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Robustness of Optimal Synchronization in Real Networks
topology Networks coupling matrix nodes link
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...
Network topology and collapse of collective stable chaos
Network topology collapse of collective stable chaos
2010/12/28
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 ...
The Topology of Scaling Limits of Positive Genus Random Quadrangulations
Topology of Scaling Limits Positive Genus Random Quadrangulations
2011/2/22
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
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
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)...
On the pre-image of a point under an isogeny and Siegel's theorem
pre-image of a point under an isogeny Siegel's theorem
2010/11/30
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...
Geodesic diameter of sets defined by few quadratic equations and inequalities
Geodesic diameter of sets defined quadratic equations nequalities
2010/11/29
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 ...
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Surface measures convergence of the Ornstein-Uhlenbeck semigroup Wiener spaces
2010/11/26
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...
Point sets that minimize $(\le k)$-edges, $3$-decomposable drawings, and the rectilinear crossing number of $K_{30}$
k–edges 3-decomposability rectilinear crossing number
2010/12/10
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 3k+2
2(≤ k)...
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
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...
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...
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
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 ...
A Furstenberg-Katznelson-Weiss type theorem on (d + 1)-point configurations in sets of positive density in finite field geometries
positive density finite field geometries
2010/12/9
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&#...