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It was 1,229 CE in the monastery of St Sabas, near Jerusalem, and a monk named Johannes Myronas was in need of some parchment. He had evidently been tasked with creating a copy of the Euchologion – an important book of prayer and worship directions for Eastern Orthodox and Byzantine Catholic churches.

The problem was, parchment was expensive and hard to come by. Recycling was the name of the game, and Johannes had just the thing: a 200-year-old manuscript filled with old math notes that nobody was all that interested in anymore. Compared with the Holy Word, there was no contest: he pulled it apart, scraped the old text off, and used the pages for the new book – a technique known as palimpsesting.

You probably know where this is going. In creating his Euchologion, Johannes had – presumably unwittingly – destroyed one of the most valuable relics of Archimedes’s work. Not just some notebook or single treatise, even: the manuscript now known as “Codex C” contained multiple works from the ancient polymath, some of which now exist nowhere else in the world.

In the fast-paced world of electric vehicles (EVs), a major breakthrough in battery technology is set to significantly enhance energy storage capacity. This development arrives at a crucial moment, as the EV industry is experiencing rapid growth, making it an ideal time for such a transformative advancement.

Researchers at Pohang University of Science & Technology (POSTECH) have introduced a revolutionary technique that can amplify the energy storage capacity of batteries by an astonishing tenfold. This leap forward not only propels battery technology to new heights but also has the potential to reshape the entire landscape of electric vehicles.

The key to understanding battery function lies in the anode, the component responsible for storing power during charging and then releasing it when the battery is in use. In most modern lithium batteries, graphite is the predominant material used for anodes.

In a Mn3Sn/W epitaxial bilayer, spin–orbit torque induces the coherent rotation of spins, which can couple to microwave currents. Unlike in ferromagnets, the resulting conversion of AC current to DC voltage remains robust at higher frequencies, which may facilitate the development of high-speed electronic devices.

All DNA is prone to fragmentation, whether it is derived from a biological matrix or created during gene synthesis; thus, any DNA sample will contain a range of fragment sizes. To really exploit the true benefits of long read sequencing, it is necessary to remove these shorter fragments, which might other wise be sequenced preferentially.

DNA size selection can exclude short fragments, maximizing data yields by ensuring that those fragments with the most informational content are not blocked from accessing detection centers (for example, ZMWs) by shorter DNA fragments.

Next-generation size-selection solutions Starting with clean, appropriate-length fragments for HiFi reads can accelerate research by reducing the computation and data processing time needed post-sequencing. Ranger Technology from Yourgene Health is a patent-protected process for automating electrophoresis-based DNA analysis and size selection. Its fluorescence machine vision system and image analysis algorithms provide real-time interpretation of the DNA separation process.

Another well-known method for physical learning is Equilibrium Propagation (EP), sharing similar procedure with coupled learning and being able to define the arbitrary differentiable loss function32. This method has been demonstrated in various physical systems, numerically in nonlinear resistor networks33 and coupled phase oscillators34, experimentally on Ising machines35.

So far, the MNNs based on the physical learning have been developed using the platform of origami structures28,36 and disordered networks29,37 to demonstrate machine learning through simulations. The experimental proposals involve using directed springs with variable stiffness38 and manually adjusting the rest length of springs31.

Here, we present a highly-efficient training protocol for MNNs through mechanical analogue of in situ backpropagation, derived from the adjoint variable method, in which theoretically the exact gradient can be obtained from only the local information. By using 3D-printed MNNs, we demonstrate the feasibility of obtaining the gradient of the loss function experimentally solely from the bond elongation of MNNs in only two steps, using local rules, with high accuracy. Besides, leveraging the obtained gradient, we showcase the successful training in simulations of a mechanical network for behaviors learning and various machine learning tasks, achieving high accuracy in both regression and Iris flower classification tasks. The trained MNNs are then validated both numerically and experimentally. In addition, we illustrate the retrainability of MNNs after switching tasks and damage, a feature that may inspire further inquiry into more robust and resilient design of MNNs.