Geometry of Deligne cohomology

It is well known that degree two Deligne cohomology groups can be identified with groups of isomorphism classes of holomorphic line bundles with connections. There is also a geometric description of degree three Deligne cohomology, due to J-L. Brylinski and P. Deligne, in terms of gerbes with connective structures and curvings. This paper gives a geometric interpretation of Deligne cohomology of all degrees, in terms of equivalence classes of higher line bundles with $k$-connections. It is also shown that the classical Abel-Jacobi isomorphism $Pic^0(X) \cong J(X)$ generalizes to the isomorphism between groups of equivalence classes of topologically trivial 1-holomorphic higher line bundles with $k$-connections and Griffiths intermediate Jacobians.Comment: 51 pages, uses XY-pic, author-supplied PostScript and DVI files available at http://www.math.tamu.edu/~pawel.gajer/gdc.html . LaTeX2

Implementation of group-based genetic algorithms for economic dispatch problem in an electrical energetic system

Tematyka artykułu dotyczy zastosowania nowej wersji algorytmu genetycznego, określanej mianem grupowego algorytmu genetycznego, w celu rozwiązania zagadnienia ekonomicznego rozdziału obciążeń pomiędzy cieplne bloki energetyczne występujące w systemie elektroenergetycznym. Główną zaletą grupowego algorytmu genetycznego jest fakt, że wartość funkcji dopasowania wyznaczana jest jednocześnie dla większej grupy osobników, co zapobiega przedwczesnej zbieżności tego rodzaju algorytmu do jednego z licznych optimów lokalnych.The topic of the paper is about implementation of a novel version of genetic algorithm, which is called a group-based genetic algorithm. We use this kind of algorithm in order to solve an economic dispatch problem among energetic blocks in the electrical energetic system. The main merit of the group-based genetic algorithm is that the fitness function is calculated simultaneously for a larger group of individuals which disables the premature convergence to some of the numerous local optima

The Intercultural Workplace: An Emirati Perspective

The diverse environment of workplaces in the United Arab Emirates (UAE) means that Emirati employees find themselves in daily contact with people from a wide range of different cultures. One prominent outcome of this scenario is that the potential for intercultural misunderstanding and miscommunication between the local population and expat employees increases. This applied research investigation proposes to explore the most common areas of cultural misunderstanding in a higher education institution in the UAE from the perspective of Emirati nationals and to examine the role education plays in raising awareness of cultural issues of both Emiratis and expat employees. In this qualitative research project, 16 working professionals of both genders in varying positions were interviewed. With one exception, they were all either employees or graduates of the same higher education institution. Of the many facets and aspects of culture that were discussed, stereotyping, gender, language and a lack of future preparedness for international work environments were the emergent themes to which more attention needs to be given. Confronting these issues, this study suggests implementing a mandatory intercultural communication component at all levels of education, a needs analysis for new Emirati employees that would focus on culture-specific training needs, an on-site language support for new hires, creating a cross-cultural buddy system and building multicultural teams

Holonomy and parallel transport for Abelian gerbes

In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This result is a higher-order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds. The holonomy of a gerbe with group $S^1$ on a simply connected manifold $M$ is a group morphism from the thin second homotopy group to $S^1$, satisfying a smoothness condition, where a homotopy between maps from $[0,1]^2$ to $M$ is thin when its derivative is of rank $\leq 2$. For the non-simply connected case, holonomy is replaced by a parallel transport functor between two monoidal Lie groupoids. The reconstruction of the gerbe and connection from its holonomy is carried out in detail for the simply connected case. Our approach to abelian gerbes with connections holds out prospects for generalizing to the non-abelian case via the theory of double Lie groupoids.Comment: Final version. Improved readibility (hopefully). LaTeX, 60 pages, 14 figures. To appear in Advances in Mathematic

Optimal Pacing for Running 400 m and 800 m Track Races

Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and field. Races are almost always won, and records set, in 400 m and 800 m running events by people who run the first half of the race faster than the second half, which is not true of shorter races, nor of longer. There is general agreement that performance in the 400 m and 800 m is limited somehow by the amount of anaerobic metabolism that can be tolerated in the working muscles in the legs. A toy model of anaerobic metabolism is presented, from which an optimal pacing strategy is analytically calculated via the Euler-Lagrange equation. This optimal strategy is then modified to account for the fact that the runner starts the race from rest; this modification is shown to result in the best possible outcome by use of an elementary variational technique that supplements what is found in undergraduate textbooks. The toy model reproduces the pacing strategies of elite 400 m and 800 m runners better than existing models do. The toy model also gives some insight into training strategies that improve performance.Comment: 14 pages, 4 figures, submitted to the American Journal of Physic

Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants

We study the space of positive scalar curvature (psc) metrics on a 4-manifold, and give examples of simply connected manifolds for which it is disconnected. These examples imply that concordance of psc metrics does not imply isotopy of such metrics. This is demonstrated using a modification of the 1-parameter Seiberg-Witten invariants which we introduced in earlier work. The invariant shows that the diffeomorphism group of the underlying 4-manifold is disconnected. We also study the moduli space of positive scalar curvature metrics modulo diffeomorphism, and give examples to show that this space can be disconnected. The (non-orientable) 4--manifolds in this case are explicitly described, and the components in the moduli space are distinguished by a Pin^c eta invariant.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper28.abs.htm