A Relational Derivation of a Functional Program

This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard $quot;column of half-adders$quot;, but the derivation illustrates a number of points about working with relations rather than with functions

The Ruby Interpreter

Ruby is a relational calculus for designing digital circuits. This document is a guide to the Ruby interpreter, which allows a special class of $quot;implementable$quot; Ruby programs to be executed. The Ruby interpreter is written in the functional programming language Lazy ML, and is used under the interactive Lazy ML system

Analysis of Hardware Descriptions

The design process for integrated circuits requires a lot of analysis of circuit descriptions. An important class of analyses determines how easy it will be to determine if a physical component suffers from any manufacturing errors. As circuit complexities grow rapidly, the problem of testing circuits also becomes increasingly difficult. This thesis explores the potential for analysing a recent high level hardware description language called Ruby. In particular, we are interested in performing testability analyses of Ruby circuit descriptions. Ruby is ammenable to algebraic manipulation, so we have sought transformations that improve testability while preserving behaviour. The analysis of Ruby descriptions is performed by adapting a technique called abstract interpretation. This has been used successfully to analyse functional programs. This technique is most applicable where the analysis to be captured operates over structures isomorphic to the structure of the circuit. Many digital systems analysis tools require the circuit description to be given in some special form. This can lead to inconsistency between representations, and involves additional work converting between representations. We propose using the original description medium, in this case Ruby, for performing analyses. A related technique, called non-standard interpretation, is shown to be very useful for capturing many circuit analyses. An implementation of a system that performs non-standard interpretation forms the central part of the work. This allows Ruby descriptions to be analysed using alternative interpretations such test pattern generation and circuit layout interpretations. This system follows a similar approach to Boute's system semantics work and O'Donnell's work on Hydra. However, we have allowed a larger class of interpretations to be captured and offer a richer description language. The implementation presented here is constructed to allow a large degree of code sharing between different analyses. Several analyses have been implemented including simulation, test pattern generation and circuit layout. Non-standard interpretation provides a good framework for implementing these analyses. A general model for making non-standard interpretations is presented. Combining forms that combine two interpretations to produce a new interpretation are also introduced. This allows complex circuit analyses to be decomposed in a modular manner into smaller circuit analyses which can be built independently

A Relational Derivation of a Functional Program

This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard $quot;column of half-adders$quot;, but the derivation illustrates a number of points about working with relations rather than with functions

Topological Flat Band Models and Fractional Chern Insulators

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with non-zero Chern number, $C$. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with non-trivial topology, $C\neq 0$, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with $|C|>1$. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.Comment: Invited review. 46 pages, many illustrations and references. V2: final version with minor improvements and added reference

Multi-stage languages in hardware design

As circuits increase in size and complexity, hardware description techniques have been trying to adopt features already well- established in software languages. In this paper, we investigate how different hardware description languages implement levels of abstraction over the hardware designs, and we examine how improvements have lead to features like parameterised circuits and generic descriptions, that enable users to efficiently model and reason about large regular-shaped structures and connection patterns. Nonetheless, the ability to include non-functional properties of circuits in the same description is still an open issue. Lately, proposed solutions are looking into meta-functional languages and multi-staging techniques. We examine how hardware description languages can benefit from the capabilities of meta-functional languages, which are able to reason about, and transform the circuit generators as data objects, thus providing a means to access both the functional and non-functional aspects of the generated circuits.peer-reviewe

Size-Aware Hypergraph Motifs

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs, and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motif mining holds promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge intersections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least correlated with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most correlated with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation

Maps for the lost: A collection of short fiction And Human / nature ecotones: Climate change and the ecological imagination: A critical essay

