Download Geometry of Knowledge for Intelligent Systems by Germano Resconi PDF

By Germano Resconi

The publication is at the geometry of agent wisdom. the real thought studied during this publication is the sphere and its Geometric illustration. To enhance a geometrical photograph of the gravity , Einstein used Tensor Calculus yet this can be very various from the information tools used now, as for example suggestions of information mining , neural networks , formal suggestion research ,quantum computing device and different subject matters. the purpose of this e-book is to rebuild the tensor calculus with a purpose to supply a geometrical illustration of agent wisdom. by utilizing a brand new geometry of data we will be able to unify the entire subject matters which have been studied in recent times to create a bridge among the geometric illustration of the actual phenomena and the geometric illustration of the person and subjective wisdom of the brokers.

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13). w = Hz = j j ⎡ h11 ⎢h ⎢ 21 ⎢ ... ⎣⎢ hq1 h12 h22 ... hq 2 ... h ⎤ ⎡ z ⎤ 1p j ,1 ⎥ ... h ⎥ ⎢ z 2 p ⎥ ⎢ j ,2 ⎥ ... ⎥ ⎢ ... ⎥ ... 53) ⎦ or w j ⎡ h1 p ⎤ ⎡ h11 ⎤ ⎡ h12 ⎤ ⎢h ⎥ ⎢ h21 ⎥ ⎢ h22 ⎥ =z ⎢ +z + ..... + z j , p ⎢ 2 p ⎥ = j ,1 ... ⎥ j ,2 ⎢ ... ⎥ ⎢ ... ⎥ ⎢h ⎥ ⎢h ⎥ ⎢⎣ hqp ⎥⎦ ⎣⎢ q1 ⎦⎥ ⎣⎢ q 2 ⎦⎥ z H +z H + .... 45), we have y h,k ⎡ y11 ⎢y = ⎢ 21 ⎢ ... ⎢⎣ yq1 ⎡ ∑p z h ⎤ h12 ... j k . j ⎥ p ⎥ h22 ... j k . 48) ... ... ⎥ ⎢ ... ⎥ i j ⎢⎣ hq1 hq 2 ... j k . j ⎥⎦ y 12 y 22 ... y ⎤ ⎡h 1p 11 ...

We term them Agents of the Second Order. 3. 4. In a new image we show both the task and the sources by the symbols Sk and Tk. 3 where at any node of the graph the tasks and the sources with the same number are the same entity. Source 1 Source Task 4 Task 2 Action Source Task Source Source Task 3 Task Fig. 2 Network showing the Action between Different sources and the task. For example from the source 1, we can obtain two different actions tasks 2 and the task 4 S1 1 S1 Action T2 2 T1 S2 T4 4 S3 S4 T3 3 T3 Fig.

2 Field, Neural Network Geometry and Coherence 43 For dS = G −1dS C , using the language of the tensor calculus we have dS = G −1dS C In the Einstein notation we have dS i = G −1dS j = G i , j dS j Where dS i = dS are the controvariant basis (ρ,θ) and dS j = dS C are the covariant basis We will show geometric examples of the controvariant and covariant basis. Given the transformation x1 = x'1 + x'2cos(α) x2 = x'2 sin(α) Geometrically, it can be shown as follows x2 P(x1,x2) α x’2 x’1 Fig. 2 Field, Neural Network Geometry and Coherence 45 Geometrically, the basis and the conjugate basis are represented as follows: dS2C x2 P dS2 ds P’ dS1C dS1 α x1 Fig.

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