### Table 1. Probabilistic User Model

2006

"... In PAGE 4: ... In these studies, users marked 85% of formula cells on average when testing and debugging spreadsheets, often placing check-marks on cells, and rarely placing a23-marks on cells. Of the cells that users marked, users in our earlier studies made mistakes according to the probabilities given in Table1 , so for our study, we simulated user behavior based on these probabilities. The bold numbers in Table 1 highlight false positive (check on incorrect value) and false negative (a23 on correct value) oracle mistakes.... ..."

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### Table 14. Summary of probabilistic model lemmas Function Probability Assumption

2002

"... In PAGE 3: ...able 13. Optimum value of k determined for each benchmark programs by simulation............. 25 Table14 .... In PAGE 46: ...I.2. Cell Array- Ripple Carry Adder Let us denote signal names by bold letters and corresponding transition probabilities by italic letters. Table14 summarizes several lemmas presented in [Parker 75a], which relates Boolean operations to corresponding operations on probabilities. Their proofs can be found in [Parker... ..."

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### Table 1. Empirical Results

"... In PAGE 11: ...INSERT FIGURE 5 (A) TO (F) Empirical Results We present the results of the estimation in Table1 , together with the results of a linear regression of the selected macroeconomic variables on the devaluation probability. The linear regression might also be seen as the estimation of the model presented earlier with Eq.... In PAGE 11: ... The expected signs are, therefore, opposite to those assigned in the case of Jeanne apos;s model. Table1 shows that, for the non-linear case, the level of international reserves is the only variable that is significant and has the expected sign. This points to the importance of this variable in the determination of the fundamental of the Brazilian economy.... In PAGE 12: ...he evolution of the estimated fundamental can be seen in Fig.7. Fig.9 shows the separate contribution of each macroeconomic variable in the composition of the fundamental. One can see clearly the importance of the level of international reserves in this composition, in accordance with the empirical results presented in Table1 . Observing Fig.... ..."

### Table 1: Parameters and Measures of Probabilistic Checkpointing Cost Model

"... In PAGE 2: ... state vector is saved after an event is executed 5. memory space is su cient to complete the simula- tion Table1 contains a list of parameters used to derive the rollback probability. We assume that the inter-LVT advancement time has an exponential distribution of mean 1 , where is the LVT advancement rate de ned as follows: = 2 if lt; + otherwise where is the arrival rate, and the service rate.... ..."

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### Table 5 Probabilistic model parameters

2006

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### Table1. Parameter definitions and estimates used in the mathematical model. Empirical values for apartridge and dpartridge have not yet been determined.

"... In PAGE 3: ...ig.1. Flow diagram of the basic two-host/shared-parasite model, where W denotes the number of parasite eggs in a com- mon infective pool while, for the ith host, Pi denotes the adult parasite and Hi the host populations. See Table1 for para- meter definitions and estimates. Table1.... In PAGE 7: ... Daily rates of worm ingestion were thus estimated as 17 12 eggs bird 1 for the pheasants, and 14 70 eggs bird 1 for the partridges. MODEL PARAMETERIZATION Model parameters, and the sources from which they were estimated, are listed in Table1 . The experi- ments detailed in this study were used to quantify parasite transmission, establishment, fecundity and mortality.... In PAGE 9: ... In the two-host simulations, this equilibrium is not stable against invasion by the other host if we assume rj gt;0 ( j 6 i). From the parameter values listed in Table1 we infer that the pheasant co-exists in equilibrium with the parasite when the partridge is absent since R0pheasant 1 23. The average worm burden is 235 worms host 1 and the pheasant popu- lation is 0 94 birds ha 1.... ..."

### 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 2: Empirical probability of rejecting linearity when the process follows a vector TAR model, using 5% asymptotic critical value. The simulation is repeated three times.

1998

"... In PAGE 8: ... To study the power of the test, we employ two 2-dimensional threshold autoregressive models yt = ( (1) 1 yt?1 + (1) t if y1;t?1 lt; 0:0 (2) 1 yt?1 + (2) t if y1;t?1 0:0 (15) where (1) 1 = quot; 0:7 0:0 0:3 0:7 # ; 1 = quot; 1:0 0:2 0:2 1:0 # ; (2) 1 = quot; ?0:7 0:0 ?0:3 ?0:7 # ; 2 = quot; 1:0 ?0:3 ?0:3 1:0 # ; yt = 8 gt; gt; lt; gt; : (1) 1 yt?1 + t if y1;t?1 lt; ?3:3 (2) 1 yt?1 + t if ?3:3 y1;t?1 lt; 3:3 (3) 1 yt?1 + t if y1;t?1 3:3 (16) where (1) 1 = quot; ?0:9 0:0 0:2 ?0:9 # ; (2) 1 = quot; 1:2 0:0 0:0 0:6 # ; (3) 1 = quot; ?0:8 0:0 0:2 0:8 # ; = I: Again, the innovations are independent multivariate normal with mean zero and variance j. Table2 gives the empirical probabilities of rejecting linearity using the critical value 12.59, which is the 5% signi cance level of a chi-square distribution with 6 degrees of freedom.... ..."

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### Table 4: Empirically determined parameters for single-

2006

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### Table 1: Empirical Task Size Model

1999

"... In PAGE 8: ... Recentwork has found that a hybrid distribution, consisting of a body following a lognormal distribution and a tail that declines via a power-law, seems to t well some Web le size measurements [4, 5]. Our results use such a model for task sizes, whichwe call the empirical model;; parameters of the empirical model are shown in Table1 . The empirical le size model has a very heavy tail, as evidenced by the low value of in the Bounded Pareto distribution.... In PAGE 16: ... This is reasonable as a approximation;; a more accurate model including a xed startup cost for each task would not a ect our results signi cantly. Thus, we use as our task size distribution the empirical le size distribution as shown in Table1 (the same as that generated by Surge). 6.... ..."

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