Death of the sampling theorem?


A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem [1,2]. Apparently anti-aliasing filters are superfluous now because one can reconstruct the aliased noise after sampling. Sounds crazy? Yes it is. I offer $1000 to the first person who proves otherwise. To collect your cool cash be sure to read to the end.

“Filter before sampling!”

This mantra has been drilled into generations of engineering students. “Sampling” here refers to the conversion of a continuous function of time into a series of discrete samples, a process that happens wherever a computer digitizes a measurement from the world. “Filter” means the removal of high-frequency components from the signal. That filtering process, because it happens in the analog world, requires real analog hardware: so-called “anti-aliasing” circuits made of resistors, capacitors, and amplifiers. That can be tedious, for example because there isn’t enough space on the electronic chips in question. This is the constraint considered by Shepard’s team, in the context of a device for recording signals from nerve cells [2].

Now these authors declare that they have invented an “acquisition paradigm that negates the requirement for per-channel anti-aliasing filters, thereby overcoming scaling limitations faced by existing systems” [2]. Effectively they can replace the anti-aliasing hardware with software that operates on the digital side after the sampling step. “Another advantage of this data acquisition approach is that the signal processing steps (channel separation and aliased noise removal) are all implemented in the digital domain” [2].

This would be a momentous development. Not only does it overturn almost a century of conventional wisdom. It also makes obsolete a mountain of electronic hardware. Anti-alias filters are ubiquitous in electronics. Your cell phone contains multiple digital radios and an audio digitizer, which between them may account for half a dozen anti-alias circuits. If given a chance today to replace all those electronic components with a few lines of code, manufacturers would jump on it. So this is potentially a billion dollar idea.

Unfortunately it is also a big mistake. I will show that these papers do nothing to rattle the sampling theorem. They do not undo aliasing via post-hoc processing. They do not obviate analog filters prior to digitizing. And they do not even come close to the state of the art for extracting neural signals from noise. Continue reading “Death of the sampling theorem?”

The fable of the missing log units

Some time ago I published a critique of attempts at “magnetogenetics” – specifically the approach based on coupling a ferritin complex to an ion channel. See my article along with the original authors’ reply here:

Meister, M. (2016). Physical limits to magnetogenetics. eLife 5, e17210.

I argued that the effects of magnetic fields on ferritin are much too weak to account for the reported observations of neural modulation. The discrepancy is 5 to 10 orders of magnitude. Several people have asked what that means. How much of a problem does this really represent? To illustrate that, here is a short fable…

Earlier this year, a team of engineers announced a discovery that could go a long way to solving the world’s energy problems. Their article, published in Nature Automotive, reports the invention of an electric car that can run for an entire year on a single AA battery. “It took a lot of persistence on the part of my students”, says the senior author. “We literally tried 21 different brands of AA battery before we found one that worked” [1].

Now a paper in eCars casts doubt on the discovery. The author performed some calculations on the amount of work needed to push a car around for a year and the amount of electrical energy stored in a battery. He says there is a discrepancy of 7 orders of magnitude, and that makes the claims very improbable: “If the car really drove around for a year it is unlikely to have anything to do with the AA battery.” The author also faults the reviewers of the original article for not recognizing how improbable the claims are, and thus failing to raise the bar for the empirical evidence accordingly. He concedes it is possible that the claimed discovery opens a window on entirely new physics, but says: “Both batteries and cars have been studied for a long time, and we have a very successful model of how they work”.

The Nature Automotive authors reply that they never proposed a mechanism for the remarkable result. They stand by their data and state that empirical observation must take priority over any theory. Because they are not experts in physics, they should not be expected to explain how the data came about.

The critic points out that Nature Automotive and similar journals have had a rather poor track record: About half of the studies published there cannot be replicated for one reason or another. Not long ago, the journal reported the invention of a car that actually produced fuel while driving, such that the gas tank needed to be emptied at regular intervals [2]. A magician dispatched by the journal subsequently debunked that report, and explained it as a mixture of wishful thinking and self-deception [3]. Nature Automotive and other journals like it profess to be concerned about the profusion of false claims, and want to improve their ability to spot those before publication. The eCars critic suggests that one ought to start with the manuscripts whose claims fly in the face of everything we know about how things work. No word yet from the editor or the referees of the original article.

[1] Vogt, N. (2016). Neuroscience: Manipulating neurons with magnetogenetics. Nature Methods 13, 394.

[2] Davenas, E., Beauvais, F., Amara, J., Oberbaum, M., Robinzon, B., Miadonnai, A., Tedeschi, A., Pomeranz, B., Fortner, P., Belon, P., et al. (1988). Human basophil degranulation triggered by very dilute antiserum against IgE. Nature 333, 816.

[3] Maddox, J., Randi, J., and Stewart, W.W. (1988). “High-dilution” experiments a delusion. Nature 334, 287–291.

Control theory meets connectomes?

My colleagues and I have been working through this intriguing paper [1] from a few weeks ago:

Yan, G., Vértes, P.E., Towlson, E.K., Chew, Y.L., Walker, D.S., Schafer, W.R., and Barabási, A.-L. (2017). Network control principles predict neuron function in the Caenorhabditis elegans connectome. Nature advance online publication.

This seems like a very important contribution. It promises detailed insights about the function of a neural circuit based on its connectome alone, without knowing any of the synaptic strengths. The predictions extend to the role that individual neurons play for the circuit’s operation. Seeing how a great deal of effort is now going into acquiring connectomes [2] – mostly lacking annotations of synaptic strengths – this approach could be very powerful.

The starting point is Barabási’s “structural controllability theory” [3], which makes statements about the control of linear networks. Roughly speaking a network is controllable if its output nodes can be driven into any desired state by manipulating the input nodes. Obviously controllability depends on the entire set of connections from inputs to outputs. Structural controllability theory derives some conclusions from knowing only which connections have non-zero weight. This seems like a match made in heaven for the structural connectomes of neural circuits derived from electron microscopic reconstructions. In these data sets one can tell which neurons are connected but not what the strength is of those connections, or even whether they are excitatory or inhibitory. Unfortunately the match is looking more like a forced marriage… Continue reading “Control theory meets connectomes?”