"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

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

A cooperative interaction between LPHN3 and 11q doubles the risk for ADHD

In previous studies of a genetic isolate, we identified significant linkage of attention deficit hyperactivity disorder (ADHD) to 4q, 5q, 8q, 11q and 17p. The existence of unique large size families linked to multiple regions, and the fact that these families came from an isolated population, we hypothesized that two-locus interaction contributions to ADHD were plausible. Several analytical models converged to show significant interaction between 4q and 11q (P<1 × 10−8) and 11q and 17p (P<1 × 10−6). As we have identified that common variants of the LPHN3 gene were responsible for the 4q linkage signal, we focused on 4q–11q interaction to determine that single-nucleotide polymorphisms (SNPs) harbored in the LPHN3 gene interact with SNPs spanning the 11q region that contains DRD2 and NCAM1 genes, to double the risk of developing ADHD. This interaction not only explains genetic effects much better than taking each of these loci effects by separated but also differences in brain metabolism as depicted by proton magnetic resonance spectroscopy data and pharmacogenetic response to stimulant medication. These findings not only add information about how high order genetic interactions might be implicated in conferring susceptibility to develop ADHD but also show that future studies of the effects of genetic interactions on ADHD clinical information will help to shape predictive models of individual outcome

Epigenetics and obesity: the devil is in the details

Obesity is a complex disease with multiple well-defined risk factors. Nevertheless, susceptibility to obesity and its sequelae within obesogenic environments varies greatly from one person to the next, suggesting a role for gene × environment interactions in the etiology of the disorder. Epigenetic regulation of the human genome provides a putative mechanism by which specific environmental exposures convey risk for obesity and other human diseases and is one possible mechanism that underlies the gene × environment/treatment interactions observed in epidemiological studies and clinical trials. A study published in BMC Medicine this month by Wang et al. reports on an examination of DNA methylation in peripheral blood leukocytes of lean and obese adolescents, comparing methylation patterns between the two groups. The authors identified two genes that were differentially methylated, both of which have roles in immune function. Here we overview the findings from this study in the context of those emerging from other recent genetic and epigenetic studies, discuss the strengths and weaknesses of the study and speculate on the future of epigenetics in chronic disease research

Female Genitalia Concealment Promotes Intimate Male Courtship in a Water Strider

Violent coercive mating initiation is typical for animals with sexual conflict over mating. In these species, the coevolutionary arms-race between female defenses against coercive mating and male counter-adaptations for increased mating success leads to coevolutionary chases of male and female traits that influence the mating. It has been controversial whether one of the sexes can evolve traits that allow them to “win” this arms race. Here, we use morphological analysis (traditional and scanning electron micrographs), laboratory experiments and comparative methods to show how females of a species characterized by typical coercive mating initiation appear to “win” a particular stage of the sexual conflict by evolving morphology to hide their genitalia from direct, forceful access by males. In an apparent response to the female morphological adaptation, males of this species added to their typically violent coercive mounting of the female new post-mounting, pre-copulatory courtship signals produced by tapping the water's surface with the mid-legs. These courtship signals are intimate in the sense that they are aimed at the female, on whom the male is already mounted. Females respond to the signals by exposing their hidden genitalia for copulatory intromission. Our results indicate that the apparent victory of coevolutionary arms race by one sex in terms of morphology may trigger evolution of a behavioral phenotype in the opposite sex

Using the social entrepreneurship approach to generate innovative and sustainable malaria diagnosis interventions in Tanzania: a case study

<p>Abstract</p> <p>Background</p> <p>There have been a number of interventions to date aimed at improving malaria diagnostic accuracy in sub-Saharan Africa. Yet, limited success is often reported for a number of reasons, especially in rural settings. This paper seeks to provide a framework for applied research aimed to improve malaria diagnosis using a combination of the established methods, participatory action research and social entrepreneurship.</p> <p>Methods</p> <p>This case study introduces the idea of using the social entrepreneurship approach (SEA) to create innovative and sustainable applied health research outcomes. The following key elements define the SEA: (1) identifying a locally relevant research topic and plan, (2) recognizing the importance of international multi-disciplinary teams and the incorporation of local knowledge, (3) engaging in a process of continuous innovation, adaptation and learning, (4) remaining motivated and determined to achieve sustainable long-term research outcomes and, (5) sharing and transferring ownership of the project with the international and local partner.</p> <p>Evaluation</p> <p>The SEA approach has a strong emphasis on innovation lead by local stakeholders. In this case, innovation resulted in a unique holistic research program aimed at understanding patient, laboratory and physician influences on accurate diagnosis of malaria. An evaluation of milestones for each SEA element revealed that the success of one element is intricately related to the success of other elements.</p> <p>Conclusions</p> <p>The SEA will provide an additional framework for researchers and local stakeholders that promotes innovation and adaptability. This approach will facilitate the development of new ideas, strategies and approaches to understand how health issues, such as malaria, affect vulnerable communities.</p