Nosimpler

How does the brain navigate uncertainty in a dynamic environment? In this study, Hosford, Mei, et al. show that computations implemented across a network of thalamic and cortical circuits continuously update internal representations of recent experiences to help mice make decisions based on limited or ambiguous information.

Nature, Published online: 27 May 2026; doi:10.1038/s41586-026-10496-6

Uniformly doped, ultrathin single-crystalline silicon nanomembranes can be vertically stacked at low temperature using a roll-transfer-printing process that is scalable to wafer scale and tolerant to substrate topology and surface roughness for constructing high-performance monolithic three-dimensional integrated circuits.

arXiv:2605.27159v1 Announce Type: new Abstract: In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state. Inspired by the fact that Dyck language provides an example of the emergence of the Catalan numbers in linguistic framework analysis, we show that these numbers are central when numbering the terms remaining when eliminating vanishing contributions detected by our application of Dyck language to fermionic second quantization. From the translation of creation and annihilation operator - or of pairs of operators - into a bracket alphabet, we derive simple and intuitive sufficient conditions for the nullity of expectation values that does not require an explicit application of Wick's theorem. This is done here with respect to the physical vacuum or relatively to a one-determinant state. We also extend this translation into a diagrammatic framework that allows a visual determination of the signature of fully contracted terms, reproducing the results of Wick's theorem. This approach has been extended to the case of (nested) commutators of pairs of fermionic second quantization including at least one excitation or deexcitation operator. Our results have been implemented in a software, MobiDyck, whose source code is freely available on the web. The algorithmic approach inspired by our work on Dyck language is detailed in this paper. Finally, a comparison of our diagrammatic approach with Goldstone diagrams is provided and closes the article.

Nature Neuroscience, Published online: 25 May 2026; doi:10.1038/s41593-026-02314-z

Lozano et al. show that REM sleep is gated by low-dimensional brainstem network dynamics, in which opposing neuron populations across the midbrain and pons determine when transitions into REM sleep can occur.

During wakefulness, neuromodulators operate largely independently to support behavior and cognition. By contrast, sleep reorganizes their activity into a coordinated brain rhythm. During sleep, the major neuromodulators—norepinephrine, acetylcholine, ...

Theo Baker spills Silicon Valley secrets and revisits his efforts to expose a shocking breach of research integrity

Stereoisomers of C13Cl2 exhibiting helical orbitals around a ring of carbon atoms were synthesized by atom manipulation on NaCl surfaces. We resolved the enantiomeric geometries of the singlet states by atomic force microscopy and mapped their helical ...

Speech requires precise serial ordering of words and phonemes into novel combinations. To accomplish this, the brain is believed to flexibly prepare utterances before producing them, even allowing pronunciation of never-before spoken words. To discover how neural populations achieve this, intracortical activity from premotor cortex was recorded while two speech neuroprosthesis pilot clinical trial participants attempted to speak factorially-balanced phoneme sequences. During preparation, activity encoded not only the next-phoneme, but multiple upcoming phoneme positions spanning whole words. We found that word-level plans were formed by compositionally combining phoneme representations, a mechanism that may enable efficient planning of novel sequences. When utterances contained more than one word, premotor cortex activity was largely limited to the first word, suggesting that articulatory planning is segmented by higher-order features. Together, these results reveal a compositional, hierarchically-segemented planning geometry, potentially a universal neural strategy for sequence organization across higher levels of language.

Gene syntax—the order and arrangement of genes and their regulatory elements—shapes the dynamic coordination of both natural and synthetic gene circuits. Transcription at one locus perturbs the transcription of adjacent genes, but the molecular basis of ...

