Investigating Information Flows in Spiking Neural Networks With High Fidelity

The brains of many organisms are capable of a wide variety of complex computations. This capability must be undergirded by a more general purpose computational capacity. The exact nature of this capacity, how it is distributed across the brains of organisms and how it arises throughout the course of development is an open topic of scientific investigation. Individual neurons are widely considered to be the fundamental computational units of brains. Moreover, the finest scale at which large scale recordings of brain activity can be performed is the spiking activity of neurons and our ability to perform these recordings over large numbers of neurons and with fine spatial resolution is increasing rapidly. This makes the spiking activity of individual neurons a highly attractive data modality on which to study neural computation. The framework of information dynamics has proven to be a successful approach towards interrogating the capacity for general purpose computation. It does this by revealing the atomic information processing operations of information storage, transfer and modification. Unfortunately, the study of information flows and other information processing operations from the spiking activity of neurons has been severely hindered by the lack of effective tools for estimating these quantities on this data modality. This thesis remedies this situation by presenting an estimator for information flows, as measured by Transfer Entropy (TE), that operates in continuous time on event-based data such as spike trains. Unlike the previous approach to the estimation of this quantity, which discretised the process into time bins, this estimator operates on the raw inter-spike intervals. It is demonstrated to be far superior to the previous discrete-time approach in terms of consistency, rate of convergence and bias. Most importantly, unlike the discrete-time approach, which requires a hard tradeoff between capturing fine temporal precision or history effects occurring over reasonable time intervals, this estimator can capture history effects occurring over relatively large intervals without any loss of temporal precision. This estimator is applied to developing dissociated cultures of cortical rat neurons, therefore providing the first high-fidelity study of information flows on spiking data. It is found that the spatial structure of the flows locks in to a significant extent. at the point of their emergence and that certain nodes occupy specialised computational roles as either transmitters, receivers or mediators of information flow. Moreover, these roles are also found to lock in early. In order to fully understand the structure of neural information flows, however, we are required to go beyond pairwise interactions, and indeed multivariate information flows have become an important tool in the inference of effective networks from neuroscience data. These are directed networks where each node is connected to a minimal set of sources which maximally reduce the uncertainty in its present state. However, the application of multivariate information flows to the inference of effective networks from spiking data has been hampered by the above-mentioned issues with preexisting estimation techniques. Here, a greedy algorithm which iteratively builds a set of parents for each target node using multivariate transfer entropies, and which has already been well validated in the context of traditional discretely sampled time series, is adapted to use in conjunction with the newly developed estimator for event-based data. The combination of the greedy algorithm and continuous-time estimator is then validated on simulated examples for which the ground truth is known. The new capabilities in the estimation of information flows and the inference of effective networks on event-based data presented in this work represent a very substantial step forward in our ability to perform these analyses on the ever growing set of high resolution, large scale recordings of interacting neurons. As such, this work promises to enable substantial quantitative insights in the future regarding how neurons interact, how they process information, and how this changes under different conditions such as disease

Signal restoration for a mass transport problem involving shear dispersion

An inverse problem associated with mass transport down a tube, when the flowing medium has a two-dimensional velocity profile, is examined. The inverse problem of estimation of a temporally varying concentration at one end of a long tube, from the measurement of the cross-sectional average concentration at the opposite end, is solved. It is shown that this inverse problem, which is associated with shear dispersion, is an ill-posed deconvolution problem. Mollification is used to produce a well-conditioned problem

Exploring Exploration Catastrophes in Various Network Models

It has been argued that much of evolution takes place in the absence of fitness gradients. Such periods of evolution can be analysed by examining the mutational network formed by sequences of equal fitness, that is, the neutral network. It has been demonstrated that, in large populations under a high mutation rate, the population distribution over the neutral network and average mutational robustness are given by the principal eigenvector and eigenvalue, respectively, of the network’s adjacency matrix. However, little progress has been made towards understanding the manner in which the topology of the neutral network influences the resulting population distribution and robustness. In this work, we use numerical methods and network models to enhance our understanding of how populations distribute themselves over neutral networks. We demonstrate that, in the presence of certain topological features, the population will undergo an exploration catastrophe and become confined to a small portion of the network. These results provide insight into the behaviour of populations on neutral networks, demonstrating that neutrality does not necessarily lead to an exploration of genotype/phenotype space or an associated increase in population diversity