The thesis comprises a collection of short fiction, Maps for the Lost, and a critical essay, “Human / Nature Ecotones: Climate Change and the Ecological Imagination.” In ecological terms, areas of interaction between adjacent ecosystems are known as ecotones. Sites of relationship between biotic communities, they are charged with fertility and evolutionary possibility. While postcolonial scholarship is concerned with borders as points of cross-cultural contact, ecocritical thought focuses upon the ecotone that occurs at the interface between human and non-human nature. In their occupation of the liminal zones between human and natural realms, the characters and narratives of Maps for the Lost reveal and nurture the porosity of conventional demarcations. In the title story, a Czech artist maps the globe by night in order to find his lover. The buried geographies of human landscapes coalesce with those of the non-human realm: the territories of wolves and the scent-trails of a fox mingle imperceptibly with nocturnal Prague and the ransacked villages of post-war Croatia. In “Seeds,” a narrative structured around the process of biological growth, the lost memories of an elderly woman are returned to her by her garden. “The Skin of the Ocean” traces the obsession of a diver who sinks his yacht under the weight of coral and fish, while in “Drift,” an Iranian refugee writes letters along the tide-line of a Tasmanian beach. The essay identifies the inadequacy of literature and literary scholarship’s response to the threat of climate change as a failure of the imagination, reflecting the transgressive dimension of the crisis itself, and the dualistic legacy which still informs Western discourse on non-human nature. In order to redress this shortfall, which I argue the current generations of writers have an urgent moral responsibility to do, it is critical that we learn to understand the natural world of which we are a part, in ways that cast off the limitations of conventional representation. Paradoxically, it is the profoundly disruptive (apocalyptic?) nature of the climate crisis itself, which may create the imaginative traction for that shift in comprehension, forcing us, through loss, to interpret the world in ways that have been forgotten, or are fundamentally new. By analysing Alexis Wright’s The Swan Book, and Les Murray’s “Presence” sequence, the essay explores the correlation between imaginative and ecological processes, and the role of voice, embodiment, patterning and story in negotiations of nature and place. In the context of the asymptotical essence of the relation between text and world, and the paradox of phenomenological representation, it calls for a deeper cultural engagement with scientific discourse and indigenous philosophy, in order to illuminate the multiplicity and complexity of human connections to the non-human natural worl

Graduate Scholar 2023: Journal of Scholarship and Recognition

https://thekeep.eiu.edu/graduate_scholar/1009/thumbnail.jp

Boffin\u27s Books and Darwin\u27s Finches: Victorian Cultures of Collecting

Although wealthy continental virtuosos had passionately and selectively accumulated a variety of natural and artificial objects from the Renaissance onwards, not until the nineteenth century did collecting become a conspicuous national pastime among all classes in Britain. As industry and empire made available many new and exotic goods for acquisition and display, the collection as a cultural form offered the Victorians a popular strategy of self-fashioning that was often represented in the literature of the age as a source of prestige and social legitimation. Through interdisciplinary readings of Victorian fiction, narrative nonfiction, and poetry, my study examines how textual representations of collecting helped to define nation, class, and gender in Britain from the 1830s to the turn of the century and beyond. Combining literary analysis with cultural criticism, including approaches from museum studies, I explain how Victorian writing about collecting, from Charles Dickens\u27s earliest works to fin-de-siècle lepidopteran narratives, participated in the formation of individual and collective identities. During the first half of the nineteenth century, prominent author-collectors asserted their specifically male authority and British dominion abroad through travel narratives about acquiring exotic artifacts for the nation or assembling proprietary collections exhibited back home. Meanwhile, Victorian novels included an array of collectors of all ranks, many of whom seek to enhance their professional or social status through their collections, which are often the products of competition or emulation. However, from mid-century on, a period in which museums proliferated and the British empire grew during the age of the New Imperialism, authors increasingly turned to the figure of the collector to convey anxieties about habits of consumption that threatened personal identity or social stability and a world of objects that were not necessarily under the consumer\u27s control. Thus, even as collecting helped to order knowledge, material culture, and social relations in nineteenth-century Britain, it also posed certain challenges to the social identities and forms of subjectivity the Victorians attempted to forge for themselves, as their collections and texts show