Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction

Theorem acquisition and deductive proof have always been core elements in the study and teaching of Euclidean geometry. The introduction of dynamic geometry environments,DGE (e.g., Cabri-Géomètre, Geometer's Sketchpad), into classrooms in the past decade has posed a challenge to this praxis. Student scan experiment through different dragging modalities on geometrical objects that they construct, and consequently infer properties(generalities, theorems) about the geometrical artefacts. Because of the inductive nature of the DGE, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical and epistemological concern. In this paper, we will describe and study a ‘Cabri proof by contradiction’ of a theorem on cyclic quadrilaterals given by a pair of 16 year-old students in a Hong Kong secondary school. We will discuss how their construction motivates a visual-cognitive scheme on `seeing' proof in DGE, and how this scheme could fit into the theoretical construct of cognitive unity of theorems proposed by Boero, Garuti and Mariotti(1996). The issue of a cognitive duality and its relation to visualization will be raised and discussed. Finally, we propose a possible perspective to bridge the experimental-theoretical gap in DGE by introducing the idea of a dynamic template as a visualizer to geometrical theorem justification and acquisition.postprin

Properties of tangential and cyclic polygons: an application of circulant matrices

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon Pn with n even is slippable (or conformable) and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain equalities. On the other hand, for a tangential (or cyclic) polygon Pn with n odd, it is rigid and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain inequalities. These inequalities give a definite answer to the question raised by Lopez-Real concerning the alternating sum of interior angles of a cyclic polygon.postprin

Superparamagnetic particles in ZSM-5-type ferrisilicates

As-synthesized, low iron content, ferrisilicates of ZSM-5-type contain well-separated Fe(III) ions in a tetrahedral environment and display paramagnetic behavior. After hydrothermal treatment, the iron ions are partially extracted from the framework, generating nanosize iron oxide or oxyhydroxide ferrimagnetic particles. This process has been studied by transmission electron microscopy (TEM), Mossbauer spectroscopy, magnetic ac susceptibility (chi(ac)), and field dependent magnetization, on samples containing up to 6.7 wt. % Fe. The experiments evidence the growth of nonaggregated particles, with a typical size around 3 nm, presumably located at the surface of the ferrisilicate crystallites, From a thorough granulometric analysis involving TEM and chi(ac) data, it is concluded that, in the range from 1.5 to 4.6 wt. % Fe, the particle size distributions are significantly independent of the iron content

Monovinyl sulfone beta-cyclodextrin. A flexible drug carrier system

Cyclodextrins have been conjugated to target various receptors and have also been functionalized with carbohydrates for targeting specific organs. However, this approach is based on a rigid design that implies the ad hoc synthesis of each cyclodextrin-targeting agent conjugate. We hypothesized that: 1) a modular design that decouples the carrier function from the targeting function leads to a flexible system, 2) combining the reactivity of the vinyl sulfone group toward biomolecules that act as targeting agents with the ability of cyclodextrin to form complexes with a wide range of drugs may yield a versatile system that allows the targeting of different organs with different drugs, and 3) the higher reactivity of histidine residues toward the vinyl sulfone group can be exploited to couple the cyclodextrin to the targeting system with a degree of regioselectivity. As a proof of concept, we synthesized a monovinyl sulfone beta-cyclodextrin (module responsible for the payload), which, after coupling to recombinant antibody fragments raised against Trypanosoma brucei (module responsible for targeting) and loading with nitrofurazone (module responsible for therapeutic action) resulted in an effective delivery system that targets the surface of the parasites and shows trypanocidal activity

Response-adapted treatment with rituximab, bendamustine, mitoxantrone, and dexamethasone followed by rituximab maintenance in patients with relapsed or refractory follicular lymphoma after first-line immunochemotherapy: Results of the RBMDGELTAMO08 phase II trial

