Given a set of unit disks in the plane with union area A, what fraction of A can be covered by selecting a pairwise disjoint subset of the disks? Richard Rado conjectured 1/4 and proved 1/4.41. In this thesis, we consider a variant of this problem where the disjointness constraint is relaxed: selected disks must be k-colourable with disks of the same colour pairwise-disjoint. Rado’s problem is ...

The zenith tropospheric delay (ZTD) is an important atmospheric parameter in the wide application of global navigation satellite systems (GNSS) technology in geoscience. Given that the temporal resolution of the current global zenith tropospheric delay model (GZTD) is only 24 h, an improved model, GZTD2, has been developed by taking the diurnal variations into consideration and modifying the mo...

This report investigates the feasibility of using smartphones as wireless reflector tags. A smartphone communicates its GNSS positioning data via peer-to-peer connections to nearby road users to notify its presence. Appropriate use cases are studied based on accident data. Different communication protocols and a pseudo differencing positioning technique are evaluated. Possibilities and obstacle...

Packaging constraints motivate a two-level interconnection network for a multiprocessor. A single node in the global network contains multiple processors connected by a local network. An important issue in two-level networks is how alternative numbers of processors per node changes the per link traac in the global network. In the case of a hypercube global network we consider three communicatio...

In this report, we study the positioning accuracy of Cooperative Localization and Target Tracking (CLATT) in a network of mobile robots, and derive analytical upper bounds for the positioning uncertainty. The obtained bounds provide a description for the asymptotic positioning performance of the robots and the targets as a function of the sensor characteristics, and the structure of the graph o...

We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any > 0, we construct an algorithm which has error converging to zero at rate n ?(1?) in the number of function evaluations n. This convergence rate ...

Deviations from the average can provide valuable insights about the organization of natural systems. This article extends this important principle to the more systematic identification and analysis of singular local connectivity patterns in complex networks. Four measurements quantifying different and complementary features of the connectivity around each node are calculated and multivariate st...

For developing countries like Pakistan, the paucity of reliable solar radiation data necessitates the development of empirical models. To develop such a model one could use various parameters. In this study, linear regression models are developed to estimate the monthly average daily global radiation using cloudiness data for Karachi, Pakistan for the period of 20 years (1990-2010). The results...