Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

This thesis is concerned with developing new methods for performing weak gravitational lensing with the aim of addressing specific systematic effects in weak lensing surveys. The first of these effects is the multiplicative biases which arise as a result of isotropic smearing. This smearing may be due to atmospheric seeing or an instrumental PSF. Isotropic smearing circularizes a galaxy image and leads to a systematic under-estimate of the modulus of the observed ellipticity. The orientation of the observed galaxy is, however, unaffected. We exploit this property by formulating a weak lensing shear estimator that requires measurements of galaxy position angles only, thereby avoiding the contribution from this systematic. We demonstrate the method on simulations and the CFHTLenS data by reconstructing convergence maps and comparing the results with the standard full ellipticity based approach. We show that the difference between the reconstructed maps for the two approaches is consistent with noise in all of the tests performed. We then apply the technique to the GREAT3 challenge data using three distinct methods to measure the position angles of the galaxies. For all three methods, we find that the position angle-only approach yields shear estimates with a performance comparable with current well established shape based techniques. The second effect addressed arises from the intrinsic alignment of the source galaxies. This alignment mimics a shear signal, and hence biases estimates of the shear. To mitigate this effect, we develop three shear estimators that include polarization information from radio observations as a tracer of a galaxy’s intrinsic orientation. In addition to the shear estimator, we also develop estimators for the intrinsic alignment signal. We test these estimators by successfully reconstructing the shear and intrinsic alignment auto and cross-power spectra across three overlapping redshift bins.

A photon asymmetry measurement in radiative muon capture (RMC) on ⁴⁰Ca has been carried out in order to determine a value for the induced-pseudoscalar coupling constant (ցƿ), thereby allowing us to investigate the possible renormalisation effect for this coupling constant inside nuclear matter. Negative muons from the M20A channel at TRIUMF were stopped in a ⁴⁰Ca target. The resulting RMC photons were then converted by a 5 cm thick Nal converter placed immediately in front of our main detector, a Nal crystal of size 46 cm∅x51 cm. The purpose of the converter was to provide discrimination against the prolific high energy neutron background. From a fit to our time spectrum for the high-energy (57 MeV< E⋎ <95 MeV) photons, we were able to extract a value for the RMC photon asymmetry (⍺⋎). This time spectrum, with 5200 "clean" photons and a signal to noise ratio of ~7, showed the photon asymmetry quite clearly. With our measured value for the photon asymmetry: ⍺⋎ = 1.00±0.23, the predicted value of the induced-pseudoscalar coupling constant becomes: ցƿ = (0.0±⁸‧⁰₆․₇) ցA;, this range contains the (theoretical) unrenormalised value of Goldberger-Treiman: ցƿ ≈ 7 ցA⋅ / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The photon asymmetry (⍺⋎) and partial branching ratio (Rk>57), for radiative muon capture on ⁴⁰Ca, have been measured in order to determine the magnitude of the induced-pseudoscalar coupling constant, gp. A large Nal(Tl) crystal (46cm ϕ x 51cm) was used with an active Nal(Tl) converter (36cm x 30cm x 5cm) as the photon detector. The combined system had an energy resolution of 15% at 70 MeV; a factor of two improvement over previous similar experiments. Simultaneous measurements of the photon asymmetry and the partial branching ratio have been performed twice in the past. From a theoretical stand-point the photon asymmetry measurement is of greater interest as it represents the least nuclear model-dependent way of extracting gp. In the present experiment we have observed 3100 photons with energies greater than 57 MeV, after background subtraction. Of these, 2500 could be used in the determination of ⍺⋎. A value of ⍺⋎ = 1.32+⁺⁰֗⁵⁴˗₀․₄₇ is obtained from a fit to the photon time distribution. For the first time in such measurements the photon asymmetry was visible in the time spectrum and an unconstrained fit is able to reproduce its known frequency and phase. The extracted asymmetry allows for the first time a meaningful limit to be placed on gp which is free of the uncertainties associated with the extraction of gp from the partial branching ratio. Our asymmetry result implies gp < 5Agp, favouring a renormalization of the induced-pseudoscalar coupling constant. The partial branching ratio determined in this experiment is consistent with previous measurements. A model-dependent extraction of gp from Rk>57 yields gP ~ (7 ± 2)gA. As a consequence of this work an improved experiment has recently been successfully performed at TRIUMF with increased statistics, improved energy resolution, and an improvement of approximately a factor of 15 in the signal-to-noise ratio. We have also identified a potential systematic error of as large as 15% in the normalization of the photon asymmetry in past experiments. Such an error occurs from the use of the V—A asymmetry distribution rather than a bound decay asymmetry distribution when performing Monte Carlo calculations of the decay electron asymmetry. This error affects the estimation of the residual muon polarization which is used to normalize the photon asymmetry. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This dissertation explores the interplay of grammar and context in the interpretation of modal words like ought, necessary, and need. The empirical foci of the discussion are patterns in the use of strong and weak necessity modals in conversation, and the interpretation of syntactically and semantically versatile modals like need in the various grammatical configurations they appear in across languages. It is argued that a sensitivity to collective commitments in a conversation is necessary for understanding certain aspects of modal strength, in particular the traditional distinction between strong and weak necessity modals (exhibited by must and ought to in English). It is proposed that strong necessity modals can only reference priorities that are presupposed to be collectively committed to, whereas weak necessity modals are evaluated with respect to a mixed bag of priorities, crucially including ones that are presupposed not to be collectively committed to. A domain restriction approach to weak necessity is adopted, following a demonstration that it is superior to a number of probabilistic alternatives. Modal verbs and adjectives that take both infinitival and nominal complements are shown to pattern alike across languages in requiring a teleological, or goal-oriented interpretation when their complements are not infinitives (but rather noun phrases or certain Complementizer Phrases). This limitation is lifted with infinitival complements, showing that transitive configurations of certain intensional verbs are not semantically equivalent to the infinitival configurations of the same verbs. A result of this research is a fine grained analysis of the differences between closely related necessity modals and attitude verbs.

