Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Holocene environmental changes in the lower Thames Valley, London, UK: implications for our understanding of the history of Taxus woodland

A radiocarbon-dated multiproxy palaeoenvironmental record from the Lower Thames Valley at Hornchurch Marshes has provided a reconstruction of the timing and nature of vegetation succession against a background of Holocene climate change, relative sea level movement and human activities. The investigation recorded widespread peat formation between c. 6300 and 3900 cal. yr BP (marine ‘regression’), succeeded by evidence for marine incursion. The multiproxy analyses of these sediments, comprising pollen, Coleoptera, diatoms, and plant and wood macrofossils, have indicated significant changes in both the wetland and dryland environment, including the establishment of Alnus (Alder) carr woodland, and the decline of both Ulmus (Elm; c. 5740 cal. yr BP) and Tilia (Lime; c. 5600 cal. yr BP, and 4160–3710 cal. yr BP). The beetle faunas from the peat also suggest a thermal climate similar to that of the present day. At c. 4900 cal. yr BP, Taxus (L.; Yew) woodland colonised the peatland forming a plant community that has no known modern analogue in the UK. The precise reason, or reasons, for this event remain unclear, although changes in peatland hydrology seem most likely. The growth of Taxus on peatland not only has considerable importance for our knowledge of the vegetation history of southeast England, and NW Europe generally, but also has wider implications for the interpretation of Holocene palaeobotanical records. At c. 3900 cal. yr BP, Taxus declined on the peatland surface during a period of major hydrological change (marine incursion), an event also strongly associated with the decline of dryland woodland taxa, including Tilia and Quercus, and the appearance of anthropogenic indicators.

Holocene palaeoenvironmental history and the impact of prehistoric salt production in the Seille Valley, Eastern France

The Seille Valley in eastern France was home to one of Europe’s largest Iron Age salt industries. Sedimentology, palynology and geochronology have been integrated within ongoing archaeological investigations to reconstruct the Holocene palaeoenvironmental history of the Seille Valley and to elucidate the human–environment relationship of salt production. A sedimentary model of the valley has been constructed from a borehole survey of the floodplain and pollen analyses have been undertaken to reconstruct the vegetation history. Alluvial records have been successfully dated using optically stimulated luminescence and radiocarbon techniques, thereby providing a robust chronological framework. The results have provided an insight into the development of favourable conditions for salt production and there is evidence in the sedimentary record to suggest that salt production may have taken place during the mid-to-late Bronze Age. The latter has yet to be identified in the archaeological record and targeted excavation is therefore underway to test this finding. The development of the Iron Age industry had a major impact on the hydrological regime of the valley and its sedimentological history, with evidence for accelerated alluviation arising from floodplain erosion at salt production sites and modification of the local fluvial regime due to briquetage accumulation on the floodplain. This research provides an important insight into the environmental implications of early industrial activities, in addition to advancing knowledge about the Holocene palaeoenvironmental and social history of this previously poorly studied region of France.

The domestication of water: water management in the ancient world and its prehistoric origins in the Jordan Valley

The ancient civilizations were dependent upon sophisticated systems of water management. The hydraulic engineering works found in ancient Angkor (ninth to thirteenth century AD), the Aztec city of Tenochtitlan (thirteenth to fifteenth century AD), Byzantine Constantinople (fourth to sixth century AD) and Nabatean Petra (sixth century BC to AD 106) are particularly striking because each of these is in localities of the world that are once again facing a water crisis. Without water management, such ancient cities would never have emerged, nor would the urban communities and towns from which they developed. Indeed, the ‘domestication’ of water marked a key turning point in the cultural trajectory of each region of the world where state societies developed. This is illustrated by examining the prehistory of water management in the Jordan Valley, identifying the later Neolithic (approx. 8300–6500 years ago) as a key period when significant investment in water management occurred, laying the foundation for the development of the first urban communities of the Early Bronze Age.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Synthesis of a mononuclear oxidovanadium(V) complex by bridge-splitting of the corresponding binuclear precursor

The mononuclear oxidovanadium(V) complex VO(OEt)L (2), where L2- is the dianion of a diprotic tridentate ONO donor ligand, 2-hydroxyacetophenone-2-aminobenzoylhydrazone (H2L), has been synthesized by oxido-bridge splitting of the corresponding binuclear complex V2O3L2 (1) and structurally characterized by single crystal X-ray diffraction analysis, together with electrochemical and spectral studies. Splitting of the oxido-bridge was effected by refluxing 1 with excess triphenylphosphine in ethanol medium. The crystal structure of 2 is compared with that of the precursor binuclear complex 1.

A climate of control: flooding, displacement and planned resettlement in the Lower Zambezi River valley, Mozambique

In recent years, the potential role of planned, internal resettlement as a climate change adaptation measure has been highlighted by national governments and the international policy community. However, in many developing countries, resettlement is a deeply political process that often results in an unequal distribution of costs and benefits amongst relocated persons. This paper examines these tensions in Mozambique, drawing on a case study of flood-affected communities in the Lower Zambezi River valley. It takes a political ecology approach – focusing on discourses of human-environment interaction, as well as the power relationships that are supported by such discourses – to show how a dominant narrative of climate change-induced hazards for small-scale farmers is contributing to their involuntary resettlement to higher-altitude, less fertile areas of land. These forced relocations are buttressed by a series of wider economic and political interests in the Lower Zambezi River region, such dam construction for hydroelectric power generation and the extension of control over rural populations, from which resettled people derive little direct benefit. Rather than engaging with these challenging issues, most international donors present in the country accept the ‘inevitability’ of extreme weather impacts and view resettlement as an unfortunate and, in some cases, necessary step to increase people’s ‘resilience’, thus rationalising the top-down imposition of unpopular social policies. The findings add weight to the argument that a depoliticised interpretation of climate change can deflect attention away from underlying drivers of vulnerability and poverty, as well as obscure the interests of governments that are intent on reordering poor and vulnerable populations.

Ensemble projections for wine production in the Douro Valley of Portugal

Wine production is largely governed by atmospheric conditions, such as air temperature and precipitation, together with soil management and viticultural/enological practices. Therefore, anthropogenic climate change is likely to have important impacts on the winemaking sector worldwide. An important winemaking region is the Portuguese Douro Valley, which is known by its world-famous Port Wine. The identification of robust relationships between atmospheric factors and wine parameters is of great relevance for the region. A multivariate linear regression analysis of a long wine production series (1932–2010) reveals that high rainfall and cool temperatures during budburst, shoot and inflorescence development (February-March) and warm temperatures during flowering and berry development (May) are generally favourable to high production. The probabilities of occurrence of three production categories (low, normal and high) are also modelled using multinomial logistic regression. Results show that both statistical models are valuable tools for predicting the production in a given year with a lead time of 3–4 months prior to harvest. These statistical models are applied to an ensemble of 16 regional climate model experiments following the SRES A1B scenario to estimate possible future changes. Wine production is projected to increase by about 10 % by the end of the 21st century, while the occurrence of high production years is expected to increase from 25 % to over 60 %. Nevertheless, further model development will be needed to include other aspects that may shape production in the future. In particular, the rising heat stress and/or changes in ripening conditions could limit the projected production increase in future decades.