### Table 1 Critical exponents of the three dimensional O(4) [10] and O(2) [11] Heisenberg models, the mean eld theory, and NF = 2 QCD with staggered quarks [12]. O(4) O(2) MF Karsch-Laermann

in 1

"... In PAGE 2: ... These critical exponents satisfy the following two scaling relations: = 2 ? ( + 1) and = ( ? 1), so that only two of the four ex- ponents are independent. Some O(4) exponents are listed in Table1 . In QCD, h corresponds to the quark mass and M corresponds to the chiral condensate.... In PAGE 2: ...0125 and Nt = 4 [14,15]. The last two columns in Table1 show the nu- merical results for critical exponents by Karsch and Laermann obtained at mqa = 0:02 { 0.075 on an 83 4 lattice [12].... In PAGE 7: ... 6 shows the result for the scaling function f(t=h1= ) = h isub=h1= with the identi ca- tion M = h isub, h = 2mqa and t = ? ct. With xing the exponents to O(4) and MF val- ues given in Table1 , we adjust ct to obtain the best t. With the O(4) exponents, we nd that the scaling ansatz works remarkably well as shown in Fig.... ..."

### Tables Table-1.Ground state energy per site for standard RG, exact results and modi ed RG for xxz spin=1 2 chain

### Table 1: The one-loop Euler-Heisenberg coe cients a(1) n from (4) and their magnitudes ja(1) n j. The last two columns list the calculated two-loop Euler-Heisenberg coe cients a(2) n in (21), and their

"... In PAGE 8: ... Instead, we have made an algebraic expansion of this integral, using MATHEMATICA and MAPLE. When combined with the exact expansion (20) of the mass renormalization term we obtain an expansion of the form: L(2) = m4 (4 )3 eB m2 4 1 X n=0 a(2) n eB m2 2n (21) The expansion coe cients a(2) n are listed in Table1 , up to n = 15. Note that those coe cients are in some sense less universal than their one-loop counterparts, since they depend on the one-loop normalization condition imposed on the renormalized electron mass.... ..."

### Table 1: Static and dynamical properties of a 2 8 ( rst set of numbers) and a 2 16 (last set of numbers) Heisenberg ladder. Quantities in parenthesis represent the discrepancy with the exact or DMRG values, respectively. Observable

"... In PAGE 3: ...02%; the discrepancy for the rst excited state is even smaller. Our present calculations of the energy/site and the gap are summarized in Table1 . We compare our range-3 results with either exact (for 2 8) or DMRG [12] (for 2 16) calculations.... In PAGE 4: ...014%. All our calculations of S(~ q ; ) are summarized in Table1 and in Figure 2. There we see that the range-3 renormalization corrections to the spin operator [Eq.... ..."

### Table 2: The critical temperatures from a linear t of the high temperature data be Tc = 0:6825 instead of Tc = 0:2413, a considerable di erence. As can be seen the Tc predicted for the range of D studied in our simulations are considerably lower than the mean eld value 0.333 which shows that the approach to the mean eld limit is slow. The mean eld spin glass susceptibility for an Heisenberg system in the paramagnetic phase can be shown to be:

"... In PAGE 5: ... From the linear ts we were able to estimate by extrapolation the critical temperatures for the di erent D studied and compare with the results of the Bethe-Peierls approximation. The results are summarized in Table2 and show a very good agreement with the analytic ones of Table 1. 4 Conclusions We have presented evidence that isotropic Heisenberg spin glasses with nite connectivities present, at low temperatures, a spin glass transition for not too small connectivities.... ..."

### Table 1: A classi cation of user interface speci cation nota- tionss with respect to status and event.

"... In PAGE 2: ... Where possible, wehave included references to work that speci cally relate to the speci cation of interactivesys- tems or user interfaces. There are a couple of important points to makeinref- erence to Table1 . We can ask about the compositionality provided byany speci cation approach.... In PAGE 3: ...The last entry in Table1 refers to the new model of speci cation that we will present in the next section. This classi cation of previous approaches points quite clearly to the absence of any one approach that treats both status and event information symmetrically.... ..."

### TABLE II. The contributions to the helicity amplitudes of Eq. (15) from the Euler-Heisenberg Lagrangian used to one-loop are given in the rst three rows. In addition, Ts +??+(z) = Ts +?+?(?z) while Tt +??+(z) = Tu +?+?(?z), Tu +??+(z) = Tt +?+?(?z) and Ti +++?(z) = Ti ++?+(z) = 0 for i = s; t; u. The last row is the sum needed in Eq. (16).

### Table 1 - Extended usage-centered design notation for activity modeling

"... In PAGE 7: ... The objective is a simple notation that expresses clear distinctions where needed with minimal additions. The notation for activity modeling summarized in Table1 adds to the established notation already used in usage-centered design four new symbols for activities, actions, artifacts, and non-actor participants. It is important to keep in mind that these models are being introduced to maximize utility and efficiency in representing activity context for interaction design purposes rather than for software engineering.... In PAGE 9: ... competing activities involving shared resources in common with proximate activities 4. adjacent activities in the same setting but otherwise unrelated to proximate activities Activities are represented in an Activity Map by the block shape shown in Table1 . A line or arrow connecting one activity to another represents a relationship.... In PAGE 13: ... In this context, actions refer to goal-directed interactions among actors or players and between them and artifacts other than the system of reference. Actions are represented by a distinct symbol (the barred ellipse seen in Table1 ), a variation of the symbol already generally used to represent task cases. The Task Map, a model used to represent the interrelationships among task cases in usage- centered design, can be extended to incorporate activities and actions.... ..."

### Table VII. Model Fitting Results for the CBCL Aggression as Reported by the Teacher

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### Table 2: Normalized Synchrony Results with Standard Error.

"... In PAGE 13: ... We broke our results into three categories: those correlations computed only between neurons in the deafferented region, those computed between neurons in the normal range and those in the deafferented range, and those computed only between neurons in the normal region. The results can be seen in Figure 4 and Table2 . In all cases, synchrony was higher for the im- paired model with changes than for the other models.... ..."