By Professor Dr. Alexei Gvishiani, Professor Dr. Jacques Octave Dubois (auth.)
The publication offers new clustering schemes, dynamical structures and trend popularity algorithms in geophysical, geodynamical and common possibility functions. the unique mathematical procedure relies on either classical and fuzzy units versions. Geophysical and normal danger functions are quite often unique. in spite of the fact that, the bogus intelligence strategy defined within the e-book could be utilized a ways past the bounds of Earth technological know-how purposes. The ebook is meant for learn scientists, tutors, graduate scholars, scientists in geophysics and engineers
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Additional resources for Artificial Intelligence and Dynamic Systems for Geophysical Applications
Ti) on the existi ng cones K 1, " ' , Kn. Therefor e, for t = t n +! we obt ain. l(Sn+1, s). 61 , p,( x , S,t n+! is a possibility of the fact that in the moment of time t n +! the signal S will arrive from x . e. Sn+1 and s. We are interested in S = Sn+1. 62 ) op en s new opp ortuniti es in the pr oblem of SOD(sn+d ca lculat ions. These opportunities come from th e theory of functions: st ep fun ction s, ty pe of approxirna t ion to moment of time t n + 1 , etc . 34 Dynamic Classification Approach Coneluding , we can formu late that the basis of wh at has been said in this chapter is aetually the following chain of im plications.
The above exam ples show the capa bility of the introd uced intensity to "catc h" clustering and to quantitatively int erpret t he integral concentration of subset A aroun d t he poi nt .. x" . T he higher t he intensity PA(x) at t he point x the more eviden ce we have t hat .. x" may be "a center" for t he subs et A (even if it is not one in a geometrical sense, espe cially if x 1. A ) . T he const ru ct ion PA (x) depends both on .. x" an d .. A" . T he followin g fact is fundament al. T h e ore m 1.
Representi ng t he signal sE S as a veetor of its components seismF(s)seismogram recorded at the station F , mF(s)-magnitude, ß F(s )-epi cent ral distance, hF(s)-depth , tF( s)-time in the sour ce, we obtain t he appearence of I as a funetion of a given database. 47 ) We assume that the region X under considerat ion is divided int o sub regions tc X= UX i, Xi nXj =0. 4 9) i= l If we have a signa l s in a certain moment t n +1 the problem is to affiliate it to a subregion X j, j = 1, . , J( . 1) does it using metric clas sification produced by Levenstein distance.
Artificial Intelligence and Dynamic Systems for Geophysical Applications by Professor Dr. Alexei Gvishiani, Professor Dr. Jacques Octave Dubois (auth.)