We prove that the scaling limit of loop-erased random walk in a simply connected domain D $ C is equal to the radial SLE2 path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that ∂D is a C1 simple closed curve, the same method is applied to show that th...

A one dimensional (1-D) based tree structure algorithm is proposed for estimating the 2D-DOAs of the signals impinging on a uniform rectangular array. The key idea of the proposed algorithm is to successively utilize the 1-D MUSIC algorithm several times, in tree structure, to estimate the azimuth and the elevation angles independently. Subspace projectors are exploited in conjunction with the ...

Splay and randomized search trees (RSTs) are self-balancing binary tree structures with little or no space overhead compared to a standard binary search tree (BST). Both trees are intended for use in applications where node accesses are skewed, for example in gathering the distinct words in a large text collection for index construction. We investigate the efficiency of these trees for such voc...

In this paper, we address the problem of closed pattern mining from n-ary relations. We propose CnS-Miner algorithm which enumerates all the closed patterns of the given n-dimensional dataset in depth first manner satisfying the user specified minimum size constraints. From the given input, the CnS-Miner algorithm generates an n-ary tree and visits the tree in depth first manner. We have propos...

Given a set L of n points in the d-dimensional Cartesian space E d , and a query specifying a domain q in E d , the Range Search problem consists in identifying the subset R(q) of the points of L contained in q. The Range Tree data-structure represents a particularly good balance between storage space and search time. The structure requires O(n log d?1 n) space and construction time, but suppor...

Background and objectives: Plumeria rubra L. (Apocynaceae) is a deciduous shrub or small tree cultivated in subtropical and tropical countries.  Its bark is prescribed to treat amoebic dysentery,   dropsy, jaundice, scabies, gonorrhea, venereal affections and wounds. In the present research, we aimed to isolate and identify the chemical constituents of the bark of ...

Bottom-up tree series transducers (tst) over the semiring A are implemented with the help of bottom-up weighted tree automata (wta) over an extension of A. Therefore bottom-up D-weighted tree automata (D-wta) with D a distributive Ω-algebra are introduced. A D-wta is essentially a wta but uses as transition weight an operation symbol of the Ω-algebra D instead of a semiring element. The given t...

We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d0 such that, for any d ≥ d0, the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi-infinite interva...

We provide an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propa...