VALORES Y METAS EN LOS CONCEPTOS PSICOANALÍTICOS DE FREUD

In this section, I analyze the dynamics of growth of in silico fungus colony in various statistical modes: ‘Actual Data’, ‘Gauss’, and ‘Kernel’. I analyze the first five experiments from every mode by counting the number of branches that crosses the designated “geographical zones” at certain times. “Geographical zones” are the box-shaped boundaries numbered from 1 (the most interior part of the colony) to 12 (the most exterior part of the colony). This approach allows to measure and compare the pace of the colonies growth. I start with the analysis of the outcomes of the individual experiments, then compare experiments within one statistical mode. At the end of this section, I compare all three statistical modes (‘Actual Data’, ‘Gauss’, and ‘Kernel’). There are a few major observations made as a result of running this exercise. Firstly, the ‘Kernel’ algorithm produces the largest number of branches, while the ‘Gauss’ algorithm generates the fewest number of daughters and further generation hyphae. Secondly, in each statistical mode the number of generated hyphae increases with time. Moreover, ‘Gauss’ mode gives step-wise curves (functions). In practice, it means that, on average, one box is crossed by one hypha at certain time step. Interestingly, ‘Actual Data’ and ‘Kernel’ modes give smooth curves. The presence of smooth curves can be explained by several branches crossing individual boxes at the same time contributing to the very specific overall pattern of growth that resembles a wave propagation. In silico fungus that follows ‘Gauss’ algorithm branches in a more discrete and asynchronous way compared to the ‘Actual Data’ and ‘Kernel’ fungi. Furthermore, ‘Kernel’ algorithm gives more predictable patterns, while the ‘Actual Data’ outcomes, although similar, are subjected to more variability. It might be easier for ‘Kernel’ fungus to generate branches that satisfy program conditions as the simulated values are withdrawn from the area under the curve (continuous distribution) while the ‘Actual Data’ fungus has restricted number of simulation values to choose. Once the simulated value does not fit the kinetic equations, the algorithm looks for another value within a specified set of numbers based on the measurements of Neurospora crassa. Therefore, the ‘Actual Data’ algorithm although similar, in general, is less efficient than the ‘Kernel’ algorithm. For every experiment, I plot the number of branches crossing particular box at a certain time. The boxes are colour-coded, the data points between consecutive time steps joined and displayed as lines in the graphs. On the right side of every graphic panel, I provide the final frame from the analyzed experiments with the indicated numbers of the boxes. Numerical data used to produced the plots in this section is available here: Fungi Dynamics - Numerical Data.

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Figure 98 Growth Dynamics of In Silico Fungus – Experiment II, ‘Actual Data’ algorithm The picture on the right comes from the experiment series (indicated as seed number two in the series) presented in the previous sections (Figure 75) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern resembles a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae increases significantly at 100 time step (~50 minutes), what is in a good agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew), that is available under the following link:Real world example (Movie no 6). One can see that the curves indicated with pink, red, blue, and black colours (1-4, in the plot on the left side of the panel) are crossed by the hyphae most frequently. Interestingly, the plot on the left side reveals existence of 3 “geographical” zones that are crossed by the similar number of hyphae at similar times: boxes 1 to 4 are crossed the earliest, by the highest number of hyphae, then boxes 5, 6, and 7 are crossed at 80-100 Time Steps by the moderate number of hyphae; and finally, the boxes no 8-12 are crossed the latest, at ~120 Time Step by the lowest number of hyphae. This level of discreteness, in terms of existence certain values bands for certain boxes, is not observed/recorded for in silico fungus in, similar, ‘Kernel’ mode.

Figure 97Growth Dynamics of In Silico Fungus – Experiment I, ‘Actual Data’ algorithm. The picture on the right comes from the experiment series (indicated as seed number one in the series) presented in the previous sections (Figure 75) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does not resemble a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae increases significantly at 110 time step (~55 minutes), what is in a good agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6). One can see that the curves indicated with pink, red, blue, and black colours (1-4, on the left side of the panel) are the ones crossed by the hyphae most frequently.

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Figure 100 Growth Dynamics of In Silico Fungus – Experiment IV, ‘Actual Data’ algorithm. The picture on the right comes from the experiment series (indicated as seed number four in the series) presented in the previous sections (Figure 75) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern resembles to certain degree a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae increases significantly at 100 time step (~50 minutes), what is in a good agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6). One can see that the curves indicated with pink, red, blue, and black colours (1-4, in the plot on the left side panel) are the ones crossed by the hyphae most frequently.

Figure 99Growth Dynamics of In Silico Fungus – Experiment III, ‘Actual Data’ algorithm. The picture on the right comes from the experiment series (indicated as seed number three in the series) presented in the previous sections (Figure 75) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern resembles a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae start increasing significantly at 60 time step (~30 minute) what is in a perfect agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6). One can see that the curves indicated with pink, red, blue, and black colours (1-4, in the plot on the left side panel) are the ones crossed by the hyphae most frequently. In this case the decline in the number of generated branches towards the boxes with the highest ID numbers (10, 11, and 12) is more equally distributed, compared to the simulations shown in the previous figures (Figures 101,102.)