Natural image representations are distributed across many dimensions of visual cortex activity, but little is known about how the multidimensional structure of these representations evolves over time following stimulus onset. Here we examined the temporal dynamics and latent dimensional structure of natural object representations in large-scale EEG and MEG data. We also compared these data with leading representational models derived from large-scale human similarity judgments and deep neural networks. Our findings reveal a rapid expansion of stimulus dimensionality in the brain, which peaks within 100 milliseconds and gradually decays over hundreds of milliseconds. The dynamics of these dimensionality changes tracked the decoding accuracy for both behavioral embeddings and neural network features, suggesting that dimensionality may be a general indicator of representational expressivity. Interestingly, the dimensionality of the neural representations could not be fully explained by leading behavior-based or neural network models. Follow-up experiments showed that the remaining neural variance carried additional perceptually relevant information not yet explained by leading models. Together, these findings reveal previously unrecognized complexity in measurements of dynamic human brain responses to natural objects.

Nature, Published online: 22 April 2026; doi:10.1038/d41586-026-01338-6

Webs of star-shaped cells called astrocytes connect distant parts of the brain, allowing long-distance exchange of molecules.

Recent studies describe Eye Movement-related Eardrum Oscillations (EMREOs), low-frequency signals recorded in the ear canal that arise from the tympanic membrane and are triggered by saccadic eye movements. Because EMREOs are thought to arise from motor elements in the peripheral auditory system, we examined how two known modulators of these elements affect the EMREO time course. First, the activity of outer hair cells (OHC) can be suppressed by the medial olivocochlear reflex (MOCR). If OHCs contribute to the generation of EMREOs, activation of this reflex should reduce EMREO amplitude. To test this, we compared EMREO amplitudes elicited by saccades performed in silence and in the presence of contralateral noise. Second, gravitational cues linked to head orientation may influence EMREOs via oculomotor control circuits that possibly modulate middle ear muscles. To test this, we recorded EMREOs while participants made saccades with their head upright (0 degrees azimuth) and with their head tilted 30 degrees in either direction. Across both experiments our data reveal no clear modulation of the EMREO time course by these experimental manipulations. Together with other recent studies these findings advocate for a stability of the EMREO time course towards multiple experimental modulations and fuel speculations that the signal may serve as a temporal reference frame when combining signals across the senses.

Proceedings of the National Academy of Sciences, Volume 123, Issue 16, April 2026.
SignificanceWe present sparse identification of nonlinear dynamics with shallow recurrent decoders (SINDy-SHRED), which jointly solves the sensing, model reduction and model identification problem with simple implementation, efficient computation, and ...

Author(s): Gabriel Sorci, Joshua Foo, Dietrich Leibfried, Christian Sanner, and Igor Pikovski

High-precision clocks based on quantum systems will work in a regime where a quantum description of proper time might be necessary.

[Phys. Rev. Lett. 136, 163602] Published Mon Apr 20, 2026

The impressive progresses in machine learning have revived the fear that humans might eventually be wiped out or enslaved by artificial superintelligences. This is hardly a new fear. For example, this fear is the basis of most of Isaac Asimov’s books, who imagined that robots are built with three laws to protect humans.

My point here is not to demonstrate that such events are impossible. On the contrary, my point is that autonomous human-made entities already exist, and cause the exact same risks that AI alarmists are talking about, except they are real. In this context, evil AI fantasies are an anthropomorphic distraction.

Let me quickly dismiss some misconceptions. Does ChatGPT understand language? Of course not. Large language models are (essentially) algorithms tuned to predict the next words. But here we don’t mean “word” in the human sense. In the human sense, a word is a symbol that means something. In the computer sense, a word is a symbol, to which we humans attribute meaning. When ChatGPT talks about bananas, it has no idea what a banana tastes like (well, it has no idea). It has never seen a banana or tasted a banana (well, it has never seen or tasted). “Banana” is just a node in a big graph of other nodes, totally disconnected from the outside world, and in particular from what “banana” might actually refer to. This is known in cognitive science as the “symbol grounding problem”, and it is a difficult problem that LLMs do not solve. So, maybe LLMs “understand” language, but only if you are willing to define “understand” in such a way that it is not required to know what words mean.

Machine learning algorithms are not biological organisms, they do not perceive, they are not conscious, they do not have intentions in the human sense. But it doesn’t matter. The broader worry about AI is simply that these algorithms are generally designed so as to optimize some predefined criterion (e.g., prediction error), and if we give them very powerful means to do so, in particular means that involve real actions in the world, then who knows whether using those means might not be harmful to us? At some point, without necessarily postulating any kind of evil mind, we humans might become means in the achievement of some optimization criterion. We built some technical goals into the machine, but it is very difficult to ensure that those are aligned with human values. This is the so-called “alignment” problem.

