In this paper we analyze different models of deformable linear objects (DLOs) in terms of efficient computation and preciseness. Our approach is to minimize the potential energy (computed as the sum of gravitational and bending energy) of the DLO. To model our DLOs, we approximate the bending of the DLO using a weighted sum of approximation functions. Our objective is to identify the optimal ty...

We consider region of interest (ROI) tomography of piecewise constant functions. We prove that continuous ROI data determine piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted `p–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We p...

The local zeta functions (also called Igusa’s zeta functions) over p-adic fields are connected with the number of solutions of congruences and exponential sums mod pm. These zeta functions are defined as integrals over open and compact subsets with respect to the Haar measure. In this paper, we introduce new integrals defined over submanifolds, or more generally, over non-degenerate complete in...

The new class of weights called A p weights is introduced. We prove that a characterization and an unconditional basis of the weighted Lp space Lp(Rn,w(x)dx) with w ∈ A p (1 < p < ∞) are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.

We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-local...

AbstractPseudorandom quantum states (PRS) are efficiently constructible that computationally indistinguishable from being Haar-random, and have recently found cryptographic applications. We explore new definitions, properties applications of pseudorandom states, present the following contributions: 1. New Definitions: study variants function-like state (PRFS) generators, introduced by Ananth, Q...

Let f : X → Y be a based map of simply connected spaces. The corresponding evaluation map ω : map(X, Y ; f)→ Y induces a homomorphism of homotopy groups whose image in πn(Y ) is called the nth evaluation subgroup of f . The nth Gottlieb group of X occurs as the special case in which Y = X and f = 1X . We identify the homomorphism induced on rational homotopy groups by this evaluation map, in te...

An orthogonal Haar scattering transform is a deep network computed with a hierarchy of additions, subtractions and absolute values over pairs of coefficients. Unsupervised learning optimizes Haar pairs to obtain sparse representations of training data with an algorithm of polynomial complexity. For signals defined on a graph, a Haar scattering is computed by cascading orthogonal Haar wavelet tr...