Optimizing the representation of orientation preference maps in visual cortex

The colorful representation of orientation preference maps in primary visual cortex has become iconic. However, the standard representation is misleading because it uses a color mapping to indicate orientations based on the HSV (hue, saturation, value) color space, for which important perceptual features such as brightness, and not just hue, vary among orientations. This means that some orientations stand out more than others, conveying a distorted visual impression. This is particularly problematic for visualizing subtle biases caused by slight overrepresentation of some orientations due to, for example, stripe rearing. We show that displaying orientation maps with a color mapping based on a slightly modified version of the HCL (hue, chroma, lightness) color space, so that primarily only hue varies between orientations, leads to a more balanced visual impression. This makes it easier to perceive the true structure of this seminal example of functional brain architecture

From perception to behavior: The neural circuits underlying prey hunting in larval zebrafish

A key challenge for neural systems is to extract relevant information from the environment and make appropriate behavioral responses. The larval zebrafish offers an exciting opportunity for studying these sensing processes and sensory-motor transformations. Prey hunting is an instinctual behavior of zebrafish that requires the brain to extract and combine different attributes of the sensory input and form appropriate motor outputs. Due to its small size and transparency the larval zebrafish brain allows optical recording of whole-brain activity to reveal the neural mechanisms involved in prey hunting and capture. In this review we discuss how the larval zebrafish brain processes visual information to identify and locate prey, the neural circuits governing the generation of motor commands in response to prey, how hunting behavior can be modulated by internal states and experience, and some outstanding questions for the field

A unifying objective function for topographic mappings

Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practical application of topographic mapping methods

Auto-SOM: recursive parameter estimation for guidance of self-organizing feature maps

An important technique for exploratory data analysis is to forma mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achieve good performance. Here we present the Auto-SOM, an algorithm that estimates the learning parameters during the training of SOMs automatically. The application of Auto-SOM provides the facility to avoid neighborhood violations up to a user-defined degree in either mapping direction. Auto-SOM consists of a Kalman filter implementation of the SOM coupled with a recursive parameter estimation method. The Kalman filter trains the neurons' weights with estimated learning coefficients so as to minimize the variance of the estimation error. The recursive parameter estimation method estimates the width of the neighborhood function by minimizing the prediction error variance of the Kalman filter. In addition, the "topographic function" is incorporated to measure neighborhood violations and prevent the map's converging to configurations with neighborhood violations. It is demonstrated that neighborhoods can be preserved in both mapping directions as desired for dimension-reducing applications. The development of neighborhood-preserving maps and their convergence behavior is demonstrated by three examples accounting for the basic applications of self-organizing feature maps

The influence of restricted orientation rearing on map structure in primary visual cortex

Visual experience is critical to the development of the structure of the primary visual cortex and, in turn, normal functional vision. The primary visual cortex contains maps of multiple features of the visual input, and these maps are characterised by specific types of geometric relationships. Manipulations of the visual environment during development in animals such as ferrets, cats and monkeys provide an opportunity to probe the rules governing map formation via their effect on these relationships. Here we use a computational model of map formation based on dimension-reduction principles to predict the effect on map relationships of presenting only a single orientation to one eye and the orthogonal orientation to the other eye. Since orientation preference and ocular dominance are now tightly coupled one might expect orientation and ocular dominance contours to lose their normally orthogonal relationship and instead run parallel to each other. However, surprisingly, the model predicts that orthogonal intersection can sometimes be preserved in this case. The model also predicts that orientation pinwheels can migrate from the centre to the borders of ocular dominance columns, and that the wavelengths of the ocular dominance and orientation maps can become coupled. These predictions provide a way to further test the adequacy of dimension reduction principles for explaining map structure under perturbed as well as normal rearing conditions, and thus allow us to deepen our understanding of the effect of the visual environment on visual cortical development

Statistical structure of lateral connections in the primary visual cortex

The statistical structure of the visual world offers many useful clues for understanding how biological visual systems may understand natural scenes. One particularly important early process in visual object recognition is that of grouping together edges which belong to the same contour. The layout of edges in natural scenes have strong statistical structure. One such statistical property is that edges tend to lie on a common circle, and this 'co-circularity' can predict human performance at contour grouping. We therefore tested the hypothesis that long-range excitatory lateral connections in the primary visual cortex, which are believed to be involved in contour grouping, display a similar co-circular structure.By analyzing data from tree shrews, where information on both lateral connectivity and the overall structure of the orientation map was available, we found a surprising diversity in the relevant statistical structure of the connections. In particular, the extent to which co-circularity was displayed varied significantly.Overall, these data suggest the intriguing possibility that V1 may contain both co-circular and anti-cocircular connections

The role of weight normalization in competitive learning

The effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed. It is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount (''divisive enforcement'') or subtracting a fixed amount from each weight (''subtractive enforcement''). For the divisive cases weight vectors spread out over the space so as to evenly represent ''typical'' inputs, whereas for the subtractive cases the weight vectors tend to the axes of the space, so as to represent ''extreme'' inputs. The consequences of these differences are examined

The combinatorics of neurite self-avoidance

During neural development in Drosophila, the ability of neurite branches to recognize whether they are from the same or different neurons depends crucially on the molecule Dscam1. In particular, this recognition depends on the stochastic acquisition of a unique combination of Dscam1 isoforms out of a large set of possible isoforms. To properly interpret these findings, it is crucial to understand the combinatorics involved, which has previously been attempted only using stochastic simulations for some specific parameter combinations. Here we present closed-form solutions for the general case. These reveal the relationships among the key variables and how these constrain possible biological scenarios