Why not. We are clearly not there, but maybe, in a hypothetical future, or at least as a thought experiment. But what strikes me with the misalignment narrative is that this scenario is not at all hypothetical if you are willing to look beyond anthropomorphic evil robots. Have you really never heard of any human-made entities with their own goals, which might be misaligned with human values? Entities that are powerful and hard to control by humans?

There is an obvious answer if you look at the social rather than technological domain: it is the modern financialized multinational corporation. The modern corporation is a human-made organization that is designed in such a way as to maximize profit. It does not have intentions or goals in a human sense, but exactly like in the AI alignment narrative, it is simply designed in such a way that it will use all means available in order to maximize a predefined criterion, which may or may not be perfectly aligned with human values. Let’s call these companies “profit robots”.

To what extent are profit robots autonomous from humans? Today’s modern large corporations are owned not by people but in majority by institutional stakeholders, such as mutual funds, i.e., other organizations with the same goals. As is well known, their multinational nature makes them largely immune to the legislation of states (hence the issues of fiscal optimization, social dumping, etc). As is also well known, a large part of the resources of a profit robot is devoted to marketing and advertisement, that is, in manipulating humans into buying their products.

Profit robots also engage in intense lobbying to bend human laws in their favor. But more to the point, the very notion of law is not the same for a profit robot as for humans. For humans, a law is something that sets boundaries on what could be done or should not be done, morally. But a profit robot is not a person. It has no moral principles. So, law is just one particular constraint, in fact a financial cost or risk – a company does not go to prison. A striking example of this is the “Dieselgate”: Volkswagen (also not owned by humans) intentionally programmed their engines so that their car emissions remained hidden during the pollution tests required to authorize their cars on the US market. As far as I know, shareholders were not informed, and neither were consumers. The company autonomously decided to break the law for profit. Again, the company is not evil: it is not a person. It behaves in this non-human way because it is a robot, exactly like in the AI misalignment narrative.

We often hear that ultimately, it is the consumers who have power, by deciding what to buy. This is simply false. Consumers did not know that Volkswagen cheated on pollution tests. Consumers rarely know in what exact conditions the products are made, or even to what corporation the products belong. This type of crucial information is deliberately hidden. Profit robots, on the other hand, actively manipulate consumers into buying their products. What to think of planned obsolescence? Nobody wants products that are deliberately designed to break down prematurely, yet that is what a profit robot makes. So yes, profit robots are largely autonomous from the human community.

Are profit robots an existential risk for humans? That might be a bit dramatic, but they certainly do cause very significant risks. A particular distressing fact illustrates this. As the Arctic ice melts because of global warming, oil companies get ready to drill the newly available resources. Clearly this is not in the interest of humans, but this is what a company like Shell, who is only directly owned by humans in the proportion of 6%, needs to do to pursue its goals, which as any other profit robot, is to generate profit by whatever means.

So yes, there is a risk that powerful human-made entities get out of control and that their goals are misaligned with human values. This worry is reasonable because it is already realized, except not in the technological domain. It is ironic (but not so surprising) that billionaires buy into the AI misalignment narrative but fail to see that the same narrative fully applies to the companies that their wealth depends on, except it is realized.

The reasonable worry about AI is not that AI takes control of the world: the worry is that AI provides even more powerful means for the misaligned robots that are already out of control now. In this context, evil AI fantasies are an anthropomorphic distraction from the actual problems we have already created.

Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would enjoy more. Click here to watch his talk!

What’s great is that Tymoczkyo not faking it: he’s really found deep ways in which symmetry shows up pervasively in music.

At first he tried to describe them geometrically using orbifolds, which are spaces in which some singular points have nontrivial symmetry groups, like the tip of a cone formed by modding out the plane by the action of the group ℤ/n\mathbb{Z}/n. But then he realized that the geometry was less important than the symmetry, which you can describe using groupoids. That’s why his talk is called “Beyond the geometry of music”.

