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We use time-resolved thermometry to monitor the decay of nonequilibrium quasiparticles in superconducting Al in the temperature range from $0.3\,$K to $1.2\,$K. The quasiparticle lifetime at higher temperatures ($T>0.7\,$K) agrees well with the calculated energy flow from electrons to phonons, but at lower temperatures it is significantly shorter than the theory predicts. We show well-defined internal equilibrium of quasiparticle system in the studied thermal transients, which implicates that quasiparticle-quasiparticle relaxation is much faster than electron-phonon interaction.

Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects called Cartesian currents. Essentially nothing is known about these limits. We show that such limits can have surprisingly large interior vertical and non-minimal portions. This demonstrates a striking discrepancy between the parametric and non-parametric area minimization problems in higher codimension. Moreover, our construction has the smallest possible dimension ($n = 3$) and codimension $(m = 2)$., Comment: 18 pages

Prediction is a fundamental capability of all living organisms, and has been proposed as an objective for learning sensory representations. Recent work demonstrates that in primate visual systems, prediction is facilitated by neural representations that follow straighter temporal trajectories than their initial photoreceptor encoding, which allows for prediction by linear extrapolation. Inspired by these experimental findings, we develop a self-supervised learning (SSL) objective that explicitly quantifies and promotes straightening. We demonstrate the power of this objective in training deep feedforward neural networks on smoothly-rendered synthetic image sequences that mimic commonly-occurring properties of natural videos. The learned model contains neural embeddings that are predictive, but also factorize the geometric, photometric, and semantic attributes of objects. The representations also prove more robust to noise and adversarial attacks compared to previous SSL methods that optimize for invariance to random augmentations. Moreover, these beneficial properties can be transferred to other training procedures by using the straightening objective as a regularizer, suggesting a broader utility for straightening as a principle for robust unsupervised learning., Comment: Accepted at NeurIPS 2024

Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.

The multiplicities of positive and negative pions, kaons and unidentified hadrons produced in deep-inelastic scattering are measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the fraction of the virtual-photon energy transferred to the final-state hadron $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam of both electric charges and a liquid hydrogen target. These measurements cover the kinematic domain with photon virtuality $Q^2 > 1$ (GeV/$c)^2$, $0.004 < x < 0.4$, $0.1 < y < 0.7$ and $0.2 < z < 0.85$, in accordance with the kinematic domain used in earlier published COMPASS multiplicity measurements with an isoscalar target. The calculation of radiative corrections was improved by using the Monte Carlo generator DJANGOH, which results in up to 12\% larger corrections in the low-$x$ region., Comment: 19 pages, 29 figures

We present revised point-spread functions (PSFs) for the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). These PSFs provide a robust estimate of the light diffracted by the meshes holding the entrance and focal plane filters and the light that is diffusely scattered over medium- to long-distance by the micro-roughness of the mirrors. We first calibrate the diffracted light using flare images. Our modeling of the diffracted light provides reliable determinations of the mesh parameters and finds that about 24 to 33% of the collected light is diffracted, depending on the AIA channel. Then, we fit for the diffuse scattered light using partially lunar occulted images. We find that the diffuse scattered light can be modeled as a superposition of two power law functions that scatter light over the entire length of the detector. The amount of diffuse scattered light ranges from 10 to 35 %, depending on the AIA channel. In total, AIA diffracts and scatters about 40 to 60 % of the collected light over medium to long distances. When correcting for this, bright image regions increase in intensity by about 30 %, dark image regions decrease in intensity by up to 90 %, and the associated differential emission measure analysis of solar features are affected accordingly. Finally, we compare the image reconstructions using our new PSFs to those using the AIA team PSFs and the PSFs of Poduval et al. (2013). We find that our PSFs outperform the others; our PSFs correct well for the flare diffraction pattern and predict accurately the long-distance scattered light in lunar occultations.

Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite fermion framework used to explain fractional quantum Hall states (such as Laughlin states). Crucially, they hold promise for hosting non-Abelian excitations, which are essential for developing topological qubits - key components for fault-tolerant quantum computing. In this work, we show that these coveted half-quantized plateaus can appear in more than one unexpected way. We report the observation of fractional states with conductance quantization at $\nu_H = 5/2$ arising due to charge equilibration in the confined region of a quantum point contact in monolayer graphene., Comment: 30 pages, 18 figures, and 2 tables

In this article we obtain certain inequalities involving the entropy of a positive integer and divergence of two positive integers, respectively the entropy of an ideal and divergence of two ideals of a ring of algebraic integers., Comment: 16 pages, 1 figure. Key words and phrases. entropy, divergence, numbers, ideals, ramification theory in algebraic number fields

This perspective piece is the result of a Generative Adversarial Collaboration (GAC) tackling the question `How does neural activity represent probability distributions?'. We have addressed three major obstacles to progress on answering this question: first, we provide a unified language for defining competing hypotheses. Second, we explain the fundamentals of three prominent proposals for probabilistic computations -- Probabilistic Population Codes (PPCs), Distributed Distributional Codes (DDCs), and Neural Sampling Codes (NSCs) -- and describe similarities and differences in that common language. Third, we review key empirical data previously taken as evidence for at least one of these proposal, and describe how it may or may not be explainable by alternative proposals. Finally, we describe some key challenges in resolving the debate, and propose potential directions to address them through a combination of theory and experiments., Comment: 35 pages, 8 figures

Solar physicists routinely utilize observations of Ar-like Fe IX and Cl-like Fe X emission to study a variety of solar structures. However, unidentified lines exist in the Fe IX and Fe X spectra, greatly impeding the spectroscopic diagnostic potential of these ions. Here, we present measurements using the Lawrence Livermore National Laboratory EBIT-I electron beam ion trap in the wavelength range 238-258 A. These studies enable us to unambiguously identify the charge state associated with each of the observed lines. This wavelength range is of particular interest because it contains the Fe IX density diagnostic line ratio 241.74 A/244.91 A, which is predicted to be one of the best density diagnostics of the solar corona, as well as the Fe X 257.26 A magnetic-field-induced transition. We compare our measurements to the Fe IX and Fe X lines tabulated in CHIANTI v10.0.1, which is used for modeling the solar spectrum. In addition, we have measured previously unidentified Fe X lines that will need to be added to CHIANTI and other spectroscopic databases.

We have experimentally studied dissociative recombination (DR) of electronically and vibrationally relaxed ArH$^+$ in its lowest rotational levels, using an electron--ion merged-beams setup at the Cryogenic Storage Ring. We report measurements for the merged-beams rate coefficient of ArH$^+$ and compare it to published experimental and theoretical results. In addition, by measuring the kinetic energy released to the DR fragments, we have determined the internal state of the DR products after dissociation. At low collision energies, we find that the atomic products are in their respective ground states, which are only accessible via non-adiabatic couplings to neutral Rydberg states. Published theoretical results for ArH$^+$ have not included this DR pathway. From our measurements, we have also derived a kinetic temperature rate coefficient for use in astrochemical models., Comment: Main paper: PDFLaTeX with 12 pages, 7 figures, 1 table. Appendix starting on page 12: PDFLaTeX with 10 pages, 4 figures, 2 tables. This is the Accepted Manuscript version of an article accepted for publication in the Physical Review A

We investigate a fully nonlinear two-phase free boundary problem with a Neumann boundary condition on the boundary of a general convex set $K \subset \mathbb{R}^n$ with corners. We show that the interior regularity theory developed by Caffarelli for the classical two-phase problem in his pioneer works \cite{C1,C2}, can be extended up to the boundary for the Neumann boundary condition under very mild regularity assumptions on the convex domain $K$. To start, we establish a general existence theorem for the Dirichlet two-phase problem driven by two different fully nonlinear operators, which is a result of independent interest.

Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to reference data is used, and the method is applicable to ground and excited states. The formulas derived are rigorous when the physical interaction is approached. In this regime, the second-order expression provides a lower bound to the long-range full configuration interaction energy. A long-range/short-range separation of the interaction between electrons at a distance of the order of one atomic unit provides total energies within chemical accuracy, and, for the systems studied, provide better results than short-range density functional approximations.