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We investigate weak Cayley table isomorphisms, a generalization of group isomorphisms. Suppose G and H are groups. A bijective map phi : G to H is a weak Cayley table isomorphism if it satisfies two conditions:(1) If x is conjugate to y, then phi(x) is conjugate to phi(y); (2) For all x, y in G, phi(xy) is conjugate to phi(x)phi(y).If there exists a weak Cayley table isomorphism between two groups, then we say that the two groups have the same weak Cayley table.This dissertation has two main goals. First, we wish to find sufficient conditions under which two groups have the same weak Cayley table. We specifically study Frobenius groups and groups which satisfy the Camina pair condition. Second, we consider the group of all weak Cayley table isomorphisms between G and itself. We call this group the weak Cayley table group of G and denote it by W(G). Any automorphism of G is an element of W. The inverse map on G is also an element of W. We say that the weak Cayley table group is trivial if it is generated by the set of all automorphisms of G and the inverse map. Stephen Humphries proved that the symmetric groups S_n, the dihedral groups D_{2n} and the free groups F_n (n not equal to 3) all have trivial weak Cayley table groups. We will investigate the weak Cayley table groups of the alternating groups, certain types of Coxeter groups, the projective special linear groups and certain sporadic simple groups.

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.

The NPDGamma Experiment is used to study the n + p to d + g reaction for the purpose of examining the hadronic weak interaction. The nucleon-nucleon interaction is overwhelmingly mediated by the strong force, however, the weak part can be extracted by a study of its parity violating manifestations. When neutrons are incident on protons, deuterons and 2.2 MeV gamma rays are produced. If the incoming neutrons are polarized, the parity violating weak interaction gives rise to a measured spatial asymmetry, Ag, in the outgoing gamma rays, as sn · kg is parity odd. At low energies, the weak nucleon-nucleon interaction can be modeled as meson exchange and characterized with six parameters. NPDGamma is sensitive to one of these parameters, hp. Previous measurements that extrapolate hp from more complicated interactions disagree, and disagree with the theoretical reasonable range. Additionally, a previous iteration of the NPDGamma Experiment performed at Los Alamos National Lab was statistics limited in its measurement of Ag. For this reason, a new measurement was performed at the high neutron flux Spallation Neutron Source at Oak Ridge National Lab. In the experiment, a high flux of cold neutrons was polarized to ~ 95% by a supermirror polarizer, the spins flipped in a defined sequence by a radio-frequency spin rotator, and then the neutrons captured on a 16 L liquid para-hydrogen target, which emits gamma-rays asymmetrically upon capture. The gamma-rays are detected in a 3pi array of 48 CsI crystal detectors. This thesis discusses the NPDGamma Experiment in detail, and includes an analysis of subset of the NPDGamma data that has unique timing and data acquisition properties that preclude it being analyzed with the combined data set. Ag was extracted with a result of (6.254 ± 37.694) × 10-9