I’m helping him with his work on groupoids, and I hope he explains his work to mathematicians someday without pulling his punches. I didn’t get to interview him yesterday, but I’ll try to do that soon.

For now you can read his books A Geometry of Music and Harmony: an Owner’s Manual along with many papers. What I’ve read so far is really exciting.

The principle of explosion is that in an inconsistent system everything is provable: if you prove both and not- for any , you can then conclude for any :

$$(P \land \lnot P) \to Q.$$

This is, to put it briefly, not intuitive. But it is awfully hard to get rid of because it appears to follow immediately from two principles that are intuitive:

1. If we can prove that is true, then we can prove that at least one of or is true. (In symbols, .)

2. If we can prove that at least one of or is true, and we can prove that is false, then we may conclude that that is true. (Symbolically, .).

Then suppose that we have proved that is both true and false. Since we have proved true, we have proved that at least one of or is true. But because we have also proved that is false, we may conclude that is true. Q.E.D.

This proof is as simple as can be. If you want to get rid of this, you have a hard road ahead of you. You have to follow Graham Priest into the wilderness of paraconsistent logic.

Raymond Smullyan observes that although logic is supposed to model ordinary reasoning, it really falls down here. Nobody, on discovering the fact that they hold contradictory beliefs, or even a false one, concludes that therefore they must believe everything. In fact, says Smullyan, almost everyone does hold contradictory beliefs. His argument goes like this:

1. Consider all the things I believe individually, . I believe each of these, considered separately, is true.

2. However, I also believe that I'm not infallible, and that at least one of is false, although I don't know which ones.

3. Therefore I believe both (because I believe each of the separately) and (because I believe that not all the are true).

And therefore, by the principle of explosion, I ought to believe that I believe absolutely everything.

Well anyway, none of that was exactly what I planned to write about. I was pleased because I noticed a very simple, specific example of something I believed that was clearly inconsistent. Today I learned that K2, the second-highest mountain in the world, is in Asia, near the border of Pakistan and westernmost China. I was surprised by this, because I had thought that K2 was in Kenya somewhere.

But I also knew that the highest mountain in Africa was Kilimanjaro. So my simultaneous beliefs were flatly contradictory:

1. K2 is the second-highest mountain in the world.
2. Kilimanjaro is not the highest mountain in the world, but it is the highest mountain in Africa
3. K2 is in Africa

Well, I guess until this morning I must have believed everything!

The Law of Excluded Middle says that for any statement P, “P or not P” is true.

Is this law true? In classical logic it is. But in intuitionistic logic it’s not.

So, in intuitionistic logic we can ask what’s the probability that a randomly chosen statement obeys the Law of Excluded Middle. And the answer is “at most 2/3—or else your logic is classical”.

This is a very nice new result by Benjamin Bumpus and Zoltan Kocsis:

• Benjamin Bumpus, Degree of classicality, Merlin’s Notebook, 27 February 2024.

Of course they had to make this more precise before proving it. Just as classical logic is described by Boolean algebras, intuitionistic logic is described by something a bit more general: Heyting algebras. They proved that in a finite Heyting algebra, if more than 2/3 of the statements obey the Law of Excluded Middle, then it must be a Boolean algebra!

Interestingly, nothing like this is true for “not not P implies P”. They showed this can hold for an arbitrarily high fraction of statements in a Heyting algebra that is still not Boolean.

Here’s a piece of the free Heyting algebra on one generator, which some call the Rieger–Nishimura lattice:

I disagree with this statement, but boy, Hilbert sure could write!

