Creation of blenders in the conservative setting

In this work we prove that each C^r conservative diffeomorphism with a pair of hyperbolic periodic points of co-index one can be C^1-approximated by C^r conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure

Mean Field Theory For Non-Equilibrium Network Reconstruction

There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically-coupled, synchronously-updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one time step-delayed correlation functions.Comment: new version, accepted in PRL. For the Supp. Mat. (ref. 11), please contact the author

p>2 spin glasses with first order ferromagnetic transitions

We consider an infinite-range spherical p-spin glass model with an additional r-spin ferromagnetic interaction, both statically using a replica analysis and dynamically via a generating functional method. For r>2 we find that there are first order transitions to ferromagnetic phases. For r<p there are two ferromagnetic phases, one non-glassy replica symmetric and one exhibiting glassy one-step replica symmetry breaking and aging, whereas for r>=p only the replica symmetric phase exists.Comment: AMSLaTeX, 13 pages, 23 EPS figures ; one figure correcte