Generational Neuro-Evolution: Restart and Retry for Improvement

This paper proposes a new Neuro-Evolution (NE) method for automated controller design in agent-based systems. The method is Generational Neuro-Evolution (GeNE), and is comparatively evaluated with established NE methods in a multi-agent predator-prey task. This study is part of an ongoing research goal to derive efficient (minimising convergence time to optimal solutions) and scalable (effective for increasing numbers of agents) controller design methods for adapting agents in neuro-evolutionary multi-agent systems. Dissimilar to comparative NE methods, GeNE employs tiered selection and evaluation as its generational fitness evaluation mechanism and, furthermore, re-initializes the population each generation. Results indicate that GeNE is an appropriate controller design method for achieving efficient and scalable behavior in a multi-agent predator-prey task, where the goal was for multiple predator agents to collectively capture a prey agent. GeNE outperforms comparative NE methods in terms of efficiency (minimising the number of genotype evaluations to attain optimal task performance)

The Evolution of Evolvability in Evolutionary Robotics

Previous research has demonstrated that computational models of Gene Regulatory Networks (GRNs) can adapt so as to increase their evolvability, where evolvability is defined as a population’s responsiveness to environmental change. In such previous work, phenotypes have been represented as bit strings formed by concatenating the activations of the GRN after simulation. This research is an extension where previous results supporting the evolvability of GRNs are replicated, however, the phenotype space is enriched with time and space dynamics with an evolutionary robotics task environment. It was found that a GRN encoding used in the evolution of a way-point navigation behavior in a fluctuating environment results in (robot controller) populations becoming significantly more responsive (evolvable) over time. This is as compared to a direct encoding of controllers which was unable to improve it’s evolvability in the same task environment

The Relationship Between Evolvability and Robustness in the Evolution of Boolean Networks

Robustness and evolvability have traditionally been seen as conflicting properties of evolutionary systems, due to the fact that selection requires heritable variation on which to operate. Various recent studies have demonstrated that organisms evolving in environments fluctuating non-randomly become better at adapting to these fluctuations, that is, increase their evolvability. It has been suggested that this is due to the emergence of biases in the mutational neighborhoods of genotypes. This paper examines a potential consequence of these observations, that a large bias in certain areas of genotype space will lead to increased robustness in corresponding phenotypes. The evolution of boolean networks, which bear similarity to models of gene regulatory networks, is simulated in environments which fluctuate between task targets. It was found that an increase in evolvability is concomitant with the emergence of highly robust genotypes, where evolvability was defined as the population’s adaptability. Analysis of the genotype space elucidated that evolution finds regions containing robust genotypes coding for one of the target phenotypes, where these regions overlap or are situated in close proximity. Results indicate that genotype space topology impacts the relationship between robustness and evolvability, where the separation of robust regions coding for the various targets was detrimental to evolvability

Neutral Network Assortativity Shapes Whether Selective Pressure Promotes or Hinders Robustness

Due to the friendship paradox, the average robustness of the single mutation neighbours (µn) of genotypes on a neutral network is larger than the average robustness of the genotypes (µg). Random walks on neutral networks have an average degree equal to µn and, intuitively, we expect that evolution will not converge on populations whose average degree is considerably lower than this. This paper argues that a population achieving an average robustness higher than µn is facilitated by nodes of degree higher than µn being mutationally biased towards other nodes of degree higher than µn. Thus, we present the hypothesis that, for biologically realistic degree distributions, assortativity allows selection to increase robustness above µn. Furthermore, although counterexamples do exist, it is argued that it is highly plausible that in the majority of cases in which selection increases robustness above µn, that the neutral network is assortative. These arguments are reinforced by simulations of evolution on randomly generated Erdos-Renyi and power-law networks. Elucidating the role of assortativity provides valuable insight into the mechanisms by which robustness evolves as well as the conditions under which it will do so. Moreover, it demonstrates the large influence that higher-order mutational biases can have on evolutionary dynamics