Existence results for primitive elements in cubic and quartic extensions of a finite field

With \Fq the finite field of $q$ elements, we investigate the following question. If $\gamma$ generates \Fqn over \Fq and $\beta$ is a non-zero element of \Fqn, is there always an a \in \Fq such that $\beta(\gamma + a)$ is a primitive element? We resolve this case when $n=3$, thereby proving a conjecture by Cohen. We also improve substantially on what is known when $n=4$.Comment: To appear in Math. Com

Continental shelf archaeology : where next?

Until very recently the case for systematic exploration of the now submerged landscapes of the continental shelf was taken seriously by rather few mainstream archaeologists, and advocacy in support of underwater prehistory was usually regarded as evidence of enthusiasm for diving, hopeless optimism with regard to the prospects of discovering useful information, or indulgence in fanciful speculation. Developments in the technology of underwater exploration, the steady accumulation of fi nds, the quality of preservation of organic materials, and above all the realization that coastal regions for most of human prehistory are now submerged and most likely played a key role in many of the most important developments in prehistory, are slowly shifting the climate of opinion. Th e question now is not whether we should undertake underwater exploration, but how we should go about it. Here, there are still powerful inhibitions and uncertainties, especially when it comes to the deeper areas of the shelf and to the systematic discovery of archaeological sites. Large-scale international collaboration, engagement with industrial and commercial partners, development of purposeful and realistic strategies of exploration, a new and growing generation of trained practitioners, an expanding knowledge base about the taphonomy of underwater landscapes and archaeological remains, and the progressive extension of experience from land to shallow water, and from shallow to deeper water, are all foreseeable ingredients of the next phase of investigation

Landscapes and their relation to hominin habitats : case studies from Australopithecus sites in eastern and southern Africa

We examine the links between geomorphological processes, specific landscape features, surface water drainage, and the creation of suitable habitats for hominins. The existence of mosaic (i.e. heterogeneous) habitats within hominin site landscape reconstructions is typically explained using models of the riverine and gallery forest settings, or the pan or lake setting. We propose a different model: the Tectonic Landscape Model (TLM), where tectonic faulting and volcanism disrupts existing pan or river settings at small scales (~ 10–25 km). Our model encompasses the interpretation of the landscape features, the role of tectonics in creating these landscapes, and the implications for hominins. In particular, the model explains the underlying mechanism for the creation and maintenance of heterogeneous habitats in regions of active tectonics. We illustrate how areas with faulting and disturbed drainage patterns would have been attractive habitats for hominins, such as Australopithecus, and other fauna. Wetland areas are an important characteristic of surface water disturbance by fault activity; therefore we examine the tectonically-controlled Okavango Delta (Botswana) and the Nylsvley wetland (South Africa) as modern examples of how tectonics in a riverine setting significantly enhances the faunal and floral biodiversity. While tectonic landscapes may not have been the only type of attractive habitats to hominins, we propose a suite of landscape, faunal, and floral indicators, which when recovered together suggest that site environments may have been influenced by tectonic and/or volcanic activity while hominins were present. For the fossil sites, we interpret the faulting and landscapes around australopithecine-bearing sites of the Middle Awash (Ethiopia) and Makapansgat, Taung, and Sterkfontein (South Africa) to illustrate these relationships between landscape features and surface water bodies. Exploitation of tectonically active landscapes may explain why the paleoenvironmental signals, anatomy, diets, as well as the fauna associated with Australopithecus appear largely heterogeneous through time and space. This hypothesis is discussed in light of potential preservation and time-averaging effects which may affect patterns visible in the fossil record. The model, however, offers insight into the landscape processes of how such habitats are formed. The landscape features and range of habitat conditions, specifically the wetter, down-dropped plains and drier, uplifted flanks persist in close proximity for as long as the fault motion continues. The Tectonic Landscape Model provides an alternative explanation of why mixed habitats may be represented at certain sites over longer timescales

Coastal adaptations and submerged landscapes : Where world prehistory meets underwater archaeology

Studies in world prehistory, which include the transition between the Pleistocene and Holocene and the cultural shift from Forager to Farmer, remain incomplete, particularly along the coastal margins. Submerged landscape archaeology has begun to emerge as a serious sub-discipline of both maritime archaeology and world prehistory, with a largely untapped potential to fill in significant gaps in the archaeological record. This chapter reviews the current state of submerged landscape archaeology and considers important elements, both theoretical and practical, and discusses how future generations of prehistorians must be willing and able to engage with archaeology on the continental shelves, worldwide

Better communication research project : language and literacy attainment of pupils during early years and through KS2 : does teacher assessment at five provide a valid measure of children's current and future educational attainments?