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. As a by-product, a topological classifier is defined that uses an open sub-covering of the data set. This sub-covering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

Primates can recognize objects despite 3D geometric variations such as in-depth rotations. The computational mechanisms that give rise to such invariances are yet to be fully understood. A curious case of partial invariance occurs in the macaque face-patch AL and in fully connected layers of deep convolutional networks in which neurons respond similarly to mirror-symmetric views (e.g., left and right profiles). Why does this tuning develop? Here, we propose a simple learning-driven explanation for mirror-symmetric viewpoint tuning. We show that mirror-symmetric viewpoint tuning for faces emerges in the fully connected layers of convolutional deep neural networks trained on object recognition tasks, even when the training dataset does not include faces. First, using 3D objects rendered from multiple views as test stimuli, we demonstrate that mirror-symmetric viewpoint tuning in convolutional neural network models is not unique to faces: it emerges for multiple object categories with bilateral symmetry. Second, we show why this invariance emerges in the models. Learning to discriminate among bilaterally symmetric object categories induces reflection-equivariant intermediate representations. AL-like mirror-symmetric tuning is achieved when such equivariant responses are spatially pooled by downstream units with sufficiently large receptive fields. These results explain how mirror-symmetric viewpoint tuning can emerge in neural networks, providing a theory of how they might emerge in the primate brain. Our theory predicts that mirror-symmetric viewpoint tuning can emerge as a consequence of exposure to bilaterally symmetric objects beyond the category of faces, and that it can generalize beyond previously experienced object categories.

In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is viewed as a trajectory evolving within a network of non-chaotic, dynamically unstable, time-invariant solutions embedded in the chaotic attractor of the system. While equilibria, periodic orbits and invariant tori can be constructed using existing methods, computations of heteroclinic and homoclinic connections mediating the evolution between the former invariant solutions remain challenging. We propose a robust matrix-free variational method for computing connecting orbits between equilibrium solutions of a dynamical system that can be applied to high-dimensional problems. Instead of a common shooting-based approach, we define a minimization problem in the space of smooth state space curves that connect the two equilibria with a cost function measuring the deviation of a connecting curve from an integral curve of the vector field. Minimization deforms a trial curve until, at a global minimum, a connecting orbit is obtained. The method is robust, has no limitation on the dimension of the unstable manifold at the origin equilibrium, and does not suffer from exponential error amplification associated with time-marching a chaotic system. Owing to adjoint-based minimization techniques, no Jacobian matrices need to be constructed and the memory requirement scales linearly with the size of the problem. The robustness of the method is demonstrated for the one-dimensional Kuramoto-Sivashinsky equation.

Merriam-Webster's Word of the Day for January 27, 2023 is:

wangle • \WANG-gul\  • verb

Wangle means “to get (something) by trickery or persuasion.” It can also mean “to adjust or manipulate for personal or fraudulent ends.”

// He managed to wangle his way into the party.

// They wangled me into pleading guilty.

See the entry >

Examples:

“Discussions of how to wangle free shipping or discounts dovetailed with a proposition that the group start a fund-raiser for a family in need—a worthy use for money saved.” — Hannah Goldfield, The New Yorker, 27 Mar. 2021

Did you know?

You may have noticed a striking resemblance between wangle and wrangle, both of which have a sense meaning “to obtain or finagle.” But the two do not share a common history: wrangle is centuries older than wangle, and despite their overlap in both meaning and appearance, wangle is believed to have evolved separately by way of waggle, meaning “to move from side to side.” (Wrangle, by contrast, comes from the Old High German word ringan, meaning “to struggle.”) It’s possible, though, that wangle saved the “obtain” sense of wrangle from the brink of obsolescence—until recent decades, this usage had all but disappeared, and its revival may very well have been influenced by wangle. We wish we could wangle conclusive evidence to support this theory, but alas!

Nature, Published online: 27 January 2023; doi:10.1038/d41586-023-00197-9

Prairie voles lacking oxytocin receptors bonded with mates and cared for pups.

