Multiscale edge point

More precisely, a point (x,y) is a multiscale edge point at scale 2 if the magnitude of the gradient p jl attains a local maximum there along the gradient direction 02jl, defined by... 

Fig. 35 A2jl[x,y) > T2/ y=2i thresholded wavelet gradient maxima at scales 2 and 2 of the images in Fig. 31. The first and second columns display the thresholded multiscale edges of the EPMA and SIMS micrographs. The scale increases from top to bottom. Black pixels correspond to wavelet maxima points. The corresponding thresholds at scale 2 and 2 are X22 = 12 and X21 = 3.5 for the EPMA image, and X21 = 5 and X2S = 2 for the SIMS...

If the reader can use these properties (when it is necessary) without additional clarification, it is possible to skip reading Section 3 and go directly to more applied sections. In Section 4 we study static and dynamic properties of linear multiscale reaction networks. An important instrument for that study is a hierarchy of auxiliary discrete dynamical system. Let A, be nodes of the network ("components"), Ai Aj be edges (reactions), and fcy,- be the constants of these reactions (please pay attention to the inverse order of subscripts). A discrete dynamical system

dynamical system for a given network we find for each A,- the maximal constant of reactions Ai Af k ( i)i>kji for all j, and — i if there are no reactions Ai Aj. Attractors in this discrete dynamical system are cycles and fixed points. 

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