Background Consensus is lacking regarding the optimal salvage therapy for patients with follicular lymphoma who relapse after or are refractory to immunochemotherapy. Methods This phase II trial evaluated the efficacy and safety of response-adapted therapy with rituximab, bendamustine, mitoxantrone, and dexamethasone (RBMD) in follicular lymphoma patients who relapsed after or were refractory to first-line immunochemotherapy. Sixty patients received three treatment cycles, and depending on their response received an additional one (complete/unconfirmed complete response) or three (partial response) cycles. Patients who responded to induction received rituximab maintenance therapy for 2 years. Results Thirty-three (55%) and 42 (70%) patients achieved complete/unconfirmed complete response after three cycles and on completing induction therapy (4-6 cycles), respectively (final overall response rate, 88.3%). Median progression-free survival was 56.4 months (median follow-up, 28.3 months; 95% CI, 15.6-51.2). Overall survival was not reached. Progression-free survival did not differ between patients who received four vs six cycles (P = .6665), nor between patients who did/did not receive rituximab maintenance after first-line therapy (P = .5790). Median progression-free survival in the 10 refractory patients was 25.5 months (95% CI, 0.6-N/A) and was longer in patients who had shown progression of disease after 24 months of first-line therapy (median, 56.4 months; 95% CI, 19.8-56.4) than in those who showed early progression (median, 42.31 months; 95% CI, 24.41-NA) (P = .4258). Thirty-six (60%) patients had grade 3/4 neutropenia. Grade 3/4 febrile neutropenia and infection were recorded during induction (4/60 [6.7%] and 5/60 [8.3%] patients, respectively) and maintenance (2/43 [4.5%] and 4/43 [9.1%] patients, respectively). Conclusions This response-adapted treatment with RBMD followed by rituximab maintenance is an effective and well-tolerated salvage treatment for relapsed/refractory follicular lymphoma following first-line immunochemotherapy

Association of VAV2 and VAV3 polymorphisms with cardiovascular risk factors

Hypertension, diabetes and obesity are cardiovascular risk factors closely associated to the development of renal and cardiovascular target organ damage. VAV2 and VAV3, members of the VAV family proto-oncogenes, are guanosine nucleotide exchange factors for the Rho and Rac GTPase family, which is related with cardiovascular homeostasis. We have analyzed the relationship between the presence of VAV2 rs602990 and VAV3 rs7528153 polymorphisms with cardiovascular risk factors and target organ damage (heart, vessels and kidney) in 411 subjects. Our results show that being carrier of the T allele in VAV2 rs602990 polymorphism is associated with an increased risk of obesity, reduced levels of ankle-brachial index and diastolic blood pressure and reduced retinal artery caliber. In addition, being carrier of T allele is associated with increased risk of target organ damage in males. On the other hand, being carrier of the T allele in VAV3 rs7528153 polymorphism is associated with a decreased susceptibility of developing a pathologic state composed by the presence of hypertension, diabetes, obesity or cardiovascular damage, and with an increased risk of developing altered basal glycaemia. This is the first report showing an association between VAV2 and VAV3 polymorphisms with cardiovascular risk factors and target organ damage

Lipoprotein-associated phospholipase A2 (Lp-PLA2) as a therapeutic target to prevent retinal vasopermeability during diabetes

Lipoprotein-associated phospholipase A2 (Lp-PLA2) hydrolyses oxidized low-density lipoproteins into proinflammatory products, which can have detrimental effects on vascular function. As a specific inhibitor of Lp-PLA2, darapladib has been shown to be protective against atherogenesis and vascular leakage in diabetic and hypercholesterolemic animal models. This study has investigated whether Lp-PLA2 and its major enzymatic product, lysophosphatidylcholine (LPC), are involved in blood-retinal barrier (BRB) damage during diabetic retinopathy. We assessed BRB protection in diabetic rats through use of species-specific analogs of darapladib. Systemic Lp-PLA2 inhibition using SB-435495 at 10 mg/kg (i.p.) effectively suppressed BRB breakdown in streptozotocin-diabetic Brown Norway rats. This inhibitory effect was comparable to intravitreal VEGF neutralization, and the protection against BRB dysfunction was additive when both targets were inhibited simultaneously. Mechanistic studies in primary brain and retinal microvascular endothelial cells, as well as occluded rat pial microvessels, showed that luminal but not abluminal LPC potently induced permeability, and that this required signaling by the VEGF receptor 2 (VEGFR2). Taken together, this study demonstrates that Lp-PLA2 inhibition can effectively prevent diabetes-mediated BRB dysfunction and that LPC impacts on the retinal vascular endothelium to induce vasopermeability via VEGFR2. Thus, Lp-PLA2 may be a useful therapeutic target for patients with diabetic macular edema (DME), perhaps in combination with currently administered anti-VEGF agents