Memories initially formed in hippocampus gradually stabilize to cortex, over weeks-to-months, for long-term storage. The mechanistic details of this brain re-organization process remain poorly understood. In this study, we developed a virtual-reality based behavioral task and observed neural activity patterns associated with memory reorganization and stabilization over weeks-long timescales. Initial photometry recordings in circuits that link hippocampus and cortex revealed a unique and prominent neural correlate of memory in anterior thalamus that emerged in training and persisted for several weeks. Inhibition of the anteromedial thalamus-to-anterior cingulate cortex projections during training resulted in substantial memory consolidation deficits, and gain amplification more strikingly, was sufficient to enhance consolidation of otherwise unconsolidated memories. To provide mechanistic insights, we developed a new behavioral task where mice form two memories, of which only the more salient memory is consolidated, and also a technology for simultaneous and longitudinal cellular resolution imaging of hippocampus, thalamus, and cortex throughout the consolidation window. We found that whereas hippocampus equally encodes multiple memories, the anteromedial thalamus forms preferential tuning to salient memories, and establishes inter-regional correlations with cortex, that are critical for synchronizing and stabilizing cortical representations at remote time. Indeed, inhibition of this thalamo-cortical circuit while imaging in cortex reveals loss of contextual tuning and ensemble synchrony in anterior cingulate, together with behavioral deficits in remote memory retrieval. We thus identify a thalamo-cortical circuit that gates memory consolidation and propose a mechanism suitable for the selection and stabilization of hippocampal memories into longer term cortical storage.

Author(s): Yang Long and Baile Zhang

An unsupervised learning approach leads to the classification of topological gapped systems without a priori knowledge of topological invariants.

[Phys. Rev. Lett. 130, 036601] Published Wed Jan 18, 2023

Just a total shocker that only every journalist knows but won't explain.

Federal prosecutors say the former head of counterintelligence for the FBI’s New York office laundered money, violated sanctions against Russia while working with a Russian oligarch and while still at the FBI took hundreds of thousands of dollars from a foreign national and former foreign intelligence official.

With two hands tied behind my back, I could not solve this mystery!

...ahaha a direct connection.

So to be clear, McGonigal was running the FBI's Trump-Russia probe at the moment this story -- at the most critical moment of the 2016 -- was leaked to the New York Times https://t.co/K4FfJW5pz6

— Will Bunch (@Will_Bunch) January 23, 2023

Systematic spatial variation in micro-architecture is observed across the cortex. These micro-architectural gradients are reflected in neural activity, which can be captured by neurophysiological time-series. How spontaneous neurophysiological dynamics are organized across the cortex and how they arise from heterogeneous cortical micro-architecture remains unknown. Here we extensively profile regional neurophysiological dynamics across the human brain by estimating over 6,800 time-series features from the resting state magnetoencephalography (MEG) signal. We then map regional time-series profiles to a comprehensive multi-modal, multi-scale atlas of cortical micro-architecture, including microstructure, metabolism, neurotransmitter receptors, cell types and laminar differentiation. We find that the dominant axis of neurophysiological dynamics reflects characteristics of power spectrum density and linear correlation structure of the signal, emphasizing the importance of conventional features of electromagnetic dynamics while identifying additional informative features that have traditionally received less attention. Moreover, spatial variation in neurophysiological dynamics is co-localized with multiple micro-architectural features, including genomic gradients, intracortical myelin, neurotransmitter receptors and transporters, and oxygen and glucose metabolism. Collectively, this work opens new avenues for studying the anatomical basis of neural activity.

Brilliant young scientists are struggling to obtain a stable faculty position, all over the world. It seems that “publish or perish” was actually quite hopeful. Now clearly, at least in biology, it is more like “publish in Science, Nature or Cell every other year or perish”. Only a small proportion of PhD holders manage to obtain a stable academic position, and only at an advanced age after multiple postdocs. Of course, this competition for publishing in certain venues also has a great impact on science; encouraging dishonesty and discouraging both long-term creative work and solid incremental science. Everyone complains about the situation.

What should we do about it? What I hear most frequently is that governments should increase the budget and create more faculty positions. That is certainly necessary but I think it is a reductionist view that largely misses the point. Of course, at the time when you start hiring more faculty, the proportion of young scientists who get a faculty position increases. However, if each of them then opens their lab and hire dozens of postdocs, then this proportion quickly reverts to what it was before.

What is at stakes is the general organization of research, in particular the “X lab” model (e.g. the Brette lab), with one group leader (the “PI”) surrounded by a number of graduate students and postdocs (I will discuss only the research staff here), with a complete turnover every few years. It seems that in many countries, to get a faculty position means to start their “own” lab. This is not the case yet in France, but this lab model is spreading very, very fast. With the new law on research currently in discussion (“discussion” might not be the appropriate word, though), it is planned that about 25% of all new recruitments will follow this model (a tenure-track system).

