Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associated with the universal complexes of singular fibers give complete invariants for all these cobordism groups. We also discuss invariants derived from hypercohomologies of the universal homology complexes of singular fibers. Finally, as an application of the theory of universal complexes of singular fibers, we show that for generic smooth map germs g: (R^3, 0) --> (R^2, 0) with R^2 being oriented, the algebraic number of cusps appearing in a stable perturbation of g is a local topological invariant of g.Comment: This is the version published by Algebraic & Geometric Topology on 7 April 200

W mass measurement at LEP

In 1998, the four experiments of LEP, i.e. ALEPH, DELPHI, L3 and OPAL, collected data of about 175 /pb per experiment at the center-of-mass energy of 189 GeV. Using these data, the mass of W boson was directly measured by reconstructing the decay products of two W bosons from the e+e- collisions. The W mass measurement was combined personally with the results obtained from data at 161, 172, and 183 GeV. This yielded the private LEP2 average of Mw = 80.350 +/- 0.056 GeV.Comment: 6 pages, 2 figures; uses Moriond.sty; to appear in the proceedings of the XXXIVth Recontres de Moriond QCD, March 199

The Chess conjecture

We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure Math., 40 (1983) 221-224] and [VI Arnol'd, VA Vasil'ev, VV Goryunov, OV Lyashenko, Dynamical systems VI. Singularities, local and global theory, Encyclopedia of Mathematical Sciences - Vol. 6 (Springer, Berlin, 1993)]. Also, in view of the Saeki-Sakuma theorem [O Saeki, K Sakuma, Maps with only Morin singularities and the Hopf invariant one problem, Math. Proc. Camb. Phil. Soc. 124 (1998) 501-511] on the Hopf invariant one problem and Morin mappings, this implies that a manifold P^p with odd Euler characteristic does not admit Morin mappings into R^{2k+1} for p > 2k not equal to 1,3 or 7.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-26.abs.htm

Simplified broken Lefschetz fibrations and trisections of 4-manifolds

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only allow us to produce various interesting families of examples, but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.Comment: 17 pages, 7 figure

Developmental and gender trends in emotional literacy and interpersonal competence among Japanese children

This study explored cross-sectional gender and grade level trends in emotional literacy and interpersonal competence among 913 elementary and middle school students in Japan. Students were presented with two hypothetical scenarios involving mixed emotions and potential interpersonal dilemmas. Results indicated that older children possess greater emotional literacy when compared to younger children. Additionally, girls identified a greater number of emotions, were better able to identify mixed emotions, and were more likely to identify empathic interpersonal behaviours. These gender and grade level considerations may be incorporated into social-emotional learning curricula to enhance the utility and effectiveness of programs for diverse populations.peer-reviewe

Obstructions to the existence of fold maps

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in terms of characteristic classes, which arise as Postnikov invariants, and can be interpreted as primary and secondary obstructions to the elimination of certain singularities. We also discuss the relationship between the existence problem of fold maps and that of vector fields of stabilized tangent bundles.Comment: 17 pages; the final version of the preprint will be published in the Journal of the LM

The Impact of Systematic Edits in History Slicing

While extracting a subset of a commit history, specifying the necessary portion is a time-consuming task for developers. Several commit-based history slicing techniques have been proposed to identify dependencies between commits and to extract a related set of commits using a specific commit as a slicing criterion. However, the resulting subset of commits become large if commits for systematic edits whose changes do not depend on each other exist. We empirically investigated the impact of systematic edits on history slicing. In this study, commits in which systematic edits were detected are split between each file so that unnecessary dependencies between commits are eliminated. In several histories of open source systems, the size of history slices was reduced by 13.3-57.2% on average after splitting the commits for systematic edits.Comment: 5 pages, MSR 201