'La Violence et la mauvaise foi': Context and rhetoric in Pierre Bayle's Ce que c'est que la France toute Catholique

My thesis presents an examination of Ce que c'est que la France toute Catholique (1686) by Pierre Bayle, a prominent figure in the Republic of Letters and the Huguenot Refuge in the seventeenth century. This pamphlet was the first occasional text that Bayle published following the Revocation of the Edict of Nantes in which the religious toleration afforded to the Huguenot minority in France was repealed, a pivotal moment in the history of early modern France. In my thesis, I analyse the specific context within which Bayle wrote this pamphlet as a means of addressing a number of issues, including the legitimacy of forced conversions, the impact of the religious controversy upon exchanges in the Republic of Letters, the nature of religious zeal and finally the alliance of Church and state discourses in the early modern period. An examination of this context provides a basis from which to re-interpret the rhetorical strategies at work within the pamphlet, and also to come to an increased understanding of how, why and to what end he wrote it. In turn this allowed me to examine the relationship between this often overlooked pamphlet and the more extensively studied Commentaire Philosophique, in which Bayle argued in favour of religious toleration. Ultimately, understanding the relationship between these two texts proves essential in order to characterise his response to the Revocation of the Edict of Nantes and to understand the place of the pamphlet within his oeuvre. Furthermore, an analysis of the pamphlet and the Commentaire Philosophique provide a lens through which to elucidate both Bayle's intellectual development at this early stage in his career, and also the wider context of the rise of toleration theory and the evolution of modes of civility within the Republic of Letters on the eve of the Enlightenment.

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.

The Celtic dragon slayer - a literary analysis of Tochmarc Emire in connection with Tristan et Iseut

As Celtic scholars have long noted, the medieval Irish tale Tochmarc Emire “The Courtship of Emer” is heavily indebted to other medieval Irish texts. In this tale of courtship and otherworldly quests, the Irish hero Cú Chulainn must prove himself worthy of the hand of the noblewoman Emer. Among his overseas adventures, Cú Chulainn rescues a princess from three attackers of the Fomoire. This episode may represent the only medieval Irish example of AT300 “The Dragon Slayer”, a story pattern known from classical models such as the stories of Perseus and Andromeda; and Hercules and Hesione. Moreover, in the company of Cú Chulainn we find a character otherwise unknown to Irish tradition by the name of Drust mac Seirb. This has led scholars to argue that Tochmarc Emire may preserve a Celtic precursor of the Continental Tristan legend, seeing in Drust the Pictish origin of the character Tristan, himself a famous dragon slayer. In this interdisciplinary dissertation, a number of questions are addressed. If the redactor of Tochmarc Emire drew on material from outside Irish tradition, what does this tell us about medieval Irish concepts of literature and genre? Further, what evidence do we have for tracing the origin of the Continental Tristan legend back to Pictland, and what explanation might we offer for a putative Pictish prince featuring in an Irish Dragon Slayer story? Finally, what place does the Dragon Slayer episode occupy within Tochmarc Emire and can we find other narratives, Celtic or classical or other, fitting the pattern of AT300, which may strengthen the link between Tochmarc Emire and Tristan?