With our theory, we can also quantify just how much more information about spatial position these populations encode than if they all shared the same size/shape. [14/n]

With our new method in hand, we turned back to rodent place fields. As the theory predicts, place fields appear to exhibit high degrees of size and shape heterogeneity! (ticks in d,e are sessions) [13/n]

We show that doing this overcomes the issues we identified with tuning measurement based on the STA. With it, we can identify shape and size heterogeneity in simulated populations far more accurately. Our method is also less biased by the occupancy pattern of the animal. [12/n]

We propose a new Bayesian approach. We use it to explicitly quantify how uncertain we are about a field’s tuning based on how limited data is. Then we use this uncertainty to weight our estimates of field properties when measuring the degrees of shape and size heterogeneity. [11/n]

In the context of place cells, this refers to the rat not traversing the environment perfectly uniformly. These biases can skew the measurements of shape and size heterogeneity. So, we figured that a different way of measuring receptive fields was necessary to test our theory.[10/n]

So, we introduced shape heterogeneity. When receptive fields vary in size and shape, populations can better encode 2- and 3-D quantities. But this property reverses for higher-dimensional stimuli. Size heterogeneity remains useful, while shape heterogeneity becomes harmful. [7/n]

Let’s start with size heterogeneity, where we find dimensionality-dependence: Heterogeneously sized RFs increase info of one dimensional stimuli (head direction, eg). And >3-D stimuli. Strikingly, size heterogeneity isn’t helpful for encoding 2- or 3-D variables. [5/n]

…until now! We derived the amount of information encoded about a stimulus in spiking activity as a function of the degree of the population’s RF heterogeneity. To make the theory general, we derived this relationship for arbitrary stimulus dimensionalities. [4/n]

Populations across the brain have differently sized and shaped receptive fields. A striking example of this is hippocampal CA1 place cells, whose receptive fields can be mere centimeters across or as large as a few meters in size (fig from Rich et al., 2014) . [2/n]