In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.

In an article of a few years ago [2] Kerékjartó obtained interesting results about certain types of transformations which he called similitudes. With a few modifications and extensions his methods can be used to gain information about the structure of measure preserving transformations at fixed points. For simplicity the results are formulated for Euclidean w-space although they could easily be...

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

Article history: Received 26 June 2008 Received in revised form 28 October 2008 Accepted 3 November 2008

We develop a general formalism for the construction of (supersymmetric) gauge theories of volume-preserving diffeomorphisms (SDiff), focusing on the D = 3 superconformal SDiff3 invariant ‘BLG’ theory describing a condensate of M2-branes. 1 igor [email protected]; supported by the Basque Science Foundation Ikerbasque. 2 [email protected]

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and it...

This paper presents an efficient and novel geometric flow-driven method for mesh optimization of segmented tetrahedral meshes with non-manifold boundary surfaces. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of vertices are optimized. Non-manifold boundary can be divided into manifold surface patches hav...

Let Fd be the collection of all d-dimensional probability distribution functions on [0, 1]d, d ≥ 2. The metric entropy of Fd under the L2([0, 1]d) norm is studied. The exact rate is obtained for d = 1, 2 and bounds are given for d > 3. Connections with small deviation probability for Brownian sheets under the sup-norm are established.

We present a straightforward, yet effective approach to volume-preserving mesh skinning. After each skinned mesh deformation, a volume correction is applied which moves the vertices along an automatically constructed displacement field. The volume correction is exact and is computed directly by a closed-form solution. The animator can control the volume correction interactively to achieve custo...

Let φt be a three dimensional contact Anosov flow. Then we prove that its cohomological pressure coincides with its metric entropy if and only if φt is C ∞ flow equivalent to a special time change of a three dimensional algebraic contact Anosov flow.