### Table 2. Results of the first inversion phase

1994

"... In PAGE 7: ... The main memory required by the second phase is thus given by . The results of the first pass on the trial data appear in Table2 . It is apparent that the main memory requirements (which are the only additional storage requirements apart from the text data) are quite modest.... In PAGE 9: ...ode. The relative size of each part of the system is summarised in Table 3. System Part Lines of Code Document conversion 124 Inversion first pass 452 Inversion second pass 915 Query processing engine 1001 User interface shell 2570 Table 3. Implementation of system parts For the text data described in Table2 the first pass of the inversion process (lexi- con construction and word frequency counting) took 8 minutes, while the second pass (search structure creation) took 27 minutes. It is apparent that our process will still ter- minate in manageable execution times even for an order of magnitude more data (both passes use algorithms where is the number of distinct words in the text).... ..."

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### Table 1. Various estimators for the reflection coefficients of inverse NUT lattice filters, where A6D4 denotes the sum of all the delays from order BD to order D4.

### TABLE VII Comparison of Different Tree Structures for TLUT inverse halftoning of clustered dot ordered dithered images.

### Table 1 Structural and elastic properties of bilayer membranes formed by amphiphilic diblock copolymers, biological lipids and a coarse-grained lattice model

2006

"... In PAGE 9: ... Additional characteristics, such as the bending rigidity, or the area compressibility modulus, then can be combined in dimensionless ratios. A comparison of such dimensionless ratios between liposomes, polymersomes, and the bond fluctuation model is presented in Table1 . One observes that these mesoscopic characteristics do not strongly differ between membranes formed by long amphiphilic diblock copolymers and biological lipids in aqueous solution and that the lattice model is able to reproduce the order of magnitude estimate of these properties.... In PAGE 32: ...Althoughthemodelcaptures only the universal amphiphilic characteristics of the membrane components, it provides a reasonable description of bilayer properties (cf. Table1 ). This efficient model allowed us to study rather large systems that contain several thousand amphiphiles, and to observe 32 fusion events for one set of parameters.... ..."

### TABLE VI Initial template TCD9 used in tree structure LUT inverse halftoning of clustered dot ordered dithered images.

### TABLE IX Initial template TOD8 used in tree structure LUT inverse halftoning of dispersed dot ordered dithered images.

### Table 2. KB statistics to simplify the presentation, we also consider inverse rela- tions, that is, attributes of some other frame pointing to the frame in question, as attributes of the latter for the purposes of the pattern induction process. For example, the vehicle involved in a motion is actually expressed via an inverse relation in the physics knowledge base as follows:

"... In PAGE 5: ...66% - 30% of the sentences. Table2 gives some figures about the under- lying KBs, giving the number of frames, average number of attributes per frame as well as the average number of inverse relations per frame. In fact, though we have not mentioned this in the description of the approach in Section 2 in order... ..."

### Table 2: The number of maxima for the molecular skin of the 1brs protein structure obtained via traditional persistence (second row) and the additional maxima obtained by its extension (third row).

"... In PAGE 8: ... The computed triangulation displayed in Figure 10 has slightly more than 50 thousand vertices after some simplification. Table2 gives the number of maxima of each type computed for this triangulation. We show in a seperate row the number of additional maxima paired by extended persistence as introduced in Section 2.... ..."

### Table 1 Arithmetic cost for di erent sizes of the diagonal blocks. V is the lattice volume. D(12) D(6) D(3) D(1)

"... In PAGE 13: ... (4). Accordingly, ignoring the parameters and cSW , four consecutive 3 3 blocks in D(3) are given by 1 + F1, 1 ? F1, 1 + F1, 1 ? F1 and two consecutive 6 6 diagonal blocks in D(6) are identical and given by 1 + F1 F2 F y 2 1 ? F1 ! : (23) Table1 quanti es the arithmetic e ort for computing a matrix-vector product with each of the matrices D(12), D(6), D(3) and D(1). We count this e ort in units of c ops, which represent one multiplication of complex numbers followed by one summation.... In PAGE 14: ... Precise numbers will depend on the particular algorithm chosen for the inversion. The estimates in Table1 are based on a particularly e cient way for computing the inverse, which uses Cramer apos;s rule on 3 3 blocks and which exploits the additional block structure within each of the D(6) ii and D(12) ii . The percentages given in brackets quantify these numbers in terms of the cost for a single matrix-vector multiply with M.... ..."

### Table 6: A framework for gradient descent image alignment algorithms. Gradient descent image alignment algorithms can be either additive or compositional, and either forwards or inverse. The inverse algorithms are computationally efficient whereas the forwards algorithms are not. The various algorithms can be applied to different sets of warps. Most sets of warps in computer vision form groups and so the forwards additive, the forwards compositional, and the inverse compositional algorithms can be applied to most sets of warps. The inverse additive algorithm can only be applied to a very small class of warps, mostly linear 2D warps. Algorithm For Example Efficient? Can be Applied To

2004

"... In PAGE 25: ...teration to first order in A1D4. In Section 3.4 we validated this equivalence empirically. The four algorithms do differ, however, in two other respects. See Table6 for a summary. Although the computational requirements of the two forwards algorithms are almost identical and... ..."

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