Rank Maximal Matchings -- Structure and Algorithms

Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank post and so on. In this paper, we develop a switching graph characterization of rank-maximal matchings, which is a useful tool that encodes all rank-maximal matchings in an instance. The characterization leads to simple and efficient algorithms for several interesting problems. In particular, we give an efficient algorithm to compute the set of rank-maximal pairs in an instance. We show that the problem of counting the number of rank-maximal matchings is #P-Complete and also give an FPRAS for the problem. Finally, we consider the problem of deciding whether a rank-maximal matching is popular among all the rank-maximal matchings in a given instance, and give an efficient algorithm for the problem

Moir\'e patterns in quantum images

We observed moir\'e fringes in spatial quantum correlations between twin photons generated by parametric down-conversion. Spatially periodic structures were nonlocally superposed giving rise to beat frequencies typical of moir\'e patterns. This result brings interesting perspectives regarding metrological applications of such a quantum optical setup.Comment: 4 pages, 5 figure

A determination of the strange quark mass for unquenched clover fermions using the AWI

Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (nf=2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Results indicate a value for the strange quark mass (in the MSbar-scheme at a scale of 2GeV) in the range 100 - 130MeV.Comment: 6 pages, contribution to Lattice2005(Hadron spectrum and quark masses), uses PoS.cl

Socially stable matchings in the hospitals / residents problem

In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings. In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for three special cases of the problem

Equine or porcine synovial fluid as a novel ex vivo model for the study of bacterial free-floating biofilms that form in human joint infections

Bacterial invasion of synovial joints, as in infectious or septic arthritis, can be difficult to treat in both veterinary and human clinical practice. Biofilms, in the form of free-floating clumps or aggregates, are involved with the pathogenesis of infectious arthritis and periprosthetic joint infection (PJI). Infection of a joint containing an orthopedic implant can additionally complicate these infections due to the presence of adherent biofilms. Because of these biofilm phenotypes, bacteria within these infected joints show increased antimicrobial tolerance even at high antibiotic concentrations. To date, animal models of PJI or infectious arthritis have been limited to small animals such as rodents or rabbits. Small animal models, however, yield limited quantities of synovial fluid making them impractical for in vitro research. Herein, we describe the use of ex vivo equine and porcine models for the study of synovial fluid induced biofilm aggregate formation and antimicrobial tolerance. We observed Staphylococcus aureus and other bacterial pathogens adapt the same biofilm aggregate phenotype with significant antimicrobial tolerance in both equine and porcine synovial fluid, analogous to human synovial fluid. We also demonstrate that enzymatic dispersal of synovial fluid aggregates restores the activity of antimicrobials. Future studies investigating the interaction of bacterial cell surface proteins with host synovial fluid proteins can be readily carried out in equine or porcine ex vivo models to identify novel drug targets for treatment of prevention of these difficult to treat infectious diseases

A Determination of the Lambda Parameter from Full Lattice QCD

We present a determination of the QCD parameter Lambda in the quenched approximation (n_f=0) and for two flavours (n_f=2) of light dynamical quarks. The calculations are performed on the lattice using O(a) improved Wilson fermions and include taking the continuum limit. We find Lambda_{n_f=0} = 259(1)(20) MeV and Lambda_{n_f=2} = 261(17)(26) MeV}, using r_0 = 0.467 fm to set the scale. Extrapolating our results to five flavours, we obtain for the running coupling constant at the mass of the Z boson alpha_s(m_Z) = 0.112(1)(2). All numbers refer to the MSbar scheme.Comment: 25 pages, 9 figure

Integer programming methods for special college admissions problems

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones

Popular Matchings in the Capacitated House Allocation Problem

We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matching M′ such that the number of agents who prefer their allocation in M′ to that in M exceeds the number of agents who prefer their allocation in M to that in M′. Here, we give an O(√C+n1m) algorithm to determine if an instance of CHA admits a popular matching, and if so, to find a largest such matching, where C is the total capacity of the houses, n1 is the number of agents and m is the total length of the agents’ preference lists. For the case where preference lists may contain ties, we give an O(√Cn1+m) algorithm for the analogous problem

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to