Inverse Function: Pre-Service Teachers’ Techniques and Meanings

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss our inferences of their meanings based on their activities. We conclude with implications for the teaching and learning of inverse function and areas for future research

Variable EBV DNA load distributions and heterogeneous EBV mRNA expression patterns in the circulation of solid organ versus stem cell transplant recipients

Epstein-Barr virus (EBV) driven post-transplant lymphoproliferative disease (PTLD) is a heterogeneous and potentially life-threatening condition. Early identification of aberrant EBV activity may prevent progression to B-cell lymphoma. We measured EBV DNA load and RNA profiles in plasma and cellular blood compartments of stem cell transplant (SCT; n = 5), solid organ transplant recipients (SOT; n = 15), and SOT having chronic elevated EBV-DNA load (n = 12). In SCT, EBV DNA was heterogeneously distributed, either in plasma or leukocytes or both. In SOT, EBV DNA load was always cell associated, predominantly in B cells, but occasionally in T cells (CD4 and CD8) or monocytes. All SCT with cell-associated EBV DNA showed BARTs an

Simulating Cosmic Microwave Background maps in multi-connected spaces

This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multi-connected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.Comment: 33 pages, 55 figures, submitted to PRD. Higher resolution figures available on deman

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Dynamics of an ensemble of $N$-unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original $2 N$-dimensional {\it stochastic} differential equations are replaced by 8-dimensional {\it deterministic} differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice

Origins of the Ambient Solar Wind: Implications for Space Weather

The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue connected with a 2016 ISSI workshop on "The Scientific Foundations of Space Weather." 44 pages, 9 figure

Fine-mapping of prostate cancer susceptibility loci in a large meta-analysis identifies candidate causal variants

Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Peer reviewe

Large-scale transcriptome-wide association study identifies new prostate cancer risk regions

Although genome-wide association studies (GWAS) for prostate cancer (PrCa) have identified more than 100 risk regions, most of the risk genes at these regions remain largely unknown. Here we integrate the largest PrCa GWAS (N = 142,392) with gene expression measured in 45 tissues (N = 4458), including normal and tumor prostate, to perform a multi-tissue transcriptome-wide association study (TWAS) for PrCa. We identify 217 genes at 84 independent 1 Mb regions associated with PrCa risk, 9 of which are region