1,721,638 research outputs found
Length functions on groups and actions on graphs
No full textWe study generalizations of Chiswell’s theorem that 0-hyperbolic Lyndon length functions on groups always arise as based length functions of the group acting isometrically on a tree. We produce counter-examples to show that this Theorem fails if one replaces 0-hyperbolicity with δ-hyperbolicity. We then propose a set of axioms for the length function on a finitely generated group that ensures the function is bi-Lipschitz equivalent to a (or any) length function of the group acting on its Cayley graph with respect to some finite generating set.</p
On-Chip time measurement architectures and implementation
No full textIn recent years, system on chip (SoC) devices have become increasingly popular in many applications, such as automotive, signal processing, portable electronic devices and communication products. This has led to more functionality being integrated onto a single piece of silicon. As the level of technology decreases down to smaller geometries, not only has the design become more complicated but also the verification of such devices has become significantly complex that it has led to stringent timing requirements being placed on such devices. With the continuing integration and speed scaling to higher frequencies into the low giga Hertz range, limitations in the effectiveness of traditional production testing have been introduced. The increase in cost of automatic test equipment (ATE) and the fact that the electrical distance between the tester and the embedded core under test (CUT) has got wider has made the verification of such devices challenging.To alleviate this cost test problem, this research investigates the design and methods associated with high resolution on-chip time measurement systems and proposes the design of a low cost, high resolution, programmable time measurement architecture for characterizing on-chip time measurements. This new architecture is based on the time-to-digital conversion (TDC) method and uses the dual-slope technique to perform the timing measurement. The proposed architecture can perform a number of different types of time measurements, such as rise and fall time, pulse width and propagation delay type measurements, without the need for additional circuitry or circuit duplication that would add to the overall cost of the time measurement architecture. Each of the critical building blocks are analysed and a description of the final implementation of a prototype chip using a 0.12µm CMOS process is described.As the on-chip clock speeds of high performance VLSI devices increase into the tens of Gigahertz range, time measurement architectures with timing resolutions of tens of femtoseconds will be required. Current high resolution time measurements architectures based on vernier and flash time measurement architectures use latches and flip-flops in the main timing measurement technique and can suffer from the inherited metastability phenomenon. To address this problem, current research solutions are analysed in this thesis and an on-chip time measurement architecture that is also based on the time-to-digital conversion method but uses the homodyne technique is proposed. The architecture is described and finally simulations using transistors based on a 0.12µm CMOS process are presented and suggest that timing resolutions in the tens of femtosecond range are attainable
Groups acting on graphs: Their automorphisms and their length functions
No full textActions on frees are powerful tools for understanding the structure of a group and its automorphisms. In this thesis, we generalise several existing results in this field to larger classes of groups.This is a three paper thesis; the main body of the work is contained in the following papers:[1] Matthew Collins. Fixed points of irreducible, displacement one automorphisms of free products. Preprint, May2023, available at arXiv:2305.01451.[2] Matthew Collins. Growth and displacement of free product automorphisms. Preprint, July 2023, available at arXiv:2307.13502.[3] Matthew Collins and Armando Martino. Length functions on groups and actions on graphs. Preprint, July 2023, available atarXiv:2307.10760.In [1], we prove that an irreducible, growth rate1 automorphism of a free product fixes a single point in outer space. This can be thought of as a generalisation of Dicks & Ventura’s classification of the irreducible, growth rate 1 automorphisms of free groups. It is well known for an irreducible free group automorphism that its growth rate is equal to the minimal Lipschitz displacement of its action on Culler-Vogtmann space. This follows as a consequence of the existence of train track representatives for the automorphism. In [2], we extend this result to the general - possibly reducible - case as well as to the free product situation where growth is replaced by ‘relative growth’. In [3], we study generalisations of Chiswell’s Theorem that 0-hyperbolic Lyndon length functions on groups always arise as based length functions of the group acting isometrically on a tree. We produce counter-examples to show that this Theorem fails if one replaces 0-hyperbolicitywith δ-hyperbolicity. We then propose a set of axioms for the length function on a finitely generated group that ensures the function is bi-Lipschitz equivalent to a (or any) length function of the group acting on its Cayley graph.</p
Matthew Henry: The Bible, Prayer, and Piety – A Tercentenary Celebration
