A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

The effects of attractiveness and underlying components on the motivational salience and the memorability of face photographs

Facial attractiveness is a particularly salient social cue that influences many important social outcomes. Using a standard key-press task to measure motivational salience of faces and an old/new memory task to measure memory for face photographs, this thesis investigated both within-woman and between-women variations in response to facial attractiveness. The results indicated that within-woman variables, such as fluctuations in hormone levels, influenced the motivational salience of facial attractiveness. However, the between-women variable, romantic relationship status, did not appear to modulate women’s responses to facial attractiveness. In addition to attractiveness, dominance also contributed to both the motivational salience and memorability of faces. This latter result demonstrates that, although attractiveness is an important factor for the motivational salience of faces, other factors might also cause faces to hold motivational salience. In Chapter 2, I investigated the possible effects of women’s salivary hormone levels (estradiol, progesterone, testosterone, and estradiol-to-progesterone ratio) on the motivational salience of facial attractiveness. Physically attractive faces generally hold greater motivational salience, replicating results from previous studies. Importantly, however, the effect of attractiveness on the motivational salience of faces was greater in test sessions where women had high testosterone levels. Additionally, the motivational salience of attractive female faces was greater in test sessions where women had high estradiol-to-progesterone ratios. While results from Chapter 2 suggested that the motivational salience of faces was generally positively correlated with their physical attractiveness, Chapter 3 explored whether physical characteristics other than attractiveness contributed to the motivational salience of faces. To address this issue, I first had the faces rated on multiple traits. Principal component analysis of third-party ratings of faces for these traits revealed two orthogonal components that were highly correlated with trustworthiness and dominance ratings respectively. Both components were positively and independently related to the motivational salience of faces. While Chapter 2 and 3 did not examine the between-woman differences in response to facial attractiveness, Chapter 4 examined whether women’s responses to facial attractiveness differed as a function of their romantic partnership status. As several researchers have proposed that partnership status influences women’s perception of attractiveness, in Chapter 4 I compared the effects of men’s attractiveness on partnered and unpartnered women’s performance on two response measures: memory for face photographs and the motivational salience of faces. Consistent with previous research, women’s memory was poorer for face photographs of more attractive men and more attractive men’s faces held greater motivational salience. However, in neither study were the effects of attractiveness modulated by women’s partnership status or partnered women’s reported commitment to or happiness with their romantic relationship. A key result from Chapter 4 was that more attractive faces were harder to remember. Building on this result, Chapter 5 investigated the different characteristics that contributed to the memorability of face photographs. While some work emphasizes relationships with typicality, familiarity, and memorability ratings, more recent work suggests that ratings of social traits, such as attractiveness, intelligence, and responsibility, predict the memorability of face photographs independently of typicality, familiarity, and memorability ratings. However, what components underlie these traits remains unknown, as well as whether these components relate to the actual memorability of face photographs. Principal component analysis of all these face ratings produced three orthogonal components that were highly correlated with trustworthiness, dominance, and memorability ratings, respectively. Importantly, each of these components also predicted the actual memorability of face photographs.