Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Minimal flavour violation extensions of the seesaw

We analyze the most natural formulations of the minimal lepton flavour violation hypothesis compatible with a type-I seesaw structure with three heavy singlet neutrinos N, and satisfying the requirement of being predictive, in the sense that all LFV effects can be expressed in terms of low energy observables. We find a new interesting realization based on the flavour group $SU(3)_e\times SU(3)_{\ell+N}$ (being $e$ and $\ell$ respectively the SU(2) singlet and doublet leptons). An intriguing feature of this realization is that, in the normal hierarchy scenario for neutrino masses, it allows for sizeable enhancements of $\mu \to e$ transitions with respect to LFV processes involving the $\tau$ lepton. We also discuss how the symmetries of the type-I seesaw allow for a strong suppression of the N mass scale with respect to the scale of lepton number breaking, without implying a similar suppression for possible mechanisms of N productionComment: 14 pages, 6 figure

Decaying Dark Matter in the Supersymmetric Standard Model with Freeze-in and Seesaw mechanims

Inspired by the decaying dark matter (DM) which can explain cosmic ray anomalies naturally, we consider the supersymmetric Standard Model with three right-handed neutrinos (RHNs) and R-parity, and introduce a TeV-scale DM sector with two fields \phi_{1,2} and a $Z_3$ discrete symmetry. The DM sector only interacts with the RHNs via a very heavy field exchange and then we can explain the cosmic ray anomalies. With the second right-handed neutrino N_2 dominant seesaw mechanism at the low scale around 10^4 GeV, we show that \phi_{1,2} can obtain the vacuum expectation values around the TeV scale, and then the lightest state from \phi_{1,2} is the decay DM with lifetime around \sim 10^{26}s. In particular, the DM very long lifetime is related to the tiny neutrino masses, and the dominant DM decay channels to \mu and \tau are related to the approximate \mu-\tau symmetry. Furthermore, the correct DM relic density can be obtained via the freeze-in mechanism, the small-scale problem for power spectrum can be solved due to the decays of the R-parity odd meta-stable states in the DM sector, and the baryon asymmetry can be generated via the soft leptogensis.Comment: 24 pages,3 figure

Interplay of LFV and slepton mass splittings at the LHC as a probe of the SUSY seesaw

We study the impact of a type-I SUSY seesaw concerning lepton flavour violation (LFV) both at low-energies and at the LHC. The study of the di-lepton invariant mass distribution at the LHC allows to reconstruct some of the masses of the different sparticles involved in a decay chain. In particular, the combination with other observables renders feasible the reconstruction of the masses of the intermediate sleptons involved in $\chi_2^0\to \tilde \ell \,\ell \to \ell \,\ell\,\chi_1^0$ decays. Slepton mass splittings can be either interpreted as a signal of non-universality in the SUSY soft breaking-terms (signalling a deviation from constrained scenarios as the cMSSM) or as being due to the violation of lepton flavour. In the latter case, in addition to these high-energy processes, one expects further low-energy manifestations of LFV such as radiative and three-body lepton decays. Under the assumption of a type-I seesaw as the source of neutrino masses and mixings, all these LFV observables are related. Working in the framework of the cMSSM extended by three right-handed neutrino superfields, we conduct a systematic analysis addressing the simultaneous implications of the SUSY seesaw for both high- and low-energy lepton flavour violation. We discuss how the confrontation of slepton mass splittings as observed at the LHC and low-energy LFV observables may provide important information about the underlying mechanism of LFV.Comment: 50 pages, 42 eps Figures, typos correcte

Radiative contribution to neutrino masses and mixing in μν\mu\nuSSM

In an extension of the minimal supersymmetric standard model (popularly known as the $\mu\nu$SSM), three right handed neutrino superfields are introduced to solve the $\mu$-problem and to accommodate the non-vanishing neutrino masses and mixing. Neutrino masses at the tree level are generated through $R-$parity violation and seesaw mechanism. We have analyzed the full effect of one-loop contributions to the neutrino mass matrix. We show that the current three flavour global neutrino data can be accommodated in the $\mu\nu$SSM, for both the tree level and one-loop corrected analyses. We find that it is relatively easier to accommodate the normal hierarchical mass pattern compared to the inverted hierarchical or quasi-degenerate case, when one-loop corrections are included.Comment: 51 pages, 14 figures (58 .eps files), expanded introduction, other minor changes, references adde

