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.

A study of the electrical basis for the inhibition and excitation in autonomically innervated smooth muscle

The aim of this thesis was to investigate the electrical and mechanical responses to inhibitory non-adrenergic noncholinergic (NANC) nerve stimulation in the bovine retractor penis muscle (BRP) and compare them with those to an inhibitory extract made from this muscle. The extract may contain the NANC inhibitory transmitter of the BRP and possibly of other smooth muscles. Because of species differences in the electrical response to NANC nerves in the rat and rabbit anococcygeus the effects of the extract on these tissues was also investigated. Prior to the investigation of the extract, both the excitatory and inhibitory responses to field stimulation in the BRP, and the effects of passive membrane potential displacement were studied using conventional intra- or extracellular (sucrose gap) recording techniques. The majority of cells in the BRP were electrically quiescent independent of the resting tone. The most frequent (in approximately 25% of preparations) form of spontaneous activity, oscillations in membrane potential and tone, may represent a pacemaker activity. The BRP had cable properties; the time constant and space constant indicated a high membrane resistance. In the absence of tone, field stimulation of the BRP evoked excitatory junction potentials (ejps) in every cell impaled and contractions, graded with the strength, frequency and number of pulses; spikes were not observed. Guanethidine (1-3 x 10-5M) abolished the ejps and contractions, confirming their adrenergic origin. Noradrenaline added exogenously depolarised and contracted the muscle. These effects were blocked by the a-adrenoceptor antagonists, phentolamine and prazosin. However, phentolamine (2.5x 10-6M) inhibited the contraction without reducing the ejp significantly. These effects may be independent of adrenoceptor blockade or the ejp may be mediated by a substance other than noradrenaline (e.g. ATP) released from adrenergic nerves. Prazosin (1.4 x lO-6M) failed to block either the ejp or contraction, indicating the possible existence of two types of adrenoceptor in the BRP; one activated by neuronally-released and the other by exogenously-added noradrenaline. ATP, a contaminant in the extract, also depolarised and contracted the BRP. Physostigmine reduced whilst atropine enhanced the ejps and contractions without similarly affecting the response to exogenous noradrenaline. This confirmed the presence of a cholinergic inhibitory innervation acting on the excitatory adrenergic fibres (Klinge and Sjostrand, 1977). TEA (1 x lO-4M) enhanced the ejp and contraction. Higher concentrations (0.5 to 10 x 10-3M) depolarised, increased the tone and evoked electrical and mechanical oscillations but no spikes. The depolarisation and contraction to exogenous noradrenaline were not enhanced, indicating that TEA acts on the adrenergic nerves. Some post-synaptic effect to block K+ channels also seems likely. The relationship between ejp amplitude and membrane potential in the double sucrose gap was linear and indicated a reversal potential more positive than -30mV. Electrotonic pulse amplitude decreased during the ejp, indicating an increased membrane conductance. Ejps and contractions were reduced following the replacement of the NaCl of the Krebs solution with sodium glutamate. This may be due to the effects of glutamate itself (e.g. Ca2+ chelation) rather than reduction in the membrane Cl- gradient. Tone usually developed spontaneously and was accompanied by membrane depolarisation (from -53 to -45mV) which may open voltage-dependent channels, causing Ca2+ entry and/or its release from intracellular binding sites. Field stimulation produced inhibitory potentials (ijps) and relaxations graded with the strength and number of pulses but showing little frequency dependence. Rebound depolarisation and contraction often followed the ijp and relaxation. Tetrodotoxin (3 x IO-6M), but not adrenergic or cholinergic antagonists, abolished the ijp and relaxation, confirming their non-adrenergic non-cholinergic neurogenic nature. The extract, prepared and acid-activated as described by Gillespie, Hunter and Martin (1981), hyperpolarised and relaxed the BRP, as did sodium nitroprusside and adenosine triphosphate (ATP). Unlike the activated extract or sodium nitroprusside, desensitisation to ATP occurred rapidly and without any change in the inhibitory electrical or mechanical responses to field stimulation. The ijp and relaxation in the BRP were insensitive to apamin but abolished by oxyhaemoglobin (4-8 x 10-6M), as were the responses to extract and sodium nitroprusside. In TEA (10-2M), field stimulation evoked relaxations with no accompanying electrical change. The ijp may be unconnected with or additional to another mechanism producing relaxation. The relationship between membrane potential and ijp in the BRP was non-linear. Ijp amplitude was initially increased during membrane potential displacement from -45mV to approximately -60mV. Thereafter (-60 to -l03mV) the ijp was reduced. Ijps were abolished at -27 and -103mV; reversal was not observed. The hyperpolarisation to extract was also enhanced during passive displacement of the membrane potential to more negative values (-57mV). Membrane resistance increased during the ijp. The extract produced inconsistent changes in membrane resistance, possibly because of the presence of more than one active component. K+ withdrawal failed to enhance the ijp or hyperpolarisation to extract and 20mM K+ did not abolish the the ijp at membrane potentials exceeding EK (-49mV). Thus, the ijp or hyperpolarisation to extract are unlikely to be mediated by an increased K+ conductance. Reducing the Cl- abolished the hyperpolarisation to field stimulation and extract. This occurred more quickly than the anticipated reduction in the Cl- gradient and may be due to Ca2+ chelation by the anion substitute (glutamate or benzenesulphonate) or blockade of the resting conductance which is normally inactivated by the transmitter. Ouabain (1-5x 10-5M), which reduces both the Na+ and Cl- gradients, abolished the ijp, implicating either of these ions as the ionic species involved. In the rat and rabbit anococcygeus, field stimulation and extract each reduced guanethidine-induced tone. This was unaccompanied in the majority of cells in the rat by any significant electrical response. In the remaining cells, inhibition of the membrane potential oscillations occurred. The rabbit anococcygeus differed in that inhibition of the electrical oscillations was observed in every cell exhibiting this behaviour. However, the majority of cells in the rabbit were electrically quiescent and showed only small hyperpolarisations to field stimulation and no electrical response to extract. Apamin (1 x 10-7M) failed to block the electrical and mechanical response to field stimulation in the rabbit but did inhibit transiently that to extract. The latter effect may be due to the initial excitatory effects of apamin. The similarities between the electrical effects of the extract and those of inhibitory nerve stimulation in the BRP, rat and rabbit anococcygeus muscles are generally consistent with their being mediated by the same active component. Moreover, the ijp in the BRP shows properties which have not been reported in other non-adrenergic noncholinergically innervated smooth muscles.

