Muhammed Moran posted an update 2 years, 11 months ago
Now we can define the mutual contagion I fi ; gj = P(fi |gj ) 1 1 log P f – log P f |g = log P(fi ) , where P(f i ) is an “a ( i) ( i j) priori” estimate. Thus: I fi ; gj = I(gj ; fi ); I fi ; gj = log P fi gj + I fi ; I(fi ; gj ) I fi ; P fi ; gj = P fi P gj I fi ; gj = 0. = Now since I F; gj = i P fi gj I fi ; gj P(fi |gj ) , and I fi ; G = i P fi gj i P fi gj log P(fi ) P(g |f ) log P jg i , we will have I (F; G) = i P fi I fi ; G = ( j) P(fi |gj ) i j P fi ; gj log P(fi )P(gj ) = I (G; F) . Then, I (F; G) 0, I (F; G) = 0 P (F, G) = P (F) P (G) , and I is symmetric in F and G (I (F; G) = I (G; F)). Furthermore, S (F) =n i=1 P 1 n i=1 Pn -li = i = 1 pi log (K) – log n n log (K) + i = 1 pi li log () log() i = 1 pi li . Thus, S (B) Llog (), where L = n= 1 pi li . So the MedChemExpress Salinomycin entropy provide a lowerifi logn i=gj log1 P(gj ), S (F | G) =n i=1 m j=1 P1 , S (G) P(fi ) m j = 1 P fi g j 1 P(fi ,gj )=log P f |g , S(F, G) = , fi , gj log ( i j) S (F, G) = S (F) + S (G | F) = S (G) + S (F | G), I (F, G) = I (F)+I (G)-I (F, G) = I (F)-I (F | G) = I (G)-I (G | F) 0, thus, we can write the mutual contagion I (F, G) as a difference between the marginal entropy and the conditional entropy. is fi =have only one code with length l1 , l2 , . . . , ln iif K 1 where li = e(ai ) , i = 1, 2, . . . , n; and ai A. Let consider, now kn =n 1 i = 1 li ngeneralsolution,= k,Nk nl i = 1 k ,withl = Max l1 , l2 , . . . , ln . Of course Nk thus k nl k = n k = nl – n + 1 nl. Thus, K 1. Now define,-li n for 0 < Gi 1, and i = 1 Gi = 1, Gi = K . Applying the Gibbs inequality, given pi the probability to observe hi , we 1 will obtain: n= 1 pi log Gii 0 or n= 1 pi log pi n= 1 i i i pKn, where r represents the standard exp – – r r multiplayer of Lagrange. We can define H (1 , 2 , . . . , K ) = (r) . i exp – r r si Thus, e = H or = ln (H). The mathematical analytics allows researcher to study the dynamics in a formal and elegant way, but unfortunately a model calibration to real behavior is very complex, being more adapted to a theoretical approach to computational communication than to real behavioral systems. However, the above equationspi log1 Gi.Frontiers in Psychology | http://www.frontiersin.orgNovember 2015 | Volume 6 | ArticleCipressoModeling behavior dynamicsrepresent the fundamental basis for the statistical mechanics approach, which we analyze below.MODELING BEHAVIOR DYNAMICS AMONG MANY INDIVIDUALS Modeling Behavior Dynamics through "Difference Equation"There are many ways to model behavior dynamics in complex systems (Bar-Yam, 1997). However, it is important to keep in mind that a model is only a representation of the real world; t.