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Nature, Published online: 11 December 2024; doi:10.1038/d41586-024-03651-4
It has been hard to find fungi that normally reside in the mouse gut. The identification of one such fungus deepens our understanding of how resident fungi drive immune responses in their natural hosts.
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Researchers have shown in mice experiments that an mRNA-based therapy can reverse the underlying causes of pre-eclampsia, a deadly complication of pregnancy for which treatment options are limited. Inspired by the success of mRNA vaccines, the team behind the work designed a method to deliver the genomic instructions for a blood-vessel growth factor directly into mouse placentas. This stimulated the production of extra blood vessels reducing the very high-blood pressure associated with the condition. Pre-eclampsia causes 15% of maternal deaths and 25% of foetal and newborn deaths worldwide and although the work is early and human trials will be required, the team hope that this work demonstrates the potential of using this approach to treat pre-eclampsia.
Research Article: Swingle et al.
News and Views: Lipid-delivery system could treat life-threatening pregnancy complication
Stacks of mass-produced bowls suggest that people founded but then abandoned an ancient Mesopotamian civilization, and analysis of Venus’s gases suggests that the planet was always dry.
Research Highlight: Ancient stacks of dishes tell tale of society’s dissolution
Research Highlight: Has Venus ever had an ocean? Its volcanoes hint at an answer
A team of scientists have created cellular switches on the surface of cells, allowing them to control custom behaviours. Creating these switches has been a long-term goal for synthetic biologists — one target has been a group of proteins called G-protein-coupled receptors that already control many cellular processes. However, engineering these proteins has been challenging, as modifications can ruin their function. Instead, the team added another molecular component that blocked the receptors activity, but could be removed in response to specific signals. This allowed the researchers to activate these receptors on command, potentially opening up a myriad of new ways to control cell behaviour, such as controlling when neurons fire.
Research Article: Kalogriopoulos et al.
A team at Google has shown it is possible to create a quantum computer that becomes more accurate as it scales up, a goal researchers have been trying to achieve for decades. Quantum computing could potentially open up applications beyond the capabilities of classical computers, but these systems are error-prone, making it difficult to scale them up without introducing errors into calculations. The team showed that by increasing the quality of all the components in a quantum computer they could create a system with fewer errors, and that this trend of improvement continued as the system became larger. This breakthrough could mean that quantum computers are getting very close to realising the useful applications that their proponents have long promised.
Nature: ‘A truly remarkable breakthrough’: Google’s new quantum chip achieves accuracy milestone
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Some researchers worry that if AI systems become conscious and people neglect or treat them poorly, they might suffer.Credit: Pol Cartie/Sipa/Alamy
A group of philosophers and computer scientists are encouraging tech companies to assess their artificial intelligence (AI) systems for signs of consciousness, and to develop policies that safeguard the systems’ welfare should it ever happen. If they don’t do this, the group argues, companies risk causing AI systems to suffer. The notion has divided researchers — some think the idea is laughable, while others agree there’s no harm in planning. “Even an imperfect initial framework can still be better than the status quo,” says philosopher and report co-author Jeff Sebo.
Nature | 5 min read
Reference: arXiv preprint (not peer reviewed)
A year from now, children under the age of 16 in Australia will be barred from many social-media platforms — the highest minimum-age limit in the world. The government hasn’t said which platforms will be off-limits, but the legislation will include those that allow users to post content and interact with two or more users, such as Snapchat and TikTok. Many parents have applauded the approach, but some researchers question the law’s enforceability and say there is minimal evidence that it will keep children safe from online harm.
Nature | 5 min read
One year into the term of libertarian president Javier Milei, his agenda to slash Argentina’s deficit has meant that, as his administration’s slogan says, “there is no money” for science. The country’s main funder of research projects has been forced to come to a virtual halt, despite most of its money coming from international agencies. Government-funded scientists have seen salaries fall and many have recoiled from Milei’s rejection of climate science. The result is that the country is facing a huge brain drain. “With six more months like this, there will be nothing left” of the scientific community, says Mariano Cantero, the director of an institute in Bariloche.
Nature | 6 min read
Exposure to extreme heat could be linked to molecular changes that reflect accelerated ageing. Researchers looked at data from almost 4,000 people and cross-referenced their ‘epigenetic clocks’ — a collection of chemical modifications to DNA as people age — with temperature maps. The team found that people who lived in areas with more hot days had ‘older’ molecular ages than those who had experienced cooler weather. However, factors such as how long each person spent outside, and whether they had air conditioning, weren’t taken into account.
Nature | 4 min read
The vast improvements in artificial intelligence have largely been a matter of scaling — researchers build a bigger neural network and they train it on more data. But progress might be about to hit a roadblock. A study published this year projected that by 2028, the size of a typical training-data set will equal all of the text that is publicly available online. Put simply, AI is about to run out of training data. Researchers now face a dilemma: find and use training data from untapped sources, such as instant messages, or change course to focus on smaller, more efficient models.
Nature | 10 min read
Reference: Proceedings of the 41st International Conference on Machine Learning paper
Source: Ref. 1
Endocrinologist Andrew Schally, whose most enduring legacy lies in his groundbreaking discovery of brain hormones that regulate the pituitary gland, has died aged 97. His decades-long rivalry with his former supervisor, neuroscientist Roger Guillemin, culminated in them sharing the Nobel Prize in Physiology or Medicine in 1977 (alongside medical physicist Rosalyn Yalow, who won for unrelated work). A child refugee from Nazi-occupied eastern Europe, Schally was particularly dedicated to advancing health care for veterans, write chemist Renzi Cai and endocrinologist Medhi Wangpaichitr.
Nature | 5 min read
Physicians are concerned about the growing number of parents giving their young children microbiome interventions such as probiotics. These live microorganisms are intended to improve health, but they are not regulated as drugs in the United States, and they can cause sepsis and increase the risk of mucosal illnesses in children. Faecal microbiota transplants (FMTs) approved to treat disorders such as inflammatory bowel disease in adults are largely unavailable to children, so parents sometimes turn to do-it-yourself options. “You may feel like you’re making people better, but you’re really taking a huge risk,” says gastroenterologist Stacy Kahn, who has treated children as young as one as the director of a FMT programme at a US children’s hospital.
Nature | 12 min read
This article is part of Nature Outlook: The human microbiome, an editorially independent supplement produced with financial support from Yakult.
Today I’m planning exactly how much swag I can stuff into my Xmas stocking by studying the long-sought solution to ‘the sofa problem’. In a preprint, mathematician Jineon Baek has shown that the maximum area of a sofa that can fit round the corner of a 1-unit-wide hallway is 2.2195 units. However, the maximum-sized sofa involved — as well as the biggest gift I can wedge into the toe of my stocking — is a slightly quirky shape, with a narrow curved seat and wide curved arms.
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We purchased V2O5 from US Research Nanomaterials and polystyrene latex spheres, 330 nm in diameter, from Thermo Fisher Scientific.