The math is easy. In a stable world, each faculty member will train on average one student to become a faculty member. For example, if a typical lab consists of 1 PI with 3 graduate students, rotating every 4 years, then over 40 years the PI will have trained 30 students, one of which would become a PI. The “success rate” would therefore be 1/30. Even with just one student at any given time, the chance for a student to end up getting a faculty position is 1/10.

Of course, one does not necessarily pursue a PhD with the goal of obtaining a faculty position. It is completely respectable to do a PhD then go to the industry. In many countries, holding a PhD is an asset. It is generally not the case in France, though. One may also want to do a PhD not for career, but because it is interesting in itself. This seems perfectly valid. Note that in that case, implementing a subtask of the PI’s project and doing all the tedious bench work might not be ideal. In any case, it must be emphasized that in this lab model, training students for research is only a marginal aim of a PhD.

How about postdocs? A postdoc is not a diploma. It typically doesn’t improve employability much. Of course, it could be done just for its own interest. But the experience I hear is mostly that of a highly stressful situation, because many if not most postdocs are hoping to secure a stable faculty position. Let us do the math again, with a simplified example. Suppose each lab has just 1 postdoc, rotating every 4 years. Compared to the above situation, it means that 1 out of 3 graduate students go on to do a postdoc. Then each of these postdocs has a 10% chance of getting a faculty position.

Let us have a look at funding questions now. What seems very appreciated is that when you start a lab, you get a “start-up package”. There is a blog post on Naturejobs entitled “The faculty series: Top 10 tips on negotiating start-up packages” that describes it. We can read for example: “There’s no point having equipment if you don’t have any hands to use it. One of the largest costs you can expect to come out of your start-up fund are the salaries of PhD students and postdocs. They’re the most crucial components of the lab for almost all researchers.”. It is very nice to provide the PI with these “components of the lab”, but as argued above, a direct consequence is to organize academic precarity on a massive scale. This remains true even if the entire budget of the State is allocated to research.

The same goes for the rest of the funding system. Project-based funding is conceived so that you hire people to implement your project, which you supervise. Part of these people are students and postdocs. For example, an ERC Starting Grant is 1.5 million euros for 5 years, or 300 k€ per year. In France, a PhD student costs about 30 k€ / year and a postdoc about the double. Of course, to that must be added the indirect costs (25%) and the grant also covers equipment and your own salary. But this is generally sufficient to hire a few students and postdocs, especially as in many countries graduate students are funded by other sources. Then the budget goes up to 2 million € for the consolidator grant and 2.5 million € for the advanced grant. The ERC has become a sort of model for good funding schemes in Europe, because it is so generous. But is it? Certainly it is for the PI who receives the grant, but a world where this mode of funding is generalized is a world where research is done by a vanishingly small proportion of permanent researchers. It is a world that is extremely cruel to young scientists, and with a very worrying demographic structure, most of the work being done by an army of young people with high turnover. You might increase the ERC budget several fold because it is such a great scheme, it will not improve this situation, at all.

Ending academic precarity is a noble cause, but one has to realize that it is inconsistent with the one PI - one lab model, as well as with project-based funding. I want to add a couple of remarks. Precarity is obviously bad for the people who experience it, but it is also bad more generally for the academic system. The excessive competition it generates encourages bad practices, and discourages long-term creative work and solid incremental science. We must also look beyond research per se. The role of academia in society is not just to produce new science. It is also to teach and to provide public expertise. We need to have some people with a deep understanding of epidemiology that we can turn to for advice when necessary. You would not just hire a bunch of graduate students after a competitive call for projects to do this advising job when a new virus emerges. But with a pyramidal organization, a comparatively low proportion of the budget is spent on sustaining the most experienced persons, so for the same budget, you would have much lower expertise than in an organization with more normal demographics. This is incredibly wasteful.

