The determinant bundle on the moduli space of stable triples over a curve

We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (E1, E2, Φ), where E1 and E2 are holomorphic vector bundles over a fixed compact Riemann surface X, and Φ: E2 → E1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kahler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed C∞ Hermitian vector bundle over a compact Riemann surface

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Quantitative ethology of social wasps: time-activity budgets and caste differentiation in Ropalidia marginata (Lep.) (Hymenoptera: Vespidae)

Time-activity budgets of several individually identified members of Ropalidia marginata colonies have been constructed with the aim of studying caste differentiation in social wasps that show no morphological differences between individuals. Analysis of these data by multivariate statistical techniques including principal components analysis and hierarchical cluster analysis has demonstrated the presence of three different behavioural castes which we have named Sitters, Fighters and Foragers. The Sitters in a colony consist of the queen and also some non-egg-laying individuals. The Fighters are non-egg-layers that show alarm reactions in response to disturbances and also fight with other individuals on the nest to a very large extent. The Foragers are also non-egg-layers and they spend a large proportion of their time making trips to places away from the nest to collect food, building material etc

Behaviour of the Indian social wasp Ropalidia cyathiformis on a nest of separate combs (Hymenoptera: Vespidae)

Observations were made on a nest of Ropa/idia cyathiformis consisting of three combs. The number of eggs, larvae, pupae and adults were monitored at about 3-day intervals for a 2-month period. The behaviour of the adults was observed with special reference to the proportion of time spent on each of the three combs, the proportion of time spent away from the.nest site and the frequencies of dominance interactions and egg laying. The adults moved freely between the three combs suggesting that all of them and all the three combs belonged to one nest. However, most of the adults preferred combs 2 and 3 over comb I. Of the 10 animals chosen for a detailed analysis of behaviour, seven spent varying periods of time away from the nest site and often brought back food or building material. Five of the 10 animals laid at least one egg each but two adults monopolized most of the egg-laying. The animals showed a variety of dominance interactions on the basis of which they have been arranged in a dominance hierarchy. The dominant individuals laid most of the eggs and spent little or no time foraging, while the subordinate individuals spent more time foraging and laid few eggs or none. It is argued that R. cyathiformis is different from R. marginata, the only other Indian social wasp whose behaviour has been studied, in being at a more primitive stage of social organization

Multi-objective optimization for preemptive & predictive supply chain operation

At present, the manufacturing industry has undergone a tremendous change in its operating principle with respect to the supply chain management system where the demands of consumers are dynamically and exponentially rising. Although Industry 4.0 offers a significant solution to this principle with the aid of its predictive automated operating process, till date there is less number of fault tolerant model that can effectively meet the standard demands of supply chain planning. Therefore, the proposed system introduces an analytical model where predictive optimization is carried out towards bridging the gap between supply and demands in supply chain 4.0. An analytical framework is a design from constraints derived from practical environment in order to offer better applicability of it. The study outcome shows that the proposed model could offer better performance in comparison to the existing optimization method with respect to the better budget control system for offering predictive and preemptive model design