The examined pillar was extracted from a sintered millimetre-sized pellet. This was prepared from a mixture of nanocrystalline V2O5 and polystyrene spheres (85/15 wt%). Mortar and pestle (10 min) was used to homogenize the mixture before the pellet was pressed using a 17 mm die set (3 min, 1.2 t uniaxial load). To increase the V2O5 grain size, sinter and create the desired porous structure, we heated the pellet to 590 °C for 5 h (Supplementary Fig. 1 and Supplementary Note 2). The polycrystalline V2O5 pillar was prepared by mechanically fracturing the sintered pellet, after which a fracture piece was mounted on an OMNY tomography pin51 using epoxy resin. The pillar was then pre-shaped using a microlathe52, before being reduced in diameter to 6 µm using focused ion beam (FIB) milling. This pillar was then transferred onto a second OMNY pin51. The tip of the second OMNY pin was sharpened using FIB milling before transferring the pillar. This was necessary to facilitate tomography measurements with a 30° stage tilt26. See Supplementary Fig. 3 for micrographs of the prepared pillar.
Scanning electron microscopy and FIB milling were performed using a Zeiss NVision 40 dual-beam FIB. Powder X-ray diffraction measurements of the sample before and after sintering were acquired using a Cu K-α radiation source with a step size of 0.02° 2θ, (refs. 53,54) (Supplementary Fig. 2). The sintered sample consists of α-V2O5 with a grain size >100 nm.
V2O5 has a layered orthorhombic crystal structure consisting of distorted [VO5] pyramids, shown schematically in Fig. 1b. These pyramids tile along the a–b plane and are bound with van der Waals interactions along the c axis. The apical, vanadyl bond of these pyramids, aligned with the crystallographic c axis, is shorter (1.57 Å) compared with the bonds on the base of the pyramid (1.87 Å). This shorter bond breaks the symmetry of an otherwise regular square pyramid55. To examine the spatial orientation of the apical bond and, in turn, the orientation of entire grains and deviations within them, the energy of the incident X-rays was set to that of the vanadium K pre-edge peak55. This peak arises from the V (1 s) to V (4p-3d) transition, more specifically, to V (3d eg + 4p) + O 2pz mixing states, which become accessible as a result of the deviation of the V coordination from the octahedral symmetry. When the apical bond is parallel to the direction of the electric field of the incident X-rays, the interaction is strong, as the transition V (1 s) to V (4p-3d) is allowed. When the apical bond is instead perpendicular to the incident polarization, the interaction is weaker29,55. An illustration of the different absorption strengths that result from the relative orientation between the incident X-ray polarization and the apical bond, known as linear dichroism, is shown in Fig. 1b. The X-ray near-edge absorption and phase spectra of V2O5 measured using LH and LV polarizations are shown in Supplementary Fig. 4 and a schematic of the layered crystal structure is provided in ref. 29.
In the above-described relationship between the polarization state of the illumination and the examined asymmetry or anisotropy, the linearly polarized light acts as a ‘search light’ for the resonant bond to which the polarization is parallel. This relationship applies, in principle, to all cases of natural linear dichroism16,42. The connection between the investigated anisotropy orientation and the unit-cell orientation of the material can be obtained through the use of reference samples, as showcased in 2D linear dichroic microscopy applications36, and is already available in the literature for numerous materials. It can also be readily determined with previous knowledge of the material’s crystal structure (or molecular arrangement)55.
Ptychography is a lensless imaging technique in which the phase problem is solved by means of iterative phase-retrieval algorithms27. By applying ptychography to solve the phase problem at different projection angles, its tomographic extension, ptychographic X-ray computed tomography (PXCT)56, is able to retrieve the complex-valued transmissivity of the specimen, providing quantitative tomograms of both phase and amplitude contrast32. Both the individual images—or projections—and resulting tomograms obtained using X-ray ptychography are sensitive to changes in the complex-valued refractive index, η. The real part of the refractive index decrement, δ, corresponds to the phase, whereas the imaginary part of the refractive index corresponds to the amplitude, β. The refractive index is fundamentally an expression of the complex atomic scattering factor, f = f1 + if2. The refractive index is therefore given by:
$$n=1-\delta -{\rm{i}}\beta =1-\frac{{r}_{{\rm{e}}}}{2{\rm{\pi }}}{\lambda }^{2}\sum _{k}{n}_{{\rm{at}}}^{k}({f}_{1}^{k}\,+{if}_{2}^{k}),$$
(1)
with re being the classical electron radius and λ the illumination wavelength57,58. The images and tomograms resulting from measurements performed with incident X-ray energies away from sample-relevant absorption edges can, in the case of tomograms, be converted to quantitative electron-density, ne, and absorption index, µ, tomograms32. Measurements conducted near sample-relevant absorption edges, that is, examining specific electronic transitions and the associated increase in the photoabsorption cross-section, are subject to anomalous scattering effects57,58, including dichroism.
The angular dependence of the linear dichroism has previously been used in a microscopy context, in particular in X-ray linear dichroism microscopy with secondary imaging modalities such as photoemission electron microscopy, to provide a 2D spatially resolved microstructural characterization tool16,29,30,36,59,60. The reader is directed to the initial work of Ade and Hsiao16 and the more recent works of Gilbert et al.36,61,62,63 and Collins et al.59,60,64. In the present work, we have developed the capability to map the orientation in 3D by combining X-ray linear dichroism microscopy with PXCT (XL-DOT).
Although XL-DOT can be applied with a range of imaging techniques, such as scanning transmission X-ray microscopy, we have selected X-ray ptychography as the imaging modality, a choice motivated by three factors. (1) PXCT provides quantitative or absolute contrast tomograms, which is ideal for material or component identification and for the detection of marginal signal variations11,30. (2) As a lensless imaging technique, ptychography excels in terms of signal-to-noise ratio (SNR), spatial resolution and dose efficiency (per resolution element) compared with other methods65,66,67,68. Given its superior SNR, it is ideal for measuring the relatively weak linear dichroism signal exhibited by V2O5 (refs. 30,61). (3) Ptychography can access the phase component. Phase changes at the vanadium K-edge are twice as large as changes in the absorption, so that the retrieved phase projections have a higher spatial resolution and superior SNR; see Supplementary Figs. 5 and 6 (ref. 58). We performed all data analysis on the phase component of the projections and tomograms only.
Experiments were carried out at the coherent small-angle X-ray scattering (cSAXS) beamline of the Swiss Light Source. The photon energy was selected using a double-crystal Si(111) monochromator. The horizontal aperture of slits located 22 m upstream of the sample was set to 20 μm, creating a virtual source point that coherently illuminates a 220-μm-diameter Fresnel zone plate with an outermost zone width of 60 nm and with engineered aberrations designed to improve reconstruction contrast and spatial resolution50. Coherent diffraction patterns were acquired using an in-vacuum Eiger 1.5M area detector, with a 75 µm pixel size, placed 5.235 m downstream of the sample inside an evacuated flight tube. Tomography experiments were performed using the positioning instrument described in ref. 69.
