Optimal Estimation ofParameters ofTransient Mixture Processes UsingDynamicLogicApproach

Inthis workwegeneralize dynamic logic ap- proach forthecaseoftimetransient processes withtime- dependent energy function. Earlier studies haslaid downthe firm foundations ofDLtopattern recognition inthepresence ofveryhighnoiseandclutter We derive DL equations withtime-dependent energy function andapplyittothe detection oftransient processes in2-dimensional images. The developed methods hasbeentested onsimulated data. The results showgoodaccuracy oftheestimation oftransient parameters, including thegradient ofspatial propagation, andrateoftheenergyincrease/decrease inthecaseof processes withexplosive/implosive processes, respectively. I.INTRODUCTION Dynamiclogic isa novelmathematical methodwhich follows theflexibility ofthelearning process inthehuman mind.Itovercomes thecurrent limitations ofartificially intelligent systems caused bythecombinatorial complexity (CC)inherent inthemanipulation oflarge datasets. CC refers tomultiple combinations ofelements inacomplex system. CCisrelated tothetypeoflogic underlying various algorithms. Itwasrelated tothefundamental inconsistency oflogic discovered byGdel(Perlovsky, 2001). Multivalued logic andfuzzylogic wereproposed toovercome these limitations (Cherkassy, Mullier, 1998), yetcomplexity of multi-valued logic isthesameasformal logic. Fuzzylogic iseither toofuzzyandnotprecise enough, ortoocrisp andsimilar toformal logic. Neither approach overcame the difficulty. Butthehumanmindisable tosortitallout, and solve these complex problems. Whatkindoflogic doesit use? Thenewtypeoflogic, Dynamiclogic, associates signals withmodelsaccording tosimilarities amongthem.Asan example, consider amixture process withK components. Eachcomponent ischaracterized bya conditional partial similarity using theconditional probability distribution. In theprocess ofassociation-recognition, models areadapted to fit thedataandsimilarity measures areadapted sothat their fuzziness ismatched tothemodeluncertainty. Theinitial uncertainty oftheknowledge ishighandsoisthefuzziness ofthesimilarity measure. Depending onthetarget problem andtheselected adaptation rule, various modelscanbe specified. During learning, themodels become moreaccurate andthesimilarity morecrisp, thevalue ofthesimilarity measure increases. Itisproposed thatbrains perform fast androbust recognition byadapting theaccuracy oftheir approximation basedontheavailable information onthe problem, asitisdescribed bydynamic logic (Perlovsky, 2001).