The transformation of Ireland 1958 - 93: the role of ideas in punctuating institutional path dependency at critical junctures

Ireland experienced two critical junctures when its economic survival was threatened: 1958/9 and 1986/7. Common to both crises was the supplanting of long established practices, that had become an integral part of the political culture of the state, by new ideas that ensured eventual economic recovery. In their adoption and implementation these ideas also fundamentally changed the institutions of state – how politics was done, how it was organised and regulated. The end result was the transformation of the Irish state. The main hypothesis of this thesis is that at those critical junctures the political and administrative elites who enabled economic recovery were not just making pragmatic decisions, their actions were influenced by ideas. Systematic content analysis of the published works of the main ideational actors, together with primary interviews with those actors still alive, reveals how their ideas were formed, what influenced them, and how they set about implementing their ideas. As the hypothesis assumes institutional change over time historical institutionalism serves as the theoretical framework. Central to this theory is the idea that choices made when a policy is being initiated or an institution formed will have a continuing influence long into the future. Institutions of state become ‘path dependent’ and impervious to change – the forces of inertia take over. That path dependency is broken at critical junctures. At those moments ideas play a major role as they offer a set of ready-made solutions. Historical institutionalism serves as a robust framework for proving that in the transformation of Ireland the role of ideas in punctuating institutional path dependency at critical junctures was central.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.