### Table 8 The Global Continuous Time Structural Semantics

"... In PAGE 6: ....e. initiates an update, via a so called Poisson process (see e.g. [14, Sect 2.4]). The global semantics for pKLAIM is de ned in Table8 . The transition relation _ ? tij + 3 between two network con gurations Ni and Nj is labelled by rates tij which are obtained as a product between the ring rate of the node which initiates the update and the normalised probabilities of the local tran- sitions occurring in the nodes involved in the update.... ..."

### Table 4: Parameters of the Continuous-Time Model

"... In PAGE 33: ...for assembling the various parts are Gamma random variables. Table4 contains the parameters of... ..."

### Table 3: Parameters of the Continuous-Time Model

2003

### Table 1: Two pairs of a discrete time autoregression matrix A and corresponding continuous time drift matrix A

"... In PAGE 13: ...Table 1: Two pairs of a discrete time autoregression matrix A and corresponding continuous time drift matrix A represents in fact a smaller auto-effect than 0:50 over t = 1:25. Not less paradoxical differences between the discrete time models studied in behavioral sci- ence on the one hand and the underlying continuous time models on the other hand can be ob- served in Table1 . On the basis of simple simulated autoregression matrices A (both typical in the sense of having higher diagonal than nondiagonal elements), it is shown that the conclusions drawn with respect to the cross-lagged coef cients in A may differ quite fundamentally from those drawn on the basis of the corresponding cross-effects in drift matrices A.... In PAGE 14: ... Therefore, statements about direction and strength of a causal effect in discrete time are meaningless without indicating the exact time interval t the statement refers to. This is the clear message of Figures 2 and 3, where for sev- eral of the cross-lagged coef cients in Table1 not only the value at t = 1 but the development over the whole period from t = 0 until t = 2 years according to exponential form A = eA t is given. Figures 2 and 3 give the continuous time impulse-response, that is the effects of an iso- lated unit-impulse in a single independent variable over continuously increasing time intervals on the dependent variable.... In PAGE 14: ... Figures 2 and 3 give the continuous time impulse-response, that is the effects of an iso- lated unit-impulse in a single independent variable over continuously increasing time intervals on the dependent variable. The implication of Figure 2 is that the conclusion about the relative strength of the recipro- cal causal effects between x3 and x1 (pair I of Table1 ) on the basis of the discrete time model depends on the time interval chosen in the model. Researchers choosing the discrete time in- terval t between 0 and 0:66 year will come to the conclusion that x1 has a larger effect on x3 (maximum difference reached at t = 0:27), while researchers choosing t gt; 0:66 come to the opposite conclusion (maximum difference reached at t = 2:74).... In PAGE 14: ...200 0.250 Coefficient Value Figure 2: Cross-lagged coef cients a ;31 (solid line) and a ;13 (dotted line) in autoregression matrix A of pair I in Table1 for corresponding continuous time coef cients a31 = 0:50 and a13 = 0:43 in A as functions of the time interval t 2 [0; 2]... In PAGE 15: ...150 0.200 Coefficient Value Figure 3: Cross-lagged coef cient a ;21 in autoregression matrix A of pair II in Table1 for corresponding continuous time coef cient a21 = 0:11 in A as a function of the time interval t 2 [0; 2] cients, by de nition having value 0 over t = 0, will rst once or repeatedly go up or down but eventually go to 0 for this and other asymptotically stable models (all eigenvalues of A strictly negative). Such stable models also imply a maximum value for the cross-lagged effect to be reached after some nite time interval t.... In PAGE 15: ... For a ;31 the maximum values of 0:208 is reached at t = 1:42, for a ;13 it is 0:230, reached at t = 1:70. Figure 3 describes the discrete time effect from x1 on x2 (pair II of Table1 ) in models with different t. Its clear implication is that even the sign of the cross-lagged coef cient need not be the same as the one of the true underlying continuous time effect.... ..."