To map the local orientation of the apical bond within the examined sample volume in 3D, we exploited its linear dichroism and acquired eight equiangular ptychographic tomograms over 180° at 5.469 keV for different illumination polarizations and sample tilts. Specifically, ptychographic tomograms were acquired with a LH and LV polarization of the incident illumination at 0° stage tilt and at 30° stage tilt (sample in grey and pink in the top two panels on the right of Fig. 1a). Two further tilts were measured, whereby the sample was first rotated by +90° and −90° about the main axis of the pillar, followed by a 30° stage tilt26. The last two tilts are equivalent to tilting towards and away from the beam by 30° (sample in green and blue in the bottom two panels on the right of Fig. 1a). Examination under different sample tilts and X-ray polarizations is required to have sufficient information for the construction of an orientation tomogram representative of the apical bond orientation in 3D26,47. To change the illumination source native horizontal polarization to vertical, we used a 250-µm-thick diamond crystal phase plate inserted into the illumination path upstream of the zone plate (see Fig. 1a). The phase plate absorbed approximately 65% of the incident photons70. The degree of polarization of the X-rays was determined to be approximately 60% using a polarization analyser set-up. The sample tilt was changed using a sample holder insert26. To minimize the acquisition time, we used an adaptive field of view for each group of ptychographic projections. The maximum field of view, horizontal × vertical, was about 24 × 25 μm2. The scanning followed a Fermat’s spiral pattern71. An average step size of 0.8 µm was used for all tomograms. The exposure time per scanning point was 0.1 s. 280 projections were acquired per tomogram.
Finally, using the same acquisition parameters, we acquired an off-resonance ptychographic tomogram of the pillar below the absorption edge at 5.4 keV. This tomogram, being insensitive to any dichroic effects, was used for computing the electron-density tomogram and subsequently used for compositional analysis11. It should be noted that the starting angle and angular spacing of projections was kept constant across all tomograms.
Ptychographic images (or tomographic projections) were reconstructed using the PtychoShelves package72. For each reconstruction, a region of 600 × 600 pixels of the detector was used per scanning point, resulting in an image pixel size of 30.91 nm for the pre-edge and 31.29 nm for the below-edge tomogram. Reconstructions were obtained with 200 iterations of the difference map algorithm73, followed by 300 iterations of maximum likelihood refinement74.
Before any tomogram reconstructions, we: (1) resampled all projections to a pixel size of 30.91 nm using Fourier interpolation; (2) extracted the phase from the reconstructed projections, removed constant and linear phase components and spatially aligned the projections using a tomographic consistency approach31; and (3) aligned all projections to a common pillar orientation. As a last step, the different orientations at which projections were measured were characterized by a 3D rotation matrix26, which was input into a specially developed reconstruction code (see the ‘XL-DOT reconstruction’ section below). It should be noted that, owing to the sample tilt and the fixed vertical field of view of the 2D projections, the 3D volume that is commonly sampled in all orientations, and used in the subsequent analysis and visualization, is reduced. (4) Last, to isolate the dichroic component from the isotropic electron-density contribution, the LV projection was subtracted from the LH projection. The resulting set of projections were used in the reconstruction of the XL-DOT dataset, as discussed further below.
The ptychographic tomogram, acquired with the X-ray energy tuned to below the absorption edge, was reconstructed using a modified filtered back-projection algorithm75. This off-resonance phase tomogram was used to derive the electron-density tomogram, which was then used for material component identification11,32.
A gradient-based iterative reconstruction algorithm was developed to reconstruct the orientation field in 3D. A schematic of the reconstruction process is shown in Supplementary Fig. 7. The process starts with the creation of a 3D starting, random guess of the sample. Using the sample–illumination interaction relationship in equation (2), a set of projections is simulated. These projections are then compared with the measured set of projections and their difference is used to compute a gradient to iteratively correct the initial guess.
The interaction between the electric field of the incident linearly polarized X-rays, \(\overrightarrow{E}\), and the orientation of the apical vanadyl bond, \(\overrightarrow{a}\), can be described as:
$$f={f}_{0}+{f}_{{\rm{lin}}}{(\overrightarrow{E}\cdot \overrightarrow{a})}^{2}$$
(2)
Here f is the total scattering factor, which contains the isotropic charge contribution, f0, and the linear dichroism contribution, \({(\overrightarrow{E}\cdot \overrightarrow{a})}^{2}\), with a pre-factor flin that depends on the electronic transition under resonance. Keeping with the experimental geometry (Fig. 1a); using X-rays with a LH polarization parallel to the x axis and denoting an arbitrary polarization angle as φ, in which φ = 0° is LH polarization and φ = 90° is LV polarization, the tomographic rotation and tilting of the sample can be quantitatively represented by the 3D rotation matrix R. In transmission, the measured projection can then be described by the integral given in equation (3). Index summation notation is used to give the rotation of the relevant components of the orientation, aj. The integration is evaluated along the X-ray propagation direction, the z axis.
$$P(x,y)=\int {f}_{0}({\bf{R}}\overrightarrow{r})+{f}_{{\rm{lin}}}[{R}_{1j}{a}_{j}({\bf{R}}\overrightarrow{r})\cos \varphi +{R}_{2j}{a}_{j}({\bf{R}}\overrightarrow{r})\sin \varphi {]}^{2}{\rm{d}}z$$
(3)
Knowing the form of the interaction, the reconstruction algorithm was formulated by generating a guess structure, from which projections were simulated at the same orientations that the sample was measured. These simulated projections, \(\hat{P}\), were then compared with the corresponding measured projections, P. Their square difference was used to define an error metric, ϵ, quantifying how well the guess could reproduce the measured projections, given by
$${\epsilon }=\sum _{m,x,y}{[{\widehat{P}}^{m}(x,y)-{P}^{m}(x,y)]}^{2}$$
(4)
in which m represents the projection index. The error metric was reduced using gradient descent, therefore improving the ability of the guess structure to represent the internal c-axis orientation of the measured sample. By differentiating the error metric in equation (4) with respect to each component, we obtain the following analytical expression for calculating the gradient:
$$\frac{{\rm{\partial }}{\epsilon }}{{\rm{\partial }}{a}_{k}}={4f}_{{\rm{l}}{\rm{i}}{\rm{n}}}\sum _{x,y}[{\hat{P}}^{m}(x,y)-{P}^{m}(x,y)][{R}_{1j}{a}_{j}\cos {\varphi }+{R}_{2j}{a}_{j}\sin {\varphi }]({R}_{1k}\cos {\varphi }+{R}_{2k}\sin {\varphi })$$
(5)
The gradient was evaluated and applied to the guess structure at every iteration. During the reconstruction process, the magnitude of the linear dichroic contrast, corresponding to flin, was not constrained and was therefore also optimized during gradient descent. As a result, it is not necessary to predetermine the flin value. As the iterative gradient descent reconstruction is prone to converging at local minima, 40 individual reconstructions were performed using different random, non-zero initial conditions. The individual reconstructions are combined by averaging all components to obtain a final reconstruction. The difference in the angular orientations between the individual reconstructions and the final, averaged reconstruction was used to evaluate the standard deviation of the orientation, which is an estimate of the uncertainty in orientation.
Notably, using equation (3), it can be shown that LV polarization (φ = 90°) projection measurements evaluate to
$$P(x,y)=\int ({f}_{0}({\bf{R}}\overrightarrow{r})+{f}_{{\rm{lin}}}[{{\bf{a}}}_{{\boldsymbol{y}}}({\bf{R}}\overrightarrow{r}){]}^{2}){\rm{d}}z$$
(6)
Because there are no vector rotations in this expression, it is equivalent to examining a scalar consisting of two components: the isotropic charge background, f0, and the (out-of-plane) \({a}_{y}^{2}\) component. This can be reconstructed with conventional tomography and gives contrast between grains that are in-plane (x–y plane) and out-of-plane oriented. This contrast was used for further validation of the final reconstruction, as shown in Supplementary Fig. 12.