Modeling of wrinkles and folds formation in single and multilayer graphene sheets lying on flat deformable (polymer) substrates has been carried out. It is shown that the deformability of the substrate leads to the appearance of significant features. In contrast to the flat surfaces of rigid crystals molecules of soft polymer substrates can penetrate into wrinkles and folds of the graphene sheet, completely filling the voids beneath the sheet. Moreover, the vertical folds of the sheet can be directed not only upward from the substrate, but also down into the substrate, penetrating it. By modeling the uniaxial compression of the two-component graphene/polymer system, the external pressure and thermal vibrations of the substrate molecules have been taken into account. High external pressure $p\ge 150$~bar leads to a noticeable additional stabilization of the initial ground state of the system. At uniaxial compression above the critical value, a system of localized wrinkles whose interior is filled with molecules of the substrate appears in the graphene sheet. Increasing temperature leads to an increase in the size of wrinkles and to a decrease in their number. The largest wrinkles form before the substrate begins to melt. Melting leads to the complete disappearance of all wrinkles and small folds. Cooling of the melted substrate leads to its crystallization, but the system of wrinkles in the graphene sheet on the surface is not restored. Therefore, melting of the polymer substrate and its subsequent cooling can serve as a method getting rid of localized wrinkles and folds of the graphene sheet., Comment: 11 pages, 11 figures

We establish global $C^{1,\beta}$ and $W^{2, p}$ regularity for singular Monge-Amp\`ere equations of the form \[\det D^2 u \sim \text{dist}^{-\alpha}(\cdot,\partial\Omega),\quad \alpha\in (0, 1),\] under suitable conditions on the boundary data and domains. Our results imply that the convex Aleksandrov solution to the singular Monge-Amp\`ere equation \[\det D^2 u=|u|^{-\alpha}\quad \text{in}\quad\Omega,\quad u=0\quad \text{in}\quad \partial\Omega, \quad \alpha\in (0, 1),\] where $\Omega$ is a $C^3$, bounded, and uniformly convex domain, is globally $C^{1,\beta}$ and belongs to $W^{2, p}$ for all $p<1/\alpha$.

Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes. Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs. Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process. We show that if the unsatisfied checks of an error syndrome are at distance greater or equal to 5 from each other, then the MS decoding is locally blind: the qubits in the direct neighborhood of an unsatisfied check are never aware of any other unsatisfied checks, except their direct neighbor. Moreover, we show that degeneracy is not the only cause of decoding failures for errors of weight at least 4, that is, the MS non-degenerate decoding radius is equal to 3, for any toric code of distance greater or equal to 9. Finally, complementing our theoretical analysis, we present a pre-processing method of practical relevance. The proposed method, referred to as stabiliser-blowup, has linear complexity and allows correcting all (degenerate) errors of weight up to 3, providing quadratic improvement in the logical error rate performance, as compared to MS only.

Quantization is widely used to increase deep neural networks' (DNN) memory, computation, and power efficiency. Various techniques, such as post-training quantization and quantization-aware training, have been proposed to improve quantization quality. We introduce a novel approach for DNN quantization that uses a redundant representation of DNN's output. We represent the target quantity as a point on a 2D parametric curve. The DNN model is modified to predict 2D points that are mapped back to the target quantity at a post-processing stage. We demonstrate that this mapping can reduce quantization error. For the low-order parametric Hilbert curve, Depth-From-Stereo task, and two models represented by U-Net architecture and vision transformer, we achieved a quantization error reduction by about 5 times for the INT8 model at both CPU and DSP delegates. This gain comes with a minimal inference time increase (less than 7%). Our approach can be applied to other tasks, including segmentation, object detection, and key-points prediction., Comment: 18 pages, 10 figures

The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently the singlet and triplet component of the repulsion between electrons not present in the model (its short-range part). The scaling factors depend uniquely on the parameter used in defining the model interaction, and are constructed using only exact properties. We show results for the ground states and low-lying excited states of Harmonium with two to six electrons. We obtain important improvements for the estimation of the exact energy, not only over the model energy, but also over the expectation value of the Hamiltonian.

