A new formulation of non-relativistic diffeomorphism invariance

We provide a new formulation of nonrelativistic diffeomorphism invariance. It is generated by localising the usual global Galilean Symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton - Cartan geometry from the gauge procedure.Comment: minor changes, new reference added, to appear in PL

Studies in Indian informal sector

This dissertation contributes to the literature in two ways. It explores the link between the trade liberalization policies and the informal sector wages, and examines the economy of the self-employed sector of India. Specifically, this dissertation (i) develops a general equilibrium model incorporating the self-employed sector as a separate informal sector and demonstrates the connection between the trade liberalization policies and the informal sector wages; (ii) presents a system analysis for the economy of the self-employed sector; (iii) highlights the distinctive characteristics of the self-employed sector and generates a better understanding of the difference between the self-employed and the wage-working sectors. There are a number of studies focusing on the impact of the changing policy environment in the developing countries on the informal sector. While most of them are in agreement that the size of the informal sector has grown post-trade reforms in the developing countries, there is still no consensus about the impact of the reforms on the terms of informal work, particularly the wages. The theoretical model developed in this dissertation shows that the current understanding changes significantly when the self-employed sector is incorporated into the analysis. The extent of self-employment plays a crucial role in determining the link between the trade liberalization policies and the informal sector wages. This model emphasizes that the growing self-employment and informalization of the formal sector workers in India can result in non-increasing informal sector wages. The analysis of the economic system of the self-employed sector generates important insights about the production relationships prevailing in this sector. A microcosm of self-employed occupations of India is developed and the occupations are categorized according to location, gender and types of products. The system of production is analyzed to find out the difference of this sector with other wage-working sectors. The extra-legal and extra-capitalist nature of production highlights the inadequacy of the abstract modeling in capturing the economic characteristics of this sector. The Kinship Associations build the informal institutions and determine the terms of input valuations. This dissertation also demonstrates the importance of maintaining the community ties in helping the productive capacity of the self-employed sector

Adjacency spectra of some subdivision hypergraphs

Here, we define a subdivision operation for a hypergraph and compute all the eigenvalues of the subdivision of regular and certain non-regular hypergraphs. In non-regular hypergraphs, we investigate the power of regular graphs, various types of hyperflowers, and the squid-like hypergraph. Using our subdivision operation, we also show how to construct non-regular non-isomorphic cospectral hypergraphs

A Geo-Spatial Information Model for Rurban Planning

The Indian context of planning primarily focuses on urban settlements comprising approximately 30% of our land area. The rest two-thirds are composed of spatially isolated rural communities which lack access to adequate infrastructure, services and connectivity for which the absence of a standardized planning methodology is a pertinent reason. Since a spatial entity is never disconnected from its context, planning is most effective when undertaken in the context of a region, joining settlements in need of physical, economic and social connectivity. Within a region, the availability of a multihierarchical geo-spatial database is fundamental to spatial planning, and research identifies that it requires conspicuous attention in our rural planning strategy. The proposed paper addresses this lacuna of data infrastructure at the micro-regional level. An example of micro-region is the rurban cluster, comprising several village settlements around a central town, displaying potential for spatially integrated development. The rurban cluster is in compliance with the Shyama Prasad Mukherji National Rurban Mission (SPMNRM), a flagship programme initiated by the Ministry of Rural Development (Government of India) in 2016. The planning, implementation and execution of this scheme also sufferes due to the lack of geo-spatial database management. Borrowing from past experiences in the country and abroad, this paper constructs a model for geo-spatial planning of rurban clusters. The model takes care of all the stages of rurban cluster planning such as delineation of the micro-region, database design and management, analysis, evolution of alternative scenarios and finally implementation and monitoringthrough geo-spatial information systems. Once developed and applied, it objectively evaluates the corresponding stages of the SPMNRM (non-spatial) and the new model (geo-spatial), to demonstrate how the latter adds value to the planning process and produces superior results on ground