"Almost stable" matchings in the Roommates problem

An instance of the classical Stable Roommates problem (SR) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an SR instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within n^{\frac{1}{2}-\varepsilon}, for any \varepsilon>0, unless P=NP. If the preference lists contain ties, we improve this result to n^{1-\varepsilon}. Also, we show that, given an integer K and an SR instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an SR instance I

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Unravelling the age of fine roots of temperate and boreal forests

Fine roots support the water and nutrient demands of plants and supply carbon to soils. Quantifying turnover times of fine roots is crucial for modeling soil organic matter dynamics and constraining carbon cycle–climate feedbacks. Here we challenge widely used isotopebased estimates suggesting the turnover of fine roots of trees to be as slow as a decade. By recording annual growth rings of roots from woody plant species, we show that mean chronological ages of fine roots vary from <1 to 12 years in temperate, boreal and sub-arctic forests. Radiocarbon dating reveals the same roots to be constructed from 10 ± 1 year (mean ± 1 SE) older carbon. This dramatic difference provides evidence for a time lag between plant carbon assimilation and production of fine roots, most likely due to internal carbon storage. The high root turnover documented here implies greater carbon inputs into soils than previously thought which has wide-ranging implications for quantifying ecosystem carbon allocation.Peer reviewe

Pan-Eurasian Experiment (PEEX): Towards a holistic understanding of the feedbacks and interactions in the land-Atmosphere-ocean-society continuum in the northern Eurasian region

The northern Eurasian regions and Arctic Ocean will very likely undergo substantial changes during the next decades. The Arctic-boreal natural environments play a crucial role in the global climate via albedo change, carbon sources and sinks as well as atmospheric aerosol production from biogenic volatile organic compounds. Furthermore, it is expected that global trade activities, demographic movement, and use of natural resources will be increasing in the Arctic regions. There is a need for a novel research approach, which not only identifies and tackles the relevant multi-disciplinary research questions, but also is able to make a holistic system analysis of the expected feedbacks. In this paper, we introduce the research agenda of the Pan-Eurasian Experiment (PEEX), a multi-scale, multi-disciplinary and international program started in 2012 (https://www.atm.helsinki.fi/peex/). PEEX sets a research approach by which large-scale research topics are investigated from a system perspective and which aims to fill the key gaps in our understanding of the feedbacks and interactions between the land-Atmosphere-Aquatic-society continuum in the northern Eurasian region. We introduce here the state of the art for the key topics in the PEEX research agenda and present the future prospects of the research, which we see relevant in this context

Ototoxicity of cisplatin plus standard radiation therapy vs. accelerated radiation therapy in glioblastoma patients

Purpose : To assess the effect of cisplatin (CDDP) plus concurrent radiation therapy on hearing loss. Methods : 451 patients with glioblastoma multiforme (GBM) were randomly assigned after surgery to: Arm A: Carmustine (BCNU) + standard radiation therapy (SRT); Arm B: BCNU + accelerated radiation therapy (ART: 160 cGy twice daily for 15 days); Arm C: CDDP + BCNU + SRT; or Arm D: CDDP + BCNU + ART. Patients on arms C and D received audiograms at baseline, and prior to the start of RT, and prior to cycles 3 and 6. Otologic toxicities were recorded at each visit. Results : 56% of patients had hearing loss at baseline. 13% and 50% of patients experienced worsening ototoxicity after 1 year of treatment in arms A and B vs. C and D, respectively, with 13% of those on arms C and D experiencing significant ototoxicity (≥ grade 3) at 6 months. Increasing age was associated with an increased risk of ototoxicity. Conclusions : Increased exposure to CDDP increases the risk of ototoxicity over time. Older patients are more susceptible to hearing loss with CDDP. The low proportion of patients with clinically significant ototoxicity suggests that baseline screening is unnecessary in GBM patients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43476/1/11060_2005_Article_9049.pd