Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known

Detection of an unknown rank-one component in white noise

We consider the detection of an unknown and arbitrary rank-one signal in a spatial sector scanned by a small number of beams. We address the problem of finding the maximal invariant for the problem at hand and show that it consists of the ratio of the eigenvalues of a Wishart matrix to its trace. Next, we derive the generalized-likelihood ratio test (GLRT) along with expressions for its probability density function (pdf) under both hypotheses. Special attention is paid to the case m= 2, where the GLRT is shown to be a uniformly most powerful invariant (UMPI). Numerical simulations attest to the validity of the theoretical analysis and illustrate the detection performance of the GLRT

Escaping from nonhyperbolic chaotic attractors

We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by solving the variational equations of the auxiliary Hamiltonian system and by incorporating the initial conditions on the chaotic attractor unambiguously. Our results are exemplified with the H{\'e}non and the Ikeda map and can be implemented straightforwardly to experimental data.Comment: replaced with published versio

An exploration of the post-treatment psychosocial experiences of female adult cancer patients

ABSTRACT This study explores the post-treatment psychosocial experiences of female adult cancer patients. In particular, this study aims at identifying common themes in the nature of their experiences. This research was exploratory in nature and took place within the context of the qualitative paradigm. The focus group method was utilised in collecting data. The six participants were white Christian females between the ages of 50 and 62 who had completed treatment (either chemotherapy, radiation or both) not more than four months prior to the study. Data were analysed by means of categorical content analysis. Four out of the six participants reported relief as well as mixed emotions after discovering they had survived cancer. A major finding of this research was that all of the participants were experiencing anxiety that the cancer might recur. Five out of the six participants reported ample support from their partners and other family members. The entire group of participants admitted that their genuine friends remained supportive throughout treatment, while some friends avoided them when they had cancer, but were willing to continue the friendship after treatment. This impacted negatively on their friendship. The entire group mentioned negative social experiences due to the stigma attached to having cancer. It was also found that the participants preferred spending time with people who have insight into the meaning of life. All of the participants agreed that without their relationship with God and the social support structure including churches and acquaintances at church, they would not be able to get through their experiences during and after treatment. The entire group mentioned the experience of a greater appreciation for life after having completed treatment and survived cancer. It is evident that the experiences of cancer survivors in the South African context necessitate further research and that an understanding of these experiences plays a crucial role in the development of successful interventions for survivors, their families and the wider social community in regard to cancer

The taxation of private equity carried interest in South Africa

A research report submitted to the Faculty of Commerce, Law and Management in partial fulfilment of the requirements for the degree of Master of Commerce (Specialising in Taxation)In this research report the South African taxation of carried interest in a private equity context is examined. The extent to which reform of that taxation should be considered is also presented in this report. The nature of carried interest in the South African private equity context is initially examined. Thereafter, a discussion of the relevant provisions of the Income Tax Act and related South African case law that would likely apply to the taxation of carried interest is set out. An analysis and determination of how appropriate and adequate the taxing provisions and relevant principles from case law are in the taxation of carried interest is provided. A recommendation for new legislation to deal with the taxation of carried interest has also been made.MT201