4,740 research outputs found
The hospitals/residents problem with ties
Get PDFThe hospitals/residents problem is an extensively-studied many-one stable matching problem. Here, we consider the hospitals/residents problem where ties are allowed in the preference lists. In this extended setting, a number of natural definitions for a stable matching arise. We present the first linear-time algorithm for the problem under the strongest of these criteria, so-called super-stability . Our new results have applications to large-scale matching schemes, such as the National Resident Matching Program in the US, and similar schemes elsewhere
An Orange Grove In California
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Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices
Full text linkWe present a general framework to study stability of the synchronous solution
for a hypernetwork of coupled dynamical systems. We are able to reduce the
dimensionality of the problem by using simultaneous block-diagonalization of
matrices. We obtain necessary and sufficient conditions for stability of the
synchronous solution in terms of a set of lower-dimensional problems and test
the predictions of our low-dimensional analysis through numerical simulations.
Under certain conditions, this technique may yield a substantial reduction of
the dimensionality of the problem. For example, for a class of dynamical
hypernetworks analyzed in the paper, we discover that arbitrarily large
networks can be reduced to a collection of subsystems of dimensionality no more
than 2. We apply our reduction techique to a number of different examples,
including a class of undirected unweighted hypermotifs of three nodes.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.
Reduced healthcare utilisation following successful HCV treatment in HIV co-infected patients with mild liver disease
Get PDFNew direct-acting antivirals (DAA) for hepatitis C virus (HCV) infection have achieved high cure rates in many patient groups previously considered difficult-to-treat, including those HIV/HCV co-infected. The high price of these medications is likely to limit access to treatment, at least in the short term. Early treatment priority is likely to be given to those with advanced disease, but a more detailed understanding of the potential benefits in treating those with mild disease is needed. We hypothesized that successful HCV treatment within a co-infected population with mild liver disease would lead to a reduction in the use and costs of healthcare services in the 5 years following treatment completion. We performed a retrospective cohort study of HIV/HCV-co-infected patients without evidence of fibrosis/cirrhosis who received a course of HCV therapy between 2004 and 2013. Detailed analysis of healthcare utilization up to 5 years following treatment for each patient using clinical and electronic records was used to estimate healthcare costs. Sixty-three patients were investigated, of whom 48 of 63 (76.2%) achieved sustained virological response 12 weeks following completion of therapy (SVR12). Individuals achieving SVR12 incurred lower health utilization costs (£5000 per-patient) compared to (£10 775 per-patient) non-SVR patients in the 5 years after treatment. Healthcare utilization rates and costs in the immediate 5 years following treatment were significantly higher in co-infected patients with mild disease that failed to achieve SVR12. These data suggest additional value to achieving cure beyond the prevention of complications of disease
Stable marriage and roommates problems with restricted edges: complexity and approximability
Get PDFIn the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs.
Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs.
Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs
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