On Streaming and Communication Complexity of the Set Cover Problem

We develop the first streaming algorithm and the first two-party communication protocol that uses a constant number of passes/rounds and sublinear space/communication for logarithmic approximation to the classic Set Cover problem. Specifically, for n elements and m sets, our algorithm/protocol achieves a space bound of O(m ·n [superscript δ] log[superscript 2] n logm) using O(4[superscript 1/δ]) passes/rounds while achieving an approximation factor of O(4[superscript 1/δ]logn) in polynomial time (for δ = Ω(1/logn)). If we allow the algorithm/protocol to spend exponential time per pass/round, we achieve an approximation factor of O(4[superscript 1/δ]). Our approach uses randomization, which we show is necessary: no deterministic constant approximation is possible (even given exponential time) using o(m n) space. These results are some of the first on streaming algorithms and efficient two-party communication protocols for approximation algorithms. Moreover, we show that our algorithm can be applied to multi-party communication model.National Science Foundation (U.S.) (Grant CCF-1161626)National Science Foundation (U.S.) (Grant CCF-1065125)United States. Defense Advanced Research Projects Agency (United States. Air Force Office of Scientific Research Grant FA9550-12-1-0423)David & Lucile Packard FoundationSimons FoundationDanish National Research Foundation. Center for Massiave Data Algorithmics (MADALGO

Contribution of the SPRT Calibration to Uncertainty of Temperature T 90 Measured by the Calibrated SPRT

The propagation of uncertainties, when the International Temperature Scale of 1990 (ITS-90) is used by a standard platinum resistance thermometer (SPRT) calibrated at defining fixed points (DFP), can be solved by applying several approaches. The article presents an analysis of contribution of covariance between resistances of SPRT at the defining fixed points (DFP). Its effect on temperature measured by calibrated SPRT is demonstrated by using real calibration data

Применение гидродинамического моделирования для обоснования мероприятий по борьбе с подтоплением при использовании лучевого дренажа

Развитие подтопления способно существенным образом осложнить эксплуатацию инженерных сооружений. Это требует разработки эффективных мер по предотвращению негативных последствий подъёма уровней подземных вод. В случае особо ответственных сооружений повышаются требования к надёжности прогноза изменения гидрогеологических условий под влиянием эксплуатации защитных мероприятий. В статье рассматриваются вопросы прогноза изменения гидрогеологических условий на участке хранения высокорадиоактивных отходов под влиянием лучевого дренажа. Flooding development is capable to complicate operation of engineering constructions essentially. It demands working out of effectual measures on prevention of negative consequences of ascending gradient of levels of underground waters. In case of especially responsible constructions requirements to reliability of the forecast of change of hydrogeological conditions under the influence of operation of protective actions raise. In article questions of the forecast of change of hydrogeological conditions on a lot of storage of a highly radioactive waste under the influence of a beam drainage are considered

Geochemical evidence of aeolian deposits in European soils

M. McLaughlin and R. Hoffmann are members of the GEMAS Project TeamHafnium (Hf) and zirconium (Zr) concentrations measured in over 4100 agricultural soil samples from Europe were assessed with the focus on their relationship to the distribution of aeolian deposits, such as loess and coversands. Comparison of extractable (aqua regia; ICP-MS) and total (XRFS) concentrations shows that only 1.0 to 1.7% of the total Hf and Zr is chemically extractable because of the resistant nature of their host minerals. Resistate minerals, such as zircon, are commonly found in the predominantly silty fraction of loess deposits. In this study a statistical analysis of total Hf and Zr soil data from areas with and without loess was carried out to derive threshold values of 10 mg kg⁻¹ (Hf) and 318 mg kg⁻¹ (Zr). These values were subsequently applied across the project area in an attempt to indicate the presence of aeolian deposits. The spatial distribution of above-threshold concentrations suggests a more extensive and coherent loess belt across central and eastern Europe, providing additional evidence of loess across Brittany, Aquitaine and near the Vosges mountains in France as well as in the basins of central and northern Spain. Above-threshold concentrations were also detected in loess regardless of its thickness, emphasising the importance of the abundance of zircon in the upper part of the soil profile rather than the actual thickness of the deposit. Soil data however, failed to indicate various loess facies within most of the Pannonian Basin, suggesting that this approach only works where deposits contain a sufficient amount of zircon. This may also explain why the extensive coversands across northern Germany and Poland were largely undetected. This study demonstrates that continental-scale soil geochemical data can help identify and map the distribution of zircon-rich loess and coversand, and subsequently enhance and improve current knowledge of the extent of these deposits.Andreas J. Scheib, Manfred Birke, Enrico Dinelli, GEMAS Project Tea

GEMAS: Geochemical background and mineral potential of emerging tech-critical elements in Europe revealed from low-sampling density geochemical mapping

The demand for ‘high-tech’ element resources (e.g., rare earth elements, lithium, platinum group elements) has increased with their continued consumption in developed countries and the emergence of developing economies. To provide a sound knowledge base for future generations, it is necessary to identify the spatial distribution of critical elements at a broad-scale, and to delineate areas for follow-up surveys. Subsequently, this knowledge can be used to study possible environmental consequences of the increased use of these resources. In this paper, three critical industrial elements (Sb, W, Li) from low-sampling density geochemical mapping at the continental-scale are presented. The geochemical distribution and spatial patterns have been obtained from agricultural soil samples (Ap-horizon, 0–20 cm; N ¼ 2108 samples) collected at a density of 1 site per 2500 km2 and analysed by ICP-MS after a hot aqua regia digestion as part of the GEMAS (GEochemical Mapping of Agricultural and grazing land Soil) soil-mapping project in 33 European countries. Most of the geochemical maps show exclusively natural background element concentrations with minor, or without, anthropogenic influence. The maximum extent of the last glaciation is marked as a discrete element concentration break, and a distinct difference occurs in element concentration levels between the soil of northern and southern Europe, most likely an effect of soil genesis, age and weathering. The Sb, W and Li concentrations in soil provide a general overview of element spatial distribution in relation to complexity of the underlying bedrock and element mobility in the surface environment at the continental-scale. The chemical composition of agricultural soil represents largely the primary mineralogy of the source bedrock, the effects of pre- and post-depositional chemical weathering, formation of secondary products, such as clays, and element mobility, either by leaching or mineral sorting. Observed geochemical patterns of Li, W and Sb can be often linked with known mineralisation as recorded in the ProMine Mineral Database, where elements in question occur either as main or secondary resources. Anthropogenic impact has only been identified locally, predominantly in the vicinity of large urban agglomerations. Unexplained high element concentrations may potentially indicate new sources for high-tech elements and should be investigated at a more detailed scale.Philippe Négrel, Anna Ladenberger, Clemens Reimann, Manfred Birke, Alecos Demetriades, Martiya Sadeghi, The GEMAS Project Tea