To obtain a first estimation of how many sample tilts and linear polarization states are necessary for a robust XL-DOT reconstruction, we performed a series of numerical simulations and tomographic reconstructions with fewer sample tilt axes (Supplementary Fig. 14). Preliminary reconstructions can be obtained with as little as two tilt axes using LV and LH polarizations only. Both our simulations (not shown) and recent literature30,47 indicate further that the numerous tilt axes can be replaced by measurements with extra X-ray polarizations76. Similar results can also be achieved using laminography46,48. This offers a route to fewer or even single tilt-axis measurements.
The total deposited dose over the duration of the experiment and the entire volume of the V2O5 pillar was approximately 109 Gy. This estimate is based on the mass density of the sample and the average flux density per projection77. No actions were taken to limit the dose, as V2O5 is not known to degrade under the present experimental conditions11,29. For radiation-sensitive materials, preventative measures can be used to mitigate or account for potential radiation damage78. Dose-limiting options include scanning and projection sparse acquisition schemes11,79 that reduce the total deposited dose, changes to the ptychography acquisition such as using an out-of-focus acquisition with micrometre-sized scanning probes which lead to a reduction of both the total and peak dose per area, as well as the implementation of cryogenic and inert atmosphere measurement conditions80,81.
Spatial resolution estimates of projections and tomograms were obtained using Fourier ring correlation and Fourier shell correlation, respectively82.
To evaluate the spatial resolution of the acquired projections, we acquired projections under identical conditions, that is, at the same rotation angle, calculated the correlation between these two images in the Fourier domain and estimated the spatial resolution based on the intersection with a one-bit threshold (see Supplementary Fig. 6). This gives spatial resolutions close to the pixel limit of 30.91 nm and 31.29 nm for the on-resonance (5.469 keV) and off-resonance (5.4 keV) measured projections, respectively.
To evaluate the spatial resolution of the electron-density tomogram acquired below the absorption edge, we halved the entire dataset and reconstructed two independent tomograms (Supplementary Fig. 10). This gives a 3D spatial resolution of 44 nm.
To evaluate the spatial resolution of the orientation vector field, the corresponding dataset was similarly split in half and two tomograms of the orientation vector field were calculated. Using Fourier shell correlation, we calculated spatial resolution estimates for each of the orientation scalar components (LDx, LDy, LDz), as shown in Supplementary Fig. 8, providing a lower bound for their spatial resolutions of 84 nm, 45 nm and 89 nm, respectively. Also, we measured edge profiles across sharp features such as 90° grain boundaries, which revealed a maximum edge sharpness of 40 nm, with an average edge sharpness of 73 nm, which we take as the spatial resolution of the orientation tomogram.
To estimate the voxel-level electron-density uncertainty, we calculated the standard deviation (σ) of the electron density in a region of air surrounding the imaged pillar. The average electron density in air and uncertainty was calculated as 0.004 ± 0.007 Å−3.
To estimate the uncertainty in the detected linear dichroism, that is, spatial variations in the pre-edge peak intensity, we independently reconstructed the LV and LH phase tomograms with the sample at a fixed sample tilt and then subtracted them from each other. We then isolated a region of air and calculated the standard deviation in the phase shift associated with the voxels in this region. This standard deviation of the phase associated with the air region corresponds to the uncertainty of the dichroic signal. On the basis of this procedure, the uncertainty of the dichroic signal is found to be 1.3 × 10−4 rad, which corresponds to a refractive index decrement, δ, error of 1.9 × 10−7.
To estimate the error in the determined orientation, we isolated an elongated grain with a volume of 0.85 µm3 and long-edge length of 3.2 µm that showed the least variance in electron density and V2O5 orientation, that is, which is assumed to be single crystal, and calculated the standard deviation (σ) in orientation to be ±10° for azimuth (x–y-plane angles) and ±8° for elevation (out-of-plane angles) (Supplementary Fig. 11).
The critical concentration for element detection can be estimated to correspond to a dichroic magnitude (difference between tomograms taken with different polarizations) of at least twice the reconstruction error. The dichroic contrast of the V2O5 is 1.8 × 10−3 and the noise in the reconstruction is an order of magnitude weaker at 1.3 × 10−4. As a result, in V2O5, our dichroic contrast is 12 times the error. We can estimate that, if all other parameters are held constant, the concentration of V can be decreased by a factor of 6 and still be measurable.
The total acquisition time for the XL-DOT dataset used in this work was around 85 h, including sample tilting, changing the polarization and alignment and dead-time overheads. The pure measurement time, however, was only about 24 h. This discrepancy is largely because of the lack of automation. There exist several opportunities to reduce the acquisition time as follows:
Reduce oversampling: reconstructions using 50% of the tomograms provide similar results (Supplementary Fig. 14).
Automation and imaging geometry: the measurement of intermediate linear X-ray polarization angles30,47,70,76 and/or use of the laminography geometry46,48 will eliminate most of the present acquisition overheads.
The increase in coherent flux expected from fourth-generation synchrotron light sources promises to reduce scan times for radiation-hard materials83.
Further innovations such as multibeam ptychography and sparse tomography offer routes to even faster data acquisition11,84, providing acquisition times compatible with operando measurements48,85.
Analysis of the dichroic tomogram was performed using in-house-developed MATLAB routines, ParaView and Avizo. To account for the damage caused during the FIB milling step of the sample preparation, we defined a mask that excluded the outermost 90 nm of the sample cylinder from orientation and electron-density volume analysis (Supplementary Fig. 9).
Materials were identified by comparing the tabulated electron densities of the known sample and reference components, listed in Supplementary Table 1, with the PXCT-measured electron densities. Shown in Supplementary Fig. 9 is a volume rendering and a horizontal cut slice through the electron-density tomogram with the corresponding electron-density histogram. The V2O5 volume was isolated using threshold segmentation with a lower bound of 0.74 Å−3 and an upper bound of 0.90 Å−3.
The topological charge can be determined by considering the winding number associated with a given topological defect. The winding number corresponds to how the crystallographic orientation changes when moving around a circle enclosing the defect in a clockwise manner. For the comet (trefoil) defect, the c axis rotates clockwise (anticlockwise) by +180° (−180°) for one complete revolution. As the crystallographic orientation has completed half a revolution of a full circle (360°), the topological numbers ±1/2 are assigned to them.
To isolate the V2O5 grains and facilitate a correlation between orientation and electron density, we applied the above-defined threshold mask (electron densities between 0.74 Å−3 and 0.90 Å−3) to the orientation tomogram. To identify and characterize individual V2O5 grains, we downsampled the masked XL-DOT reconstruction by a factor of three (transforming a group of 3 × 3 voxels into 1 voxel with an average intensity value of the same size), thus reducing the sensitivity to intragranular variations. Segmentation was then performed by separating regions along high-angle grain boundaries, showing a c-axis orientation difference larger than 10°. Following segmentation, we then calculated the volume of these grains, their mean diameter and their sphericity86. Shown in Supplementary Fig. 13 are the corresponding distributions and correlations of the segmented grains.
