Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

A laminar model for the joint development of ocular dominance columns and CO blobs in the primary visual cortex

In this paper, we present a multi-layer, activity-dependent model for the joint development of ocular dominance (OD) columns and cytochrome oxidase (CO) blobs in primate V1. For simplicity, we focus on layers 4C and 2/3 with both layers receiving direct thalamic inputs and layer 4C sending vertical projections to layer 2/3. Both the thalamic and the vertical connections are taken to be modifiable by activity. Using a correlation-based Hebbian learning rule with subtractive normalization, we show how the formation of an OD map in layer 4C is inherited by layer 2/3 via the vertical projections. Competition between these feedforward projections and the direct thalamic input to layer 2/3 then results in the formation of CO blobs superimposed upon the ocular dominance map. The spacing of the OD columns is determined by the spatial profile of the intralaminar connections within layer 4, while the spacing of CO blobs depends both on the width of the OD columns inherited from layer 4 and the spatial distribution of intralaminar connections within the superficial layer. The resulting CO blob distribution is shown to be consistent with experimental data. In addition, we numerically simulate monocular deprivation and find that while the CO blob distribution is unaltered, the OD pattern undergoes modification. The OD stripes of the deprived eye narrow, whereas the OD stripes for the remaining open eye widen.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Universal transition from unstructured to structured neural maps

Neurons sharing similar features are often selectively connected with a higher probability and should be located in close vicinity to save wiring. Selective connectivity has, therefore, been proposed to be the cause for spatial organization in cortical maps. Interestingly, orientation preference (OP) maps in the visual cortex are found in carnivores, ungulates, and primates but are not found in rodents, indicating fundamental differences in selective connectivity that seem unexpected for closely related species. Here, we investigate this finding by using multidimensional scaling to predict the locations of neurons based on minimizing wiring costs for any given connectivity. Our model shows a transition from an unstructured salt-and-pepper organization to a pinwheel arrangement when increasing the number of neurons, even without changing the selectivity of the connections. Increasing neuronal numbers also leads to the emergence of layers, retinotopy, or ocular dominance columns for the selective connectivity corresponding to each arrangement. We further show that neuron numbers impact overall interconnectivity as the primary reason for the appearance of neural maps, which we link to a known phase transition in an Ising-like model from statistical mechanics. Finally, we curated biological data from the literature to show that neural maps appear as the number of neurons in visual cortex increases over a wide range of mammalian species. Our results provide a simple explanation for the existence of salt-and-pepper arrangements in rodents and pinwheel arrangements in the visual cortex of primates, carnivores, and ungulates without assuming differences in the general visual cortex architecture and connectivity.

Stochastic Network Models in Neuroscience: A Festschrift for Jack Cowan. Introduction to the Special Issue

Jack Cowan's remarkable career has spanned, and molded, the development of neuroscience as a quantitative and mathematical discipline combining deep theoretical contributions, rigorous mathematical work and groundbreaking biological insights. The Banff International Research Station hosted a workshop in his honor, on Stochastic Network Models of Neocortex, July 17-24, 2014. This accompanying Festschrift celebrates Cowan's contributions by assembling current research in stochastic phenomena in neural networks. It combines historical perspectives with new results including applications to epilepsy, path-integral methods, stochastic synchronization, higher-order correlation analysis, and pattern formation in visual cortex.

Neural maps versus salt-and-pepper organization in visual cortex

Theoretical neuroscientists have long been intrigued by the spatial patterns of neuronal selectivities observed in the visual cortices of many mammals, including primates. While theoretical studies have contributed significantly to our understanding of how the brain learns to see, recent experimental discoveries of the spatial irregularity of visual response properties in the rodent visual cortex have prompted new questions about the origin and functional significance of cortical maps. Characterizing the marked differences of cortical design principles among species and comparing them may provide us with a deeper understanding of primate and non-primate vision.