A Solution to Matching with Preferences over Colleagues

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty.Matching markets, Core, Lattice, Gale-Shapley algorithm

Accelerated Asymptotics for Diffusion Model Estimation

We propose a semiparametric estimation procedure for scalar homogeneous stochastic differential equations. We specify a parametric class for the underlying diffusion process and identify the parameters of interest by minimizing criteria given by the integrated squared difference between kernel estimates of drift and diffusion function and their parametric counterparts. The nonparametric estimates are simplified versions of those in Bandi and Phillips (1998). A complete asymptotic theory for the semiparametric estimates is developed. The limit theory relies on infill and long span asymptotics and the asymptotic distributions are shown to depend on the chronological local time of the underlying diffusion process. The estimation method and asymptotic results apply to both stationary and nonstationary processes. As is standard with semiparametric approaches in other contexts, faster convergence rates are attained than is possible in the fully functional case. From a purely technical point of view, this work merges two strands of the most recent econometrics literature, namely the estimation of nonlinear models of integrated time-series [Park and Phillips (1999, 2000)] and the functional identification of diffusions under minimal assumptions on the dynamics of the underlying process [Florens-Zmirou (1993), Jacod (1997), Bandi and Phillips (1998) and Bandi (1999)]. In effect, the 'minimum distance' type of estimation that is presented in this paper can be interpreted as extremum estimation for potentially nonstationary and nonlinear continuous-time models.

Joint statistics of acceleration and vorticity in fully developed turbulence

We report results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present results concerning acceleration statistics and the statistics of trapping by vortex filaments conditioned to the local values of vorticity and enstrophy. We distinguish two different behaviors between the joint statistics of vorticity and centripetal acceleration or vorticity and longitudinal acceleration.Comment: 8 pages, 6 figure

Interaction induced Fermi-surface renormalization in the t1−t2t_1{-}t_2 Hubbard model close to the Mott-Hubbard transition

We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.Comment: 6 pages and 7 figure

Zero-Temperature Properties of the Quantum Dimer Model on the Triangular Lattice

Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. {\bf 86}, 1881 (2001)].Comment: 10 pages, 16 figure

Orientation-dependent Casimir force arising from highly anisotropic crystals: application to Bi2Sr2CaCu2O8+delta

We calculate the Casimir interaction between parallel planar crystals of Au and the anisotropic cuprate superconductor Bi2Sr2CaCu2O8+delta (BSCCO), with BSCCO's optical axis either parallel or perpendicular to the crystal surface, using suitable generalizations of the Lifshitz theory. We find that the strong anisotropy of the BSCCO permittivity gives rise to a difference in the Casimir force between the two orientations of the optical axis, which depends on distance and is of order 10-20% at the experimentally accessible separations 10 to 5000 nm.Comment: 5 pages, 3 figures. Accepted for publication in Physical Review

Improved estimates of rare K decay matrix-elements from Kl3 decays

The estimation of rare K decay matrix-elements from Kl3 experimental data is extended beyond LO in Chiral Perturbation Theory. Isospin-breaking effects at NLO (and partially NNLO) in the ChPT expansion, as well as QED radiative corrections are now accounted for. The analysis relies mainly on the cleanness of two specific ratios of form-factors, for which the theoretical control is excellent. As a result, the uncertainties on the K+ --> pi+ nu nubar and KL --> pi0 nu nubar matrix-elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contribution to KL --> pi0 l+ l-. They could be reduced even further with better experimental data for the Kl3 slopes and the K+l3 branching ratios. As a result, the non-parametric errors for B(K --> pi nu nubar) and for the direct CP-violating contributions to B(KL --> pi0 l+ l-) are now completely dominated by those on the short-distance physics.Comment: 16 pages, 1 figure. Numerical analysis updated to include the recent Kl3 data. To appear in Phys. Rev.

On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions

NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function \Psi: {\cal L}^N_K \to \Lambda_N. The probability {\cal P}_K that \Psi (f) = \Psi (f'), when f' is obtained through f by a change of one of its K-Boolean functions (b_K: \IZ_2^K \to \IZ_2), and/or connections; is calculated. The leading term of the asymptotic expansion of {\cal P}_K, for N \gg 1, turns out to depend on: the probability to extract the tautology and contradiction Boolean functions, and in the average value of the distribution of probability of the Boolean functions; the other terms decay as {\cal O} (1 / N). In order to accomplish this, a classification of the Boolean functions in terms of what I have called their irreducible degree of connectivity is established. The mathematical findings are discussed in the biological context where, \Psi is used to model the genotype-phenotype map.Comment: 17 pages, 1 figure, Accepted in Journal of Mathematical Physic