Leprosy Associated with Atypical Cutaneous Leishmaniasis in Nicaragua and Honduras

In Central America, few cases of leprosy have been reported, but the disease may be unrecognized. Diagnosis is based on clinical criteria and histology. Preliminary field work in Nicaragua and Honduras found patients, including many children, with skin lesions clinically suggestive of atypical cutaneous leishmaniasis or indeterminate leprosy. Histology could not distinguish these diseases although acid-fast organisms were visible in a few biopsies. Lesions healed after standard antimicrobial therapy for leprosy. In the present study, patients, family members, and other community members were skin-tested and provided nasal swabs and blood samples. Biopsies were taken from a subgroup of patients with clinical signs of infection. Two laboratories analyzed samples, using local in-house techniques. Mycobacterium leprae, Leishmania spp. and Leishmania infantum were detected using polymerase chain reactions. Mycobacterium leprae DNA was detected in blood samples and nasal swabs, including some cases where leprosy was not clinically suspected. Leishmania spp. were also detected in blood and nasal swabs. Most biopsies contained Leishmania DNA and coinfection of Leishmania spp. with M. leprae occurred in 33% of cases. Mycobacterium leprae DNA was also detected and sequenced from Nicaraguan and Honduran environmental samples. In conclusion, leprosy and leishmaniasis are present in both regions, and leprosy appears to be widespread. The nature of any relationship between these two pathogens and the epidemiology of these infections need to be elucidated

Stenotrophomonas maltophilia prosthetic valve endocarditis: a case report

<p>Abstract</p> <p>Introduction</p> <p><it>Stenotrophomonas maltophilia </it>is an environmental bacterium increasingly involved in nosocomial infections and resistant to most antibiotics. It is important to recognize and efficiently treat infections with this bacterium as soon as possible.</p> <p>Case presentation</p> <p>We present a case of <it>Stenotrophomonas maltophilia </it>prosthetic valve endocarditis secondary to an indwelling catheter infection. The patient was cured without surgery. We review other cases of <it>S. maltophilia </it>endocarditis from the literature and describe the peculiarities of this case.</p> <p>Conclusion</p> <p><it>S. maltophilia </it>endocarditis is a rare disease that is often hospital-acquired and related to an indwelling catheter infection. The high lethality is likely related to the intrinsic resistance of nosocomial bloodstream infections to commonly prescribed antibiotics.</p

HSP60 as a Target of Anti-Ergotypic Regulatory T Cells

The 60 kDa heat shock protein (HSP60) has been reported to influence T-cell responses in two ways: as a ligand of toll-like receptor 2 signalling and as an antigen. Here we describe a new mechanism of T-cell immuno-regulation focused on HSP60: HSP60 is up-regulated and presented by activated T cells (HSP60 is an ergotope) to regulatory (anti-ergotypic) T cells. Presentation of HSP60 by activated T cells was found to be MHC-restricted and dependent on accessory molecules - CD28, CD80 and CD86. Anti-ergotypic T cells responded to T-cell HSP60 by proliferation and secreted IFNγ and TGFβ1. In vitro, the anti-ergotypic T cells inhibited IFNγ production by their activated T-cell targets. In vivo, adoptive transfer of an anti-ergotypic HSP60-specific T-cell line led to decreased secretion of IFNγ by arthritogenic T cells and ameliorated adjuvant arthritis (AA). Thus, the presentation of HSP60 by activated T cells turns them into targets for anti-ergotypic regulatory T cells specific for HSP60. However, the direct interaction between the anti-ergotypic T regulators (anti-HSP60) and the activated T cells also down-regulated the regulators. Thus, by functioning as an ergotope, HSP60 can control both the effector T cells and the regulatory HSP60-specific T cells that control them