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Robustness of Optimal Synchronization in Real Networks     topology  Networks  coupling matrix  nodes  link       font style='font-size:12px;'> 2011/7/6
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental res...
Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotem-poral systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of ...
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every n  1, a random quadrangulation qn uniformly distributed over the set of all ro...
Lower bounds on the Hausdorff measure of nodal sets      Lower bounds  Hausdorff measure of nodal sets        font style='font-size:12px;'> 2010/12/8
Let N' be the nodal hypersurface of a -eigenfunction ' of eigenvalue 2on a smooth Riemannian manifold. We prove that Hn−1(N') ≥ C7 4− 3n 4 on the surface measure of its nodal set. Th...
Level Sets of the Takagi Function: Local Level Sets      Level Sets  Takagi Function  Local Level Sets        font style='font-size:12px;'> 2010/11/30
The Takagi function  : [0; 1] ! [0; 1] is a continuous non-di erentiable functio constructed by Takagi in 1903. This paper studies the level sets L(y) = fx :  (x) = yg of the Takagi function  (x)...
Consider a rational point on an elliptic curve under an isogeny.Suppose that the action of Galois partitions the set of its pre-images into n orbits. It is shown that all such points above a certain h...
We prove a bound for the geodesic diameter of a subset of the unit ball in Rn described by a fixed number of quadratic equations and inequalities,which is polynomial in n, whereas the known bound for ...
We study points of density 1/2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this clas...
There are two properties shared by all known crossing-minimizing geometric drawings of Kn, for n a multiple of 3.First, the underlying n-point set of these drawings has exactly 3􀀀k+2 2(≤ k)...
Metaplectic Ice      p-adic Whittaker function  metaplectic group  Gelfand-Tsetlin pattern       font style='font-size:12px;'> 2010/12/1
We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local field using lattice models from statistical mechanics.
Enriched weakness           font style='font-size:12px;'> 2010/12/1
The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the un...
Density of classical points in eigenvarieties      Density of classical points  eigenvarieties        font style='font-size:12px;'> 2010/11/26
In this short note, we study the geometry of the eigenvariety parametrising p-adic automorphic forms for GL1 over a number field, as constructed by Buzzard. We show that if K is not totally real and c...
Non-concentration of return times      Non-concentration  return times        font style='font-size:12px;'> 2010/12/1
We show that the distribution of the first return time τ to the origin, v, of a simple randomwalk on an infinite recurrent graph is heavy tailed and non-concentrated.
Moduli spaces for point modules on naive blowups      Moduli spaces  point modules  naive blowups        font style='font-size:12px;'> 2010/12/3
The na¨ıve blow-up algebras developed by Keeler-Rogalski-Stafford [KRS05], after examples of Rogalski [Rog04], are the first known class of connected graded algebras that are noetherian but not ...
We show that if E ⊂ Fdq , the d-dimensional vector space over the finite field with q elements,and |E| ≥ qd, where q−1 2 ≪  ≤ 1, then E contains an isometric copy of at least cd&#...

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