Fixed causality

There is a constraint between the causality of two or more ports of a node. This is the case for the elementary two port nodes (M)TF and (M)GY the (M)TF always has only one stroke at the node, while the (M)GY has either both strokes at the node or both open ends. The junctions also have such a causal constraint an -port 0-junction has one stroke at the node and n - 1 open ends, while an -port 1-junction has one open end at the node and n - 1 causal strokes. The same holds for the XO and the XI in principle, but in many cases they will be given a fixed causality, given the discontinuous and consequently non-invertible nature of their constitutive relations. 

Choose an unassigned port with a. fixed causality of type la, assign it, and check that the causality of the port at the other side of the bond, which is assigned as a result... 

Continue with (1) until all ports with fixed causality of type la are assigned. 

The warm bed of dynamic models in the form of a set of differential equations or a block diagram in an a priori fixed causality has been replaced by the cold floor of port-based modeling concepts with causal preferences and constraints. Hopefully the new revelation caused by this disturbing experience is the insight that the... 

This last representation is completely equivalent to the analytidty of t(ai) in Im 0 and the statement that a,t(a>) go to zero as u - oo. The analyticity property in turn is a direct consequence of the retarded or causal character of T(t), namely that it vanishes for t > 0. If t(ai) is analytic in the upper half plane, but instead of having the requisite asymptotic properties to allow the neglect of the contribution from the semicircle at infinity, behaves like a constant as o> — oo, we can apply Cauchy s integral to t(a,)j(o, — w0) where a>0 is some fixed point in the upper half plane within the contour. The result in this case, valid if t( - oo is... 

Only someone who denied the thesis of physicalism - that the physical facts fix all the biological facts - could deny the causal relevance of this vast motley of disparate macromolecular processes to the existence of (PS) and the truth of (G). 

Note that these boundary conditions break causality. The function y has the boundary at the final time t whereas m has the boundary at the initial time 0. Causality is broken because by imposing a fixed value of the work w along the paths we are constraining the time evolution of the system. 

In the previous, fixed-input determination of the IT bond indices this discontinuity in the transition from the decoupled to the coupled descriptions of the molecular fragments prevents an interpretation of the former as the limiting case of the latter, when all external communications of the subsystem in question become infinitely small. In other words, the fixed-and flexible-input approaches generate the mutually exclusive sets of bond indices, which cannot describe this transition in a continuous ("causal") fashion. As we have demonstrated in the decoupled approach of the preceding section, only the overall input normalization equal to the number of the decoupled orbital subsystems gives rise to the full agreement with the accepted chemical intuition. 

Therefore, in using the classification, the following fixed order is proposed (as indicated from top to bottom in figure 5,1.) to arrive at the best-fitting error category for causal factors of accidents and near misses first K-B errors, then R-B and finally S-B errors. In this way the above mentioned... 

It is interesting to compare Eq. (4.23) with (4.25). The difference in the numerical factors corresponds to different mathematical assumptions and approximations. While it is rather difficult to estimate the errors involved, the former case is more convenient in treating the integral equation. In addition it takes into account the chain connectivity and the causality character of the starting hydrodynamical equation somewhat better than the latter. On the other hand, the latter formalism takes into account the fact that the center of gravity is fixed in space. Thus, a rigorous theory may give a value in between the two factors. 

The alternative Bayesian interpretation of P(SC C)x 1 ) retains the idea of a single, entire universe in which values of initial conditions (S( -C)x) should be regarded as fixed aspects of a unique N, and no maximal invariant proper subset N C N exists. Although theories of initial conditions are by assumption not causal, they are expected to commit to specific forms the same way they currently specify the algorithmic structure of natural laws. A non-sharp P(SC C)x 1 ) is then associated by Bayesians with a range of... 

If we carry out such a calculation for a large number of trajectories at the same fixed energy , we obtain a unique map of the global dynamics at that energy. The map is unique because each point on it uniquely specifies a single trajectory in phase space, and trajectories in phase space do not intersea at any given instant in time. If they did intersect, they would have to arise from identical initial conditions, and then claissical mechanics would no longer be a causal theory ... 

The answer to this question would seem to be no . If we look at what is going on here and try to identify the causal mechanism at work, it is clear that the property in virtue of which the balls sort is size. If we fixed the size of a particular ball, we could vary the particular lower-level microstructure all we wanted, and as long as the size remained the same, the ball would sort to the appropriate level. We could make the ball out of wood or metal or glass, instead of plastic, and it would still sort according to its size. The particular lower-level configuration of the ball is, in a certain sense, epiphenomenal with respect to the causal mechanism at work here. But if we held the lower level as fixed as possible and varied the size of the ball, the effect would be different. So clearly the causal mechanism at work, when any ball sorts, is at the higher level of size and not at the lower-level microstructure. 

But how can this be Once we fixed the lower-level microstructure of the ball and placed it in the sorter, all the causal work for the ball to sort had already been done. The property L is sufficient to bring about the effect of the ball sorting. How can the distinct and irreducible property of size also be causal with respect to the ball sorting What additional causal work is left for the ball s size to do How can the ball s size be causally efficacious with respect to the sorting, when all the causal work has already been done at the lower level When we try to apply the exclusion principle to a case outside the case of the mental, it seems almost silly. The picture of causation created by the exclusion principle seems misguided when we apply it to a mundane case of causation... 

Ron McClamrock (1995a, ch. 3) has argued that we can use the ideas of multiple realizability and context dependence to pick out preferred levels of causation and explanation. When we have token identity at different levels, we can use the ideas of multiple realizability and context dependence to hold properties at one level fixed while varying properties at other levels, in order to try to see at which level the causal mechanism occurs. In the ball-sorter case, we see that the causation occurs in virtue of size and that the macro-level of size is the right level of explanation. 

Twenty years later, another Space Shuttle was lost. While the proximate cause for the Columbia accident (foam hitting the wing of the orbiter) was very different than that for Challenger, many of the systemic causal factors were similar and reflected either inadequate fixes of these factors after the Challenger accident or their reemergence in the years between these losses [117]. 

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