Canonical Melnikov theory for diffeomorphisms

We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation

We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2. The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems

Rationales, design and recruitment for the Elfe longitudinal study

Background Many factors act simultaneously in childhood to influence health status, life chances and well being, including pre-birth influences, the environmental pollutants of early life, health status but also the social influences of family and school. A cohort study is needed to disentangle these influences and explore attribution. Methods Elfe will be a nationally representative cohort of 20 000 children followed from birth to adulthood using a multidisciplinary approach. The cohort will be based on the INSEE Permanent Demographic Panel (EDP) established using census data and civil records. The sample size has been defined in order to match the representativeness criteria and to obtain some prevalence estimation, but also to address the research area of low exposure/rare effects. The cohort will be based on repeated surveys by face to face or phone interview (at birth and each year) as well as medical interview (at 2 years) and examination (at 6 years). Furthermore, biological samples will be taken at birth to evaluate the foetal exposition to toxic substances, environmental sensors will be placed in the child's homes. Pilot studies have been initiated in 2007 (500 children) with an overall acceptance rate of 55% and are currently under progress, the 2-year survey being carried out in October this year. Discussion The longitudinal study will provide a unique source of data to analyse the development of children in their environment, to study the various factors interacting throughout the life course up to adulthood and to determine the impact of childhood experience on the individual's physical, psychological, social and professional development

Geometry and field theory in multi-fractional spacetime

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with fixed dimension, presented in a companion paper, we generalize to a multi-fractional scenario inspired by multi-fractal geometry, where the dimension changes with the scale. This is related to the renormalization group properties of fractional field theories, illustrated by the example of a scalar field. Depending on the symmetries of the Lagrangian, one can define two models. In one of them, the effective dimension flows from 2 in the ultraviolet (UV) and geometry constrains the infrared limit to be four-dimensional. At the UV critical value, the model is rendered power-counting renormalizable. However, this is not the most fundamental regime. Compelling arguments of fractal geometry require an extension of the fractional action measure to complex order. In doing so, we obtain a hierarchy of scales characterizing different geometric regimes. At very small scales, discrete symmetries emerge and the notion of a continuous spacetime begins to blur, until one reaches a fundamental scale and an ultra-microscopic fractal structure. This fine hierarchy of geometries has implications for non-commutative theories and discrete quantum gravity. In the latter case, the present model can be viewed as a top-down realization of a quantum-discrete to classical-continuum transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and improved (especially section 4.5), typos corrected, references added; v4: further typos correcte

Descriptions of some North American Micropezidae (Diptera)

Volume: 49Start Page: 72End Page: 7

Concerning the Types of Mallophora Rex and Cheysomela Bromley

Volume: 33Start Page: 91End Page: 9

A new species of Achias-like fly from Nicaragua, apparently belonging to the little-known genus Plagiocephalus (Diptera: Ortalidae)

Volume: 34Start Page: 257End Page: 26

Some North American Diptera from the south west. Paper 1. Ortalidae

Volume: 32Start Page: 279End Page: 28

Descriptions of new North American acalyptrate Diptera--I

Volume: 25Start Page: 457End Page: 46

A new species of Micropeza from Colorado (Diptera: Micropezidae)

Volume: 46Start Page: 229End Page: 23