983 resultados para ‘I’ boundaries


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The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.

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(I): M r = 258.34, triclinic, Pi, a = 9.810 (3), b=9.635(3), e=15.015(4)A, a=79.11(2), #= 102.38 (3), y = 107.76 (3) o, V= 1308.5 A 3, Z = 4, Din= 1.318 (3) (by flotation in KI solution), D x = 1.311 g cm -3, Cu Ka, 2 = 1.5418/~, g = 20-05 cm -1, F(000) = 544, T---- 293 K, R = 0.074 for 2663 reflections. (II): M r = 284.43, monoclinic, P2~/c, a= 17.029 (5), b=6.706 (5), c= 14.629 (4), t= 113.55 (2) ° , V=1531.4A 3, Z=4, Dm=1.230(5) (by flotation in KI solution), Dx= 1.234gem -3, Mo Ka, 2 = 0.7107 A, g = 1.63 cm-1; F(000) = 608, T= 293 K, R = 0.062 for 855 reflections. The orientation of the C=S chromophores in the crystal lattice and their reactivity in the crystalline state are discussed. The C--S bonds are much shorter than the normal bond length [1.605 (4) (I), 1.665 (8) A (II) cf. 1.71 A].

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(I): Mr=274"39, orthorhombic, Pbca, a = 7.443 (1), b= 32.691 (3), c= 11.828 (2)A, V= 2877.98A 3, Z=8, Din= 1.216 (flotation in KI), D x = 1.266 g cm -3, /~(Cu Ka, 2 = 1.5418 A) = 17.55 cm -1, F(000) = li52.0, T= 293 K, R = 6.8%, 1378 significant reflections. (II): M r = 248.35, orthorhombic, P212~21, a = 5.873 (3), b = 13.677 (3), c = 15-668 (5) A, V = 1260.14 A 3, Z = 4, D,n = 1.297 (flotation in KI), Dx= 1.308 g cm -a, /t(CuKa, 2=1.5418 A) = 19.55 cm -~, F(000) = 520.0, T= 293 K, R = 6.9%, 751 significant reflections. Crystals of (I) and (II) undergo photo-oxidation in the crystallinestate. In (I) the dihedral angle between the phenyl rings of the biphenyl moiety is 46 (1) °. The C=S bond length is 1.611(5) A in (I) and 1.630 (9)/~ in (II). The correlation between molecular packing and reactivity is discussed.

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