In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection. Our methodology involves the use of a parameter-dependent potential dependent on a single parameter to facilitate practical computations. We analyze the energy errors and densities in a two-electron system (harmonium) under various conditions, employing different confinement potentials and interaction parameters. The study reveals that while the mean-field potential improves the expectation value of the physical Hamiltonian, it does not necessarily improve the energy of the system within the bounds of chemical accuracy. We also delve into the impact of density variations in adiabatic connections, challenging the common assumption that a mean field improves results. Our findings indicate that as long as energy errors remain within chemical accuracy, the mean field does not significantly outperform a bare potential. This observation is attributed to the effectiveness of corrections based on the short-range behavior of the wave function, a universal characteristic that diminishes the distinction between using a mean field or not.

We present a study of spectral line width measurements from the Extreme Ultraviolet Imaging Spectrometer (EIS) on {\it Hinode}. We used spectral line profiles of Fe {\sc xvi} 262.984 {\AA}, Fe {\sc xiv} 264.787 {\AA}, Fe {\sc xiv} 270.519 {\AA}, Fe {\sc xiv} 274.203 {\AA}, and Fe {\sc xv} 284.160 {\AA}, and studied 11 active regions. Previous studies of spectral line widths have shown that in hot loops in the cores of active regions, the observed non-thermal velocities are smaller than predicted from models of reconnection jets in the corona or shock heating associated with Alfv\'{e}n waves. The observed line widths are also inconsistent with models of chromospheric evaporation due to coronal nanoflares. We show that recent advances in higher resolution Alfv\'{e}n wave turbulence modeling enables us to obtain non-thermal velocities similar to those measured in active regions. The observed non-thermal velocities for the 11 active regions in our study are in the range of 17$-$30 $\rm km ~ s^{-1}$, consistent with the spectral line non-thermal widths predicted from our model of 16 interacting flux tubes, which are in the range of ~15$-$37 $\rm km ~ s^{-1}$.

An inertial navigation system (INS) utilizes three orthogonal accelerometers and gyroscopes to determine platform position, velocity, and orientation. There are countless applications for INS, including robotics, autonomous platforms, and the internet of things. Recent research explores the integration of data-driven methods with INS, highlighting significant innovations, improving accuracy and efficiency. Despite the growing interest in this field and the availability of INS datasets, no datasets are available for gyro-free INS (GFINS) and multiple inertial measurement unit (MIMU) architectures. To fill this gap and to stimulate further research in this field, we designed and recorded GFINS and MIMU datasets using 54 inertial sensors grouped in nine inertial measurement units. These sensors can be used to define and evaluate different types of MIMU and GFINS architectures. The inertial sensors were arranged in three different sensor configurations and mounted on a mobile robot and a passenger car. In total, the dataset contains 35 hours of inertial data and corresponding ground truth trajectories. The data and code are freely accessible through our GitHub repository., Comment: 10 pages, 16 figures, 6 tables

Variations of the Flip-It game have been applied to model network cyber operations. While Flip-It can accurately express uncertainty and loss of control, it imposes no essential resource constraints for operations. Capture the flag (CTF) style competitive games, such as Flip-It , entail uncertainties and loss of control, but also impose realistic constraints on resource use. As such, they bear a closer resemblance to actual cyber operations. We formalize a dynamical network control game for CTF competitions and detail the static game for each time step. The static game can be reformulated as instances of a novel optimization problem called Adversarial Knapsack (AK) or Dueling Knapsack (DK) when there are only two players. We define the Adversarial Knapsack optimization problems as a system of interacting Weighted Knapsack problems, and illustrate its applications to general scenarios involving multiple agents with conflicting optimization goals, e.g., cyber operations and CTF games in particular. Common awareness of the scenario, rewards, and costs will set the stage for a non-cooperative game. Critically, rational players may second guess that their AK solution -- with a better response and higher reward -- is possible if opponents predictably play their AK optimal solutions. Thus, secondary reasoning which such as belief modeling of opponents play can be anticipated for rational players and will introduce a type of non-stability where players maneuver for slight reward differentials. To analyze this, we provide the best-response algorithms and simulation software to consider how rational agents may heuristically search for maneuvers. We further summarize insights offered by the game model by predicting that metrics such as Common Vulnerability Scoring System (CVSS) may intensify the secondary reasoning in cyber operations., Comment: 26 pages

In this paper, we introduce a new class of quaternions called Lucas-Leonardo p-quaternions and derive several fundamental properties of these numbers. Furthermore, we investigate some applications related to companion sequences associated with Leonardo quaternions. In particular, we determine Lucas-Leonardo quaternions and Francois quaternions, which are zero divisors and invertible elements in the quaternion algebra over certain finite fields.

