Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Characterization of the procera Tomato Mutant Shows Novel Functions of the SlDELLA Protein in the Control of Flower Morphology, Cell Division and Expansion, and the Auxin-Signaling Pathway during Fruit-Set and Development

procera (pro) is a tall tomato (Solanum lycopersicum) mutant carrying a point mutation in the GRAS region of the gene encoding SlDELLA, a repressor in the gibberellin (GA) signaling pathway. Consistent with the SlDELLA loss of function, pro plants display a GA-constitutive response phenotype, mimicking wild-type plants treated with GA(3). The ovaries from both nonemasculated and emasculated pro flowers had very strong parthenocarpic capacity, associated with enhanced growth of preanthesis ovaries due to more and larger cells. pro parthenocarpy is facultative because seeded fruits were obtained by manual pollination. Most pro pistils had exserted stigmas, thus preventing self-pollination, similar to wild-type pistils treated with GA(3) or auxins. However, Style2.1, a gene responsible for long styles in noncultivated tomato, may not control the enhanced style elongation of pro pistils, because its expression was not higher in pro styles and did not increase upon GA(3) application. Interestingly, a high percentage of pro flowers had meristic alterations, with one additional petal, sepal, stamen, and carpel at each of the four whorls, respectively, thus unveiling a role of SlDELLA in flower organ development. Microarray analysis showed significant changes in the transcriptome of preanthesis pro ovaries compared with the wild type, indicating that the molecular mechanism underlying the parthenocarpic capacity of pro is complex and that it is mainly associated with changes in the expression of genes involved in GA and auxin pathways. Interestingly, it was found that GA activity modulates the expression of cell division and expansion genes and an auxin signaling gene (tomato AUXIN RESPONSE FACTOR7) during fruit-set.

Opposing Roles for Cannabinoid Receptor Type-1 (CB1) and Transient Receptor Potential Vanilloid Type-1 Channel (TRPV1) on the Modulation of Panic-Like Responses in Rats

The midbrain dorsal periaqueductal gray (dPAG) has an important role in orchestrating anxiety-and panic-related responses. Given the cellular and behavioral evidence suggesting opposite functions for cannabinoid type 1 receptor (CB1) and transient receptor potential vanilloid type-1 channel (TRPV1), we hypothesized that they could differentially influence panic-like reactions induced by electrical stimulation of the dPAG. Drugs were injected locally and the expression of CB1 and TRPV1 in this structure was assessed by immunofluorescence and confocal microscopy. The CB1-selective agonist, ACEA (0.01, 0.05 and 0.5 pmol) increased the threshold for the induction of panic-like responses solely at the intermediary dose, an effect prevented by the CB1-selective antagonist, AM251 (75 pmol). Panicolytic-like effects of ACEA at the higher dose were unmasked by pre-treatment with the TRPV1 antagonist capsazepine (0.1 nmol). Similarly to ACEA, capsazepine (1 and 10 nmol) raised the threshold for triggering panic-like reactions, an effect mimicked by another TRPV1 antagonist, SB366791 (1 nmol). Remarkably, the effects of both capsazepine and SB366791 were prevented by AM251 (75 pmol). These pharmacological data suggest that a common endogenous agonist may have opposite functions at a given synapse. Supporting this view, we observed that several neurons in the dPAG co-expressed CB1 and TRPV1. Thus, the present work provides evidence that an endogenous substance, possibly anandamide, may exert both panicolytic and panicogenic effects via its actions at CB1 receptors and TRPV1 channels, respectively. This tripartite set-point system might be exploited for the pharmacotherapy of panic attacks and anxiety-related disorders. Neuropsychopharmacology (2012) 37, 478-486; doi:10.1038/npp.2011.207; published online 21 September 2011

Reduced muscle carnosine content in type 2, but not in type 1 diabetic patients

Carnosine is present in high concentrations in skeletal muscle where it contributes to acid buffering and functions also as a natural protector against oxidative and carbonyl stress. Animal studies have shown an anti-diabetic effect of carnosine supplementation. High carnosinase activity, the carnosine degrading enzyme in serum, is a risk factor for diabetic complications in humans. The aim of the present study was to compare the muscle carnosine concentration in diabetic subjects to the level in non-diabetics. Type 1 and 2 diabetic patients and matched healthy controls (total n = 58) were included in the study. Muscle carnosine content was evaluated by proton magnetic resonance spectroscopy (3 Tesla) in soleus and gastrocnemius. Significantly lower carnosine content (-45%) in gastrocnemius muscle, but not in soleus, was shown in type 2 diabetic patients compared with controls. No differences were observed in type 1 diabetic patients. Type II diabetic patients display a reduced muscular carnosine content. A reduction in muscle carnosine concentration may be partially associated with defective mechanisms against oxidative, glycative and carbonyl stress in muscle.

