Time-Optimal Tree Computations on Sparse Meshes

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite number of processors. We then go on to show that this lower bound is tight. We also show that the task of reconstructing n-node binary trees and ordered trees from their traversais can be performed in O(1) time on the same architecture. Our algorithms rely on novel time-optimal algorithms on sequences of parentheses that we also develop

Constant-time algorithms for constrained triangulations on reconfigurable meshes

A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconfigurable mesh has been proposed: In essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. The main contribution of this paper is to show that the flexibility of the reconfigurable mesh can be exploited for the purpose of obtaining constant-time algorithms for a number of constrained triangulation problems. These include triangulating a convex planar region containing any constant number of convex holes, triangulating a convex planar region in the presence of a collection of rectangular holes, and triangulating a set of ordered line segments. Specifically with a collection of O(n) such objects as input, our algorithms run in O(1) time on a reconfigurable mesh of size n/spl times/n. To the best of our knowledge, this is the first time constant time solutions to constrained triangulations are reported on this architecture

Constant-Time Convexity Problems on Reconfigurable Meshes

The purpose of this paper is to demonstrate that the versatility of the reconfigurable mesh can be exploited to devise constant-time algorithms for a number of important computational tasks relevant to robotics, computer graphics, image processing, and computer vision. In all our algorithms, we assume that one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a reconfigurable mesh of size p n \Theta p n. In this setup, we propose constant-time solutions for testing an arbitrary polygon for convexity, solving the point location problem, solving the supporting lines problem, solving the stabbing problem, determining the minimum area/perimeter corner triangle for a convex polygon, determining the k-maximal vertices of a restricted class of convex polygons, constructing the common tangents of two separable convex polygons, deciding whether two convex polygons intersect, answering queries concerning two convex polygons, and computing the smallest distance bet..

Time-Optimal Tree Computations on Sparse Meshes

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than \Omega\Gammaan/ n) time even if the MMB has an infinite number of processors. We then go on to show that this lower bound is tight. We also show that the task of reconstructing n-node binary trees and ordered trees from their traversals can be performed in O(1) time on the same architecture. Our algorithms rely on novel time-optimal algorithms on sequences of parentheses that we also develop

Peptide Mapping, In Silico and In Vivo Analysis of Allergenic Sorghum Profilin Peptides

Background and objectives: Nearly 20−30% of the world’s population suffers from allergic rhinitis, among them 15% are progressing to asthma conditions. Sorghum bicolor profilin (Sorb PF), one of the panallergens, was identified, but the allergen specificity is not yet characterized. Materials and Methods: To map the antigenic determinants responsible for IgE binding, the present study is focused on in silico modeling, simulation of Sorb PF and docking of the Sorb PF peptides (PF1-6) against IgG and IgE, followed by in vivo evaluation of the peptides for its allergenicity in mice. Results: Peptide PF3 and PF4 displayed high docking G-scores (−9.05) against IgE only. The mice sensitized with PF3 peptide showed increased levels of IL5, IL12, TNF-alpha, and GMCSF when compared to other peptides and controls, signifying a strong, Th2-based response. Concurrently, the Th1 pathway was inhibited by low levels of cytokine IL2, IFN-γ, and IL-10 justifying the role of PF3 in allergenic IgE response. Conclusions: Based on the results of overlapping peptides PF3 and PF4, the N-terminal part of the PF3 peptide (TGQALVI) plays a crucial role in allergenic response of Sorghum profilin