### Table 4: Numerical results of the Continuous-Time formulation with GAMS 2.50/Cplex 7.0.0 Size Continuous-time model

2002

"... In PAGE 12: ...P7.CP.CL for 10 instances. The results are summarized in Table4 . Final demands vary as combinations of 0s and 20s.... In PAGE 12: ...08 seconds. The numerical results in Table4 are very encouraging. We can conclude that by applying the new continuous-time model, with a small number of events, it is not difficult to get a feasible solution; the CPU time for getting an optimal solution is acceptable.... ..."

### Table 7. Estimates of Unobserved Components Models: Discrete Time and Continuous Time

"... In PAGE 28: ... The results are contained in Tables 7 and 8. Table7 contains the results of estimating the discrete time and continuous time trend- plus-cycle models. The discrete time estimates are taken directly from Harvey (1989, p.... In PAGE 30: ...2843 Figures in parentheses are standard errors. misspeci ed in some way, and Harvey (1989) does indeed nd that the discrete time model in Table7 is inferior to a cyclical trend model in which t also depends on t 1 and yt = t+ t. Further investigations with continuous time cyclical trend models may be fruitful, but are beyond the scope of this simple illustration.... ..."

### Table 1: BNF syntax of the continuous-time part of .

"... In PAGE 4: ... For this purpose, the number of active equations must be equal to the number of continuous variables. A summary of the continuous-time language constructs in Backus-Naur Form (BNF) is given in Table1 , where r is an expression of type real. Table 1: BNF syntax of the continuous-time part of .... ..."

### Table 3: Rate Monotonic applied on a Continuous-time controller

2007

### Table I. Model Parameters. The availability (steady-state probability of being in the available state) piA can be derived using standard CTMC (continuous-time Markov chain) techniques [10]:

1993

Cited by 8

### Table 7. Continuous Time Models Estimated from Interest Rate Data: Optimized Value of the Criterion for the Semiparametric ARCH Score.

1995

"... In PAGE 27: ... To compute m( ; ) : = 1 N N Xt=0 @ @ log[f(^ ytj^ yt?L; : : : ; ^ yt?1; )] we use an explicit order 2 weak as described in Section 4 above. For this work, time t is scaled so the interval [t; t + 1] is one week and n0 = 10; which implies the simulation step size is = 0:10: ||||||||||||{ Table7 about here ||||||||||||{ Table 7 summarizes the main results. As can seen be seen from the table, YF-Diagonal and YF-Premium models fare poorly as does the YF-General.... In PAGE 27: ... To compute m( ; ) : = 1 N N Xt=0 @ @ log[f(^ ytj^ yt?L; : : : ; ^ yt?1; )] we use an explicit order 2 weak as described in Section 4 above. For this work, time t is scaled so the interval [t; t + 1] is one week and n0 = 10; which implies the simulation step size is = 0:10: ||||||||||||{Table 7 about here ||||||||||||{ Table7 summarizes the main results. As can seen be seen from the table, YF-Diagonal and YF-Premium models fare poorly as does the YF-General.... In PAGE 28: ...50 for federal funds, but not Trea- sury Bills. The middle part of Table7 reports the concentrated objective function for YF- Power speci cations with the exponents restricted to a common value, 31 = 32 = 33 = ; = 0:60; 0:70; 0:80; 0:90: These speci cations come closer to tting the Semiparametric ARCH score, with the best t at = 0:70; though the model is still rejected at conventional signi cance levels. If the common-value restriction on the exponents is maintained but treated as a free parameter, then the objective function is quite at in the region 0.... In PAGE 28: ...reated as a free parameter, then the objective function is quite at in the region 0.70{0.75, with the point estimate being 0.706 and the objective value hardly improves (YF-Power- Equal in Table7 ). Treating 1; 2; and 3 as three free parameters (YF-Power-Free), provides little improvement, suggesting that the separate exponents are not sharply estimated.... ..."