Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: taxicab sampler. We describe construction this sampler and discuss how its interpretation usage differs from that standard Metropolis-Hastings as well related Hamming ball The proposed sampling algorithm is then shown to demonstrate subst...

Let n and n be respectively the uniform empirical and quantile processes , and deene R n = n + n , which usually is referred to as the Bahadur{Kiefer process. The well-known Bahadur{Kiefer theorem connrms the following remarkable equivalence: kR n k= p k n k n ?1=4 (log n) 1=2 almost surely, as n goes to innnity, where kfk = sup 0t1 jf(t)j is the L 1-norm. We prove that kR n k 2 = p k n k 1 n ?...

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...

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

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...