Pulling Apart 2-spheres in 4-manifolds

An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection invariants provide a geometric generalization of Milnor's link-homotopy invariants, and can give the complete obstruction to pulling apart 2-spheres in certain families of 4-manifolds. It is also shown that in an arbitrary simply connected 4-manifold any number of parallel copies of an immersed surface with vanishing self-intersection number can be pulled apart, and that this is not always possible in the non-simply connected setting. The order 1 intersection invariant is shown to be the complete obstruction to pulling apart 2-spheres in any 4-manifold after taking connected sums with finitely many copies of S^2\times S^2; and the order 2 intersection indeterminacies for quadruples of immersed 2-spheres in a simply connected 4-manifold are shown to lead to interesting number theoretic questions.Comment: Revised to conform with the published version in Documenta Mathematic

A golden template self-generating method for patterned wafer inspection

This paper presents a novel golden template self-generating technique for detecting possible defects in periodic two-dimensional wafer images. A golden template of the patterned wafer image under inspection can be obtained from the wafer image itself and no other prior knowledge is needed. It is a bridge between the existing self-reference methods and image-to-image reference methods. Spectral estimation is used in the first step to derive the periods of repeating patterns in both directions. Then a building block representing the structure of the patterns is extracted using interpolation to obtain sub-pixel resolution. After that, a new defect-free golden template is built based on the extracted building block. Finally, a pixel-to-pixel comparison is all we need to find out possible defects. A comparison between the results of the proposed method and those of the previously published methods is presented

Total synthesis of a Streptococcus pneumoniae serotype 12F CPS repeating unit hexasaccharide

The Gram-positive bacterium Streptococcus pneumoniae causes severe disease globally. Vaccines that prevent S. pneumoniae infections induce antibodies against epitopes within the bacterial capsular polysaccharide (CPS). A better immunological understanding of the epitopes that protect from bacterial infection requires defined oligosaccharides obtained by total synthesis. The key to the synthesis of the S. pneumoniae serotype 12F CPS hexasaccharide repeating unit that is not contained in currently used glycoconjugate vaccines is the assembly of the trisaccharide β-D-GalpNAc-(1→4)-[α-D-Glcp-(1→3)]-β-D-ManpNAcA, in which the branching points are equipped with orthogonal protecting groups. A linear approach relying on the sequential assembly of monosaccharide building blocks proved superior to a convergent [3 + 3] strategy that was not successful due to steric constraints. The synthetic hexasaccharide is the starting point for further immunological investigations