A q-query locally testable code (LTC) is an error correcting code that can be tested by a randomized algorithm that reads at most q symbols from the given word. An important question is whether there exist LTCs that have the c3 property: constant relative rate, constant relative distance, and that can be tested with a constant number of queries. Such codes are sometimes referred to as “asymptot...

In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample set of a curve, correctly reconstructs the smooth arcs and further closed and simple curves in Riemannian manifolds. The proof is based on the behaviour of the curve segment inside the tubular neighbourh...

In this paper, we define hedge operation on a residuated skew lattice and investigate some its properties. We get relationships between some special sets as dense, nilpotent, idempotent, regular elements sets and their hedges.  By examples, we show that hedge of a dense element is not a dense and hedge of a regular element is not a regular. Also hedge of a nilpotent element is a nilpotent and h...

In this thesis we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be spectrally rigid over a stratum with enough complexity, extending a result of Duchin-LeiningerRafi. Specifically, for any stratum with more unmarked zeroes than the ...

We study geodesic flows on compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval (−∞, 1), and this is an optimal result. In higher dimensions, we obtain the same result on a neighborhood...

Let A be a locally compact group topologically generated by d elements and let k > d. Consider the action, by precomposition, of Γ = Aut(Fk) on the set of marked, k-generated, dense subgroups Dk,A := {η ∈ Hom(Fk, A) | 〈φ(Fk)〉 = A}. We prove the ergodicity of this action for the following two families of simple, totally disconnected locally compact groups: • A = PSL2(K) where K is a non-Archimed...

We introduce a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...

To address the fine-grain scalable audio compression issue, a novel combined significance tree technique is proposed for high compression efficiency. The core idea is to dynamically adopt a set of locally optimal significance trees, instead of following the common approach of using a single type of tree. Two different encoding strategies are proposed: the spectral coefficients can be encoded ei...