In this dissertation we consider the problem of cooperative sensing for secondary user access to primary user spectrum in cognitive radio systems. Using a fusion center or an access point, the cooperative users decide on the availability of spectrum for their use. Both Neyman-Pearson and Bayes criterion are considered for performance assessment. Our work on the asymptotic performance of counting rules with a very large number of sensors in decentralized detection problem shows that majority logic fusion rule has the same order of performance when compared to the best fusion rule based on the binary decisions received from the observing sensors in a network. In cognitive radio context, very large number of sensors may not be realistic and hence we would like to examine the performance of majority logic and counting rules involving a finite and small number of sensors. Uniformly most powerful test for decentralized detection for testing parameter θ when the observation is a sample from uniform (0,θ) distribution is investigated and it is shown that OR rule has the best performance among all counting rules in error free channel. The numerical study for reporting channel as a binary symmetric channel (BSC) with probability of bit error is also investigated and the results show that 2-out-of-5 or 2-out-of-10 has better performance among other k-out-of-n rules, whenever OR rule is not able to provide a probability of false alarm at the sensor, that lies over (0,1) at a given probability of bit error.

Research in many fields of life and biomedical sciences depends on the microscopic image analysis of biological images. Quantitative analysis of these images is often time-consuming, tedious, and may be prone to subjective bias from the observer and inter /intra observer variations. Systems for automatic analysis developed in the past decade determine various parameters associated with biological tissue, such as the number of cells, object volume and length of fibers to avoid problems with manual collection of microscopic data. Specifically, automatic analysis of biological microstructures using unbiased stereology, a set of approaches designed to avoid all known sources of systematic error, plays a large and growing role in bioscience research. Our aim is to develop an algorithm that automates and increases the throughput of a commercially available, computerized stereology device (Stereologer, Stereology Resource Center, Chester, MD). The current method for estimation of first and second order parameters of biological microstructures requires a trained user to manually select biological objects of interest (cells, fibers etc.) while systematically stepping through the three dimensional volume of a stained tissue section. The present research proposes a three-part method to automate the above process: detect the objects, connect the objects through a z-stack of images (images at varying focal planes) to form a 3D object and finally count the 3D objects. The first step involves detection of objects through learned thresholding or automatic thresholding. Learned thresholding identifies the objects of interest by training on images to obtain the threshold range for objects of interest. Automatic thresholding is performed on gray level images converted from RGB (red-green-blue) microscopic images to detect the objects of interest. Both learned and automatic thresholding are followed by iterative thresholding to separate objects that are close to each other. The second step, linking objects through a z-stack of images involves labeling the objects of interest using connected component analysis and then connecting these labeled objects across the stack of images to produce a 3D object. Finally, the number of linked objects in a 3D volume is counted using the counting rules of stereology. This automatic approach achieves an overall object detection rate of 74%. Thus, these results support the view that automatic image analysis combined with unbiased sampling as well as assumption and model-free geometric probes, provides accurate and efficient quantification of biological objects.

This thesis entitled “Electronic Structure and Bonding in Metallaboranes and Main Group Compounds” consists of five chapters. Chapter 1 gives an exposition of concepts and techniques used in understanding the electronic structure and bonding in some chemically interesting molecules. Heuristics concepts like isolobal analogy and electron counting rules are used in analyzing and predicting some novel chemical systems. A brief description of computational techniques such as density functional theory (DFT) based methods are used to quantitatively examine the structures and energies of these systems. In chapter 2 we present a critical analysis of bonding in neutral and dianionic stannadiphospholes and compare the potential energy surfaces with the isoelectronic Cp+ and Cp- species. The analysis indicates that Sn can be a better isolobal analogue to P+ than to BH or CH+. In chapter 3 we present new strategy to stabilize B2H4 in planar configuration using transition metal fragments. This requires the metal to donate two electrons into the empty B-B π orbital. Such complexes present a unique case study to the classical DCD model of metal-π complex. In chapter 4 we study the bonding in some recently synthesized metallaboranes which does not follow conventional electron counting rules. The complex and non-canonical nature of these metallaboranes feature some unique bonding patterns which are elucidated using theoretical techniques. In the final chapter we present new approach to build metal coated boron fullerenes. We use electron counting rules to device new structures which show enhanced metal boron bonding.