As linear dichroic phenomena occur near absorption edges or resonant X-ray energies, the X-ray penetration depth at these energies determines the sample diameter that can be investigated with XL-DOT. For most materials, it is the penetration depth at the X-ray energy of the examined chemical element that sets an upper limit on the sample diameter. Taking pure transition metals as an example, this imposes a typical upper limit to the sample size of around 10 µm. Transition-metal-rich functional materials such as catalyst bodies, cathode materials, ferroelectrics, biominerals and concrete, which are also of interest for XL-DOT measurements, exhibit a substantially larger upper sample size limit owing to their internal porosity or composite nature. For instance, a 100 µm-thick V2O5 sample transmits around 10% of the incident beam in the pre-edge region (https://henke.lbl.gov/). 3D or nanotomography measurements of such sample diameters are increasingly typical for operando measurements48,87,88,89.
Although XL-DOT measurements should ideally be performed at the X-ray energy of an absorption edge at which linear dichroic contrast is strongest to maximize contrast in the projections, the range of energies at the absorption edge at which dichroism can be measured can be large. For instance, the full width at half maximum of the near-edge peak in our V2O5 spectra used for XL-DOT is approximately 3 eV, which means that even an X-ray energy resolution of up to 3 eV would be sufficient for XL-DOT measurements, albeit at a decreased SNR. There is therefore a degree of flexibility in terms of the required energy position and resolution for XL-DOT measurements.
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MATBG devices A, B and C are devices B, F and C from ref. 11 (the full description of the fabrication procedure can be found in this reference). In brief, devices were fabricated using a ‘tear-and-stack’ method51 in which a single graphene sheet is torn in half by van der Waals interaction with hBN. The two halves were rotated relative to each other and stacked to form MATBG. Graphene, graphite (in the aligned device) and hBN were picked up with polyvinyl alcohol. Then, to flip the heterostructure upside down, the heterostructure was pressed against an intermediate structure consisting of polymethyl methacrylate/transparent tape/Sylgard 184, and the polyvinyl alcohol was dissolved by water injection. The heterostructure was then transferred to a SiO2/Si chip with pre-patterned titanium/gold electrodes. Residual polymer was dissolved in dichloromethane, water, acetone and isopropyl alcohol. These chips were annealed in ultrahigh vacuum at 170 °C overnight and at 400 °C for 2 h in previous STM and STS measurements11. The other devices shared a similar fabrication and preparation method.
Synchrotron-based μ-ARPES measurements were performed at Beamline 7.0.2 (MAESTRO) of the Advanced Light Source, USA and Beamline 07U of the Shanghai Synchrotron Radiation Facility (SSRF), China. The samples were annealed in ultrahigh vacuum at 300 °C for 3 h and measured under ultrahigh vacuum below 3 × 10−11 torr. The photon energy of the incident beam was 95 eV and the measurement was performed at room temperature. Data were collected using an R4000 analyser upgraded with deflectors (Advanced Light Source) and a DA30 analyser (SSRF). The incoming photon beam was focused down to a 2-μm spot size by using a capillary mirror28 and a 1-μm spot size using a Fresnel zone plate (SSRF). The total energy and angle resolutions were 20 meV and 0.1°, respectively.
Laplacian (sum of second partial derivatives) plots were used to highlight the non-dispersive bands, as presented in Figs. 2 and 3. These plots were generated by summing the second partial derivatives of the original ARPES spectra along both axes in pixel units, then transforming them into energy and momentum space.
We adopted the following non-interacting-electron tight-binding Hamiltonian to calculate the electronic structure and EPC of MATBG
$$H=\,-\,\sum _{Ii\alpha \,,\,Jj\beta }t({{\bf{R}}}_{Ii\alpha }-{{\bf{R}}}_{Jj\beta }){c}_{Ii\alpha }^{\dagger }{c}_{Jj\beta }$$
(1)
where \({c}_{{I}i\alpha }^{\dagger }\) and \({c}_{{J}j\beta }\) are creation and annihilation operators for the pz orbital of the iα/jβ carbon atom in the I/Jth moiré superlattice (α and β are joint indices for sublattices and layers), and R is the corresponding atomic coordinate. The impact of atomic coordinates on the hopping parameter t is approximated by the Slater–Koster formula, whose dependence on atomic coordinates sets the stage for the EPC estimation. The Slater–Koster parameters are specified in Supplementary Information section VII.
To evaluate the coupling in the mini-Brillouin zone, we further projected the coupling matrix using the truncated atomic plane wave (TAPW) method43,52. Thus, a moiré phonon near the ΓM point can be approximated by in-plane transverse optical/in-plane longitudinal acoustic/in-plane longitudinal optical phonons at graphene K/K′ points (see Supplementary Information section VIII for details). We set the moiré phonon energy ω0 = 150 meV, the mass of carbon atoms mc = 2.0 × 10−26 kg, and the characteristic phonon length \({l}_{{\rm{p}}}=\sqrt{\hbar /(2{m}_{{\rm{c}}}{\omega }_{0})}=34.0\,{\rm{m}}{\text{\AA }}.\) The TAPW electrons and projected EPC constitute the model Hamiltonian for the TBG system
$$\begin{array}{l}H\,=\,\sum _{\bar{{\bf{k}}}\sigma }{{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{T}}{\rm{A}}{\rm{P}}{\rm{W}})\dagger }{h}_{\bar{{\bf{k}}}}{{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{T}}{\rm{A}}{\rm{P}}{\rm{W}})}\\ \,\,-\frac{1}{\sqrt{{N}_{{\rm{m}}}}\,}\sum _{\bar{{\bf{k}}}\sigma \bar{{\bf{q}}}\nu }{{\bf{c}}}_{\bar{{\bf{k}}}+\bar{{\bf{q}}}\sigma }^{({\rm{T}}{\rm{A}}{\rm{P}}{\rm{W}})\dagger }{M}_{\bar{{\bf{q}}}\nu }{{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{T}}{\rm{A}}{\rm{P}}{\rm{W}})}({a}_{\bar{{\bf{q}}}\nu }+{a}_{-\bar{{\bf{q}}}\nu }^{\dagger })+\sum _{\bar{{\bf{q}}}\nu }{\omega }_{0}{a}_{\bar{{\bf{q}}}\nu }^{\dagger }{a}_{\bar{{\bf{q}}}\nu }\end{array}$$
(2)
where \({{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{TAPW}})}\) is the column vector of electron annihilation operators with moiré momentum \(\bar{{\bf{k}}}\) and spin σ in the TAPW basis and \({h}_{\bar{{\boldsymbol{k}}}}\) is the electronic hopping matrix for a specific moiré momentum \(\bar{{\bf{k}}}\). The size of its moiré mini-Brillouin zone is denoted as Nm to distinguish from the system size N. For folded phonon branches, \({a}_{\bar{{\bf{q}}}\nu }\) is the annihilation operator with moiré momentum \(\bar{{\bf{q}}}\) and ν labels the index of branches. The average distance between phonons and electrons is small compared with the moiré length scale. Therefore, the coupling matrix \({M}_{\bar{{\bf{q}}}\nu }\) can be estimated by the momentum-independent M0, which can be evaluated by the frozen-phonon calculations.
