### Table 7: Description of the input data and the output decomposition.

"... In PAGE 21: ... In ongoing work, we are exploring the application of third-order tensors to this task, com- bining ideas from Landauer and Dumais (1997) and Turney (2006). Table7 describes the input data and the output tensor decomposition. The first mode of the tensor consists of all of the 391 unique words that occur in the TOEFL questions.... ..."

### Table 1. Classification of decomposition techniques Strategy Properties of Decomposition Indexing Structures

1996

"... In PAGE 6: ...classification yields five strategies as in Table1 . We discuss a brief description with respect to five decomposition strategies and attempt to capture their particular properties concerning evaluation criteria outlined in Section 2.... ..."

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### Table 1. Classification of decomposition techniques Strategy Properties of Decomposition Indexing Structures

1996

"... In PAGE 6: ...classification yields five strategies as in Table1 . We discuss a brief description with respect to five decomposition strategies and attempt to capture their particular properties concerning evaluation criteria outlined in Section 2.... ..."

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### Table 2 Decomposition of Employment Trends

2006

"... In PAGE 44: ... This is only an accounting identity, and we need to be a little careful in drawing causal conclusions from these numbers, particularly because some of the productivity changes are induced by foreign competition. The trends since 1970 in employment and these three components of the employment identity are reported in Table2 . In durables, domestic demand has been growing smartly at the rate of 5.... ..."

### Table 5: Decomposition by income source

"... In PAGE 20: ...20 of the other geographic controls are suggestive of positive externalities from better local endowments of human and physical infrastructure; in particular, higher levels of literacy locally and higher road density promote higher consumption growth at household level. The indications of geographic externalities are also evident in the decomposition by income source ( Table5 ). Echoing the results of Table 3, here too one finds strong indications that areas with more land and more developed agriculture tend to experience higher subsequent farm income gains; this effect is particularly strong for fertilizer usage, which is probably the best indicator in these data of the adoption of modern agricultural techniques.... In PAGE 20: ... However, unlike Table 3, one now finds strong positive effects of the density of nonfarm commercial development and industrial output on farm incomes. By allowing us to break up nonfarm incomes by sector (industry, construction, transport and services) the regressions using the county administrative data in Table5 reveal that the more aggregate effects identified in Table 3 disguise some potentially important differences between sub-sectors. Indeed, while there are generally positive external effects of local industrial development, we see signs of negative external effects on farm and nonfarm income growth of greater local activity in the transport and service sub-sectors.... In PAGE 21: ... Higher fertilizer usage also has an external effect on both types of nonfarm income growth, though the dominant external effect is on farm incomes. The extended models in Table5 also point to some diverse and in some cases surprising impacts across income sources. The positive effect of higher population density on consumption growth (Table 4) appears to be transmitted entirely through nonfarm type I income growth.... ..."

### Table 1: The tensor, (JPC = 2++), mesons and the decay rates into pairs of pseudo{ scalar mesons.

"... In PAGE 3: ... In order to uniquely identify that a state belongs to a particular nonet, it is necessary to look at several properties of the state. Table1 lists the tensor mesons, JPC = 2++ along with their masses, widths, and known two pseudo{scalar decay modes. Given a series of mesons which we believe belong to the same nonet, we can use the mass relation in equation 1 to arrive at a mixing angle for the nonet.... ..."

### Table 2. Different motion patterns ( rst column) and the ranks of the generalized structure tensors for 1, 2, and 3 motions (table rows). This table summarizes our results by showing the correspondence between the different motion patterns and the tensor ranks that can, in turn, be used to estimate the con dence for a particular pattern, i.e., a proper motion model. Note that the rank of JN induces a natural order of complexity for patterns consisting of N additive layers.

"... In PAGE 5: ... 4.1 Two 1D Transparent Moving Gratings In the projective plane, two moving gratings correspond to the fline, lineg case - see Table2 . According to the theory, the perceived motion should correspond to the intersection point U of the two lines and indeed it does - see Fig.... In PAGE 7: ... In the current framework, the in- trinsic dimension corresponds to the rank of J1. As shown in Table2 , by introducing the generalized structure tensor, we can further differentiate the signal classes of a given (integer) intrinsic dimension. In some sense, we thereby de ne frac- tional intrinsic dimensions.... In PAGE 12: ... These correspond to ranks 1,4 and 2,5,7 respectively. Table2 summarizes the possibilities for the ranks of JN for N = 1; 2; 3. Cicero Mota is on leave from University of Amazonas, Brazil and is currently with the Insti- tute for Neuro- and Bioinformat- ics, University of Luebeck, Ger- many.... ..."

### Table 1. Classification of decomposition techniques Class Strategy Properties of Decomposition Indexing Structures

"... In PAGE 6: ... We classify the object decomposition techniques according to the following three properties: condition of decomposition, number of partitions, and containers of components. This classification yields five strategies (see Table1 ). We briefly describe the five decomposition strategies, and attempt to capture their particular properties concerning the evaluation criteria outlined in Section 2.... ..."

### Table 5: Attribute Tensor

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### Table 5: Attribute Tensor

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