Network governance at local — A comparative approach

Factors influencing the effectiveness of democratic institutions and to that effect processes involved at the local governance level have been the interest in the literature, given the presence of various advocacies and networks that are context-specific. This paper is motivated to understand the adaptability issues related to governance given these complexities through a comparative analysis of diversified regions. We adopted a two-stage clustering along with regression methodology for this purpose. The results show that the formation of advocacies and networks depends on the context and institutional framework. The paper concludes by exploring different strategies and dynamics involved in network governance and insists on the importance of governing the networks for structural reformation through regional policy making.

Influence of planning and governance on the level of urban services

A theoretical framework to analyse the interaction of planning and governance on the extent of outgrowth and level of services is proposed. An indicator framework for quantifying sprawl is also proposed and the same is operationalised for Bangalore. The indicators comprise spatial metrics (derived from temporal satellite remote sensing data) and other metrics obtained from a house-hold survey. The interaction of different indicators with respect to the core city and the outgrowth is determined by multi-dimensional scaling. The analysis reveals the underlying similarities (and dissimilarities) that relate with the different governance structures that prevail here. The paper concludes outlining the challenges in addressing urban sprawl while ensuring adequate level of services that planning and governance have to ensure towards achieving sustainable urbanisation.

Nodal length fluctuations for arithmetic random waves

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (''arithmetic random waves''). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy.

Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.