não Euclidiana, com recurso a artefactos e a software de geometria dinâmica, será investigada.