Complexiton Solutions of the Toda Lattice Equation

A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton solutions to the Toda lattice equation through the Casoratian formulation. An analysis is made for solving the resulting system of differential-difference equations, thereby providing the general solution yielding eigenfunctions required for forming complexitons. Moreover, a feasible way is presented to compute the required eigenfunctions, along with examples of real complexitons of lower order.Comment: 21 pages, Latex, to appear in Physica

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

A polymorphism associated with depressive disorders differentially regulates brain derived neurotrophic factor promoter IV activity

PMCID: PMC3712170Peer reviewedPublisher PD

Multiple Guidance Mechanisms Control Axon Growth to Generate Precise T-Shaped Bifurcation During Dorsal Funiculus Development in the Spinal Cord

The dorsal funiculus in the spinal cord relays somatosensory information to the brain. It is made of T-shaped bifurcation of dorsal root ganglion (DRG) sensory axons. Our previous study has shown that Slit signaling is required for proper guidance during bifurcation, but loss of Slit does not affect all DRG axons. Here, we examined the role of the extracellular molecule Netrin-1 (Ntn1). Using wholemount staining with tissue clearing, we showed that mice lacking Ntn1 had axons escaping from the dorsal funiculus at the time of bifurcation. Genetic labeling confirmed that these misprojecting axons come from DRG neurons. Single axon analysis showed that loss of Ntn1 did not affect bifurcation but rather altered turning angles. To distinguish their guidance functions, we examined mice with triple deletion of Ntn1, Slit1, and Slit2 and found a completely disorganized dorsal funiculus. Comparing mice with different genotypes using immunolabeling and single axon tracing revealed additive guidance errors, demonstrating the independent roles of Ntn1 and Slit. Moreover, the same defects were observed in embryos lacking their cognate receptors. These in vivo studies thus demonstrate the presence of multi-factorial guidance mechanisms that ensure proper formation of a common branched axonal structure during spinal cord development

A noise-reduction GWAS analysis implicates altered regulation of neurite outgrowth and guidance in autism

<p>Abstract</p> <p>Background</p> <p>Genome-wide Association Studies (GWAS) have proved invaluable for the identification of disease susceptibility genes. However, the prioritization of candidate genes and regions for follow-up studies often proves difficult due to false-positive associations caused by statistical noise and multiple-testing. In order to address this issue, we propose the novel GWAS noise reduction (GWAS-NR) method as a way to increase the power to detect true associations in GWAS, particularly in complex diseases such as autism.</p> <p>Methods</p> <p>GWAS-NR utilizes a linear filter to identify genomic regions demonstrating correlation among association signals in multiple datasets. We used computer simulations to assess the ability of GWAS-NR to detect association against the commonly used joint analysis and Fisher's methods. Furthermore, we applied GWAS-NR to a family-based autism GWAS of 597 families and a second existing autism GWAS of 696 families from the Autism Genetic Resource Exchange (AGRE) to arrive at a compendium of autism candidate genes. These genes were manually annotated and classified by a literature review and functional grouping in order to reveal biological pathways which might contribute to autism aetiology.</p> <p>Results</p> <p>Computer simulations indicate that GWAS-NR achieves a significantly higher classification rate for true positive association signals than either the joint analysis or Fisher's methods and that it can also achieve this when there is imperfect marker overlap across datasets or when the closest disease-related polymorphism is not directly typed. In two autism datasets, GWAS-NR analysis resulted in 1535 significant linkage disequilibrium (LD) blocks overlapping 431 unique reference sequencing (RefSeq) genes. Moreover, we identified the nearest RefSeq gene to the non-gene overlapping LD blocks, producing a final candidate set of 860 genes. Functional categorization of these implicated genes indicates that a significant proportion of them cooperate in a coherent pathway that regulates the directional protrusion of axons and dendrites to their appropriate synaptic targets.</p> <p>Conclusions</p> <p>As statistical noise is likely to particularly affect studies of complex disorders, where genetic heterogeneity or interaction between genes may confound the ability to detect association, GWAS-NR offers a powerful method for prioritizing regions for follow-up studies. Applying this method to autism datasets, GWAS-NR analysis indicates that a large subset of genes involved in the outgrowth and guidance of axons and dendrites is implicated in the aetiology of autism.</p

Spin Caloritronics

This is a brief overview of the state of the art of spin caloritronics, the science and technology of controlling heat currents by the electron spin degree of freedom (and vice versa).Comment: To be published in "Spin Current", edited by S. Maekawa, E. Saitoh, S. Valenzuela and Y. Kimura, Oxford University Pres

An X chromosome-wide association study in autism families identifies TBL1X as a novel autism spectrum disorder candidate gene in males

<p>Abstract</p> <p>Background</p> <p>Autism spectrum disorder (ASD) is a complex neurodevelopmental disorder with a strong genetic component. The skewed prevalence toward males and evidence suggestive of linkage to the X chromosome in some studies suggest the presence of X-linked susceptibility genes in people with ASD.</p> <p>Methods</p> <p>We analyzed genome-wide association study (GWAS) data on the X chromosome in three independent autism GWAS data sets: two family data sets and one case-control data set. We performed meta- and joint analyses on the combined family and case-control data sets. In addition to the meta- and joint analyses, we performed replication analysis by using the two family data sets as a discovery data set and the case-control data set as a validation data set.</p> <p>Results</p> <p>One SNP, rs17321050, in the transducin β-like 1X-linked (<it>TBL1X</it>) gene [OMIM:300196] showed chromosome-wide significance in the meta-analysis (<it>P </it>value = 4.86 × 10^-6) and joint analysis (<it>P </it>value = 4.53 × 10^-6) in males. The SNP was also close to the replication threshold of 0.0025 in the discovery data set (<it>P </it>= 5.89 × 10^-3) and passed the replication threshold in the validation data set (<it>P </it>= 2.56 × 10^-4). Two other SNPs in the same gene in linkage disequilibrium with rs17321050 also showed significance close to the chromosome-wide threshold in the meta-analysis.</p> <p>Conclusions</p> <p><it>TBL1X </it>is in the Wnt signaling pathway, which has previously been implicated as having a role in autism. Deletions in the Xp22.2 to Xp22.3 region containing <it>TBL1X </it>and surrounding genes are associated with several genetic syndromes that include intellectual disability and autistic features. Our results, based on meta-analysis, joint analysis and replication analysis, suggest that <it>TBL1X </it>may play a role in ASD risk.</p