Cost-effectiveness and budget impact of saxagliptine as additional therapy to metformin for the treatment of diabetes mellitus type 2 in the Brazilian private health system

Cost-effectiveness and budget impact of saxagliptine as additional therapy to metformin for the treatment of diabetes mellitus type 2 in the Brazilian private health system Objectives: To compare costs and clinical benefits of three additional therapies to metformin (MF) for patients with diabetes mellitus type 2 (DM2). Methods: A discrete event simulation model seas built to estimate the cost-utility ratio (cost per quality-adjusted life years [QALY)) of saxagliptine as an additional therapy to MF when compared to rosiglitazone or pioglitazone. A budget impact model (BIM) was built to simulate the economic impact of saxagliptine use in the context of the Brazilian private health system. Results: The acquiring medication costs for the hypothetical patient group analyzed in a time frame of three years, were R$ 10,850,185, R$ 14,836,265 and R$ 14,679,099 for saxagliptine, pioglitazone and rosiglitazone, respectively. Saxagliptine showed lower costs and greater effectiveness in both comparisons, with projected savings for the first three years of R$ 3,874 and R$ 3,996, respectively. The BIM estimated cumulative savings of R$ 417,958 with the repayment of saxagliptine in three years from the perspective of a health plan with 1,000,000 covered individuals. Conclusion: From the perspective of private paying source, the projection is that adding saxagliptine with MF save costs when compared with the addition of rosiglitazone or pioglitazone in patients with DM2 that have not reached the HbA1c goal with metformin monotherapy. The BIM of including saxagliptine in the reimbursement lists of health plans indicated significant savings on the three-year horizon.

ZETA DETERMINANT FOR DOUBLE SEQUENCES OF SPECTRAL TYPE

We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the first terms in the Laurent expansion at zero of the zeta function associated to a double sequence.

Interleukin-18 and interferon-gamma polymorphisms are implicated on proviral load and susceptibility to human T-lymphotropic virus type 1 infection

Interleukin-18 (IL-18) and interferon-gamma (IFN-?) exert important functions in both innate and adaptive immune responses against intracellular pathogens and viruses. Previous studies suggested that host genetic factors, including cytokines gene polymorphisms, could be involved in the pathogenesis of human T-cell leukemia virus type 1 (HTLV-1)-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Thus, we analyzed -137C/G and -607A/C of the IL-18 promoter and +874T/A of the IFN-? in DNA samples from 98 HTLV-1-infected individuals exhibiting or not clinical symptoms and 150 healthy control individuals. The IL-18 promoter -607CC genotype was significantly lower in HTLV-1 asymptomatic carriers (HAC) and HTLV-1-infected individuals (HAC + HAM/TSP) than healthy control group. In contrast, the -607AC genotype was significantly higher in HAC and HTLV-1-infected individuals group compared to the healthy control group. The -137G/-607A IL-18 haplotype was higher in infected group than healthy control group, and the -137C/-607C IL-18 haplotype was increased in the healthy control group compared to the others. Finally, the IFN-? polymorphism analysis showed that the HTLV-1-infected individuals with +874AT genotype presented higher proviral load than +874AA genotype. These data indicate that the IL-18-607AC genotype and -137G/-607A haplotype could be a risk factor for HTLV-1 infection, whereas the protective effect could be conferred by -607CC genotype and -137C/-607C haplotype. Also, the IFN-? could be implicated on the proviral load levels.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. (C) 2012 Elsevier B.V. All rights reserved.

Genomic analysis of ERVWE2 locus in patients with multiple sclerosis: absence of genetic association but potential role of human endogenous retrovirus type W elements in molecular mimicry with myelin antigen

Human endogenous retroviruses (HERVs) arise from ancient infections of the host germline cells by exogenous retroviruses, constituting 8% of the human genome. Elevated level of envelope transcripts from HERVs-W has been detected in CSF, plasma and brain tissues from patients with Multiple Sclerosis (MS), most of them from Xq22.3, 15q21.3, and 6q21 chromosomes. However, since the locus Xq22.3 (ERVWE2) lack the 5' LTR promoter and the putative protein should be truncated due to a stop codon, we investigated the ERVWE2 genomic loci from 84 individuals, including MS patients with active HERV-W expression detected in PBMC. In addition, an automated search for promoter sequences in 20 kb nearby region of ERVWE2 reference sequence was performed. Several putative binding sites for cellular cofactors and enhancers were found, suggesting that transcription may occur via alternative promoters. However, ERVWE2 DNA sequencing of MS and healthy individuals revealed that all of them harbor a stop codon at site 39, undermining the expression of a full-length protein. Finally, since plaque formation in central nervous system (CNS) of MS patients is attributed to immunological mechanisms triggered by autoimmune attack against myelin, we also investigated the level of similarity between envelope protein and myelin oligodendrocyte glycoprotein (MOG). Comparison of the MOG to the envelope identified five retroviral regions similar to the Ig-like domain of MOG. Interestingly, one of them includes T and B cell epitopes, capable to induce T effector functions and circulating Abs in rats. In sum, although no DNA substitutions that would link ERVWE2 to the MS pathogeny was found, the similarity between the envelope protein to MOG extends the idea that ERVEW2 may be involved on the immunopathogenesis of MS, maybe facilitating the MOG recognizing by the immune system. Although awaiting experimental evidences, the data presented here may expand the scope of the endogenous retroviruses involvement on MS pathogenesis

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.