The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics

Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue that the concept of event-rather than object-better captures the vitality of mathematics, and offers new ways of thinking about mathematics education. In this paper I draw on two different but related theories of event articulated in the philosophies of Alain Badiou and Gilles Deleuze to argue that the central activity of 'problem solving' in mathematics education should be recast in terms of a problematic of events. © 2012 Springer Science+Business Media Dordrecht

Candida albicans repetitive elements display epigenetic diversity and plasticity

Transcriptionally silent heterochromatin is associated with repetitive DNA. It is poorly understood whether and how heterochromatin differs between different organisms and whether its structure can be remodelled in response to environmental signals. Here, we address this question by analysing the chromatin state associated with DNA repeats in the human fungal pathogen Candida albicans. Our analyses indicate that, contrary to model systems, each type of repetitive element is assembled into a distinct chromatin state. Classical Sir2-dependent hypoacetylated and hypomethylated chromatin is associated with the rDNA locus while telomeric regions are assembled into a weak heterochromatin that is only mildly hypoacetylated and hypomethylated. Major Repeat Sequences, a class of tandem repeats, are assembled into an intermediate chromatin state bearing features of both euchromatin and heterochromatin. Marker gene silencing assays and genome-wide RNA sequencing reveals that C. albicans heterochromatin represses expression of repeat-associated coding and non-coding RNAs. We find that telomeric heterochromatin is dynamic and remodelled upon an environmental change. Weak heterochromatin is associated with telomeres at 30?°C, while robust heterochromatin is assembled over these regions at 39?°C, a temperature mimicking moderate fever in the host. Thus in C. albicans, differential chromatin states controls gene expression and epigenetic plasticity is linked to adaptation

Constraints from Solar and Reactor Neutrinos on Unparticle Long-Range Forces

We have investigated the impact of long-range forces induced by unparticle operators of scalar, vector and tensor nature coupled to fermions in the interpretation of solar neutrinos and KamLAND data. If the unparticle couplings to the neutrinos are mildly non-universal, such long-range forces will not factorize out in the neutrino flavour evolution. As a consequence large deviations from the observed standard matter-induced oscillation pattern for solar neutrinos would be generated. In this case, severe limits can be set on the infrared fix point scale, Lambda_u, and the new physics scale, M, as a function of the ultraviolet (d_UV) and anomalous (d) dimension of the unparticle operator. For a scalar unparticle, for instance, assuming the non-universality of the lepton couplings to unparticles to be of the order of a few per mil we find that, for d_UV=3 and d=1.1, M is constrained to be M > O(10^9) TeV (M > O(10^10) TeV) if Lambda_u= 1 TeV (10 TeV). For given values of Lambda_u and d, the corresponding bounds on M for vector [tensor] unparticles are approximately 100 [3/Sqrt(Lambda_u/TeV)] times those for the scalar case. Conversely, these results can be translated into severe constraints on universality violation of the fermion couplings to unparticle operators with scales which can be accessible at future colliders.Comment: 13 pages, 3 figures. Minor changes due to precision in numerical factors and correction in figure labels. References added. Conclusions remain unchange

Local and Global Effects of Climate on Dengue Transmission in Puerto Rico

The four dengue viruses, the agents of dengue fever and dengue hemorrhagic fever in humans, are transmitted predominantly by the mosquito Aedes aegypti. The abundance and the transmission potential of Ae. aegypti are influenced by temperature and precipitation. While there is strong biological evidence for these effects, empirical studies of the relationship between climate and dengue incidence in human populations are potentially confounded by seasonal covariation and spatial heterogeneity. Using 20 years of data and a statistical approach to control for seasonality, we show a positive and statistically significant association between monthly changes in temperature and precipitation and monthly changes in dengue transmission in Puerto Rico. We also found that the strength of this association varies spatially, that this variation is associated with differences in local climate, and that this relationship is consistent with laboratory studies of the impacts of these factors on vector survival and viral replication. These results suggest the importance of temperature and precipitation in the transmission of dengue viruses and suggest a reason for their spatial heterogeneity. Thus, while dengue transmission may have a general system, its manifestation on a local scale may differ from global expectations