Protective Role of Taurine against Arsenic-Induced Mitochondria-Dependent Hepatic Apoptosis via the Inhibition of PKCδ-JNK Pathway

BACKGROUND: Oxidative stress-mediated hepatotoxic effect of arsenic (As) is mainly due to the depletion of glutathione (GSH) in liver. Taurine, on the other hand, enhances intracellular production of GSH. Little is known about the mechanism of the beneficial role of taurine in As-induced hepatic pathophysiology. Therefore, in the present study we investigated its beneficial role in As-induced hepatic cell death via mitochondria-mediated pathway. METHODOLOGY/PRINCIPAL FINDINGS: Rats were exposed to NaAsO(2) (2 mg/kg body weight for 6 months) and the hepatic tissue was used for oxidative stress measurements. In addition, the pathophysiologic effect of NaAsO(2) (10 microM) on hepatocytes was evaluated by determining cell viability, mitochondrial membrane potential and ROS generation. As caused mitochondrial injury by increased oxidative stress and reciprocal regulation of Bcl-2, Bcl-xL/Bad, Bax, Bim in association with increased level of Apaf-1, activation of caspase 9/3, cleavage of PARP protein and ultimately led to apoptotic cell death. In addition, As markedly increased JNK and p38 phosphorylation with minimal disturbance of ERK. Pre-exposure of hepatocytes to a JNK inhibitor SP600125 prevented As-induced caspase-3 activation, ROS production and loss in cell viability. Pre-exposure of hepatocytes to a p38 inhibitor SB2035, on the other hand, had practically no effect on these events. Besides, As activated PKCdelta and pre-treatment of hepatocytes with its inhibitor, rottlerin, suppressed the activation of JNK indicating that PKCdelta is involved in As-induced JNK activation and mitochondrial dependent apoptosis. Oral administration of taurine (50 mg/kg body weight for 2 weeks) both pre and post to NaAsO(2) exposure or incubation of the hepatocytes with taurine (25 mM) were found to be effective in counteracting As-induced oxidative stress and apoptosis. CONCLUSIONS/SIGNIFICANCE: Results indicate that taurine treatment improved As-induced hepatic damages by inhibiting PKCdelta-JNK signalling pathways. Therefore taurine supplementation could provide a new approach for the reduction of hepatic complication due to arsenic poisoning

Genetic Structure and Inferences on Potential Source Areas for Bactrocera dorsalis (Hendel) Based on Mitochondrial and Microsatellite Markers

Bactrocera dorsalis (Diptera: Tephritidae) is mainly distributed in tropical and subtropical Asia and in the Pacific region. Despite its economic importance, very few studies have addressed the question of the wide genetic structure and potential source area of this species. This pilot study attempts to infer the native region of this pest and its colonization pathways in Asia. Combining mitochondrial and microsatellite markers, we evaluated the level of genetic diversity, genetic structure, and the gene flow among fly populations collected across Southeast Asia and China. A complex and significant genetic structure corresponding to the geographic pattern was found with both types of molecular markers. However, the genetic structure found was rather weak in both cases, and no pattern of isolation by distance was identified. Multiple long-distance dispersal events and miscellaneous host selection by this species may explain the results. These complex patterns may have been influenced by human-mediated transportation of the pest from one area to another and the complex topography of the study region. For both mitochondrial and microsatellite data, no signs of bottleneck or founder events could be identified. Nonetheless, maximal genetic diversity was observed in Myanmar, Vietnam and Guangdong (China) and asymmetric migration patterns were found. These results provide indirect evidence that the tropical regions of Southeast Asia and southern coast of China may be considered as the native range of the species and the population expansion is northward. Yunnan (China) is a contact zone that has been colonized from different sources. Regions along the southern coast of Vietnam and China probably served to colonize mainly the southern region of China. Southern coastal regions of China may also have colonized central parts of China and of central Yunnan