In a previous communication we have reported on the agglufinins which are formed in rabbits following systematic inoculation with concentrated culture material of Treponema pallidum. Incidentally it may be stated that a sheep has also been successfully used. The antigen used for the immunization of these animals was similar to that employed in the first agglutination experiments, except that we...

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in Algebraic Geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especiall...

The dominant view of the phylogeny of living elasmobranchs, based on morphological characters, is that batoids (skates and rays) are derived sharks, joined with saw sharks, and angel sharks in the clade Hypnosqualea [S. Shirai, Squalean Phylogeny: A New Framework of 'Squaloid' Sharks and Related Taxa, Hokkaido University Press, Sapporo, 1992]. By contrast, a recent molecular-phylogenetic study ...

I give a survey about a program which intends to find topological characterizations of a rational map and then use them to study the rigidity problem for rational maps. Thurston started this program by considering critically finite branched coverings and gave a necessary and sufficient combinatorial condition for a critically finite rational maps among all critically finite branched coverings. ...

We study the bifurcation loci of quadratic (and unicritical) polynomials and exponential maps. We outline a proof that the exponential bifurcation locus is connected; this is an analog to Douady and Hubbard’s celebrated theorem that (the boundary of) the Mandelbrot set is connected. For these parameter spaces, a fundamental conjecture is that hyperbolic dynamics is dense. For quadratic polynomi...

We consider a compact twistor space P and assume that there is a surface S ⊂ P, which has degree one on twistor fibres and contains a twistor fibre F, e.g. P a LeBrun twistor space ([20],[18]). Similar to [6] and [5] we examine the restriction of an instanton bundle V equipped with a fixed trivialisation along F to a framed vector bundle over (S,F). First we develope inspired by [13] a suitable...

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set of zero Γ-capacity. We illustrate this general principle in different problems of small divisors. As an application we obtain new richer families of non-linearizab...

Phyllotaxis, the arrangement of a plant's phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM), has intrigued natural scientists for centuries. Even today, the reasons for the observed patterns and their special properties, the physical and chemical mechanisms which give rise to strikingly similar configurations in a wide variety of plants, the almost-constant golden divergen...

Niche modelling approaches and applications R. A. Catullo, R. Lanfear, P. Doughty and J. S. Keogh: The biogeographical boundaries of northern Australia: evidence from ecological niche models and a multi-locus phylogeny of Uperoleia toadlets (Anura: Myobatrachidae) 659–672 N. E. de Lima, M. S. Lima-Ribeiro, C. F. Tinoco, L. C. Terribile and R. G. Collevatti: Phylogeography and ecological niche m...

New insights into the combinatorial structure of the the Mandelbrot set are given by ‘Correspondence’ and ‘Translation’ Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles and discuss results related to them. Stony Brook IMS Preprint #1997/14 October 1997 1. The conjectures by Lau and Schleicher Introduction. The detailed ...