The ground-state phonon pressure is an analogue to the famous Casimir pressure of vacuum produced by zero-point photons. The acoustic Casimir forces are, however, many orders of magnitude weaker than the electromagnetic Casimir forces, as the typical speed of sound is 100 000 times smaller than the speed of light. Because of its weakness, zero-point acoustic Casimir pressure was never observed, although the pressure of artificially introduced sound noise on a narrow aperture has been reported. However, the magnitude of Casimir pressure increases as $1/L^3$ with the decrease of the sample size $L$, and reaches picoNewtons in the sub-micron scales. We demonstrate and measure the acoustic Casimir pressure induced by zero-point phonons in solid helium adsorbed on a carbon nanotube. We have also observed Casimir-like "pushing out" thermal phonons with the decreasing temperature or the length. We also show that all thermodynamic quantities are size-dependent, and therefore in the mesoscopic range $L\lesssim\hbar{c}/(k_BT)$ quadruple points are possible on the phase diagram where four different phases coexist. Due to the smallness of solid helium sample, temperature of Bose-Einstein condensation (BEC) of vacancies is relatively high, $10-100$ mK. This allowed us to experimentally discover the BEC in a system of zero-point vacancies, predicted more than 50 years ago.

We study Homogeneously Precessing Domain (HPD) in superfluid $^3$He-B in a regular continuous-wave nuclear magnetic resonance (CW NMR) experiment. Using Fourier analysis of CW NMR time traces, we identify several oscillation modes with frequency monotonically increasing with the frequency shift of the HPD. Some of these modes are localized near the cell walls, while others are localized in bulk liquid and can be interpreted as oscillations of $\vartheta$-solitons. We also observe chaotic motion of the HPD in a certain range of temperatures and frequency shifts., Comment: 12 pages, 6 figures

We present a high-resolution spectral study of Fe L-shell extinction by the diffuse interstellar medium (ISM) in the direction of the X-ray binaries Cygnus X-1 and GX 339-4, using the XMM-Newton reflection grating spectrometer. The majority of interstellar Fe is suspected to condense into dust grains in the diffuse ISM, but the compounds formed from this process are unknown. Here, we use the laboratory cross sections from Kortright & Kim (2000) and Lee et al. (2009) to model the absorption and scattering profiles of metallic Fe, and the crystalline compounds fayalite (Fe$_2$SiO$_4$), ferrous sulfate (FeSO$_4$), hematite ($\alpha$-Fe$_2$O$_3$), and lepidocrocite ($\gamma$-FeOOH), which have oxidation states ranging from Fe$^{0}$ to Fe$^{3+}$. We find that the observed Fe L-shell features are systematically offset in energy from the laboratory measurements. An examination of over two dozen published measurements of Fe L-shell absorption finds a 1-2 eV scatter in energy positions of the L-shell features. Motivated by this, we fit for the best energy-scale shift simultaneously with the fine structure of the Fe L-shell extinction cross sections. Hematite and lepidocrocite provide the best fits ($\approx +1.1$ eV shift), followed by fayalite ($\approx +1.8$ eV shift). However, fayalite is disfavored, based on the implied abundances and knowledge of ISM silicates gained by infrared astronomical observations and meteoritic studies. We conclude that iron oxides in the Fe$^{3+}$ oxidation state are good candidates for Fe-bearing dust. To verify this, new absolute photoabsorption measurements are needed on an energy scale accurate to better than 0.2 eV., Comment: accepted to AAS Journals