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A comparison of Examples I-V for the ‘Actual Data’ mode is given in Figure 102 on the next page. The numbers of branches generated from the seeds (Examples) 1 and 5 are much lower compared to the seeds (Examples) 2, 3, and 4. Visual outcomes are similar to the examples 1&5, and 2&4. Simulation number 3 gives an outcome that is in between these two typical geometrical patterns (first one (seeds 1&5). The 'parent' hypha branching at the later stages and sending a fewer number of branches, and the second one (seeds 2&4) with the parent hypha branching relatively early and sending a higher number of branches). Example number 2 is an interesting case as it shows the parameter values forming certain numerical bands regarding the number of hyphae generated at certain times. Band 1 is for the boxes 1 to 4, band 2 for the boxes 5, 6, and 7; and band 3 for the boxes 8 to 12. The 2 of 5 simulation outcomes resemble a typical shape of Neurospora crassa colony grown in a laboratory conditions. This similarity can be explained by the permutation-wise way the ‘Actual Data’ algorithm works. The simulation values are withdrawn at random from the discrete set of numbers with replacement. In practice, it creates sets of numerical strings – numbers simulated in different order, so, in other words, various permutations of the same set of numbers. Therefore, if in silico fungus is “unlucky”, it cannot grow properly as the generated numerical string does not satisfy the computer program conditions.

Figure 101 Growth Dynamics of In Silico Fungus – Experiment V, ‘Actual Data’ algorithm. The picture on the right comes from the experiment series (indicated as seed number five in the series) presented in the previous sections (Figure 75) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does not resemble a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae increases significantly at 90 time step (~45 minutes), what is in a good agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6). One can see that the curves indicated with pink and blue (3&4, in the plot on the left side panel) are the ones crossed by the hyphae most frequently. In this case the overall numerical and geometrical pattern is similar to the one in the Example no 1 (Figure 101). Occurrence of two types of geometrical patterns (one that resembles to certain degree Neurospora crassa natural colonies, and the other one that does not) is typical

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On the next pages, I give a detailed analysis of in silico fungus grown in a ‘Gauss’ mode of the program. The results for this mode are significantly different from those for the ‘Actual Data’ and ‘Kernel’ modes. Firstly, characteristic step-wise curves in the plots for this mode are a reflection of in silico fungus sending single branches at certain times rather, than generating several branches simultaneously and propagating in a “heatwave” fashion on the surface, as it happens for the fungi following ‘Actual Data’ and ‘Kernel’ algorithms. Secondly, the overall number of branches is an order of magnitude lower. Finally, branch generation is not distributed equally in spatiotemporal space, e.g. in the Example no 2, at Time Step 120, boxes 5&6 are rapidly crossed by the increased number of branches. This type of parametric pattern is very characteristic for in silico fungus that follows ‘Gauss’ statistical algorithm.

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Seed 2

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Seed 3

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Seed 4

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Seed 5

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Figure 102 Growth Dynamics of In Silico Fungus – Comparison of the Experiments I- V, for the ‘Actual Data’ Algorithm.

The numbers of branches generated for the seeds 1 and 5 are much lower compared to the seeds 2, 3, and 4. Visual outcomes are similar within seeds 1&5, and 2&4. The seed number 3 gives an outcome that is in between the 2 typical geometrical patterns (first one (seeds 1&5) with the parent hypha branching at the later stages and sending fewer number of branches, and the second one (seeds 2&4) with the parent hypha branching relatively early and sending higher number of branches). Result for the seed number 2 is an interesting case as it shows the parameter values forming certain numerical bands in terms of the number of hyphae generated at certain times. Band 1 is for the boxes 1 to 4, band 2 for the boxes 5, 6, and 7; and band 3 for the boxes 8 to 12. The 2 of 5 simulation outcomes resemble a typical shape of Neurospora crassa colony grown in a laboratory conditions.

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Figure 104Growth Dynamics of In Silico Fungus – Experiment II, ‘Gauss’ algorithm. The picture on the right comes from the experiment series (indicated as seed number two in the series) presented in the previous sections (Figure 86) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does slightly resemble a typical shape of Neurospora crassa grown in laboratory conditions at the very beginning of the colony formation, however, it does not reflect the dynamics of the real-world population for this species. The number of generated hyphae increases at 100 Time Step (~50 minutes). Boxes 5&6 at 120 Time Steps rapidly start to be crossed by increased number of hyphae- this means that the colony formation in this computer mode is not equally distributed in spatiotemporal space This simulation outcome can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6).

Figure 103Growth Dynamics of In Silico Fungus – Experiment I, ‘Gauss’ algorithm. The picture on the right comes from the experiment series (indicated as seed number one in the series) presented in the previous sections (Figure 86) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does not resemble a typical shape of Neurospora crassa colony grown in laboratory conditions. The number of generated hyphae increases in a progressive way from the very beginning of the simulation and is not in a good agreement with the real world observations. This result can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6).

