### Table 1. The multi-dimensional signal set mapper

"... In PAGE 8: ...List of Tables Table1 : CCIR test channel parameters .... In PAGE 8: ............ 87 Table1 1: Summary of Search Metrics used for different channels .... In PAGE 134: ... 4. The Codes The coded-modulation scheme used for each rate is given in Table1 . All the codes shown are convolutional trellis codes.... In PAGE 134: ... A block diagram of the multi-rate encoder is shown in Figure 2. The convolutional encoder implements the convolutional codes shown in Table1 . The multi-dimensional signal set mapper then maps the coded bits into either two, four or eight signal dimensions (for the 300, 600 and 1200 bps codes this function also includes a Gray coder, see later).... In PAGE 134: ... (1) where m ek is the e th metric at time k r k is the received signal phasor at time k e is the expected signal constellation point Info. Rate Code Rate k/n Constell- ation States Generators or Parity Check Coefficients (octal) Ref 300 1/8 4xQPSK 256 g 1 =373 g 2 =353 g 3 =335 g 4 =315 g 5 =277 g 6 =251 g 7 =231 g 8 =227 [11] 600 1/4 2xQPSK 256 g 1 =365 g 2 =337 g 3 =271 g 4 =233 [11] 1200 1/2 QPSK 256 g 1 =363 g 2 =255 [11] 2400 2/3 8PSK 256 h 0 =417 h 1 =573 h 2 =621 [12] 3600 3/4 16PSK 128 h 0 =211 h 1 =307 h 2 =343 h 3 =337 [12] Table1 . Coded-Modulation Schemes Investigated.... ..."

### Table 1, i.e. k = PBc + Bp + b and l = Bc + b. The distribution basis for a multi-dimensional array can be expressed as a tensor product of the distribution bases for each dimension.

1994

"... In PAGE 5: ...Table1 : Index mapping functions for regular data distributions. BLOCK CYCLIC CYCLIC(b) local to global k = p(dN=Pe) + l k = lP + p k = (l div b)bP + bp + l mod b global to local l = k mod dN=Pe l = k div P l = (k div Pb)b + k mod b global to proc p = k div dN=Pe p = k mod P p = (k div b) mod P k global index 0 k N ? 1; l local index 0 l lt; db ?dN=(Pb)e ; p processor 0 p lt; P.... In PAGE 5: ... Techniques developed in [11] can be used for the array redistribution in the general case. For identity alignments, the relationships between the global index, the local index and the processor index for regular data distributions of a one-dimensional array are shown in Table1 . The indexing for arrays A and A loc begins at zero and the processors are numbered from 0 to P ? 1.... In PAGE 8: ... For example, under a BLOCK distribution the array is partitioned into segments of size NP . The relationship between the global index k, the processor index p, and the local index l as shown in Table1 can be represented by the equality eN k = eP p eNP l ; where p = k div NP and l = k mod NP . In the above identity, the index of vector basis eP p is associated with the processor index on which element A(k) is located after being distributed using a BLOCK distribution.... ..."

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### Table 1, i.e. k = PBc + Bp + b and l = Bc + b. The distribution basis for a multi-dimensional array can be expressed as a tensor product of the distribution bases for each dimension.

1994

"... In PAGE 5: ...Table1 : Index mapping functions for regular data distributions. BLOCK CYCLIC CYCLIC(b) local to global k = p(dN=Pe) + l k = lP + p k = (l div b)bP + bp + l mod b global to local l = k mod dN=Pe l = k div P l = (k div Pb)b + k mod b global to proc p = k div dN=Pe p = k mod P p = (k div b) mod P k global index 0 k N ? 1; l local index 0 l lt; db ?dN=(Pb)e ; p processor 0 p lt; P.... In PAGE 5: ... Techniques developed in [11] can be used for the array redistribution in the general case. For identity alignments, the relationships between the global index, the local index and the processor index for regular data distributions of a one-dimensional array are shown in Table1 . The indexing for arrays A and A loc begins at zero and the processors are numbered from 0 to P ? 1.... In PAGE 8: ... For example, under a BLOCK distribution the array is partitioned into segments of size NP . The relationship between the global index k, the processor index p, and the local index l as shown in Table1 can be represented by the equality eN k = eP p eNP l ; where p = k div NP and l = k mod NP . In the above identity, the index of vector basis eP p is associated with the processor index on which element A(k) is located after being distributed using a BLOCK distribution.... ..."

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### Table 12: Multi-dimensional categorization

2006

"... In PAGE 11: ...Multi-Conference Information Systems (MKWI06), Passau, Germany, 2006. Table12 exemplarily illustrates the multi-dimensional categorization of metrics. Table 12: Multi-dimensional categorization ... ..."

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### Table 4: Multi-Dimensional Resource Models

"... In PAGE 7: ... This will typically be a negative term (= profit per accepted customer). Non-Existent - Existent C Table 5: Cost Model Elements Table4 : Multi-Dimensional Resource Models... ..."

### Table 3: Multi-dimensional DISC algorithm

"... In PAGE 8: ... Given two locations represented by longitudes and latitudes, they are near to each other only if their longitudes and latitudes are close to each other. To cluster objects of multiple attributes, DISC can be extended to M-DISC ( Table3 ). The generated multi-dimensional TAHs are called MTAHs.... ..."

### Table 4. A multi-dimensional sequence database

2005

"... In PAGE 30: ... Example 8 (Mining multi-dimensional, multi-level sequential patterns). Con- sider a sequence database SDB in Table4 , where each sequence is associated with certain multi-dimensional, multi-level information. For example, it may contain multi-dimensional circumstance information, such as cust-grp = busi- ness, city = Boston,andage-grp = middle aged.... ..."

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### Table 1: Example data capture modalities, and their typical characteristics and representation schemes.

"... In PAGE 5: ... Digitization is the primary technology for acquiring SORs of real-life objects and phenomena. This technology, which is based on measuring various physical properties, is avail- able in a wide range of modalities as listed in Table1 . In most of these modalities, a sampling process may involve the processing of multi-channel or multi-dimensional sig- nals, including convolution and deconvolution, quantization, and signal space conversion.... ..."

### Table 1. A Typology of Multi-Dimensional Evaluation Methods* Type of

2002

"... In PAGE 4: ... There are a limited number of options (training areas) to choose from which are obviously discrete. In this study, two of the six types of models described in Table1... ..."

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