We extend the unpublished work of Handel and Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel–Miller construction of the geodesic laminations, give an axiomatic theory for pseudo-geodesic laminations, show that the geodesic laminations satisfy the axioms, and prove that pseudo-geodesic laminations satisfying our axioms are ambiently isotopic to the geodesic laminations. The axiomatic approach allows us to show that the given endperiodic automorphism is isotopic to a smooth endperiodic automorphism preserving smooth laminations ambiently isotopic to the original ones. Using the axioms, we also prove the ‘transfer theorem’ for foliations of 3-manifolds, namely that, if two depth-one foliations ${\mathcal{F}}$ and ${\mathcal{F}}^{\prime }$ are transverse to a common one-dimensional foliation ${\mathcal{L}}$ whose monodromy on the non-compact leaves of ${\mathcal{F}}$ exhibits the nice dynamics of Handel–Miller theory, then ${\mathcal{L}}$ also induces monodromy on the non-compact leaves of ${\mathcal{F}}^{\prime }$ exhibiting the same nice dynamics. Our theory also applies to surfaces with infinitely many ends.

Experimental rolling trials were performed at different temperatures on EN 1.4462 duplexsteel imposing also different reduction ratios and a possible solution quenching. A clearand significant relation between the applied thermo-mechanical process and themicrostructural evolution was shown, and it is useful for designing the steelmicrostructure. The mechanical properties, the micro-structural features and the texturecharacteristics were defined for each condition in order to point out the operativeparameters (i.e. thermal level, imposed strains and application of solution quenching)that permit to maximize the formability of the final hot-rolled products.

We have investigated the distribution of ON- and OFF-center responses in the lateral geniculate nucleus of ferrets with normal and abnormal retinal projections. Electrophysiological recordings in normal pigmented animals confirm previous studies on mustelids showing that ON-center responses are found in the anterior, inner parts of laminae A and AI and OFF-center responses in posterior, outer leaflets. In albino animals, lamina A displays normal patterns of ON/OFF segregation but in lamina AI, which receives an abnormal crossed retinal projection, no consistent patterns of segregation are found. Following monocular enucleation on the day of birth, the uncrossed projection in pigmented ferrets remains expanded across the LGN. Anatomically and physiologically, this projection is segregated into two leaflets: an anterior, inner ON-center leaflet and a posterior outer OFF-center leaflet. We conclude that the persistence of ON/OFF segregation, independent of geniculate location, suggests that self-sorting of retinal input is an important factor in generating the segregation.

The elimination of retinogeniculate afferents from one eye on embryonic day 44 (E44) has pronounced effects on the formation of the cellular laminae in the cat lateral geniculate nucleus (LGN). Only two laminae form: a dorsal, “magnocellular” layer, and a ventral, “parvocellular” layer. Soma size measurements and previously reported patterns of termination of retinogeniculate axons suggest that the dorsal lamina is a coalescence of the normal A-laminae and the dorsal, magnocellular division of layer C, while the ventral layer is a composite of the parvocellular sublamina of layer C and the remaining C-laminae. This is a novel pattern of lamination in the LGN that differs from that found in the normal nucleus, not only in that there are now only two cell layers rather than the normal five, but also in that the interlaminar zone occurs in an abnormal location. This result is markedly different from that observed in other species where interlaminar zones present after early monocular enucleation are a subset of the ones which would normally be present. We suggest that, in the absence of ongoing binocular interactions, interactions between functionally distinct retinal ganglion cell classes from the remaining eye may direct the formation of cell laminae in the LGN, even when such interactions are not normally operative.

Brain evolution is a complex weave of species similarities and differences, bound by diverse rules and principles. This book is a detailed examination of these principles, using data from a wide array of vertebrates but minimizing technical details and terminology. It is written for advanced undergraduates, graduate students, and more senior scientists who already know something about “the brain,” but want a deeper understanding of how diverse brains evolved. The book's central theme is that evolutionary changes in absolute brain size tend to correlate with many other aspects of brain structure and function, including the proportional size of individual brain regions, their complexity, and their neuronal connections. To explain these correlations, the book delves into rules of brain development and asks how changes in brain structure impact function and behavior. Two chapters focus specifically on how mammal brains diverged from other brains and how Homo sapiens evolved a very large and “special” brain.

Cells of the cat's perigeniculate nucleus (PGN), part of the visual sector of the thalamic reticular nucleus (TRN), provide GABAergic inhibition to the A and A1 layers of the dorsal lateral geniculate nucleus (LGNd) and, therefore, may control information flow from the retina to the cortex. Previous electrophysiological experiments suggested that the PGN may be subdivided on the basis of ocular dominance thus reflecting the afferent and efferent projections with lamina A and A1 of the LGNd. The present study utilized the ability of wheat germ agglutinin-horseradish peroxidase (WGA-HRP) to be transported transneuronally following intraocular injections in four cats to examine whether there is any anatomical evidence for eye specific layers within the PGN. Sections were processed with tetramethylbenzidine. Light WGA-HRP transneuronal labeling of LGNd collaterals and somata were seen in the PGN and very light labeling (but not somata) was seen in the TRN. Neither the cells of the PGN projecting to the LGNd nor the LGNd relay collaterals within the PGN were clearly organized into nonoverlapping laminae related to the eye specific layers of the LGNd. However, parts of the PGN immediately adjacent to the LGNd appear devoid of connections with lamina A1 thus creating a thin monocular segment for the contralateral eye.

We study the global behaviour of trees of Markoff triples over the complex numbers. We relate this to the space of type-preserving representations of the punctured torus group into $\mbox{SL}(2,{\Bbb C})$. In particular, we explore which Markoff triples correspond to quasifuchsian representations. We derive a variation of McShane's identity for quasifuchsian groups. In the case of non-discrete representations, we attempt to relate the asymptotic behaviour of Markoff triples to the realisability of laminations in hyperbolic 3-space. We also consider how some of these issues might be related for more general surfaces.

1991 Mathematics Subject Classification: 57M50.