Variations on Noetherianness

In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programming language. We want to say that a set is Noetherian, if, when we are shown elements from it one after another, we will sooner or later have seen some element twice. This idea can be made precise in a number of ways. We explore the properties and connections of some of the possible encodings. In particular, we show that certain implementations imply decidable equality while others do not, and we construct counterexamples in the latter case. Additionally, we explore the relation between Noetherianness and other notions of finiteness.Comment: In Proceedings MSFP 2016, arXiv:1604.0038

Exploring (un)sustainable growth of digital technologies in the home

HCI and Ubicomp research often centres around the support of humans interacting with digital technology. Despite this obvious focus, there seems to be less work on understanding how these digital technologies can lead to growth in use, dependence, and influence practices in everyday life. In this paper we discuss how digital technologies have been, and continue to be, adopted in domestic practices—and how the growth of interactions with various ecologies of digital technologies can lead to growth in use and energy consumption. We further the discussion within ICT4S and sustainable HCI on how to promote research that encourages sustainability as a core concern—socially, economically, and ecologically—emphasising that defining limits to growth are important when trying to affect change in sustainable directions. We echo calls for more significant sustainability research from HCI, and set out some avenues of design for moving in this direction

Type-Theoretic Constructions of the Final Coalgebra of the Finite Powerset Functor

The finite powerset functor is a construct frequently employed for the specification of nondeterministic transition systems as coalgebras. The final coalgebra of the finite powerset functor, whose elements characterize the dynamical behavior of transition systems, is a well-understood object which enjoys many equivalent presentations in set-theoretic foundations based on classical logic. In this paper, we discuss various constructions of the final coalgebra of the finite powerset functor in constructive type theory, and we formalize our results in the Cubical Agda proof assistant. Using setoids, the final coalgebra of the finite powerset functor can be defined from the final coalgebra of the list functor. Using types instead of setoids, as it is common in homotopy type theory, one can specify the finite powerset datatype as a higher inductive type and define its final coalgebra as a coinductive type. Another construction is obtained by quotienting the final coalgebra of the list functor, but the proof of finality requires the assumption of the axiom of choice. We conclude the paper with an analysis of a classical construction by James Worrell, and show that its adaptation to our constructive setting requires the presence of classical axioms such as countable choice and the lesser limited principle of omniscience

Finiteness in cubical type theory

This thesis will explore and explain finiteness in constructive mathematics: using this setting, it will also serve as an introduction to constructive mathematics in Cubical Agda, and some related topics