We demonstrate complete control over dynamics of a single superconducting vortex in a nanostructure which we coin the Single Vortex Box (SVB). Our device allows us to trap the vortex in a field-cooled aluminum nanosquare and expel it on demand with a nanosecond pulse of electrical current. We read-out the vortex state of the box by testing the switching current of the adjacent Dayem nanobridge. Using the time-resolving nanothermometry we measure 4$\cdot$10$^{-19}\,$J as the amount of the dissipated heat (which is the energy of a single red photon) in the elementary process of the vortex expulsion, and monitor the following thermal relaxation of the device. The measured heat is equal to the energy required to annihilate all Cooper pairs on the way of the moving vortex. Our design and measuring protocol are convenient for studying the stochastic mechanism of the vortex escape from current-driven superconducting nanowires, which has its roots either in thermal or quantum fluctuations, similar to ones widely studied in Josephson junctions or magnetic nanoclusters and molecules. Our experiment enlightens the thermodynamics of the absorption process in the superconducting nanowire single-photon detectors, in which vortices are perceived to be essential for a formation of a detectable hot spot. The demonstrated opportunity to manipulate a single superconducting vortex reliably in a confined geometry comprises in fact a proof-of-concept of a nanoscale non-volatile memory cell with sub-nanosecond write and read operations, which offers compatibility with quantum processors based either on superconducting qubits or rapid single flux quantum circuits.

We study the notion of $k$-stabilizer universal quantum state, that is, an $n$-qubit quantum state, such that it is possible to induce any stabilizer state on any $k$ qubits, by using only local operations and classical communications. These states generalize the notion of $k$-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and $k$-vertex-minor universal graphs. First, we demonstrate the existence of $k$-stabilizer universal graph states that are optimal in size with $n=\Theta(k^2)$ qubits. We also provide parameters for which a random graph state on $\Theta(k^2)$ qubits is $k$-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of $k$-stabilizer universal graph states on $n = O(k^4)$ qubits. Both rely upon the incidence graph of the projective plane over a finite field $\mathbb{F}_q$. This provides a major improvement over the previously known explicit construction of $k$-pairable graph states with $n = O(2^{3k})$, bringing forth a new and potentially powerful family of multipartite quantum resources.

We report the first experimental detection of a reflected Alfv\'en wave from an Alfv\'en-speed gradient under conditions similar to those in coronal holes. The experiments were conducted in the Large Plasma Device at the University of California, Los Angeles. We present the experimentally measured dependence of the coefficient of reflection versus the wave inhomogeneity parameter, i.e., the ratio of the wave length of the incident wave to the length scale of the gradient. Two-fluid simulations using the Gkeyll code qualitatively agree with and support the experimental findings. Our experimental results support models of wave heating that rely on wave reflection at low heights from a smooth Alfv\'en-speed gradient to drive turbulence.

New results are presented on a high-statistics measurement of Collins and Sivers asymmetries of charged hadrons produced in deep inelastic scattering of muons on a transversely polarised $^6$LiD target. The data were taken in 2022 with the COMPASS spectrometer using the 160 \gevv\ muon beam at CERN, balancing the existing data on transversely polarised proton targets. The first results from about two-thirds of the new data have total uncertainties smaller by up to a factor of three compared to the previous deuteron measurements. Using all the COMPASS proton and deuteron results, both the transversity and the Sivers distribution functions of the $u$ and $d$ quark, as well as the tensor charge in the measured $x$-range are extracted. In particular, the accuracy of the $d$ quark results is significantly improved.

The COMPASS Collaboration performed measurements of the Drell-Yan process in 2015 and 2018 using a 190 GeV/c $\pi^{-}$ beam impinging on a transversely polarised ammonia target. Combining the data of both years, we present final results on the amplitudes of the five azimuthal modulations in the dimuon production cross section. Three of these transverse-spin-dependent azimuthal asymmetries (TSAs) probe the nucleon leading-twist Sivers, transversity, and pretzelosity transverse-momentum dependent (TMD) parton distribution functions (PDFs). The other two are induced by subleading effects. These TSAs provide unique new inputs for the study of the nucleon TMD PDFs and their universality properties. In particular, the Sivers TSA observed in this measurement is consistent with the fundamental QCD prediction of a sign change of naive time-reversal-odd TMD PDFs when comparing the Drell-Yan process with semi-inclusive measurements of deep inelastic scattering. Also, within the context of model predictions, the observed transversity TSA is consistent with the expectation of a sign change for the Boer-Mulders function.