Two algorithms for the student-project allocation problem

We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals / Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation

Review of Recent Developments in the Random-Field Ising Model

A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.Comment: 11 pages, 4 figures, updated and extended version, to be published in J. Stat. Phy

Ultra-high Energy Cosmic Rays: a probe into New Physics

The most energetic particles ever detected exceed $10^{20}$ eV in energy. Their existence represents at the same time a great challenge for particle physics and astrophysics, and a great promise of providing us for a probe of the validity of the laws of Nature in extreme conditions. We review here the most recent data and the future perspectives for detection of cosmic rays at ultra-high energies, and discuss possible ways of using these data to test the possibility that new Physics and/or new Astrophsyics may be awaiting around the corner.Comment: Invited Review Talk at SpacePart 2002, La Biodola, Isola d'Elba, Italy - May 14-19, 200