Solving stable matching problems using answer set programming

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725

Local and Global Consistency Properties for Student Placement

In the context of resource allocation on the basis of priorities, Ergin (2002) identifies a necessary and sufficient condition on the priority structure such that the student-optimal stable mechanism satisfies a consistency principle. Ergin (2002) formulates consistency as a local property based on a fixed population of agents and fixed resources -- we refer to this condition as local consistency and to his condition on the priority structure as local acyclicity. We identify a related but stronger necessary and sufficient condition (unit acyclicity) on the priority structure such that the student-optimal stable mechanism satisfies a more standard global consistency property. Next, we provide necessary and sufficient conditions for the student-optimal stable mechanism to satisfy converse consistency principles. We identify a necessary and sufficient condition (local shift-freeness) on the priority structure such that the student-optimal stable mechanism satisfies local converse consistency. Interestingly, local acyclicity implies local shift-freeness and hence the student-optimal stable mechanism more frequently satisfies local converse consistency than local consistency. Finally, in order for the student-optimal stable mechanism to be globally conversely consistent, one again has to impose unit acyclicity on the priority structure. Hence, unit acyclicity is a necessary and sufficient condition on the priority structure for the student-optimal stable mechanism to satisfy global consistency or global converse consistency.acyclicity, consistency, converse consistency, student placement.

The College Admissions problem with lower and common quotas

We study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in Hungary. The first problem is an extension of the College Admissions problem in which the colleges have lower quotas as well as the normal upper quotas. Here, we show that a stable matching may not exist and we prove that the problem of determining whether one does is NP-complete in general. The second problem is a different extension in which, as usual, individual colleges have upper quotas, but, in addition, certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas. Again, we show that a stable matching may not exist and the related decision problem is NP-complete. On the other hand, we prove that, when the bounded sets form a nested set system, a stable matching can be found by generalising, in non-trivial ways, both the applicant-oriented and college-oriented versions of the classical Gale–Shapley algorithm. Finally, we present an alternative view of this nested case using the concept of choice functions, and with the aid of a matroid model we establish some interesting structural results for this case

Mental state estimation for brain-computer interfaces

Mental state estimation is potentially useful for the development of asynchronous brain-computer interfaces. In this study, four mental states have been identified and decoded from the electrocorticograms (ECoGs) of six epileptic patients, engaged in a memory reach task. A novel signal analysis technique has been applied to high-dimensional, statistically sparse ECoGs recorded by a large number of electrodes. The strength of the proposed technique lies in its ability to jointly extract spatial and temporal patterns, responsible for encoding mental state differences. As such, the technique offers a systematic way of analyzing the spatiotemporal aspects of brain information processing and may be applicable to a wide range of spatiotemporal neurophysiological signals

Monotone and Consistent discretization of the Monge-Ampere operator

We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are achieved by exploiting the arithmetic structure of the discrete domain, assumed to be a two dimensional cartesian grid. The construction of our scheme is simple, but its analysis relies on original tools seldom encountered in numerical analysis, such as the geometry of two dimensional lattices, and an arithmetic structure called the Stern-Brocot tree. Numerical experiments illustrate the method's efficiency

Death receptor 5 expression is inversely correlated with prostate cancer progression.

Prostate carcinoma (PCa) is one of the most common cancers in men. Prostate-specific antigen (PSA) has been widely used to predict the outcome of PCa and screening with PSA has resulted in a decline in mortality. However, PSA is not an optimal prognostic tool as its sensitivity may be too low to reduce morbidity and mortality. Consequently, there is a demand for additional robust biomarkers for prostate cancer. Death receptor 5 (DR5) has been implicated in the prognosis of several cancers and it has been previously shown that it is negatively regulated by Yin Yang 1 (YY1) in prostate cancer cell lines. The present study investigated the clinical significance of DR5 expression in a prostate cancer patient cohort and its correlation with YY1 expression. Immunohistochemical analysis of protein expression distribution was performed using tissue microarray constructs from 54 primary PCa and 39 prostatic intraepithelial neoplasia (PIN) specimens. DR5 expression was dramatically reduced as a function of higher tumor grade. By contrast, YY1 expression was elevated in PCa tumors as compared with that in PIN, and was increased with higher tumor grade. DR5 had an inverse correlation with YY1 expression. Bioinformatic analyses corroborated these data. The present findings suggested that DR5 and YY1 expression levels may serve as progression biomarkers for prostate cancer

A minimal statistical-mechanical model for multihyperuniform patterns in avian retina

Birds are known for their extremely acute sense of vision. The very peculiar structural distribution of five different types of cones in the retina underlies this exquisite ability to sample light. It was recently found that each cone population as well as their total population display a disordered pattern in which long wave-length density fluctuations vanish. This property, known as hyperuniformity is also present in perfect crystals. In situations like the avian retina in which both the global structure and that of each component display hyperuniformity, the system is said to be multi-hyperuniform. In this work, we aim at devising a minimal statistical-mechanical model that can reproduce the main features of the spatial distribution of photoreceptors in avian retina, namely the presence of disorder, multi-hyperuniformity and local hetero-coordination. This last feature is key to avoid local clustering of the same type of photoreceptors, an undesirable feature for the efficient sampling of light. For this purpose we formulate a simple model that definitively exhibits the required structural properties, namely an equimolar three-component mixture (one component to sample each primary color, red, green, and blue) of non-additive hard disks to which a long-range logarithmic repulsion is added between like particles. A Voronoi analysis of our idealized system of photoreceptors shows that the space-filling Voronoi polygons interestingly display a rather uniform area distribution, symmetrically centered around that of a regular lattice, a structural property also found in human retina. Disordered multi-hyperuniformity offers an alternative to generate photoreceptor patterns with minimal long-range concentration and density fluctuations. This is the key to overcome the difficulties in devising an efficient visual system in which crystal-like order is absent

Annuities and Individual Welfare

This paper advances the theory of annuity demand. First, we derive sufficient conditions under which complete annuitization is optimal, showing that this well-known result holds true in a more general setting than in Yaari (1965). Specifically, when markets are complete, sufficient conditions need not impose exponential discounting, intertemporal separability or the expected utility axioms; nor need annuities be actuarially fair, nor longevity risk be the only source of consumption uncertainty. All that is required is that consumers have no bequest motive and that annuities pay a rate of return for survivors greater than those of otherwise matching conventional assets, net of administrative costs. Second, we show that full annuitization may not be optimal when markets are incomplete. Some annuitization is optimal as long as conventional asset markets are complete. The incompleteness of markets can lead to zero annuitization but the conditions on both annuity and bond markets are stringent. Third, we extend the simulation literature that calculates the utility gains from annuitization by considering consumers whose utility depends both on present consumption and a which they have become accustomed. The value of annuitization hinges critically on the size of the initial standard-of-living relative to wealth.