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for some positive real number . Remarks 1. The bound (4.2) is sometimes called the Davies bound (Davies, 1977). 2. Proposition 4.1(b) was originally proved by Piterbarg in 1981 [see also his book (1996a)] for centered stationary Gaussian processes. In this case, under the hypotheses, 8 < . The joint distribution of X(s), X (s), X (s), X(t), X (t), X (t) does not degenerate for distinct s, t [0, T ]. (t) < 0 for 0 < t T . Aza s et al. (2001) have been able to describe more precisely the comple mentary term in the asymptotic expansion given in part (b). The result is that as u + , P(MT > u) = 1 (u) + 2 T (u) 2

18: Introducing CORBA 8. The client also creates a name component to query the naming context about that particular object reference. 9. The naming context then resolves the name component and returns the object. As the type of the returned object is generic, the object is converted to a specific object reference with the help of its Helper class. 10. Now the client can invoke the methods on that particular object and perform all the operations. Note that in Java, the naming service used is known as the COS Naming Service. All necessary interfaces required to be able to use this naming service are available in a package called org.omg.CosNaming. CORBA applications in Java need to import this package in order to use the naming service. The following example, which creates an object reference name binding using Naming Services, may help you understand Naming Services better. First, assume the existence of a CORBA application called Welcome, which welcomes a new user with the message "Welcome to CORBA." Consider the steps the server performs to add the object reference binding in the naming service: 1. Implement the interface. Assume that the implementation already exists:

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signal and the event gains more and more value In this way our brain learns to attach a value to all the events and objects and places around us Many will remain neutral, but some will acquire high value and some will acquire low value We experience this map of values within our brain when we return from a long trip abroad we feel a rising emotional response as the streets we are moving through become more and more familiar If we approached the things with high value and avoided the things with low value, we would obtain rewards and avoid punishments But this associative learning mechanism tells us only which things are valuable It doesn t tell us how to get these valuable things.

Thorndike s cat, when rst put in the puzzle box, knows that the sh is valuable, but it doesn t know what to do to get the sh A mechanism for learning exactly what to do to get rewards (or avoid punishments) also exists It s called the temporal difference (TD) algorithm This procedure allows a machine to discover the best sequence of actions to perform in order to get something of value This procedure is also known as the Actor Critic model One part of the program, the Actor, chooses the next action to perform The other part of the program, the Critic, indicates how good this action was This critic tells the actor about any errors in the prediction A good action is one in which the situation we are in now has a value that is higher than the situation we were in before performing the action.

The critic is commenting on the change in value from one time to the next (hence temporal difference ) Value is higher after an action that gets you nearer to the reward This is a way of discovering the pathways that lead to reward Value is highest in the place right next to reward As we move away from the reward, the value gets smaller By moving toward the places with higher value, we will eventually reach the reward Of course these values are not actually marked on the real world They are marked only on the internal model of the world we have in our brains, the model that has been built up by learning and experience.

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