#13. The Neural Code, Part II: the Thalamus [neuroscience, engineering]

A hypothetical scheme of the thalamus, a central part of your brain.

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Red, theory; black, fact.

Thalamic processing as Laplace transform

More in Deprecated, Part 1. I postulate that the thalamus performs a Laplace transform (LT). All the connections shown are established anatomical facts, and are based on the summary diagram of lateral geniculate nucleus circuitry of Steriade et al. (Steriade, M., Jones E. G. and McCormick, D. A. (1997) Thalamus, 2 Vols. Amsterdam: Elsevier).  What I have added is feedback from cortex as a context-sensitive enabling signal for the analytical process. I originally guessed that the triadic synapses are differentiators, but now I think that they are function multipliers.

Thalamic electrophysiology

The thalamic low-threshold spike (LTS) is a slow calcium spike that triggers further spiking that appears in extracellular recordings as a distinctive cluster of four or five sodium spikes. The thalamus also has an alternative response mode consisting of fast single spikes, which is observed at relatively depolarized membrane potentials.

The thalamic low-threshold spike as triggered by a hyperpolarization due to an electric current pulse injected into the neuron through the recording electrode. ACSF, normal conditions; TTX, sodium spikes deleted pharmacologically. From my thesis, page 167.

Network relationships of the thalamus

Depolarizing input to thalamus from cortex is conjectured to be a further requirement for the LTS-burst complex. This depolarization is conjectured to take the form of a pattern of spots, each representing a mask to detect a specific pole of the stimulus that the attentional system is looking for in that context.

The complex frequency plane is where LTs are graphed, usually as a collection of points. Some of these are "poles," where gain goes to infinity, and others are "zeroes," where gain goes to zero. I assume that the cerebral cortex-thalamus system takes care of the poles, while the superior and inferior colliculi take care of the zeroes. 

If this stimulus is found, the pattern of poles must still be recognized. This may be accomplished through a cortical AND-element wired up on Hebbian principles among cortical neurons. These neurons synapse on each other by extensive recurrent collaterals, which might be the anatomical substrate of the conjectured AND-elements. Explosive activation of the AND network would then be the signal that the expected stimulus has been recognized, as Hebb proposed long ago, and the signal would then be sent forward in the brain via white matter tracts to the motor cortex, which would output a collection of excitation spots representing the LT of the desired response.

Presumably, a reverse LT is then applied, possibly by the spinal grey, which I have long considered theoretically underemployed in light of its considerable volume. If we assume that the cerebral cortex is highly specialized for representing LTs, then motor outputs from cerebellum and internal globus pallidus would also have to be transformed to enable the cortex to represent them. In agreement with this, the motor cortex is innervated by prominent motor thalami, the ventrolateral (for cerebellar inputs) and the ventroanterior (for pallidal inputs).

Brain representation of Laplace transforms

The difficulty is to see how a two-dimensional complex plane can be represented on a two-dimensional cerebral cortex without contradicting the results of receptive field studies, which clearly show that the two long dimensions of the cortex represent space in egocentric coordinates. This just leaves the depth dimension for representing the two dimensions of complex frequency.

03-01-2020:
A simple solution is that the complex frequency plane is tiled by the catchment basins of discrete, canonical poles, and all poles in a catchment basin are represented approximately by the nearest canonical pole. It then becomes possible to distinguish the canonical poles in the cerebral cortex by the labelled-line mechanism (i.e., by employing different cell-surface adhesion molecules to control synapse formation.)

Recalling that layer 1 of cortex is mostly processes, this leaves us with five cortical cell layers not yet assigned to functions. Four of them might correspond to the four quadrants of  the complex frequency plane, which differ qualitatively in the motions they represent. The two granule-cell layers 2 and 4 are interleaved with the two pyramidal-cell layers 3 and 5. The two granule layers might be the top and bottom halves of the left half-plane, which represents decaying, stabilized motions. The two pyramidal layers might represent the top and bottom halves of the right half-plane, which represents dangerously growing, unstable motions. Since the latter represent emergency conditions, the signal must be processed especially fast, requiring fast, large-diameter axons. Producing and maintaining such axons requires correspondingly large cell bodies. This is why I assign the relatively large pyramidal cells to the right half-plane.

