Growth Cone Pathfinding: a competition between deterministic and stochastic events

Background  

Growth cone migratory patterns show evidence of both deterministic and stochastic search modes.     

Surjectivity for Hamiltonian loop group spaces

Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,), and assume that the moment map :XL ^* is proper. We consider the function ||²:X, and use a version of Morse theory to show that the inclusion map j:^-1(0)X induces a surjection j ^*:H _G ^*(X)H _G ^*(^-1(0)), in analogy with Kirwans surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces.     

Development of [j] in young, midwestern, American children

Beginning at the age of about 14 months, eight children who lived in a rhotic dialect region of the United States were recorded approximately every 2 months interacting with their parents. All were recorded until at least the age of 26 months, and some until the age of 31 months. Acoustic analyses of speech samples indicated that these young children acquired [inverted r] production ability at different ages for [inverted r]'s in different syllable positions. The children, as a group, had started to produce postvocalic and syllabic [inverted r] in an adult-like manner by the end of the recording sessions, but were not yet showing evidence of having acquired prevocalic [inverted r]. Articulatory limitations of young children are posited as a cause for the difference in development of [inverted r] according to syllable position. Specifically, it is speculated that adult-like prevocalic [inverted r] production requires two lingual constrictions: one in the mouth, and the other in the pharynx, while postvocalic and syllabic [inverted r] requires only one oral constriction. Two lingual constrictions could be difficult for young children to produce.     

Supramolecular assembly of strongly chemisorbed size- and shape-defined chiral clusters: S- and R-alanine on Cu(110)

The bonding and self-assembly of a chirally organized monolayer of alanine on the Cu(110) surface has been investigated using reflection-absorption infrared spectroscopy, low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM). This multitechnique approach has enabled an in-depth understanding of the hierarchy of chirality transfer: from a single adsorbed molecule, to size-defined chiral clusters, and then to an overall chiral assembly. The data have indicated that the alanine is in its anionic form, bound to the copper surface through the oxygens of the ionized carboxylate group and the nitrogen of the neutral amino group. Importantly, the methyl group is held away from the surface, resulting in direct chirality transfer into the footprint of the adsorbed alanine molecules, with the local adsorption motif for S-alanine being the mirror image of that created for R-alanine. STM has shown that S-alanine molecules self-organize to form size-defined chiral clusters of six or eight molecules at the surface, interspersed with chiral channels of bare metal. Together, these clusters and channels further self-assemble into a chiral array with one unique chiral domain sustained across the entire surface. A similar chiral assembly, but with the mirror organization, has been observed for R-alanine. Structural models for the individual clusters are proposed, and in conjunction with LEED data, overall models for these chiral phases of both S- and R-alanine have been constructed. Overall, this adsorption system has been found to be both strongly chemisorbed and capable of extensive intermolecular H-bonding, causing stresses that lead not only to the chiral self-organization of molecules but also to a specific self-organization of the empty chiral channels and spaces that intersperse the structure which, in turn, chirally assemble across macroscopic length scales to give a surface with global organizational chirality.     

Experimental realization of a quantum spin pump

We demonstrate the operation of a quantum spin pump based on cyclic radio-frequency excitation of a GaAs quantum dot, including the ability to pump pure spin without pumping charge. The device takes advantage of bidirectional mesoscopic fluctuations of pumped current, made spin dependent by the application of an in-plane Zeeman field. Spin currents are measured by placing the pump in a focusing geometry with a spin-selective collector.     

Synthesis of stable derivatives of c(62): the first nonclassical fullerene incorporating a four-membered ring

A rational synthetic approach to the first four-membered ring-containing derivatives of C(62) is reported. They were synthesized by an inverse electron demand Diels-Alder reaction of 3,6-diaryl-1,2,4,5-tetrazines with C(60) in o-dichlorobenzene, followed by visible light irradiation at reflux. The structure of these nonclassical fullerenes derivatives was determined by X-ray single-crystal diffraction.     

Chiral base-mediated benzylic functionalisation of tricarbonylchromium(0) complexes of benzylamine derivatives

The novel complex (eta 6-benzylamine)tricarbonylchromium(0) 11 was prepared in up to 66% yield by direct complexation with Cr(CO)6 in refluxing 1,4-dioxane. Imine derivatives of this complex were readily deprotonated at the benzylic position by diamide 5, and the resultant anions reacted regioselectively with electrophiles (Me3SiCl or MeI) to give fairly good yields of products substituted at the benzylic carbon. Products of up to 87% e.e. were obtained in these reactions, with the highest enantioselectivity being derived from the tert-butyl-substituted imine complex 25.