There has been a debate raging for as long as I can remember. Neurons fire in action potentials that seem stereotyped. Let's take the action potentials to be stereotyped for all practical purposes in reality. (Honestly, we should test this. We haven't quite tested this rigorously through mutual information calculations of, say, the mutual information between voltage time series relative to stimulus versus a point process encoding relative to stimulus. If the two are the same within error bars with a lot of data, the voltage itself provides no additional information basically about the stimulus compared to the spike itself.) We then must ask: what about the spikes carry the information?

Some said that the precise spike timing, exactly when the spikes occurred, determined the neural encoding of information. This code can contain quite a bit of information, if you just think about the entropy of a point process. This, however, is not a very robust code. Other people therefore proposed that firing rate-- the number of spikes over a larger time interval-- was a more robust code that could contain quite a bit of information. According to Izhikevich, who is a proponent of the spike timing hypothesis, firing rate might matter at the neuromuscular junction, but that's about it.

I think these debates ignore the fact that even though many neuroscience experiments involve presenting a static stimulus and then watching neurons respond, stimuli in real life are constantly fluctuating. Almost never do we see a movie that is static. In fact, our eye movements prohibit this by doing microsaccades all the time even if the image in front of us is static. As a result, we see constantly moving video no matter what, or we basically perceive nothing at all. So really, we are asking how to encode a constantly changing movie.

In reality, there is some dt on our perception. If you were to jitter that movie by just a bit, we wouldn't be able to perceive it. This is like when the fan goes too fast and it looks like it's continuous regardless of the speed past a certain point. So really, we have a discrete-time stimulus with a small dt that we constantly must encode.

The most natural code for that might actually be something that is neither based on spike timing or based on firing rate, really, but is effectively a binary vector. Basically, the neural response within a window of dt (the spike timing included) would be what encodes information. It seems like this could still allow for a firing rate code, but the refractory period prohibits multiple spikes in that window of dt, hence prohibiting a firing rate code for stimuli that must be constantly encoded. You could maybe see a spike timing code, but you have to weigh the amount of time it takes for an action potential to complete against the limits of sensory perception, this dt. In reality, dt depends on the sense being studied, and the correct calculation to this question might involve some understanding of the refractory period. This question might be incredibly complicated. But my money is on a binary vector not being such a bad representation of the actual neural code that is used in practice-- just, did each neuron spike or not. Thank goodness, because so many papers have used this neural code implicitly, including some of my own!

This question might be complicated a bit if a blocklength larger than 1 is used-- but that leads to time delays, which are quite costly for reinforcement learning reasons!

Mitt Romney famously once said, in response to a town hall question, that corporations were people too. Immediately, journalists said that corporations were psychopaths.

Well, actually, this idea has some merit. An organization can be made up of good, smart people, but can act for some reason like something with a personality disorder. This is definitely related to the field of organizational psychology, about which I know very little, but I think this topic of how collective behavior of individuals makes for an organization with a different personality makeup than its individuals is badly explored mathematically.

I have been struggling with how to even begin a model of the collective behavior of the individuals that make up an organization in a way that will identify an organization's personality disorder. In fact, I think rarely does an organization lack a personality disorder. A model of this could explain everything from why some charities have way too much overhead that goes to the fat of the people running the organization to why democracy is failing.

The first mathematical model I thought of was some simplified sensory/actuator model of every person combined with a coarse-graining to find latent emotional states of the collective behavior. In reality, I think that although this is principled, it is unlikely to succeed unless we understand how to model an organism better than we already do. I sincerely hope that this approach is studied at some point in great detail-- and I mean mathematically. Just imagine that every person is modeled as a resource-constrained reinforcement learner who interacts with reward functions that depend on the people next to it, in a multi-agent reinforcement learning setting, and that we then model the behavior of the collective to find latent emotional states that can then be mapped to personality disorders with a mathematical form of the DSM. Undoubtedly, this is the way to proceed once you understand how to set it up mathematically, but on this, I give up, I think for life.

The second mathematical model I went to was a Potts model. This reminds me of the voter models in which people are modeled as Ising spins that I always thought of as being completely made up but basically okay for understanding certain behaviors. In a Potts model, collective behavior is modeled as interactions between particles that can adopt one of N discrete states. These discrete states could be one of several personality types. You then define some sort of interaction energy between these spins that can govern dynamics under several different models, but usually just governs the state into which the collective settles. A renormalization group analysis might then find that the collective, upon decimating using a majority opinion vote or the like, adopts a different discrete state of the Potts model than one might expect. The key is that the interaction energy might lead to frustration or a flipping of states, so that even if the collective starts out as good and smart, it ends up as a narcissist (perhaps a charity with too much overhead and grandiose statements about how much they do) or a psychopath (most corporations, who will screw over their workers for a payday).

In non-mathematical terms, this comes down to saying that the organizational structure is specified by an interaction energy between particles. This includes an understanding of the lattice structure and how far away particles can interact (if they are in an office such that only people at the same desk talk or if there's some movement generally so that one side of the office talks to the other), if there is a mean-field ordering from a mission statement, if separate orders are given to separate parts of the organization so that there are different mean-fields for different parts of the organization, if there are leaders that unduly influence the spins and are themselves stubborn, if disagreement is encouraged or discouraged which could lead to frustration or alignment.

One day, I hope to come back to this mathematical idea when I understand more about personality. In the meantime, if you have a way to turn this into something, please do!