### Table 3: Average message latencies for low-order interleaved (LOI) and high-order interleaved (HOI) memory.

in Effect of Virtual Channels and Memory Organization on Cache-Coherent Shared-Memory Multiprocessors

1996

"... In PAGE 14: ... Figure 3: Tra c pattern for MATMUL. Table3 . In case of high-order interleaved memory, the execution time shows a big improve- ment when the number of virtual channels are increased from 2 to 4.... ..."

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### Table 1: High-order behaviour of perturbation expansion coe cients (see also explanations in the text)

"... In PAGE 5: ... Ogievetsky found the Borel sum in the form Z 1 0 e?m2ta(t; e)dt (6) with a(t; e) = ? 1 8 2t3[etH cot(etH) ? 1 ? (etH)2=3]; (7) which coincides with the compact expression obtained by Schwinger [5]. This important result shows that a divergent perturbative expansion does not signal an inconsistency in a theory; it also shows that there are special - but realistic - cases of Borel summability in QED, although general considerations indicate Borel non-summability (see [7, 9, 10], and Table1 and a discussion in section 2 of the present paper). Gradually, the Borel summation techniques became widely adopted in quantum theory.... In PAGE 8: ... It should be considered as very fortunate that, simultaneously, analyticity plays a crucial role also as a mathematical condition reducing the ambiguity of asymptotic series. In Section 2 of the present paper, we discuss in detail the interplay between large-order behaviour of a series (as listed in Table1 ) and the analyticity properties of the function expanded; it turns out that a balance between these two concepts is needed for a unique determination of f(z) from (3), in the sense that if more analyticity of f(z) is available, one can a ord a more violent behaviour of the an, and vice versa. In Section 3 we focus on some practical aspects of the operator-product expansion, in particular on the problem of how the remainder after subtraction of the rst n terms from the function expanded depends on the distance from euclidean region, provided that an estimate on the remainder in euclidean region is known.... In PAGE 9: ... There are types of diagrams for which the amplitude itself grows like n! [21]. A survey of the large-order behaviour of expansion coe cients in some typical theories and models is given in the Table1 . As subtle cancellations among higher-order graphs may occur, the expressions in the third column of Table 1 may sometimes give an upper bound rather than the actual high-order behaviour of the coe cients.... In PAGE 9: .... There are types of diagrams for which the amplitude itself grows like n! [21]. A survey of the large-order behaviour of expansion coe cients in some typical theories and models is given in the Table 1. As subtle cancellations among higher-order graphs may occur, the expressions in the third column of Table1 may sometimes give an upper bound rather than the actual high-order behaviour of the coe cients. Table 1 is intended for rst information and should not be used for systematic anal- yses because some important conditions or restrictions could not be mentioned.... In PAGE 9: ... As subtle cancellations among higher-order graphs may occur, the expressions in the third column of Table 1 may sometimes give an upper bound rather than the actual high-order behaviour of the coe cients. Table1 is intended for rst information and should not be used for systematic anal- yses because some important conditions or restrictions could not be mentioned. A brief explanation of its use is given below.... In PAGE 12: ... To organize the diagrams in classes, the expansion parameter 1=Nf is used, where Nf is the number of fermion species; as a consequence, diagrams suppressed in the 1=Nf expansion are not suppressed for large n and, consequently, no nite order in the 1=Nf expansion provides the correct behaviour in n in the full theory. Table1 shows the large-order behaviour of the vacuum polarization, rn being the coe cient of i n+1 in the perturbative expansion and 2 = 99=(8N2 f ) . The authors discuss extension of the formalism to non-abelian gauge theories and expect a similar result.... In PAGE 12: ... The series is not Borel summable, all its terms being positive. A look at the third column of Table1 shows that most of the theories listed are characterized by an n! large-order behaviour. This does not mean that all of them can be cured by the same resummation method: large-order behaviour is just one of aspects which determine the summation procedure.... In PAGE 12: ... This does not mean that all of them can be cured by the same resummation method: large-order behaviour is just one of aspects which determine the summation procedure. To each power series with coe cients listed in the 3rd column of Table1 , there is a whole class of functions f(z) having the same asymptotic expansion. To specify the asymptotic expansion, one has to establish the angle (ray(s)) along which z approaches the origin; further, to pick out one function f(z) of this class, one has to add some additional information, according to the theory in question.... In PAGE 17: ...i.e., = 1, (n) = n!)) plays no privileged role among the variety of possible summation methods. In many practical problems, the Borel method nevertheless seems to be preferable, because most of the large-order estimates suggest an n! behaviour of the perturbative coe cients (see Table1 ). But this method simultaneously requires analyticity and the bound (22) in the z plane in an opening angle that is equal to .... In PAGE 28: ...rom subsection 2.1 are satis ed. The condition 1) would be violated if the an were to grow faster than n!. As follows from Table1 , this is not the case in typical situations. We generally do not know the nature or distribution of singularities to assess the validity of the condition 2).... In PAGE 31: ...A further generalization of Borel transformation The functions B (t) and M(t) de ned in Table 2 are generalizations of the Borel transform, which can be used in the various situations listed in Table1 to reduce non-uniqueness, provided some additional information is available. More about the properties of B (t) and M(t) can be found in [38, 39, 40, 42] and in references therein.... ..."

### Table 7.1: The generalization and size of constructed high order perceptrons.

### Table 2: Recognition accuracy results obtained using high order neural networks proposed in this work in comparison to other approaches on dataset of Experiment1. A white Gaussian noise is added with the variances shown.

### Table 1. General types of neural networks

"... In PAGE 30: ...Tables Table1 . General types of neural networks Type of network Inputs Outputs Connectionist Channel-coded Channel-coded Time delay Temporally-coded Channel-coded Timing net Temporally-coded... ..."

### Table 2. Leakage power of two designs for high order gates at three DSM technologies

"... In PAGE 7: ... 7. 8-input COMP NAND gate We have analysed the leakage power performance of an 8-input NOR gate for a number of DSM technologies, and the results are given in Table2 . Again, this shows that the COMP design is more efficient than partitioning from a leakage power per- spective.... In PAGE 7: ... Fig. 6 and Table2 indicate that designers should choose the COMP design style to obtain leakage power efficient high order NAND and NOR gates. However, this choice is achieved with an inferior speed performance [13], particularly when the ... In PAGE 8: ...Table2 that, as the number of inputs to a gate in- creases, the average leakage power decreases. This is because a higher number of in- puts causes a longer stack, and hence a lower average leakage power.... ..."

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### Table II. Time constants for the three phases of the algorithm. Time is assumed to be a polynomial function of the number of deployed nodes n, with a high-order term of the form bna.

### Table IV. SPS rank of main effects for Xprog

### Table 3 Playout Time (msec) for different values of delay

2003

"... In PAGE 15: ...Figure 6: Playout Time (msec) for different values of delay The results in Table3 and Figure 6 show the effect of introducing the buffer, for the base case of a short 3 ms network latency, and for increased latencies of 10 ms. and 30 ms.... ..."

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