It is well-established that language skills are amongst the best predictors of educational success. Consistent with this, findings from a population-based longitudinal study of parents and children in the UK indicate that language development at the age of two years predicts children’s performance on entering primary school. Moreover, children who enter school with poorly developed speech and language are at risk of literacy difficulties and educational underachievement is common in such children. Whatever the origin of children’s problems with language and communication, the poor educational attainment of children with language learning difficulties is an important concern for educational polic

Collection and consumption of echinoderms and crustaceans at the Mesolithic shell midden site of El Mazo (northern Iberia) : Opportunistic behaviour or social strategy?

Recent studies in Atlantic Europe on crab remains, goose barnacles and sea urchins have revealed that these species can be of great help in determining patterns of shellfish collection and providing new information on subsistence strategies of hunter-fisher-gatherers. Current excavations at the Mesolithic shell midden site of El Mazo cave (Asturias, northern Iberia) have produced a sizeable amount of crustacean and echinoderm remains from a long stratigraphic sequence that covers an important part of the Mesolithic chronological range, providing the opportunity to investigate long-term exploitation patterns. Results show that echinoderms (sea urchins) and crustaceans (goose barnacles and crabs) were present throughout all of the stratigraphic units (from 8.9 to 7.6 cal kyr), suggesting that they were a persistently exploited food source. However, these resources were not intensively exploited, save perhaps sea urchins at the base of the sequence. From a quantitative perspective, these resources have been traditionally interpreted as minor resources exploited opportunistically to help group survival. However, given the pattern of continuous exploitation exhibited by these resources in northern Iberia and other areas of Atlantic Europe, we suggest that they can be interpreted from a qualitative perspective as stable resources with a significant social valu

Edaphic and Topographic Constraints on Exploitation of the Central Kenya Rift by Large Mammals and Early Hominins

Our aim in this paper is to create a large-scale palaeoenvironmental and spatio-temporal framework for interpreting human land use and exploitation of large mammals in the Central Kenya Rift over the past 2 million years, with particular reference to the Nakuru-Elmenteita-Naivasha basin and its adjacent rift flanks on the Kinangop Plateau and Mau escarpment. We pay particular attention to the tectonic and volcanic history of the region, and to the system of lakes that have undergone periodic expansion and contraction during the Pleistocene in response to climatic and tectonic controls. We use this information to reconstruct topographic features as they would have existed at different periods of the past and their likely influence on patterns of large-mammal movements. In addition we present a systematic mapping of variations in the mineral nutrients of soils – soil edaphics – based on 150 analyses of trace elements in modern soil and vegetation samples. Soil edaphics play an important role in animal and human health today, with serious deficiencies in some areas, and would have exerted an important constraint on animal distributions and movements in the past. We show how soil-edaphic properties vary across the region and demonstrate a close relationship between them and the underlying geology and sediments, which allows us to project patterns back into the past and extrapolate them over larger areas. Using this combination of variables, we construct maps that help to place archaeological sites into their wider regional setting. We show that the Acheulean site of Kariandusi occupies a unique window of opportunity in place and time for trapping mammals constrained to move through a narrowly defined topographic bottleneck between edaphically-rich areas. We infer that the site was used for a simple form of ambush hunting and briefly explore the implications for differential site use, formation, preservation and visibility

Ecosystem health towards sustainability

Ecosystems are becoming damaged or degraded as a result of stresses especially associated with human activities. A healthy ecosystem is essential to provide the services that humans and the natural environment require and has tremendous social and economic value. Exploration of the definition of ecosystem health includes what constitutes health and what it means to be healthy. To evaluate ecosystem health, it is necessary to quantify ecosystem conditions using a variety of indicators. In this paper, the main principles and criteria for indicator selection, classification of indicators for different kinds of ecosystems, the most appropriate indicators for measuring ecosystem sustainability, and various methods and models for the assessment of ecosystem health are presented. Drivers, sustainability, and resilience are considered to be critical factors for ecosystem health and its assessment. Effective integration of ecological understanding with socioeconomic, biophysical, biogeochemical, and public-policy dimensions is still the primary challenge in this field, and devising workable strategies to achieve and maintain ecosystem health is a key future challenge