A combinatorial approach to angiosperm pollen morphology

Angiosperms (flowering plants) are strikingly diverse. This is clearly expressed in the morphology of their pollen grains, which are characterized by enormous variety in their shape and patterning. In this paper, I approach angiosperm pollen morphology from the perspective of enumerative combinatorics. This involves generating angiosperm pollen morphotypes by algorithmically combining character states and enumerating the results of these combinations. I use this approach to generate 3 643 200 pollen morphotypes, which I visualize using a parallel-coordinates plot. This represents a raw morphospace. To compare real-world and theoretical morphologies, I map the pollen of 1008 species of Neotropical angiosperms growing on Barro Colorado Island (BCI), Panama, onto this raw morphospace. This highlights that, in addition to their well-documented taxonomic diversity, Neotropical rainforests also represent an enormous reservoir of morphological diversity. Angiosperm pollen morphospace at BCI has been filled mostly by pollen morphotypes that are unique to single plant species. Repetition of pollen morphotypes among higher taxa at BCI reflects both constraint and convergence. This combinatorial approach to morphology addresses the complexity that results from large numbers of discrete character combinations and could be employed in any situation where organismal form can be captured by discrete morphological characters

Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Optogenetic Interrogation of Functional Synapse Formation by Corticospinal Tract Axons in the Injured Spinal Cord

To restore function after injury to the CNS, axons must be stimulated to extend into denervated territory and, critically, must form functional synapses with appropriate targets. We showed previously that forced overexpression of the transcription factor Sox11 increases axon growth by corticospinal tract (CST) neurons after spinal injury. However, behavioral outcomes were not improved, raising the question of whether the newly sprouted axons are able to form functional synapses. Here we developed an optogenetic strategy, paired with single-unit extracellular recordings, to assess the ability of Sox11-stimulated CST axons to functionally integrate in the circuitry of the cervical spinal cord. Initial time course experiments established the expression and function of virally expressed Channelrhodopsin (ChR2) in CST cell bodies and in axon terminals in cervical spinal cord. Pyramidotomies were performed in adult mice to deprive the left side of the spinal cord of CST input, and the right CST was treated with adeno-associated virus (AAV)–Sox11 or AAV–EBFP control, along with AAV–ChR2. As expected, Sox11 treatment caused robust midline crossing of CST axons into previously denervated left spinal cord. Clear postsynaptic responses resulted from optogenetic activation of CST terminals, demonstrating the ability of Sox11-stimulated axons to form functional synapses. Mapping of the distribution of CST-evoked spinal activity revealed overall similarity between intact and newly innervated spinal tissue. These data demonstrate the formation of functional synapses by Sox11-stimulated CST axons without significant behavioral benefit, suggesting that new synapses may be mistargeted or otherwise impaired in the ability to coordinate functional output. SIGNIFICANCE STATEMENT As continued progress is made in promoting the regeneration of CNS axons, questions of synaptic integration are increasingly prominent. Demonstrating direct synaptic integration by regenerated axons and distinguishing its function from indirect relay circuits and target field plasticity have presented technical challenges. Here we force the overexpression of Sox11 to stimulate the growth of corticospinal tract axons in the cervical spinal cord and then use specific optogenetic activation to assess their ability to directly drive postsynaptic activity in spinal cord neurons. By confirming successful synaptic integration, these data illustrate a novel optogenetic-based strategy to monitor and optimize functional reconnection by newly sprouted axons in the injured CNS

On the binary codes with parameters of triply-shortened 1-perfect codes

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary $(n=2^m-3, 2^{n-m-1}, 4)$ code $C$, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable partition of the $n$-cube into six cells. An arbitrary binary $(n=2^m-4, 2^{n-m}, 3)$ code $D$, i.e., a code with parameters of a triply-shortened Hamming code, is a cell of an equitable family (but not a partition) from six cells. As a corollary, the codes $C$ and $D$ are completely semiregular; i.e., the weight distribution of such a code depends only on the minimal and maximal codeword weights and the code parameters. Moreover, if $D$ is self-complementary, then it is completely regular. As an intermediate result, we prove, in terms of distance distributions, a general criterion for a partition of the vertices of a graph (from rather general class of graphs, including the distance-regular graphs) to be equitable. Keywords: 1-perfect code; triply-shortened 1-perfect code; equitable partition; perfect coloring; weight distribution; distance distributionComment: 12 page

A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Similarity and Lexicon-Abstraction

This article discusses some general issues arising from the study of similarity in music, both human-conducted and computer-aided, and then progresses to a consideration of similarity relationships between patterns in a phrase by Beethoven, from the first movement of the Piano Sonata in A flat major op. 110 (1821), and various potential memetic precursors. This analysis is followed by a consideration of how the kinds of similarity identified in the Beethoven phrase might be understood in psychological/conceptual and then neurobiological terms, the latter by means of William Calvin’s Hexagonal Cloning Theory. This theory offers a mechanism for the operation of David Cope’s concept of the lexicon, conceived here as a museme allele-class. I conclude by attempting to correlate and map the various spaces within which memetic replication occurs

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Gender politics in 21st century literacy reform

From 2001 to 2004 Education Queensland undertook significant literacy reform in schools through the Literate Futures Project. Research into the impact of this reform has revealed that significant demands were placed on women at all levels, from those producing resources to those leading change within schools. Although the reform was a government response to globalisation, many women were driven by a commitment to a collaborative approach to professional learning that addressed equity and improving educational outcomes for all students. But what was the cost of this commitment to the project? Failure to acknowledge the emotion work demanded by educational reform effectively silences women and the significant contribution they make. This paper examining a 21st century literacy reform draws on the work of Fraser and Boler to argue for gender justice and acknowledgement of emotion work

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools

Measurement of Direct Photon Emission in K^+ -> pi^+ pi^0 gamma Decay

We have performed a measurement of the K^+ -> pi^+ pi^0 gamma decay and have observed 2 X 10^4 events. The best fit to the decay spectrum gives a branching ratio for direct photon emission of (4.7\pm0.8\pm0.3) X 10^{-6} in the pi^+ kinetic energy region of 55 to 90 MeV and requires no component due to interference with inner bremsstrahlung.Comment: 9 pages, 3 figures. To be submitted to PR