Memory capacity of flow network morphology
by Komal Bhattacharyya
Date of Examination:2022-09-16
Date of issue:2023-02-13
Advisor:Prof. Dr. Karen Alim
Referee:Prof. Dr. Karen Alim
Referee:Prof. Dr. Peter Sollich
Persistent Address:
http://dx.doi.org/10.53846/goediss-9722
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Abstract
English
Adaptive flow networks are ubiquitous in our world. From animal blood vasculature to plant water vasculature and organisms shaped as flow networks, Physarum polycephalum, flow networks are abundant in biology with their main function being the transport of resources and information throughout an organism. They continuously remodel their network morphology to optimise their function. These adaptive flow networks have shown to retain memory of flow within the network morphology. In my thesis I aim to uncover the physical principles behind memory formation and retention in flow networks adapting to minimise energy dissipation while maintaining a conserved material. The work presented here shows that such an adaptive network can retain memory of an external stimulus within its network morphology, and that this memory can be read out even after a long time of evolution without the stimulus. First, I delve into the physical principles of memory formation in such adaptive networks. Using theoretical and numerical methods I show memory is conserved in adaptive networks because of the irreversible decay of network links. I show both analytically and numerically that links weaker than a particular threshold decay irreversibly and do not grow back. An adaptive network retains the memory of the location of an applied stimulus in the location and orientation of these decaying links within the network morphology. Furthermore, that the possibility of memory formation in adaptive network relies on the constrain of material conservation. In the second part of the thesis, I focus on how the memory of a stimulus direction depends on experimental protocol parameters. In this part, I explored the possibility of storing memories of multiple stimuli in adaptive flow networks. I show that an adaptive network evolved with some stimuli can form memory of a newly applied stimulus. The memory read-out signal of a stimulus decays with the age the network has before the stimulus was applied. As the number of decaying links retaining the memory saturates over the evolution time of an adaptive flow network, the capacity to form new memories also saturates. Using theoretical and numerical methods, I show that the memory of an older stimulus cannot be overwritten by applying more new stimuli. Moreover, the memory of a stimulus in such an adaptive network increases with the time during which the stimulus is applied. I quantify the number of stimuli that can be memorised by such networks as a function of different experimental parameters to obtain the optimal parameters for storing a maximum number of memories in adaptive flow networks. With this thesis, I uncover the physical principles behind the emergence of memory in flow networks and establish the dependence of the memory capacity on parameters which can be verified experimentally.
Keywords: Flow network; Memory formation; Memory capacity; Adaptive network; Network morphology; Network optimisation; Physical network