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Figure 106Growth Dynamics of In Silico Fungus – Experiment IV, ‘Gauss’ algorithm. The picture on the right comes from the experiment series (indicated as seed number four in the series) presented in the previous sections (Figure 86) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does slightly resemble a typical shape of Neurospora crassa grown in laboratory conditions at the very beginning of the colony formation, however, it does not reflect the dynamics of the real-world population for this species. The number of generated hyphae start increasing at 90th Time Step (~45 minutes). The number of branches crossing the boxes 2, 3, and 4 increases significantly at times ~ 120, 130, and 140 respectively. The general tendency for this seed number is that one hypha crosses on box at certain time. This simulation outcome can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6).

Figure 105Growth Dynamics of In Silico Fungus – Experiment III, ‘Gauss’ algorithm. The picture on the right comes from the experiment series (indicate as seed number three in the series) presented in the previous sections (Figure 86) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The analysed pattern does slightly resemble a typical shape of Neurospora crassa grown in laboratory conditions at the very beginning of the colony formation, however, it does not reflect the dynamics of the real-world population for this species. The number of generated hyphae increases at 80 Time Step (~40 minutes). Box 4 at 140th Time Step starts to be crossed by increased number of hyphae. The general tendency for this seed number is that one hypha crosses on box at certain time. This simulation outcome can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6).

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Comparison of the simulation outcomes from the Figures 103-107 is given in Figure 108 on the next page. There are several specific features for the ‘Gauss’ mode. Firstly, in silico fungus following ‘Gauss’ algorithm tends to send one branch at the time. Secondly, the daughter and further generation branches are generated at the later times, compared to the ‘Actual Data’ and ‘Kernel’ modes. Moreover, the overall geometrical patterns only slightly resemble a typical shape of the Neurospora crassa colony, and only from the beginning stages of the colony formation. Furthermore, the biomass is not equally distributed in spatiotemporal space in this computer mode. Increased branch generation occurs in different parts of the surface at various times. Certain boxes (“geographical zones”) start to be crossed by the increased number of fungi in an asynchronous way, what is reflected in the presented graphs as lines representing various boxes “overtaking” each other. This pattern is a very characteristic one, especially for the ‘Gauss’ simulation mode and is not observed/recorded for the other two modes (‘Kernel’ and ‘Actual Data’).

Figure 107 Growth Dynamics of In Silico Fungus – Experiment V, ‘Gauss’ algorithm. The picture on the right comes from the experiment series (indicated as seed number five in the series) presented in the previous sections (Figure 86) and is a final frame of the simulation consisting of 150 time steps (~2 h 31 min in a real world setting). The outcome geometrical pattern does slightly resemble a typical shape of Neurospora crassa grown in laboratory conditions at the very beginning of the colony formation, however, it does not reflect the dynamics of the real-world population for this species. The number of generated hyphae start increasing at 80th Time Step (~40 minutes). The number of branches crossing the boxes 2, 3, and 4 increases significantly at times ~ 120, 130, and 140 respectively. The general tendency for this seed number is that one hypha crosses on box at certain time and that fungus starts sending daughter branches at the later times and at the boxes with higher ID numbers, compared to the previous cases. This simulation outcome can be compared with the real world evidence (Neurospora crassa movies provided by Prof Roger Lew) that is available under the following link:Real world example (Movie no 6).

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On the next pages, I give a detailed analysis of in silico fungus grown in a ‘Kernel’ mode of the program. The results for this mode resemble those for the ‘Actual Data’ mode. However, the biomass is distributed more equally across the surface in this mode, and the average proportion of the surface covered by the fungus is much higher. Additionally, the fungus also propagates like a wave, but even more smoothly, compared to the ‘Actual Data’ mode. The overall shape in 4/5 cases perfectly reflects a typical shape of Neurospora crassa colony grown in laboratory conditions. The pace of the increase in the number of hyphae is crossing “geographical” boundaries is similar to every box. Thus, the lines in the plots are parallel most of the time and resemble curves growing exponentially. At times, some sectors of in silico fungus colonies grow faster than the other ones or have similar parametric characteristics, e.g. in the Example number 3 in Figure 106.

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Seed 2

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Seed 3

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Seed 4

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Seed 5

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Figure 108 Growth Dynamics of In Silico Fungus – Comparison of the Experiments I- V, for the ‘Gauss’ Algorithm. In all examples in silico fungi tend to send one branch at the time. Also, the daughter and further generation

branches are generated at the later times, compared to the ‘Actual Data’ and ‘Kernel’ modes. Moreover, the

overall geometrical patterns only slightly resemble a typical shape of the Neurospora crassa colony, and only from the beginning stages of the colony formation. Furthermore, the biomass is not equally distributed in spatiotemporal space in this computer mode. Increased branch generation occurs at different parts of the surface