666 research outputs found
Convex Hulls under Uncertainty
We study the convex-hull problem in a probabilistic setting, motivated by the
need to handle data uncertainty inherent in many applications, including sensor
databases, location-based services and computer vision. In our framework, the
uncertainty of each input site is described by a probability distribution over
a finite number of possible locations including a \emph{null} location to
account for non-existence of the point. Our results include both exact and
approximation algorithms for computing the probability of a query point lying
inside the convex hull of the input, time-space tradeoffs for the membership
queries, a connection between Tukey depth and membership queries, as well as a
new notion of \some-hull that may be a useful representation of uncertain
hulls
Synthetic, Structural, and Biochemical Studies of Organotin(IV) With Schiff Bases Having Nitrogen and Sulphur Donor Ligands
Three bidentate Schiff bases having nitrogen and sulphur donor sequences were prepared by condensing S-benzyldithiocarbazate (NH(2)NHCS(2)CH(2)C(6)H(5)) with heterocyclic aldehydes. The reaction of diphenyltin dichloride with Schiff bases leads to the formation of a new series of organotin(IV) complexes. An attempt has been made to prove their structures on the basis of elemental analyses, conductance measurements, molecular weights determinations, UV, infrared, and multinuclear magnetic resonance ((1)H, (13)C, and (119)Sn) spectral studies. Organotin(IV) complexes were five- and six-coordinate. Schiff bases and their corresponding organotin complexes have also been screened for their antibacterial and antifungal activities and found to be quite active in this respect
Computing Optimal Kernels in Two Dimensions
Let be a set of points in . A subset is
an -kernel of if the projection of the convex hull of
approximates that of within -factor in every direction.
The set is a weak -kernel if its directional width
approximates that of in every direction. We present fast algorithms for
computing a minimum-size -kernel as well as a weak
-kernel. We also present a fast algorithm for the Hausdorff
variant of this problem.
In addition, we introduce the notion of -core, a convex polygon
lying inside , prove that it is a good approximation of the optimal
-kernel, present an efficient algorithm for computing it, and use
it to compute an -kernel of small size
Computing the Similarity Between Moving Curves
In this paper we study similarity measures for moving curves which can, for
example, model changing coastlines or retreating glacier termini. Points on a
moving curve have two parameters, namely the position along the curve as well
as time. We therefore focus on similarity measures for surfaces, specifically
the Fr\'echet distance between surfaces. While the Fr\'echet distance between
surfaces is not even known to be computable, we show for variants arising in
the context of moving curves that they are polynomial-time solvable or
NP-complete depending on the restrictions imposed on how the moving curves are
matched. We achieve the polynomial-time solutions by a novel approach for
computing a surface in the so-called free-space diagram based on max-flow
min-cut duality
The Maximum-Level Vertex in an Arrangement of Lines
Let be a set of lines in the plane, not necessarily in general position. We present an efficient algorithm for finding all the vertices of the arrangement of maximum level, where the level of a vertex is the number of lines of that pass strictly below . The problem, posed in Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it seems, as this vertex might not be on the upper envelope of the lines. We first assume that all the lines of are distinct, and distinguish between two cases, depending on whether or not the upper envelope of contains a bounded edge. In the former case, we show that the number of lines of that pass above any maximum level vertex is only . In the latter case, we establish a similar property that holds after we remove some of the lines that are incident to the single vertex of the upper envelope. We present algorithms that run, in both cases, in optimal time. We then consider the case where the lines of are not necessarily distinct. This setup is more challenging, and the best we have is an algorithm that computes all the maximum-level vertices in time . Finally, we consider a related combinatorial question for degenerate arrangements, where many lines may intersect in a single point, but all the lines are distinct: We bound the complexity of the weighted -level in such an arrangement, where the weight of a vertex is the number of lines that pass through the vertex. We show that the bound in this case is , which matches the corresponding bound for non-degenerate arrangements, and we use this bound in the analysis of one of our algorithms
Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search
The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a
general technique for constructing a data structure to answer approximate near
neighbor queries by using a distribution over locality-sensitive
hash functions that partition space. For a collection of points, after
preprocessing, the query time is dominated by evaluations
of hash functions from and hash table lookups and
distance computations where is determined by the
locality-sensitivity properties of . It follows from a recent
result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive
hash functions can be reduced to , leaving the query time to be
dominated by distance computations and
additional word-RAM operations. We state this result as a general framework and
provide a simpler analysis showing that the number of lookups and distance
computations closely match the Indyk-Motwani framework, making it a viable
replacement in practice. Using ideas from another locality-sensitive hashing
framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of
additional word-RAM operations to .Comment: 15 pages, 3 figure
Synthetic and Spectroscopic Characterization of Organotin(IV) Complexes of Biologically Active Schiff Bases Derived from Sulpha Drugs
A number of diorganotin(IV) complexes with Schiffbase have been synthesized and characterized by elemental analysis, conductance measurements, molecular weight determinations, infrared, electronic and multinuclear magnetic resonance ((1)H, (13)C and (119)Sn NMR) spectral data. The molar conductivity data shows non-electrolytic nature of complexes. The bidentate nature of the ligands is inferred from IR and NMR spectral studies. The antimicrobial activities of the ligands and their tin complexes have been screened in vitro against the organism Escherichia coli; Staphylococus aureus, Prouteus mirabilis, Bacillus thurengiensis, Penicillium co.,sogenum, Aspergillus niger and Fusarium oxysporum
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