What is the alternative? Well, first of all, research has not always been organized in this way, with one PI surrounded by an army of students and postdocs. The landmark series of 4 papers by Hodgkin and Huxley in 1952 on the ionic basis of neural excitability did not come out of the "Hodgkin lab"; they came out from “the Physiological Laboratory, University of Cambridge”. The Hubel and Wiesel papers on the visual cortex were not done by graduate student Hubel under the supervision of professor Wiesel. Two scientists of the same generation decided to collaborate together, and as far as I know none of their landmark papers from the 1960s involved any student or postdoc. What strikes me is that these two experienced scientists apparently had the time to do the experiments themselves (all the experiments), well after they got a stable faculty position (in 1959). How many PIs can actually do that today, instead of supervising, hiring, writing grants and filling reports? It is quite revealing to read again the recent blog post cited above: “There’s no point having equipment if you don’t have any hands to use it.” - as if using it yourself was not even conceivable.

In France, the 1 PI - 1 lab kind of organization has been taking on gradually over the last 20 years, with a decisive step presumably coming this year with the introduction of a large proportion of tenure tracks with “start-up packages”. This move has been accompanied by a progressive shift from base funding to project-based funding, and a steady increase in the age of faculty recruitment. This is not to say that the situation was great 20 years ago, but it is clearly worsening.

A sustainable, non-pyramidal model is one in which a researcher would typically train no more than a few students over her entire career. It means that research work is done by collaboration between peers, rather than by hiring (and training) less experienced people to do the work. It means that research is not generically funded on projects led by a single individual acting as a manager. In fact, a model where most of the working force is already employed should have much less use of “projects”. A few people can just decide to join forces and work together, just as Hubel and Wiesel did. Of course, some research ideas might need expenses beyond the usual (e.g. equipment), and so there is a case for project-based funding schemes to cover for these expenses. But it is not the generic case.

One of the fantasies of competitive project-based funding is that it would supposedly increase research quality by selecting the best projects. But how does it work? Basically, peers read the project and decide whether they think it is good. Free association is exactly that, except the peers in question 1) are real experts, 2) commit to actually do some work on the project and possibly to bring some of their own resources. Without the bureaucracy. Peer reviewing of projects is an unnecessary and poor substitute for what goes on in free collaboration - do I think this idea is exciting enough to devote some of my own time (and possibly budget) on it?

In conclusion, the problem of academic precarity, of the unhealthy pressure put on postdocs in modern academia, is not primarily a budget problem. At least it is not just that. It is a direct consequence of an insane organization of research, based on general managerial principles that are totally orthogonal to what research is about (and beyond: teaching, public expertise). This is what needs to be challenged.

Update:

• a presentation in French on this topic.
• an article in French: Le modèle managérial de la recherche : critique et alternative.

The so-called ``small denominator problem'' was a fundamental problem of dynamics, as pointed out by Poincar\'{e}. Small denominators appear most commonly in perturbative theory. The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators. In this paper, using the forced Duffing equation as an example, we illustrate that the famous ``small denominator problems'' never appear if a non-perturbative approach based on the homotopy analysis method (HAM), namely ``the method of directly defining inverse mapping'' (MDDiM), is used. The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained. So, from the viewpoint of the HAM, the famous ``small denominator problems'' are only artifacts of perturbation methods. Therefore, completely abandoning perturbation methods but using the HAM-based MDDiM, one would be never troubled by ``small denominators''. The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called ``small denominators''.

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system's state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary and only a specific subspace is relevant. Here, we establish the theoretic condition to reconstruct a nonlinear functional of state variables from measurement processes, generalizing the concept of functional observability to nonlinear systems. When the functional observability condition holds, we show how to construct a map from the embedding space to the desired functional of state variables, characterizing the quality of such reconstruction. The theoretical results are then illustrated numerically using chaotic systems with contrasting observability properties. By exploring the presence of functionally unobservable regions in embedded attractors, we also apply our theory for the early warning of seizure-like events in simulated and empirical data. The studies demonstrate that the proposed functional observability condition can be assessed a priori to guide time-series analysis and experimental design for the dynamical characterization of complex systems.