Two-dimensional RCFT's without Kac-Moody symmetry

Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find "dual" theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT's. The theory dual in this sense to the Ising model has central charge 47/2 and is related to the Baby Monster Module.Comment: 18 page

Choosing Products in Social Networks

We study the consequences of adopting products by agents who form a social network. To this end we use the threshold model introduced in Apt and Markakis, arXiv:1105.2434, in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with such each social network a strategic game between the agents. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining the existence of a Nash equilibrium, also of a special type, is NP-complete. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or has no source nodes. For these three classes we determine the complexity of establishing whether a (special type of) Nash equilibrium exists. We also clarify for these categories of games the status and the complexity of the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for verifying the property of being a weakly acyclic game.Comment: 15 pages. Appeared in Proc. of the 8th International Workshop on Internet and Network Economics (WINE 2012), Lecture Notes in Computer Science 7695, Springer, pp. 100-11

EMEEDP: Enhanced Multi-hop Energy Efficient Distributed Protocol for Heterogeneous Wireless Sensor Network

In WSN (Wireless Sensor Network) every sensor node sensed the data and transmit it to the CH (Cluster head) or BS (Base Station). Sensors are randomly deployed in unreachable areas, where battery replacement or battery charge is not possible. For this reason, Energy conservation is the important design goal while developing a routing and distributed protocol to increase the lifetime of WSN. In this paper, an enhanced energy efficient distributed protocol for heterogeneous WSN have been reported. EMEEDP is proposed for heterogeneous WSN to increase the lifetime of the network. An efficient algorithm is proposed in the form of flowchart and based on various clustering equation proved that the proposed work accomplishes longer lifetime with improved QOS parameters parallel to MEEP. A WSN implemented and tested using Raspberry Pi devices as a base station, temperature sensors as a node and xively.com as a cloud. Users use data for decision purpose or business purposes from xively.com using internet.Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1409.1412 by other author

Cosets of Meromorphic CFTs and Modular Differential Equations

Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are constructed. The same method also gives rise to interesting new examples of CFTs with three and four characters.Comment: 1+12 page