Intra-thalamic operations

It is beginning to look like the thalamus computes the Laplace transform just the way it is defined: the integral of the product of the input time-domain function and an exponentially decaying or growing sinusoid (eigenfunction). A pole would be recognized after a finite integration time as the integrand rising above a threshold. This thresholding is plausibly done in cortical layer 4, against a background of elevated inhibition controlled by the recurrent layer-6 collaterals that blocks intermediate calculation results from propagating further into the cortex. The direct projections from layer 6 down to thalamus would serve to trigger the analysis and rescale eigenfunction tempo to compensate for changes in behavioral tempo. Reverberation of LTS-bursting activity between thalamic reticular neurons and thalamic principal neurons would be the basis of the oscillatory activity involved in implementing the eigenfunctions. This is precedented by the spindling mechanism and the phenomenon of Parkinsonian tremor cells.

Mutual inhibition of reticular thalamic neurons would be the basis of the integrator and multiplication of functions would be done by silent inhibition in the triadic synapses (here no longer considered to be differentiators) via the known disinhibitory pathway from the reticular thalamus. 

A negative feedback system will be necessary to dynamically rejig the thalamus so that the same pole maps to the same spot despite changes in tempo. Some of the corticothalamic cells (layer 6) could be part of this system (layer 6 cells are of two quite different types), as well as the prominent cholinergic projections to the RT.

Consequences for object recognition

The foregoing system could be used to extract objects from the incoming data by in effect assuming that the elements or features of an object always share the same motion and therefore will be represented by the same set of poles. An automatic process of object extraction may therefore be implemented as a tendency for Hebbian plasticity to involve the same canonical pole at two different cortical locations that are connected by recurrent axon collaterals.

#12. The Neural Code, Part I: the Hippocampus [neuroscience, engineering]

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Red, theory; black, fact.

"Context information" is often invoked in neuroscience theory as an address for storing more specific data in memory, such as whatever climbing fibers carry into the cerebellar cortex (Marr theory), but what exactly is context, as a practical matter?

First, it must change on a much longer timescale than whatever it addresses. Second, it must also be accessible to a moving organism that follows habitual, repetitive pathways in patrolling its territory. Consideration of the mainstream theory that the hippocampus prepares a cognitive map of the organism's spatial environment suggests that context is a set of landmarks. It seems that a landmark will be any stimulus that appears repetitively. Since only rhythmically repeating functions have a classical discrete-frequency Fourier transform, the attempt to calculate such a transform could be considered a filter for extracting rhythmic signals from the sensory input. 

However, this is not enough for a landmark extractor because landmark signals are only repetitive, not rhythmic. Let us suppose, however, that variations in the intervals between arrivals at a given landmark are due entirely to programmed, adaptive variations in the overall tempo of the organism's behavior. A tempo increase will upscale all incoming frequencies by the same factor, and a tempo decrease will downscale them all by the same factor. Since these variations originate within the organism, the organism could send a "tempo efference copy" to the neuronal device that calculates the discrete Fourier transform, to slide the frequency axis left or right to compensate for tempo variations. 

Thus, the same landmark will always transform to the same set of activated spots in the frequency-amplitude-phase volume. I conjecture that the hippocampus calculates a discrete-frequency Fourier transform of all incoming sensory data, with lowest frequency represented ventrally and highest dorsally, and a with a linear temporal spectrum represented between. 

The negative feedback device that compensates tempo variations would be the loop through medial septum. The septum is the central hub of the network in which the EEG theta rhythm can be detected. This rhythm may be a central clock of unvarying frequency that serves as a reference for measuring tempo variations, possibly by a beat-frequency principle. 

The hippocampus could calculate the Fourier transform by exploiting the mathematical fact that a sinusoidal function differentiated four times in succession gives exactly the starting function, if its amplitude and frequency are both numerically equal to one. This could be done by the five-synapse loop from dentate gyrus to hippocampal CA3 to hippocampal CA1 to subiculum to entorhinal cortex, and back to dentate gyrus. The dentate gyrus looks anatomically unlike the others and may be the input site where amplitude standardization operations are performed, while the other four stages would be the actual differentiators. 

Differentiation would occur by the mechanism of a parallel shunt pathway through slowly-responding inhibitory interneurons, known to be present throughout the hippocampus. The other two spatial dimensions of the hippocampus would represent frequency and amplitude by setting up gradients in the gain of the differentiators. A given spot in the array maps the input function to itself only for one particular combination of frequency and transformed (i.e., output) amplitude. 