The deglaciation of the East Cheviot area, Northumberland

Those parts of the east Cheviot area appearing on vertical aerial photographs (scale approximately 1:10,000) held by the Scottish Development Department were studied stereoscopically as a prelude to work on the ground. The glacial landforms were mapped on a transparent overlay and then transferred to Six -inch maps (Ordnance Survey Provisional Edition) after approximate corrections for scale and distortion had been made using a Grant Projector. The drift boundaries published by the Geological Survey on the One -inch Drift maps of the area were copied and inserted on the Six -inch maps. The latter were taken into the field so that amendments could be made where necessary as the entire area was systematically investigated on foot. Since it was considered necessary to produce accurately levelled profiles on one of the more extensive landforms, a Watts microptic level (SL100) was used. All of the natural and artificial sections, together with the majority of minor exposures were systematically inspected to establish the nature of the drift and of the underlying bedrock. Since the sections are generally poor and small in number, a 3 -foot soil auger was used to provide supplementary drift information in certain places, and all available bore -hole records for the area were consulted. Where good till sections were exposed in sites that appear to be relatively undisturbed by mass movements, the preferred dip and orientation of stones were measured with a Suunto compass in an attempt to establish the formier directions of ice movement. The following procedure was adopted. Sites were chosen at least 3 feet below the ground surface, and after a vertical face had been cleared, a trench was dug inwards for at least one foot. This was to avoid all possible interference by plants and animals. At every site the dip and compass orientation of 100 stones were measured and recorded. Each stone selected for measurement possessed axes that were in the ratio of at least 1:2. Stones smaller than 1 cm. and larger than 20 cros. were avoided. Contiguous particles and particles with long areas dipping in excess of 600 were rejected, as were those in the vicinity of large boulders. The lithology and shape of each stone were also recorded. The measurements were plotted on polar equal nets (Figure 1.1, Chapter 1), on which the radial scale represents dip and the circumferential scale azimuth (Kirby 1961). The resulting scatter diagrams of axial plots give a good visual impression of the fabric characteristics.The analysis of peat layers occurring in close juxtaposition with fluvioglacial phenomena necessitated techniques of investigation beyond the writer's scope. For this reason, pollen analyses of the peat were undertaken by S. E. Durno who also produced the pollen diagram presented with this thesis.Although levelling and fabric analyses provided useful information, it should be emphasised that the majority of conclusions reached in the following chapters are based essentially on the analysis of morphological maps. The density of fluvioglacial phenomena in many parts of the east Cheviot area is so great that a valid interpretation of the deglaciation could not have been attempted if the complex interrelationships of the landforms had not first been plotted on the Six -inch scale. The landforms were later also plotted on the scale of 1 :25,000, so that the overall patterns could be more readily discerned. The latter are presented in the map pocket accompanying this volume and are referred to throughout the text as Maps 1 to 11. The list of symbols used on these maps is also located in the map pocket. Where it has been necessary to illustrate the landforms in more detail, figures drawn to a scale larger than 1 :25,000 and photographs are included with the text

Individual and collective dynamics of chemotaxing cells

The study of the dynamics of interacting self-propelled entities is a growing area of physics research. This dissertation investigates individual and collective motion of the eukaryote Dictyostelium discoideum, a system amenable to signal manipulation, mathematical modeling, and quantitative analysis. In the wild, Dictyostelium survive adverse conditions through collective behaviors caused by secreting and responding to chemical signals. We explore this collective behavior on size scales ranging from subcellular biochemistry up to dynamics of thousands of communicating cells. To study how individual cells respond to multiple signals, we perform stability analysis on a previously-developed computational model of signal sensing. Polarized cells are linearly stable to perturbations, with a least stable region at about 60 degrees off the polarization axis. This finding is confirmed through simulations of the model response to additional chemical signals. The off-axis sensitivity suggests a mechanism for previously observed zig-zag motion of real cells randomly migrating or chemotaxing in a linear gradient. Moving up in scale, we experimentally investigate the rules of cell motion and interaction in the context of thousands of cells. Migrating Dictyostelium discoideum cells communicate by sensing and secreting directional signals, and we find that this process leads to an initial signal having an increased spatial range of an order of magnitude. While this process steers cells, measurements indicate that intrinsic cell motility remains unaffected. Additionally, migration of individual cells is unaffected by changing cell-surface adhesion energy by nine orders of magnitude, showing that individual motility is a robust process. In contrast, we find that collective dynamics depend on cell-surface adhesion, with greater adhesion causing cells to form smaller collective structures. Overall, this work suggests that the underlying migration ability of individual Dictyostelium cells operates largely independent of environmental conditions. Our gradient-sensing model shows that polarized cells are stable to small perturbations, and our experiments demonstrate that the motility apparatus is robust to considerable changes in cell-surface adhesion or complex signaling fields. However, we find that environmental factors can dramatically affect the collective behavior of cells, emphasizing that the laws governing cell-cell interaction can change migration patterns without altering intrinsic cell motility

MIDDLE TO LATE HOLOCENE (7200-2900 CAL. BP) ARCHAEOLOGICAL SITE FORMATION PROCESSES AT CRUMPS SINK AND THE ORIGINS OF ANTHROPOGENIC ENVIRONMENTS IN CENTRAL KENTUCKY, USA