No full textThe summer of 2014 marked the tercentenary of the death of Matthew Henry (1662–1714), a leading figure among early eighteenth-century Dissenters and author of the six-volume Exposition of the Old and New Testaments (1707–1714/25). This monumental work, which by 1855 had already been published in twenty-five different editions, attempted a peculiarly practical approach to the biblical text and continues to be widely used and readily accessible even today in both print and online versions. The theme of foreign (or ‘strange’) wives and Israelite intermarriage is one which occurs throughout the Hebrew Bible and, accordingly, throughout Matthew Henry’s commentary upon it. Where it appears, the practice of intermarriage is characterized by Henry as (at best) unwise and (at worst) a very real threat to both social and religious cohesion. This essay explores how Henry deals with the issue of ‘strange wives’, why he believes they continue to pose a threat, and (in view of the overall intention of his commentary) what ‘practical observations’ he offers to his reader as a result. In doing so it is argued that Henry’s commentary traces a thematic thread from the ante-diluvian age to the post-exilic period of calamities resulting from mixed marriages between ‘professors of religion’ and their ‘strange wives’
On-chip timing measurement architecture with femtosecond resolution
No full textA new timing measurement architecture based on the time-to-digital conversion technique is presented. The architecture occupies a small silicon area (200x185µm) in a 0.12µm CMOS Process and can achieve tens of femtoseconds timing resolution, which is the highest reported to date
On-chip time measurement architecture with femtosecond timing resolution
No full textThis paper presents a new on-chip time measurement architecture which is based on the time-to-digital conversion (TDC) method that is capable of achieving a timing resolution of tens of femtoseconds without the use of external automatic test equipment (ATE). This is the highest temporal resolution that has been reported to-date and is achieved by the use of the homodyne technique. The proposed architecture has been designed using a 0.12mum CMOS process and simulation results based on foundry transistor models indicates that it is possible to achieve a timing resolution of 40 fs. The time measurement architecture is standalone and occupies a small silicon area, 150mum by 180mum, making it attractive for high resolution on-chip time measurement
A Programmable Time Measurement Architecture for Embedded Memory Characterization
No full textThis paper describes a programmable time measurement architecture that facilitates memory characterization. We have created a novel standalone time measurement architecture that can measure rise time, fall time, pulse width and propagation delay time measurements without the need of additional circuitry [1] or circuit duplication [2]. This is achieved by the use of Time-to-Digital Conversion (TDC) based on the dual-slope principle. The key feature of the proposed architecture is programmability through the use of a novel programmable input stage. Furthermore, a current steering Time-to-Voltage Converter (TVC) is used in order to improve the linearity and dynamic range as compared to recent designs. The proposed architecture has been designed using 0.18?m CMOS process and results from simulations using foundry models suggest it is possible to achieve a timing resolution of 103ps. The measurement core size is 110?m x 75?m
The First World War and the Mobilisation of Biblical Scholarship
No full textIn January 1917, in the midst of the First World War, a small group of biblical scholars gathered at King’s College London for the inaugural meeting of the newly-formed Society for Old Testament Study (SOTS). The decision to create such a society had been taken the previous summer at Queens’ College, Cambridge, on 29 June 1916, just two days before the commencement of the Battle of the Somme. Thus the origins of this British-based society are to be found firmly (and somewhat peculiarly) planted in the context and conflict of the Great War. As a result, the records and history of the early years of the society afford us a valuable window through which to view the landscape of biblical scholarship of the period. Likewise, the detailed minutes and papers of the wartime meetings of the larger and already established US-based Society of Biblical Literature (SBL; founded in 1880) offer a similar (yet distinct) insight into academic attitudes on the other side of the Atlantic and especially the challenges to biblical scholarship (both ideological and practical) posed by the outbreak of war. Accordingly, in thinking about the wartime mobilization of biblical studies, this essay takes as its focus the effect of the war upon British and American scholarly societies (epitomized here by SOTS and SBL) and the response(s) of those societies as indicative of shifts and trends in both wartime and post-war biblical scholarship. Although predominantly a historical survey, drawing upon the records and minutes of the two groups in order to reconstruct events, it is argued that, in both their rhetoric and the practical steps taken towards scholarly reconciliation, these societies may be seen as having actively resisted the idea of 'the enemy' prevalent in propaganda material of the time. In doing so, they were subsequently well positioned to play a significant role in the swift re-establishment of international scholarly relations after the First (and indeed later, the Second) World War. Thus, it is argued that, during wartime, these scholarly societies performed a potentially unintentional yet vital regulatory function as tools enabling and encouraging the maintenance, preservation, recovery, and continuity of international biblical scholarship
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