As the experimentally relevant electrons lie in low-energy flat bands, we further project the TAPW orbitals onto the four flat-band orbitals, which can be expressed as the projection operator \({{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{flat}})}={{P}_{\bar{{\bf{k}}}}^{\dagger }{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{TAPW}})}\), where P is the flat-band projection operator. In the projected Hamiltonian, the EPC matrix becomes a 4 × 4-dimensional \({\widetilde{{M}_{\bar{{\bf{k}}}}}(\bar{{\bf{q}}})=P}_{\bar{{\bf{k}}}{\boldsymbol{+}}\bar{{\bf{q}}}}^{\dagger }\,{M}_{\bar{{\bf{q}}}}\,{P}_{\bar{{\boldsymbol{k}}}}\). On the basis of its numerical distribution (Supplementary Information section VIII), we find that \(\widetilde{{M}_{\bar{{\bf{k}}}}}(\bar{{\bf{q}}})\) can be approximated by \({Q}_{\bar{{\bf{k}}}{\boldsymbol{+}}\bar{{\bf{q}}}}\,{g}_{\bar{{\bf{q}}}}\eta {Q}_{\bar{{\bf{k}}}}^{\dagger }\), where Q is the similarity transformation, g is the coupling strength and η is a constant diagonal matrix. Thus, the projected Hamiltonian can be written in an EPC-diagonal basis
$$\begin{array}{l}{H}_{{\rm{flat}}-{\rm{band}}}=\sum _{\bar{{\bf{k}}}\sigma }{{\bf{d}}}_{\bar{{\bf{k}}}\sigma }^{\dagger }{Q}_{\bar{{\bf{k}}}}^{\dagger }{\varepsilon }_{\bar{{\bf{k}}}}{Q}_{\bar{{\bf{k}}}}{{\bf{d}}}_{\bar{{\bf{k}}}\sigma }\\ \,\,\,\,\,-\frac{1}{\sqrt{{N}_{{\rm{m}}}}\,}\sum _{\bar{{\bf{k}}}\sigma \bar{{\bf{q}}}\nu }{g}_{\bar{{\bf{q}}}}{{\bf{d}}}_{\bar{{\bf{k}}}+\bar{{\bf{q}}}\sigma }^{\dagger }\eta {{\bf{d}}}_{\bar{{\bf{k}}}\sigma }({a}_{\bar{{\bf{q}}}\nu }+{a}_{-\bar{{\bf{q}}}\nu }^{\dagger })+\sum _{\bar{{\bf{q}}}\nu }{\omega }_{0}{a}_{\bar{{\bf{q}}}\nu }^{\dagger }{a}_{\bar{{\bf{q}}}\nu }\end{array}$$
(3)
where \({{\bf{d}}}_{\bar{{\bf{k}}}\sigma }={Q}_{\bar{{\bf{k}}}}^{\dagger }{{\bf{c}}}_{\bar{{\bf{k}}}\sigma }^{({\rm{flat}})}\) and the diagonal matrix \({\varepsilon }_{\bar{{\boldsymbol{k}}}}\) represents the energy of the flat bands.
The strong EPC for the flat-band electrons leads to non-perturbative polaronic dressing effects. We consider the Lang–Firsov transformation for the coupled Hamiltonian
$${U}_{{\rm{LF}}}={{\rm{e}}}^{-\frac{1}{\sqrt{{N}_{{\rm{m}}}}{\omega }_{0}}{\sum }_{\bar{{\bf{R}}}\sigma \bar{{\bf{q}}}\nu }{{\rm{e}}}^{-{\rm{i}}\bar{{\bf{R}}}\cdot \bar{{\bf{q}}}}{{g}_{\bar{{\bf{q}}}}{\bf{d}}}_{\bar{{\bf{R}}}\sigma }^{\dagger }\eta {{\bf{d}}}_{\bar{{\bf{R}}}\sigma }({a}_{\bar{{\bf{q}}}\nu }-{a}_{-\bar{{\bf{q}}}\nu }^{\dagger })}$$
(4)
where \({{\bf{d}}}_{\bar{{\bf{R}}}\sigma }\) is the real-space annihilation operator of electron in the EPC-diagonal basis. Owing to the separation of energy scales for electrons and phonons, we can employ the polaron ansatz for the ground-state wavefunction \(| {\varPsi }_{{\rm{G}}}\rangle ={U}_{{\rm{LF}}}^{\dagger }| {\psi }_{{\rm{e}}}\rangle \bigotimes | {\psi }_{{\rm{ph}}}\rangle \), where |ψe⟩ and |ψph⟩ are the electronic and phononic wavefunctions. Moreover, as both the transformed coupling strength \({g}_{\bar{{\bf{q}}}}\) and temperature are much less than the phonon energy ω0 = 150 meV, we further assume that the \(|{\psi }_{{\rm{ph}}}\rangle \) can be approximated by a vacuum state \(|{0}_{{\rm{ph}}}\rangle \). Thus, the electronic part \(| {\psi }_{{\rm{e}}}\rangle \) is determined by an effective Hamiltonian
$$\begin{array}{c}\langle {0}_{{\rm{ph}}}| {U}_{{\rm{LF}}}H{U}_{{\rm{LF}}}^{\dagger }| {0}_{{\rm{ph}}}\rangle =\sum _{\bar{{\bf{R}}}\bar{{{\bf{R}}}^{{\prime} }}\sigma }{{\bf{d}}}_{\bar{{\bf{R}}}\sigma }^{\dagger }\langle {0}_{{\rm{ph}}}| {h}_{\bar{{\bf{R}}}\bar{{{\bf{R}}}^{{\prime} }}}^{* }| {0}_{{\rm{ph}}}\rangle {{\bf{d}}}_{\bar{{{\bf{R}}}^{{\prime} }}\sigma }\\ -\sum _{\bar{{\bf{R}}}\bar{{{\bf{R}}}^{{\prime} }}\sigma {\sigma }^{{\prime} }\bar{{\bf{q}}}}\frac{{N}_{v}\,{| {g}_{\bar{{\bf{q}}}}| }^{2}}{{N}_{{\rm{m}}}{\omega }_{0}}{{\rm{e}}}^{{\rm{i}}(\bar{{{\bf{R}}}^{{\prime} }}{\boldsymbol{-}}\bar{{\bf{R}}})\cdot \bar{{\bf{q}}}}({{\bf{d}}}_{\bar{{\bf{R}}}\sigma }^{\dagger }\eta {{\bf{d}}}_{\bar{{\bf{R}}}\sigma })({{\bf{d}}}_{\bar{{{\bf{R}}}^{{\prime} }}{\sigma }^{{\prime} }}^{\dagger }\eta {{\bf{d}}}_{\bar{{{\bf{R}}}^{{\prime} }}{\sigma }^{{\prime} }})\end{array}$$
(5)
The \({h}_{\bar{{\bf{R}}}\bar{{{\bf{R}}}^{{\prime} }}}^{* }\) is the phonon-dressed electronic hopping matrix, whose specific form is shown in Supplementary Information section X. In the flat-band limit of TBG, this matrix is close to identity and, therefore, is irrelevant in determining the polaronic dressing. The ground state of the above equation determines the \(| {\psi }_{{\rm{e}}}\rangle \) in \(| {\varPsi }_{{\rm{G}}}\rangle \).