The self-mapping sets up a reverberation around the loop that makes the spot stand out functionally. All the concurrently active spots would constitute the context. This context could in principle reach the entire cerebral cortex via the fimbria fornix, mammillary bodies, and tuberomamillary nucleus of the hypothalamus, the latter being histaminergic.

The cortex may contain a novelty-detection function, source of the well-documented mismatch negativity found in oddball evoked-potential experiments. A stimulus found to be novel would go into a short term memory store in cortex. If a crisis develops while it is there, it is changed into a flash memory and wired up to the amygdala, which mediates visceral fear responses. In this way, a conditioned fear stimulus could be created. If a reward registers while the stimulus is in short term memory, it could be converted to a conditioned appetitive stimulus by a similar mechanism.

 I conjecture that all a person's declarative and episodic memories together are nothing more nor less than those that confer conditioned status on particular stimuli.

To become such a memory, a stimulus must first be found to be novel, and this is much less likely in the absence of a context signal; to put it another way, it is the combination of the context signal and the sensory stimulus that is found to be novel. Absent the context, and almost no simple stimulus will be novel. This may be the reason why at least one hippocampus must be functioning if declarative or episodic memories are to be formed.

#5. Why We Dream [neuroscience]

NE
Red, theory; black, fact.

The Melancholy Fields

Something I still remember from Psych 101 is the prof's statement that "operant conditioning" is the basis of all voluntary behavior. The process was discovered in lab animals such as pigeons by B.F. Skinner in the 1950s and can briefly be stated as "If the ends are achieved, the means will be repeated." (Gandhi said something similar about revolutionary governments.)

I Dream of the Gruffalo. Pareidolia as dream imagery.

Let's say The Organism is in a supermarket checkout line and can't get the opposite sides of a plastic grocery bag unstuck from each other no matter how it rubs, blows, stretches, picks at, or pinches the bag. At great length, a rubbing behavior by chance happens near the sweet spot next to the handle, and the bag opens at once. Thereafter, when in the same situation, The Organism goes straight to the sweet spot and rubs, for a great savings in time and aggravation. This is operant conditioning, which is just trial-and-error, like evolution itself, only faster. Notice how it must begin: with trying moves randomly--behavioral mutations. However, the process is not really random like a DNA mutation. The Organism never tries kicking out his foot, for example, when it is the hand that is holding the bag. Clearly, common sense plays a role in getting the bag open, but any STEM-educated person will want to know just what this "common sense" is and how you would program it. Ideally, you want the  creativity and genius of pure randomness, AND the assurance of not doing anything crazy or even lethal just because some random-move generator suggested it. You vet those suggestions.

That, in a nutshell, is dreaming: vetting random moves against our accumulated better judgment to see if they are safe--stocking the brain with pre-vetted random moves for use the next day when stuck. This is why the emotions associated with dreaming are more often unpleasant than pleasant: there are more ways to go wrong than to go right (This is why my illustrations for this post are melancholy and monster-haunted.) The vetting is best done in advance (e.g., while we sleep) because there's no time in the heat of the action the next day, and trial-and-error with certified-safe "random" moves is already time-consuming without having to do the vetting on the spot as well.

Dreams are loosely associated with brain electrical events called "PGO waves," which begin with a burst of action potentials ("nerve impulses") in a few small brainstem neuron clusters, then spread to the visual thalamus, then to the primary visual cortex. I theorize that each PGO wave creates a new random move that is installed by default in memory in cerebral cortex, and is then tested in the inner theater of dreaming to see what the consequences would be. In the event of a disaster foreseen, the move is scrubbed from memory, or better yet, added as a "don't do" to the store of accumulated wisdom. Repeat all night.

If memory is organized like an AI knowledge base, then each random move would actually be a connection from a randomly-selected but known stimulus to a randomly-selected but known response, amounting to adding a novel if-then rule to the knowledge base. Some of the responses in question could be strictly internal to the brain, raising or lowering the firing thresholds of still other rules.

(Deprecated, Part 3)

In "Evolution in Four Dimensions" [1st ed.] Jablonka and Lamb make the point that epigenetic, cultural, and symbolic processes can come up with something much better than purely random mutations: variation that has been subjected to a variety of screening processes.

Nightmares involving feelings of dread superimposed on experiencing routine activities may serve to disrupt routine assumptions that are not serving you well (that is, you may be barking up the wrong tree).