Criteria for Optimizing Cortical Hierarchies with Continuous Ranges

In a recent paper (Reid et al., 2009) we introduced a method to calculate optimal hierarchies in the visual network that utilizes continuous, rather than discrete, hierarchical levels, and permits a range of acceptable values rather than attempting to fit fixed hierarchical distances. There, to obtain a hierarchy, the sum of deviations from the constraints that define the hierarchy was minimized using linear optimization. In the short time since publication of that paper we noticed that many colleagues misinterpreted the meaning of the term “optimal hierarchy”. In particular, a majority of them were under the impression that there was perhaps only one optimal hierarchy, but a substantial difficulty in finding that one. However, there is not only more than one optimal hierarchy but also more than one option for defining optimality. Continuing the line of this work we look at additional options for optimizing the visual hierarchy: minimizing the number of violated constraints and minimizing the maximal size of a constraint violation using linear optimization and mixed integer programming. The implementation of both optimization criteria is explained in detail. In addition, using constraint sets based on the data from Felleman and Van Essen (1991), optimal hierarchies for the visual network are calculated for both optimization methods

Hierarchy and Dynamics of Neural Networks

Contains fulltext : 88364.pdf (publisher's version ) (Open Access

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

From Caenorhabditis elegans to the Human Connectome: A Specific Modular Organisation Increases Metabolic, Functional, and Developmental Efficiency

The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values but otherwise maximally random. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of C. elegans and human connectomes are both higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in C. elegans connectome or each region of interest (ROI) in human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared to the alternative arrangements. This implies that fewer rules are needed to encode for the organisation of neural systems

Multiple perspectives of the functional status of stroke survivors at 3 months post-stroke

Stroke is one of the leading causes of disability. Using an understandable measure to describe subsequent disabilities, namely, activities of daily living (ADL), is important for clinical practice. The three studies in this dissertation describe ADL task disability of stroke survivors at 3 months post-stroke, from multiple perspectives. The first study compared the constructs of five commonly used ADL measurement tools which used different scoring systems and assessment methods. Rasch analysis, using the partial credit model, confirmed that the performance-based and task-specific (criterion-referenced) ADL assessment, Performance Assessment of Self-Care Skills (PASS), had excellent unidimensionality for measuring independence in stroke survivors. It was also more valid and reliable than the other informant-based, and global non-summative (Glasgow Outcome Scale, 5-point [GOS5], Glasgow Outcome Scale, 5-point [GOS8], Modified Rankin Scale [mRS]) and global summative (Barthel Index [BI]) measures. The second study went on to develop an item difficulty hierarchy with the combined items from the PASS and the BI, and establish the person abilities of the stroke survivors. Rasch analysis and common person equating method revealed that the PASS was more difficult for the stroke survivors than the BI, and the participants had the greatest difficulty performing PASS instrumental ADL (IADL). The third study further delineated the independence of the stroke survivors with left and right hemispheric stroke (LHS and RHS) at the overall, domain, and task levels of the PASS. Rasch analysis, differential group functioning, and differential item functioning showed that the LHS group performed significantly more independently than the RHS group in the functional mobility domain, and better, but not significantly better on the overall PASS, and the personal care, physical IADL, and cognitive IADL domains. The findings of clinically significant differences in specific tasks between the two stroke groups (side of lesion, gender, and age) will advance the knowledge related to specific disabilities of stroke survivors, especially for IADL tasks. Further studies were recommended to explore the independence of the stroke survivors in performing ADL subtasks, with more homogeneous samples and at multiple time points

Single Biological Neurons as Temporally Precise Spatio-Temporal Pattern Recognizers

This PhD thesis is focused on the central idea that single neurons in the brain should be regarded as temporally precise and highly complex spatio-temporal pattern recognizers. This is opposed to the prevalent view of biological neurons as simple and mainly spatial pattern recognizers by most neuroscientists today. In this thesis, I will attempt to demonstrate that this is an important distinction, predominantly because the above-mentioned computational properties of single neurons have far-reaching implications with respect to the various brain circuits that neurons compose, and on how information is encoded by neuronal activity in the brain. Namely, that these particular "low-level" details at the single neuron level have substantial system-wide ramifications. In the introduction we will highlight the main components that comprise a neural microcircuit that can perform useful computations and illustrate the inter-dependence of these components from a system perspective. In chapter 1 we discuss the great complexity of the spatio-temporal input-output relationship of cortical neurons that are the result of morphological structure and biophysical properties of the neuron. In chapter 2 we demonstrate that single neurons can generate temporally precise output patterns in response to specific spatio-temporal input patterns with a very simple biologically plausible learning rule. In chapter 3, we use the differentiable deep network analog of a realistic cortical neuron as a tool to approximate the gradient of the output of the neuron with respect to its input and use this capability in an attempt to teach the neuron to perform nonlinear XOR operation. In chapter 4 we expand chapter 3 to describe extension of our ideas to neuronal networks composed of many realistic biological spiking neurons that represent either small microcircuits or entire brain regions