The photoemission spectrum also involves excited states (denoted as \(| \varPhi \rangle \))
$$A(\bar{{\bf{k}}},\omega )={\rm{Im}}\left\{\frac{1}{{N}_{{\rm{m}}}}\sum _{\bar{{\bf{R}}}\bar{{{\bf{R}}}^{{\prime} }}}{{\rm{e}}}^{-{\rm{i}}(\bar{{\bf{R}}}{\boldsymbol{-}}\bar{{{\bf{R}}}^{{\prime} }})\cdot \bar{{\bf{k}}}}\sum _{\sigma \alpha ,\Phi }\langle {\varPsi }_{{\rm{G}}}| {c}_{\bar{{\bf{R}}}\sigma \alpha }^{\dagger ({\rm{flat}})}| \varPhi \rangle \langle \varPhi | {c}_{\bar{{{\bf{R}}}^{{\prime} }}\sigma \alpha }^{({\rm{flat}})}| {\varPsi }_{{\rm{G}}}\rangle \frac{1}{\omega -{\rm{i}}\varGamma +{E}_{\varPhi }-{E}_{{\rm{G}}}}\right\}$$
(6)
where Γ is the Lorentzian broadening. With the aforementioned ground-state ansatz, the intensity of the Mth replica peak is explicitly determined as
$$\,\frac{1}{M!}\exp \left(-\sum _{\bar{{\bf{q}}}}\frac{{N}_{v}{| {g}_{\bar{{\bf{q}}}}| }^{2}}{{N}_{{\rm{m}}}{\omega }_{0}^{2}}\right){\left(\sum _{\bar{{\bf{q}}}}\frac{{N}_{v}{| {g}_{\bar{{\bf{q}}}}| }^{2}}{{N}_{{\rm{m}}}{\omega }_{0}^{2}}{{\rm{e}}}^{{\rm{i}}\bar{{\bf{R}}}\cdot \bar{{\bf{q}}}}\right)}^{M}$$
(7)
It follows a Poisson distribution with the factor \(\sum _{\bar{{\bf{q}}}}\frac{{N}_{v}\,{| {g}_{\bar{{\bf{q}}}}| }^{2}}{{N}_{{\rm{m}}}\,{\omega }_{0}^{2}}\approx 0.11\), according to the frozen-phonon simulations. Focusing on the relative intensity of replica features and ignoring the interacting nature of electrons inside each replica, we produce the spectral simulation in Fig. 4d.
The Lang–Firsov transformation is suitable for the flat-band TBG model. The experiments presented in this paper also include TBG under more complicated conditions, including with hBN substrates and finite bandwidth away from the magic angle. These generalized cases can be modelled in the form of
$$H=\,\sum _{\bar{{\bf{k}}}\sigma }{{\bf{d}}}_{\bar{{\bf{k}}}\sigma }^{\dagger }{h}_{\bar{{\bf{k}}}}{{\bf{d}}}_{\bar{{\bf{k}}}\sigma }-\frac{1}{\sqrt{{N}_{{\rm{m}}}}\,}\sum _{\bar{{\bf{k}}}\sigma }{{\bf{d}}}_{\bar{{\bf{k}}}+\bar{{\bf{q}}}\sigma }^{\dagger }{M}_{\bar{{\bf{q}}}}{{\bf{d}}}_{\bar{{\bf{k}}}\sigma }({a}_{\bar{{\bf{q}}}}+{a}_{\bar{{\bf{q}}}}^{\dagger })+\sum _{{\bf{q}}}{\omega }_{{\bf{q}}}{a}_{\bar{{\bf{q}}}}^{\dagger }{a}_{\bar{{\bf{q}}}}$$
(8)
where \({h}_{\bar{{\bf{k}}}}\) describes the band structure in general. The derivation and specific forms of Hamiltonian with hBN and bandwidth are detailed in the Supplementary Information sections X and XI.
It is important to note that the first term in equation (8) does not commute with the second term in this generalized case, making the Lang–Firsov transformation unsuitable for this case. To simulate the polaronic dressing in this generalized Hamiltonian, we employ a variational ansatz of the ground state \(| {\varPsi }_{{\rm{G}}}\rangle ={U}_{{\rm{NGS}}}^{\dagger }(\lambda )| {\psi }_{{\rm{e}}}\rangle | {0}_{{\rm{ph}}}\rangle \) with
$${U}_{{\rm{NGS}}}^{\dagger }(\lambda )=\exp \left[\frac{\lambda }{\sqrt{{N}_{{\rm{m}}}}}\sum _{\bar{{\bf{R}}}\sigma \bar{{\bf{q}}}\nu }\,{{\rm{e}}}^{-{\rm{i}}\bar{{\bf{R}}}\cdot \bar{{\bf{q}}}}{{\bf{d}}}_{\bar{{\bf{R}}}\sigma }^{\dagger }\eta {{\bf{d}}}_{\bar{{\bf{R}}}\sigma }({a}_{\bar{{\bf{q}}}\nu }-{a}_{-\bar{{\bf{q}}}\nu }^{\dagger })\right]$$
(9)
where λ is the variational parameter in contrast to the fixed g/ω0 of the Lang–Firsov transformation for TBG. Owing to the high phonon energy compared with any energy scales in equation (8), we still assume the post-transformation phonon state is vacuum. Therefore, the variational ansatz gives the total energy as a function of λ:
$$\begin{array}{l}{E}_{{\rm{tot}}}(\lambda )=\langle {0}_{{\rm{ph}}}| \langle {\psi }_{{\rm{e}}}| {U}_{{\rm{NGS}}}(\lambda )H{U}_{{\rm{NGS}}}^{\dagger }(\lambda )| {\psi }_{{\rm{e}}}\rangle | {0}_{{\rm{ph}}}\rangle \\ \,\,\,=\,{E}_{{\rm{kin}}}-\frac{{N}_{v}}{{N}_{{\rm{m}}}}(2g\lambda -{\omega }_{0}{\lambda }^{2})\sum _{\bar{{\bf{R}}}{\bar{{\bf{R}}}}^{{\prime} }\sigma {\sigma }^{{\prime} }\bar{{\bf{q}}}}{{\rm{e}}}^{{\rm{i}}(\bar{{{\bf{R}}}^{{\prime} }}-\bar{{\bf{R}}})\cdot \bar{{\bf{q}}}}\\ \,\,\,\,\langle {\psi }_{{\rm{e}}}| ({{\bf{d}}}_{\bar{{\bf{R}}}\sigma }^{\dagger }\eta {{\bf{d}}}_{\bar{{\bf{R}}}\sigma })({{\bf{d}}}_{\bar{{{\bf{R}}}^{{\prime} }}{\sigma }^{{\prime} }}^{\dagger }\eta {{\bf{d}}}_{\bar{{{\bf{R}}}^{{\prime} }}{\sigma }^{{\prime} }})| {\psi }_{{\rm{e}}}\rangle \end{array}$$
(10)
with the normalized kinetic energy Ekin follows the expression in Supplementary Information sections X and XI. Unlike the analytically solvable Lang–Firsov transformation, the variational parameter λ is obtained by numerical optimization of Etot(λ). The self-consistent equations for different situations of the generalized Hamiltonian are derived in Supplementary Information sections X and XI. This numerically determined λ describes the relative strength of the polaronic dressing, where λ reproduces g/ω0 when H takes the flat-band TBG form in equation (3). The Poisson factor for the relative replica intensity is then obtained by p = Nvλ2.
