We are studying the polymerization of mono-mono and dimethoxymer mixtures. In Figure 4, the average weight size, the gel fraction and the network structures are represented for three polymerization systems with different proportions of mono- and divinylmono V_2 V_1 meren: (a) linear chains (V_1: “V_2-1”: 0, b) “Little Connected Network” (V_1″: V_2-0.97, 0.0.03, c) V_2 V_1 dense network The random color diagram forecast is compared to the SSA data and the diagram randomly uncollected. In Figure 1, we illustrate the concept with a simple example of linear polymer chains: the original structure, which we want to restore from the random diagram, consists of three polymer chains of length 6. We take degree distributions of different random diagram models: (1) oriented, (2) untrained and colorful, (3) directed and colored. If the degree distribution contains only information on the number of half-edges (degrees) and their orientation (left), chains of different lengths will be obtained. In the second case, the degree distribution contains information on degrees and color, but the edges are considered unated (middle), in turn different chain lengths are obtained. Only if the degree distribution contains information about both, the orientation and color of the edge, the correct structure is restored (right). A striking feature of history-dependent processes is that the time when a large cluster, i.e. the frost point13, differs from the percolation threshold value found when randomly deleting links in the final network. This contrasts sharply with network formation by step growth polymerization, in which the polymerization process corresponds to random percolation on the final network topology21,23,24. However, in some cases, the non-coloured random diagram provides a surprisingly good estimate of phase passage and frost fraction13, suggesting that the polymerization of chain growth may not, under certain conditions, lead to a significant dependence on history. Beyond polymers, a strong dependence on history is characteristic of processes on networks that can be reformulated as a recticulated dynamic.33 Some network characteristics in this model require only the first and second mixed moments of degree distribution (u (`varvec`k`)` and we simply write `(`mathbb`[X]) to designate the expectation of a random X variable in relation to this distribution. We define the vector “” and “matrix” (“varvec”) as “Varvec” obtained during the complete conversion, because it contains information about the entire polymerization process.

If the half-edges of types i and J are at “M_” i, j “, half-edges of types i and I are rarely found simultaneously on a monomer. Match the system “” to a system with randomized colors, a system with a dependence on `erased` history. Figure 5 shows the structures of ” (`varvec`M`) and “tilde“varvec`M`) for: (a) linear living polymerization with initial radical concentration, (p_, `ini`-0.0.0 (b) Dense living polymerization with initial radical concentration (text p_ “ini” 0.01), c) dense living polymerization with a high initial concentration (p_ text, ini-0,1). To quantify the importance of a system`s historical dependence, we compare its matrix to the “matrix” (with randomized colors that represent a system of dependence “erased” from history. The randomized system responds to the same distribution in relation to edge alignment, but with a random distribution of edge colors. The derivative of the Varvec-M “tilde” zone is given in the “Randomized Matrix” section.