Bull's eye leaky wave antenna for terrestrial and space applications

This work presents the study of Bull's eye antenna designs, a type of leaky wave antenna (LWA), operating in the 60 GHz band. This band emerged as a new standard for specific terrestrial and space applications because the radio spectrumbecomes more congested up to the millimetre-wave band, starting at 30 GHz. Built on existing Bull's eye antenna designs, novel structures were simulated, fabricated and measured, so as to provide more exibility in the implementation of wireless solutions at this frequency. Firstly, the study of a 60 GHz Bull's eye antenna for straightforward integration onto a CubeSat is presented. An investigation of the design is carried out, from the description of the radiation mechanism supported by simulation results, to the radiation pattern measurement of a prototype which provides a gain of 19.1 dBi at boresight. Another design, based on a modified feed structure, uses a microstrip to waveguide transition to provide easier and inexpensive integration of a Bull's eye antenna onto a planar circuit. Secondly, the design of Bull's eye antennas capable of creating beam deflection and multi-beam is presented. In particular, a detail study of the deflection mechanism is proposed, followed by the demonstration of a Bull's eye antenna generating two separate beams at ±16° away from the boresight. In addition, a novel mechanically steerable Bull's eye antenna, based on the division of the corrugated area in paired sectors is presented. A prototype was fabricated and measured. It generated double beams at ±8° and ±15° from the boresight, and a single boresight beam. Thirdly, a Bull's eye antenna capable of generating two simultaneous orbital angular momentum (OAM) modes l = 3 is proposed. The design is based on a circular travelling wave resonator and would allow channel capacity increase through OAM multiplexing. An improved design based on two stacked OAM Bull's eye antennas capable of producing four orthogonal OAM modes l = (±3,±13) simultaneously is presented. A novel receiving scheme based on discretely sampled partial aperture receivers (DSPAR) is then introduced. This solution could provide a lower windage and a lower cost of implementation than current whole or partial continuous aperture.