The genomes of two key bumblebee species with primitive eusocial organization

Background: The shift from solitary to social behavior is one of the major evolutionary transitions. Primitively eusocial bumblebees are uniquely placed to illuminate the evolution of highly eusocial insect societies. Bumblebees are also invaluable natural and agricultural pollinators, and there is widespread concern over recent population declines in some species. High-quality genomic data will inform key aspects of bumblebee biology, including susceptibility to implicated population viability threats. Results: We report the high quality draft genome sequences of Bombus terrestris and Bombus impatiens, two ecologically dominant bumblebees and widely utilized study species. Comparing these new genomes to those of the highly eusocial honeybee Apis mellifera and other Hymenoptera, we identify deeply conserved similarities, as well as novelties key to the biology of these organisms. Some honeybee genome features thought to underpin advanced eusociality are also present in bumblebees, indicating an earlier evolution in the bee lineage. Xenobiotic detoxification and immune genes are similarly depauperate in bumblebees and honeybees, and multiple categories of genes linked to social organization, including development and behavior, show high conservation. Key differences identified include a bias in bumblebee chemoreception towards gustation from olfaction, and striking differences in microRNAs, potentially responsible for gene regulation underlying social and other traits. Conclusions: These two bumblebee genomes provide a foundation for post-genomic research on these key pollinators and insect societies. Overall, gene repertoires suggest that the route to advanced eusociality in bees was mediated by many small changes in many genes and processes, and not by notable expansion or depauperation

Socio-cultural determinants of adiposity and physical activity in preschool children: A cross-sectional study

BACKGROUND: Both individual socio-cultural determinants such as selected parental characteristics (migrant background, low educational level and workload) as well as the regional environment are related to childhood overweight and physical activity (PA). The purpose of the study was to compare the impact of distinct socio-cultural determinants such as the regional environment and selected parental characteristics on adiposity, PA and motor skills in preschool children. METHODS: Forty preschools (N = 542 children) of two culturally different urban regions (German and French speaking part of Switzerland) participated in the study (Ballabeina Study). Outcome measures included adiposity (BMI and skinfold thickness), objectively measured sedentary activities and PA (accelerometers) and agility performance (obstacle course). Parental characteristics (migrant status, educational level and workload) were assessed by questionnaire. RESULTS: Children from the French speaking areas had higher adiposity, lower levels of total and of more intense PA, were more sedentary and less agile than children from the German speaking regions (percent differences for all outcome parameters except for BMI ≥10%; all p ≤ 0.04). Differences in skinfold thickness, sedentary activities and agility, but not in PA, were also found between children of Swiss and migrant parents, though they were ≤8% (p ≤ 0.02). While paternal workload had no effect, maternal workload and parental education resulted in differences in some PA measures and/or agility performance (percent differences in both: ≤9%, p ≤ 0.008), but not in adiposity or sedentary activities (p = NS). Regional differences in skinfold thickness, PA, sedentary activities and agility performance persisted after adjustment for parental socio-cultural characteristics, parental BMI and, where applicable, children's skinfolds (all p ≤ 0.01). CONCLUSIONS: The regional environment, especially the broader social environment, plays a prominent role in determining adiposity, PA and motor skills of young children and should be implicated in the prevention of obesity and promotion of PA in children

Australia's Dengue Risk Driven by Human Adaptation to Climate Change

Current and projected rainfall reduction in southeast Australia has seen the installation of large numbers of government-subsidised and ad hoc domestic water storage containers that could create the possibility of the mosquito Ae. aegypti expanding out of Queensland into southern Australian's urban regions. By assessing the past and current distribution of Ae. aegypti in Australia, we construct distributional models for this dengue vector for our current climate and projected climates for 2030 and 2050. The resulting mosquito distribution maps are compared to published theoretical temperature limits for Ae. aegypti and some differences are identified. Nonetheless, synthesising our mosquito distribution maps with dengue transmission climate limits derived from historical dengue epidemics in Australia suggests that the current proliferation of domestic water storage tanks could easily result in another range expansion of Ae. aegypti along with the associated dengue risk were the virus to be introduced