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

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

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.

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.

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

Testing Feedback-Modified Dark Matter Haloes with Galaxy Rotation Curves: Estimation of Halo Parameters and Consistency with Λ\LambdaCDM

Cosmological $N$-body simulations predict dark matter (DM) haloes with steep central cusps (e.g. NFW, Navarro et al. 1996). This contradicts observations of gas kinematics in low-mass galaxies that imply the existence of shallow DM cores. Baryonic processes such as adiabatic contraction and gas outflows can, in principle, alter the initial DM density profile, yet their relative contributions to the halo transformation remain uncertain. Recent high resolution, cosmological hydrodynamic simulations (Di Cintio et al. 2014, DC14) predict that inner density profiles depend systematically on the ratio of stellar to DM mass (M$_*$/M$_{\text{halo}}$). Using a Markov Chain Monte Carlo approach, we test the NFW and the M$_*$/M$_{\text{halo}}$-dependent DC14 halo models against a sample of 147 galaxy rotation curves from the new {\it Spitzer} Photometry and Accurate Rotation Curves (SPARC) data set. These galaxies all have extended H{\small I} rotation curves from radio interferometry as well as accurate stellar mass density profiles from near-infrared photometry. The DC14 halo profile provides markedly better fits to the data compared to the NFW profile. Unlike NFW, the DC14 halo parameters found in our rotation curve fits naturally fall within two standard deviations of the mass-concentration relation predicted by $\Lambda$CDM and the stellar mass-halo mass relation inferred from abundance matching with few outliers. Halo profiles modified by baryonic processes are therefore more consistent with expectations from $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology and provide better fits to galaxy rotation curves across a wide range of galaxy properties than do halo models that neglect baryonic physics. Our results offer a solution to the decade long cusp-core discrepancy.Comment: 23 Pages, 18 Figures, MNRAS Accepte

On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by `Statistically Preserved Structures' which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.Comment: revised version with new data on Navier-Stokes eq