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The Internet is a vast ocean of human knowledge, but it isn’t infinite. And artificial intelligence (AI) researchers have nearly sucked it dry.
The past decade of explosive improvement in AI has been driven in large part by making neural networks bigger and training them on ever-more data. This scaling has proved surprisingly effective at making large language models (LLMs) — such as those that power the chatbot ChatGPT — both more capable of replicating conversational language and of developing emergent properties such as reasoning. But some specialists say that we are now approaching the limits of scaling. That’s in part because of the ballooning energy requirements for computing. But it’s also because LLM developers are running out of the conventional data sets used to train their models.
A prominent study1 made headlines this year by putting a number on this problem: researchers at Epoch AI, a virtual research institute, projected that, by around 2028, the typical size of data set used to train an AI model will reach the same size as the total estimated stock of public online text. In other words, AI is likely to run out of training data in about four years’ time (see ‘Running out of data’). At the same time, data owners — such as newspaper publishers — are starting to crack down on how their content can be used, tightening access even more. That’s causing a crisis in the size of the ‘data commons’, says Shayne Longpre, an AI researcher at the Massachusetts Institute of Technology in Cambridge who leads the Data Provenance Initiative, a grass-roots organization that conducts audits of AI data sets.
The imminent bottleneck in training data could be starting to pinch. “I strongly suspect that’s already happening,” says Longpre.
Source: Ref. 1
Although specialists say there’s a chance that these restrictions might slow down the rapid improvement in AI systems, developers are finding workarounds. “I don’t think anyone is panicking at the large AI companies,” says Pablo Villalobos, a Madrid-based researcher at Epoch AI and lead author of the study forecasting a 2028 data crash. “Or at least they don’t e-mail me if they are.”
For example, prominent AI companies such as OpenAI and Anthropic, both in San Francisco, California, have publicly acknowledged the issue while suggesting that they have plans to work around it, including generating new data and finding unconventional data sources. A spokesperson for OpenAI, told Nature: “We use numerous sources, including publicly available data and partnerships for non-public data, synthetic data generation and data from AI trainers.”
Even so, the data crunch might force an upheaval in the types of generative AI model that people build, possibly shifting the landscape away from big, all-purpose LLMs to smaller, more specialized models.
LLM development over the past decade has shown its voracious appetite for data. Although some developers don’t publish the specifications of their latest models, Villalobos estimates that the number of ‘tokens’, or parts of words, used to train LLMs has risen 100-fold since 2020, from hundreds of billions to tens of trillions.
In AI, is bigger always better?
That could be a good chunk of what’s on the Internet, although the grand total is so vast that it’s hard to pin down — Villalobos estimates the total Internet stock of text data today at 3,100 trillion tokens. Various services use web crawlers to scrape this content, then eliminate duplications and filter out undesirable content (such as pornography) to produce cleaner data sets: a common one called RedPajama contains tens of trillions of words. Some companies or academics do the crawling and cleaning themselves to make bespoke data sets to train LLMs. A small proportion of the Internet is considered to be of high quality, such as human-edited, socially acceptable text that might be found in books or journalism.
The rate at which usable Internet content is increasing is surprisingly slow: Villalobos’s paper estimates that it is growing at less than 10% per year, while the size of AI training data sets is more than doubling annually. Projecting these trends shows the lines converging around 2028.
At the same time, content providers are increasingly including software code or refining their terms of use to block web crawlers or AI companies from scraping their data for training. Longpre and his colleagues released a preprint this July showing a sharp increase in how many data providers block specific crawlers from accessing their websites2. In the highest-quality, most-often-used web content across three main cleaned data sets, the number of tokens restricted from crawlers rose from less than 3% in 2023 to 20–33% in 2024.
Several lawsuits are now under way attempting to win compensation for the providers of data being used in AI training. In December 2023, The New York Times sued OpenAI and its partner Microsoft for copyright infringement; in April this year, eight newspapers owned by Alden Global Capital in New York City jointly filed a similar lawsuit. The counterargument is that an AI should be allowed to read and learn from online content in the same way as a person, and that this constitutes fair use of the material. OpenAI has said publicly that it thinks The New York Times lawsuit is “without merit”.
If courts uphold the idea that content providers deserve financial compensation, it will make it harder for both AI developers and researchers to get what they need — including academics, who don’t have deep pockets. “Academics will be most hit by these deals,” says Longpre. “There are many, very pro-social, pro-democratic benefits of having an open web,” he adds.
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A study finds that many published papers are not accessible to low-vision and blind readers.Credit: Getty
Around three out of every four PDF versions of scholarly papers are largely inaccessible to low-vision and blind readers, a study has found1.
Researchers looked at how often around 20,000 studies published between 2014 and 2023 were compliant with 6 accessibility criteria. That includes providing alternative text for figures and headers for tables, as well as adding the tags necessary to make PDF files accessible to low-vision and blind readers, who typically access these files using assistive reading devices.
Only around 3% of the analysed studies met all six criteria, the analysis found, and just under 75% met none of the criteria at all.
“After 2019, there was a very sharp decline across almost all of the criteria that we measured,” says study co-author Anukriti Kumar, an information scientist at the University of Washington in Seattle. The authors attribute that trend to the move towards rapid-publishing methods such as preprints and online-first publishing, and say that it was exacerbated by the COVID-19 pandemic, which demanded quick communication of research findings.
The analysis was presented in October at the 26th International ACM SIGACCESS Conference on Computers and Accessibility in St. John’s, Canada.
Lucy Lu Wang, also an information scientist at the University of Washington and a co-author of the study, published2 a similar analysis of accessibility of more than 11,000 PDFs in 2021. “Things were mostly improving,” she recalls. But with new global open-access policies and changes with how publishers are producing PDFs, accessibility overall has decreased since then,” she says.
“Accessibility often falls to the wayside, because it disproportionately affects a smaller group of people,” Wang says, “or the kind of people who don’t have as much clout.”
For the 2021 analysis, the authors interviewed several low-vision and blind scientists, some of whom said that they chose their fields of study in part because of how easily accessible the associated literature was. “People were drawn to fields that had more accessible papers,” Wang says. “The barriers to working in those fields were lower.”
Sheri Wells-Jensen, a linguistics researcher at Bowling Green State University in Ohio, who is fully blind, tells Nature that the hassle of finding accessible papers is such that she sometimes doesn’t even try. “I never expect to be able to go to an open-access journal and just get the PDF and read it with the same level of ease and convenience as other scientists do,” she says. “We’ve got different software that could do some scanning, but you have to be a little bit of a wizard sometimes.”
Wells-Jensen notes that academic journals rarely provide information about accessibility for scientists with visual impairment in the ‘information for authors’ sections of their websites, making it unclear how researchers should prepare their manuscripts for optimal accessibility. Manuscript-submission systems themselves are also often inaccessible, she adds.
Addressing such accessibility shortfalls will require “systemic changes” from authors, publishers and others, Kumar says.
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Nature, Published online: 11 December 2024; doi:10.1038/d41586-024-04027-4
ResearchHub Journal launches latest attempt to compensate referees for their labour.
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