Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics

We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G_{n,p} -model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n^{c\log n}, which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be normal. The approach we develop is of some generality and is amenable for other graph algorithms.Comment: 35 page

MHD activity in FTU plasmas with reversed magnetic shear

Abstract. The MHD activity of plasma configurations with reversed magnetic shear has been investigated on the FTU tokamak. In the presence of pairs of surfaces with the same rational value q D m=n of the safety factor, double-tearing modes are excited which give rise in most cases to bursts of sawtooth-like profile rearrangements. More stable regimes have also been found, in which the activity is dominated by rotating saturated modes. In a particular case with q.0 / 2:8 and qmin 2:5 a discharge without any detectable MHD activity during the current flat-top has been obtained. In high-temperature regimes (Te 8 keV at ne 0:81020 m−3), an irregular activity has been detected near the plasma centre which could be due to the excitation of resistive interchange modes. 1

Sectoral approaches to improve regional carbon budgets

Humans utilise about 40% of the earth’s net primary production (NPP) but the products of this NPP are often managed by different sectors, with timber and forest products managed by the forestry sector and food and fibre products from croplands and grasslands managed by the agricultural sector. Other significant anthropogenic impacts on the global carbon cycle include human utilization of fossil fuels and impacts on less intensively managed systems such as peatlands, wetlands and permafrost. A great deal of knowledge, expertise and data is available within each sector. We describe the contribution of sectoral carbon budgets to our understanding of the global carbon cycle. Whilst many sectors exhibit similarities for carbon budgeting, some key differences arise due to differences in goods and services provided, ecology, management practices used, landmanagement personnel responsible, policies affecting land management, data types and availability, and the drivers of change. We review the methods and data sources available for assessing sectoral carbon budgets, and describe some of key data limitations and uncertainties for each sector in different regions of the world. We identify the main gaps in our knowledge/data, show that coverage is better for the developed world for most sectors, and suggest how sectoral carbon budgets could be improved in the future. Research priorities include the development of shared protocols through site networks, a move to full carbon accounting within sectors, and the assessment of full greenhouse gas budgets