Let S be a set of N grid points in the plane, and let G a graph with n vertices (n ≤ N). An orthogeodesic point-set embedding of G on S is a drawing of G such that each vertex is drawn as a point of S and each edge is a chain of horizontal and vertical segments with bends on grid points whose length is equal to the Manhattan distance of its end vertices. We study the following problem. Given a ...

We consider an instance of the Earth Mover’s Distance (EMD) useful for comparing rhythmical patterns. To make searches for r-near neighbours efficient, we decompose our search space into disjoint metric subspaces, in each of which the EMD reduces to the l1 norm. We then use a combined approach of two methods, one for searching within the subspaces, the other for searching between them. For the ...

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. In the hyperbolic space, we show that if the volume of M is 1, then there exists a constant C depending on the dimension of M and the L-norm of the second fundamental form B such that the pinching condition tanh(R) < 1 ||H||∞ + C (where H is the mean curvature) implies that M is diffeomorphic to an ...

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

Swapan Rana,1, ∗ Preeti Parashar,2 Andreas Winter,3, 4 and Maciej Lewenstein1, 4 1ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain 2Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 BT Road, Kolkata, India 3Departament de Física: Grup d’Informació Quàntica, Universitat Autònoma de Barcelona, ES-08193 Bell...

An l1-norm function is introduced as a computational tool to estimate the Dehn function of a finite presentation and settle certain imbedding questions for finitely presented groups.

For a prime p and a vector ᾱ = (α1, . . . , αk) ∈ Zp let f (ᾱ, p) be the largest n such that in each set A ⊆ Zp of n elements one can find x which has a unique representation in the form x = α1a1 + · · · + αkak, ai ∈ A. Hilliker and Straus [2] bounded f (ᾱ, p) from below by an expression which contained the L1-norm of ᾱ and asked if there exists a positive constant c (k) so that f (ᾱ, p) > c (k...

We obtain estimates in Besov, Triebel–Lizorkin and Lorentz spaces of differential forms on Rn in terms of their L1 norm.

Given access to independent samples of a distribution A over [n℄ [m℄, we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is -close in the L1 norm to the product distribution A1 A2 for some distributionsA1 over [n℄ and A2 over [m℄. The sample complexity of our test is ~ O(n2=3m1=3poly( 1)), assuming without loss of generality ...