Minimum Equivalence in Random Boolean Networks, Elementary Cellular Automata, and Beyond

Random Boolean networks (RBN) and Cellular Automata (CA) operate in a very similar way. They update their state with simple deterministic functions called Boolean function or Transition Table (TT), both being essentially the same mechanism under different names. This paper applies a concept most known from CA called Minimum Equivalence (ME). ME is applied to RBN and shows how to calculate the number of unique computations for a given number of neighbours. Crucially, it is shown how RBN rules are even more equivalent than in CA, how the set can be reduced into even fewer unique rules, and how the concept becomes more relevant with larger neighbourhoods. For example, switching transformation alone reduces the number of unique rules in RBN with 4 neighbours from 65 536 to only 3 984 (6.1%) rules. Additionally, this paper examines the ME and transformations in substrates beyond Elementary CA (ECA), such as CA with additional spatial dimensions and number of states.publishedVersio

Assessment and manipulation of the computational capacity of in vitro neuronal networks through criticality in neuronal avalanches

In this work, we report the preliminary analysis of the electrophysiological behavior of in vitro neuronal networks to identify when the networks are in a critical state based on the size distribution of network-wide avalanches of activity. The results presented here demonstrate the importance of selecting appropriate parameters in the evaluation of the size distribution and indicate that it is possible to perturb networks showing highly synchronized—or supercritical—behavior into the critical state by increasing the level of inhibition in the network. The classification of critical versus non-critical networks is valuable in identifying networks that can be expected to perform well on computational tasks, as criticality is widely considered to be the state in which a system is best suited for computation. In addition to enabling the identification of networks that are well-suited for computation, this analysis is expected to aid in the classification of networks as perturbed or healthy. This study is part of a larger research project, the overarching aim of which is to develop computational models that are able to reproduce target behaviors observed in in vitro neuronal networks. These models will ultimately be used to aid in the realization of these behaviors in nanomagnet arrays to be used in novel computing hardwares

Hallmarks of Criticality in Neuronal Networks Depend on Cell Type and the Temporal Resolution of Neuronal Avalanches

The human brain has a remarkable capacity for computation, and it has been theorized that this capacity arises from the brain self-organizing into the critical state, a dynamical state poised between ordered and dis- ordered behavior and widely considered to be well-suited for computation. Criticality is commonly identified in in vitro neuronal networks using an analytical approach based on the size distribution of cascades of activity called neuronal avalanches. In this study, criticality analysis was applied to different in vitro neuronal networks with two areas of focus: evaluating the effect of the size of the time bins used for neuronal avalanche detection and observation of the development of networks of neurons derived from human induced pluripotent stem cells. This pre- preliminary study is expected to aid in the construction of models capable of emulating neuronal behaviors identified as well-suited for computation and ultimately inform the development of brain-inspired computing substrates that are better able to keep pace with increased demand for data storage and processing power

Evolving spiking neuron cellular automata and networks to emulate in vitro neuronal activity

Neuro-inspired models and systems have great potential for applications in unconventional computing. Often, the mechanisms of biological neurons are modeled or mimicked in simulated or physical systems in an attempt to harness some of the computational power of the brain. However, the biological mechanisms at play in neural systems are complicated and challenging to capture and engineer; thus, it can be simpler to turn to a data-driven approach to transfer features of neural behavior to artificial substrates. In the present study, we used an evolutionary algorithm to produce spiking neural systems that emulate the patterns of behavior of biological neurons in vitro. The aim of this approach was to develop a method of producing models capable of exhibiting complex behavior that may be suitable for use as computational substrates. Our models were able to produce a level of network-wide synchrony and showed a range of behaviors depending on the target data used for their evolution, which was from a range of neuronal culture densities and maturities. The genomes of the top-performing models indicate the excitability and density of connections in the model play an important role in determining the complexity of the produced activity

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed “neuronal avalanches.” The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other’s functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network’s computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered

Evolving spiking neuron cellular automata and networks to emulate in vitro neuronal activity

Neuro-inspired models and systems have great potential for applications in unconventional computing. Often, the mechanisms of biological neurons are modeled or mimicked in simulated or physical systems in an attempt to harness some of the computational power of the brain. However, the biological mechanisms at play in neural systems are complicated and challenging to capture and engineer; thus, it can be simpler to turn to a data-driven approach to transfer features of neural behavior to artificial substrates. In the present study, we used an evolutionary algorithm to produce spiking neural systems that emulate the patterns of behavior of biological neurons in vitro. The aim of this approach was to develop a method of producing models capable of exhibiting complex behavior that may be suitable for use as computational substrates. Our models were able to produce a level of network-wide synchrony and showed a range of behaviors depending on the target data used for their evolution, which was from a range of neuronal culture densities and maturities. The genomes of the top-performing models indicate the excitability and density of connections in the model play an important role in determining the complexity of the produced activity

Structuring a multi-nodal neural network in vitro within a novel design microfluidic chip

Neural network formation is a complex process involving axon outgrowth and guidance. Axon guidance is facilitated by structural and molecular cues from the surrounding microenvironment. Micro-fabrication techniques can be employed to produce microfluidic chips with a highly controlled microenvironment for neural cells enabling longitudinal studies of complex processes associated with network formation. In this work, we demonstrate a novel open microfluidic chip design that encompasses a freely variable number of nodes interconnected by axon-permissible tunnels, enabling structuring of multi-nodal neural networks in vitro. The chip employs a partially open design to allow high level of control and reproducibility of cell seeding, while reducing shear stress on the cells. We show that by culturing dorsal root ganglion cells (DRGs) in our microfluidic chip, we were able to structure a neural network in vitro. These neurons were compartmentalized within six nodes interconnected through axon growth tunnels. Furthermore, we demonstrate the additional benefit of open top design by establishing a 3D neural culture in matrigel and a neuronal aggregate 3D culture within the chips. In conclusion, our results demonstrate a novel microfluidic chip design applicable to structuring complex neural networks in vitro, thus providing a versatile, highly relevant platform for the study of neural network dynamics applicable to developmental and regenerative neuroscience