By Germano Resconi

The publication is at the geometry of agent wisdom. the $64000 inspiration studied during this ebook is the sphere and its Geometric illustration. To enhance a geometrical photo of the gravity , Einstein used Tensor Calculus yet this can be very diversified from the information tools used now, as for example strategies of knowledge mining , neural networks , formal thought research ,quantum desktop and different issues. the purpose of this e-book is to rebuild the tensor calculus with the intention to provide a geometrical illustration of agent wisdom. through the use of a brand new geometry of data we will unify all of the subject matters which have been studied lately to create a bridge among the geometric illustration of the actual phenomena and the geometric illustration of the person and subjective wisdom of the agents.

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**Example text**

9) h1,jh1,i h1,jh2,i h2,jh2,i h2,jh1,i Rj,i = h3,jh1,i h2,jh3,i h1,jh3,i h3,jh2,i h3,jh3,i Fig. 9 The basic set of 9 relations between three elements. We move from one relation to another by the variation of the index j and the index i. 10. z12 z11 z22 z21 Z= z31 z32 z13 z23 z33 Fig. 11 shows the tensor y and the components in the objects space. y12 y11 y22 y21 Y= y31 y32 y13 y23 y33 Fig. 11. This is done by using the components in the space of the objects in H. 3 there are two colours “Red” and “Yellow”, The book has only one colour “Yellow” and the Pencil has two colours “Red” and “Green”.

Let τ be the intensity of trail on the edge (i,j) at time t. Each Ant at time t chooses the next point, where it will be at time t+1. When the time is t+n each ant will have completed a tour. The trail intensity is then updated according to the formula. 22) k =1 Here Δτ ik, j is the quantity which is laid per unit of length of the trail substance laid on edge (i,j) by the k-th ant between time t and t+n. The coefficient ρ must be set to a value <1 to avoid an unlimited accumulation of the substance laid by Real Ants known as the pherormone.

This is a di , j quantity not modified during the runningof the the Ant System. The normalised decision making index from point i to point j for the k-th Ant is Di , j (t ) = τ iα, j (t )ηiβ. j Here α and β are the parameters which control the relative importance of the trial versus the visibility. Where the ant decides to generate the Sp trial with the task T to change the field S. From S the task T1 is to mantain the field S in time in the way to be used by the other ants. 21 with a different assignment of the sources and task.