Though some researchers have argued that the Big Barrens grasslands of Kentucky were the product of anthropogenic land clearing practices by Native Americans, heretofore, this hypothesis had not been tested archaeologically. More work was needed to refine chronologies of fire activity in the region, determine the extent to which humans played a role in the process, and integrate these findings with the paleoenvironmental and archaeological record. With these goals in mind, I conducted archaeological and geoarchaeological investigations at Crumps Sink in the Sinkhole Plain of Kentucky. The archaeological record and site formation history of Crumps Sink were compared with environmental and archaeological data from the Interior Low Plateaus and Southern Appalachian Mountains for an understanding of how the site fits into the larger story of human-environmental interactions in the Eastern Woodlands. Based on the data recovered, I argue that through land burning Archaic hunter-gatherers were active managers of ecosystems to a greater degree than previously acknowledged. Excavations at Crumps Sink revealed stratified archaeological deposits spanning the late Middle Archaic to Terminal Late Archaic periods. Radiocarbon dates and an analysis of projectile point typologies provided information on the chronological and cultural history of the site. Magnetic susceptibility, loss-on-ignition, plant available phosphorous, and soil micromorphological analyses were conducted to examine landform dynamics in response to environmental change and to trace the anthropogenic signature created by human activities at the site. Masses of lithic debitage, animal bone, and burned sediment nodules per ten-cm-level provide an indication of human occupation intensity and shifting activities over time. Radiocarbon dates were used to reconstruct rates of sediment accumulation in the sink. These varying datasets were considered together for a holistic understanding of localized environmental and anthropogenic impacts on the landform. Between 7200 and 5600 cal. BP, during the Middle Holocene Thermal Maximum and corresponding with the late Middle Archaic period, sediment accumulation was sustained with one identifiable episode of very weak soil development. Background magnetic and chemical signatures in the soils were greater than they were at pre-occupation levels, demonstrating that human activities left a lasting imprint in soils as early as the late Middle Archaic period. Between 5600 and 3900 cal. BP, periods of diminished sedimentation led to more pronounced episodes of soil formation. However, these soil horizons are interposed by pulses of enhanced sediment accumulation. These soil data may signal shifting environmental regimes during the Middle to Late Holocene transition. Between 5600 and 3900 cal. BP scattered plant ash, elevated masses of burned sediment nodules, and pestle fragments in Late Archaic deposits suggest that hunter-gatherers were intensively processing nut mast, potentially in association with early forest clearance and silviculture. Botanical assemblages from a coincident archaeological sequence at the Carlston Annis site in the nearby middle Green River region has demonstrated woodland disturbance and potential silviculture in central Kentucky during this time. During the Late Archaic and Terminal Late Archaic periods (3900-3000 cal. BP), substantial plant ash deposition occurred in a stratum that accumulated relatively quickly. Very low burned sediment nodule masses in this deposit indicate that combustion features were not common in the immediate vicinity and that elevated frequencies of plant ash were the result of burning on a broader expanse of the surrounding landform. Chronologically, the zone with enhanced plant ash deposition is coeval with previously demonstrated occurrences of increased forest fires, grassland expansion, and a shift to early horticultural economies throughout the region. Soil development occurred after 3000 cal. BP, and this episode of landform stability may have lasted for over two millennia until being capped by sediment accumulation from historic agriculture. The late Middle Archaic through Terminal Late Archaic data from Crumps Sink demonstrate that hunter-gatherer activities left lasting signatures in soils in Kentucky. The data from the Late Archaic to Terminal Late Archaic periods (ca. 5600-3000 cal. BP) may indicate intentional land burning by hunter-gatherers to create anthropogenic environments, first for silviculture and then for early plant domestication. This forces a rethinking of labor and subsistence systems within hunter-gatherer societies. Thus, if hunter-gatherers were utilizing long-term forest management methods, they were employing a delayed-return economic system relying on labor investment and negotiated understandings about land tenure. Further characterization of the origin of fire management activities will help us to elucidate the nature of incipient indigenous plant domestication in the Eastern Woodlands