England and Autism

The history of Autism is a discourse (Waltz 2013), a journey through a disputed landscape, whose territories are alternatively staked by Politics, Education, Society, and Culture. It is diachronic in nature, as the knowledge of the present is built upon the past, but a diachronic that has progressed differently in different states, at different rates as each impact upon each other. Essentially its origins are lost in myth (Frith 1992) but its presence has always been felt in one way or another, even before the concept of autism was framed in the Western psychiatric narrative

The parabola theorem on continued fractions

Using geometric methods borrowed from the theory of Kleinian groups, we interpret the parabola theorem on continued fractions in terms of sequences of Möbius transformations. This geometric approach allows us to relate the Stern–Stolz series, which features in the parabola theorem, to the dynamics of certain sequences of Möbius transformations acting on three-dimensional hyperbolic space. We also obtain a version of the parabola theorem in several dimensions

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings

The stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a "surface \`a godets". It is shown that the information on the profile is encoded in the Jacobian of a conformal mapping (the coefficient of deformation) corresponding to an isometric embedding of a uniform Cayley tree into the 3D Euclidean space. The geometric characteristics of the leaf's boundary (like the perimeter and the height) are calculated. In addition a symbolic language allowing to investigate statistical properties of a "surface \`a godets" with annealed random defects of curvature of density $q$ is developed. It is found that at $q=1$ the surface exhibits a phase transition with critical exponent $\alpha=1/2$ from the exponentially growing to the flat structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics

Boundary Conformal Field Theories, Limit Sets of Kleinian Groups and Holography

In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the possibility of extension of work of Belavin, Polyakov and Zamolodchikov to higher dimensions is investigated. Known in physical literature objections against such extension are removed and the possibility of an extension is convincingly demonstrated.Comment: 62 pages, 5 figure

Autism community research priorities: the potential of future research to benefit autistics

Despite the enormous amounts of money spent on autism research, there has been little focus to date on what members of the autistic community believe should be prioritised by autism researchers. Our systematic review of the literature identified three published studies that had developed wide-ranging autism research priority sets. We undertook an in-depth analysis of these priorities sets to determine whether research focused on each priority had the potential to benefit the well-being of and/or emancipate autistic individuals. For this purpose, we used published ‘inclusive research’ criteria. We also compared the three sets of autism research priorities in the context of autistic well-being and emancipation. Our findings demonstrated substantial differences between the priorities in the studies in terms of whether they might benefit and/or be emancipatory for autistic people. Autistic people were a small minority of participants in studies where participant numbers had been recorded. There has yet to be a study focused solely on understanding the autism research priorities of autistic adults

Reflections on the role of the ‘users’: challenges in a multi-disciplinary context of learner-centred design for children on the autism spectrum

Technology design in the field of human–computer interaction has developed a continuum of participatory research methods, closely mirroring methodological approaches and epistemological discussions in other fields. This paper positions such approaches as examples of inclusive research (to varying degrees) within education, and illustrates the complexity of navigating and involving different user groups in the context of multi-disciplinary research projects. We illustrate this complexity with examples from our recent work, involving children on the autism spectrum and their teachers. Both groups were involved in learner-centred design processes to develop technologies to support social conversation and collaboration. We conceptualize this complexity as a triple-decker ‘sandwich’ representing Theory, Technologies and Thoughts and argue that all three layers need to be appropriately aligned for a good quality ‘product’ or outcome. However, the challenge lies in navigating and negotiating all three layers at the same time, including the views and experiences of the learners. We question the extent to which it may be possible to combine co-operative, empowering approaches to participatory design with an outcome-focused agenda that seeks to develop a robust learning technology for use in real classrooms

Generalized algebra within a nonextensive statistics

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g., associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element is no more universal within the generalized algebra.Comment: 11 pages, no figure, TeX. Reports on Mathematical Physics (2003), in pres

Invariant varieties of periodic points for some higher dimensional integrable maps

By studying various rational integrable maps on $\mathbf{\hat C}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\ge p$ for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: {\it `If there is an invariant variety of periodic points of some period, there is no set of isolated periodic points of other period in the map.'}Comment: 24 page