Papers

We propose the electric Edelstein effect (EEE) in two-dimensional (2D) systems, where crossed out-of-plane and in-plane electric fields generate a spin polarization. The gate field converts the Edelstein response from a material-fixed spin polarization into a gate-tunable one. A symmetry analysis over all magnetic layer point groups shows that the EEE is allowed in a wide range of magnetic and nonmagnetic systems, including ferromagnets, antiferromagnets, and altermagnets. The EEE plays two distinct roles: it generates spin polarization where the linear Edelstein effect (EE) is symmetry-forbidden, as in centrosymmetric materials; and it adds a new gate-tunable component, generally non-collinear with the conventional one, where the EE is already present. The two fields then act as independent knobs and raise the control dimension of the spin polarization from one to two. Our microscopic theory traces the EEE to band-geometric quantities, which are strongly enhanced near small band gaps. First-principles calculations predict pronounced effects in the centrosymmetric ferromagnet MnSe2, where the linear EE is symmetry-forbidden. In the nonmagnet SnSe where the EE and EEE coexist, the two knobs cover an extended region of the spin sphere. Our findings establish the EEE as a symmetry-guided, gate-tunable route to electrical spin manipulation and open avenues for multistate spintronics in 2D quantum materials.

Early warning signals are key tools for anticipating qualitative changes in the dynamics of complex systems. In this work, we investigate whether an information-theoretic measure designed to characterize directional causal dependencies between observables can provide early warning of the approach to bifurcations. The measure considered is the rate of information transfer, which has been successfully applied to characterize directional dependencies in a broad range of fields, from economics to climate science. Three fundamental local bifurcations are considered: saddle-node, pitchfork, and Hopf bifurcations. We first investigate idealized (quasi-)potential stochastic systems for which analytical expressions for the rate of information transfer can be derived. Distinct signatures are found for the three bifurcation types. In particular, the rate of information transfer displays a strong increase and divergence when approaching the saddle-node bifurcation, whereas smoother but systematic changes are found near the pitchfork and Hopf bifurcations. The approach is then tested using low-order climate models exhibiting the same types of bifurcations. The results confirm that changes in the rate of information transfer can precede the corresponding dynamical transitions, suggesting that directional information transfer provides a useful complementary early-warning indicator for detecting the approach to critical transitions in nonlinear stochastic systems.

In this paper, we study planar compressible cavity flows fast-decaying vorticity and establish a Schauder estimate in large scale. As an application, we obtain an a priori asymptotic growth rate estimate of the cavity, that $s^{\frac{1}{2}-\delta}\lesssim h(s)\lesssim s^{\frac{1}{2}+\delta}$. This is by far the most accurate asymptotic estimate for compressible cavity flows and is probably the first paper that takes vorticity into account in the asymptotic analysis.

We introduce a parallel decoder for quantum low-density parity-check (QLDPC) codes based on probabilistic bits (p-bits), tunable stochastic binary units controlled by local fields. The idea is that predicted error configurations, interpreted as explanations of the observed syndrome, are updated stochastically using local Gibbs conditionals, while a progressively strengthened parity penalty drives the search toward syndrome-valid configurations. A coloring of the decoding graph enables parallel block updates, and independent replicas and restarts provide trajectory diversity. The best candidate encountered during the search is returned, mirroring the candidate-selection strategy of recent ensemble decoders. At the stated update budgets, the resulting logical error rates are on par with leading decoders under both code-capacity and circuit-level noise. While the total number of variable resamplings can be substantially larger than the message-update count of BP-based alternatives, the numerical results establish constraint-annealed p-bit dynamics as a competitive stochastic alternative for QLDPC decoding and motivate further study of hardware-native implementations.

Accurate lens surface metrology is essential to determine the manufactured geometry of refractive optical elements and their deviation from the specified design. We demonstrate a transmission metrology method that reconstructs refractive lens surfaces from the displacement of a wavelet-noise-patterned mask. Lens-induced distortion is represented by a dense displacement field. A differentiable ray tracer fits the lens geometry using a calibrated near-telecentric camera model with an effective finite ray origin. We validate the method on commercial lenses. The recovered geometries agree with nominal specifications, and the plano-aspheric reconstruction is compared with chromatic confocal profilometry.

Simple aggregation of independent responses ("wisdom of crowds") generally improves collective performance through statistical facilitation, but interaction among members can sometimes hinder group outcomes. However, under certain circumstances, coordination studies show that interacting groups can outperform their individual members and nominal groups, and interaction can also be more efficient than independence. We present a reservoir computing model to investigate how interaction can enhance joint performance in terms of accuracy and efficiency. Echo state networks were trained independently to identify Japanese speakers from vowel recordings and tested jointly with and without coupled feedback. Model pairs reproduced the dyadic advantage reported by Bahrami et al. (2010) with interaction via pooled-feedback, but not when independent responses were aggregated together. Model dynamics revealed that interaction was beneficial whereas aggregated outputs were prone to diverging from runaway feedback over time. In terms of efficiency, larger groups of smaller interacting models outperformed smaller groups of larger models while equating for total amount of group computation. Our results offer a formal framework for explaining when and why interaction enhances collective intelligence.

Blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI) has revolutionized noninvasive imaging of human brain function, but it indirectly senses deoxyhemoglobin through water-proton relaxation and relies on bulky, costly, noisy, enclosed, superconducting-magnet scanners. In contrast, photoacoustic computed tomography (PACT) directly probes hemoglobin absorption using a more compact, lower-cost, quieter, open, magnet-free system. However, functional PACT of the adult human brain has so far been demonstrated only after surgical skull removal, because the skull strongly attenuates optical and acoustic signals. Here, we demonstrate non-invasive transcranial functional PACT (T-fPACT) through the intact adult skull. A densely packed, high-channel-count (3,072-element) hemispherical ultrasonic array provides near-$2\pi$-steradian simultaneous acquisition, enabling high sensitivity and single-shot three-dimensional imaging at 20 Hz that eliminates motion blurring. Participant-specific stabilization further enables measurement of small task-evoked hemodynamic responses over the entire task duration. In healthy adults, T-fPACT localized responses to expected sensorimotor regions, distinguished task-specific motor representations, and yielded consistent localizations across repeated task runs and visits. Comparison with high-field (7 T) fMRI showed spatially corresponding functional regions, while dual-wavelength imaging revealed distinct hemoglobin-weighted responses. These findings overcome the long-standing skull barrier in human brain PACT and establish non-invasive, rapid volumetric photoacoustic imaging of brain function.

We study the sharp constant in the differential inequality \[ I(t)I''(t)\geq c\,[I'(t)]^2 \] for Fisher information along the probability-normalized heat flow on $\mathbb R^2$. The unrestricted log-convexity value $c=1$ is false in two dimensions, whereas the known square-root convexity theorem gives the universal value $c=1/2$. We construct an exact, machine-verifiable sum-of-squares certificate proving the stronger universal bound \[ c\geq \frac{231691}{250000}=0.926764. \] Together with an independent exact Fourier/Gaussian-envelope construction, this gives \[ 0.926764\leq c_*<0.94176665012062, \] where $c_*$ is the sharp constant for positive-time Gaussian convolutions of arbitrary probability measures on $\mathbb R^2$. We formulate the proof in explicit two-dimensional index notation. The lower bound follows from an exact rational polynomial identity involving a strictly positive denominator, a weighted total derivative, and eleven positive rational Gram matrices. All $491$ recorded leading principal minors are strictly positive and the complete polynomial identity has zero residual. No symmetry, log-concavity, finite-variance, or finite-entropy assumption is imposed on the initial measure. The sharp value remains open.

A pressure-swirl nozzle converts the feed pressure into a swirling conical sheet that breaks into ligaments and then into drops. The size of the drops governs the deposition and drift of agricultural sprays, the capture of airborne dust and the combustion efficiency of fuel injectors. The standard tool for measuring the drop size is laser diffraction, which returns a spatial, concentration-weighted distribution at the beam station. However, the dependence of the measured drop size on the nozzle-to-beam distance has not been quantified alongside a Weber-number scaling, so prefactors reported at different distances cannot be compared on an equal footing. To this end, we measure the drop-size distribution of two full-cone pressure-swirl nozzles by laser diffraction at a range of distances, pressures and orientations, together with high-speed imaging of the sheet breakup. We find that the volume-median diameter $D_{v50}$ decreases with the measurement distance $L$ as $D_{v50} \sim L^{-0.18}$ beyond the drop-formation region. A joint fit over both nozzles gives $D_{v50}/d_0 \sim \mathrm{We}^{-0.31}\,(L/d_0)^{-0.21}$, where $d_0$ is the orifice diameter and $\mathrm{We}$ the Weber number, which separates the pressure and distance effects. At a fixed distance the two nozzles collapse onto the $\mathrm{We}^{-1/3}$ scaling of Kooij et al. (2018), and the measured distance dependence may account for part of the offset between our near-field prefactor and the far-field value. Thus, a drop size obtained by laser diffraction is meaningful only when the measurement distance is reported with it, and a spray should be characterized at the actual distance between the nozzle and its target.

Interpreting electron paramagnetic resonance (EPR) spectra commonly requires repeated forward simulation and optimization of spin Hamiltonian parameters. Established software provides mature simulation and fitting methods, but these calculations are not generally available as differentiable components within machine-learning workflows. We present TorchSpin, an open-source PyTorch framework that ports the organization and numerical conventions of EasySpin into a tensor-based computational environment. Representative calculations spanning continuous-wave EPR, ENDOR, pulse EPR, spin dynamics, trajectory simulation, and magnetometry closely reproduced corresponding EasySpin results. In matched benchmarks, TorchSpin CPU execution was faster than EasySpin for six of nine workloads although performance depended strongly on the calculation. We therefore focused on the capabilities enabled by automatic differentiation in PyTorch. In a Cu(II) powder-spectrum demonstration, feedback propagated through TorchSpin improved the quality of a supervised convolutional neural network (CNN) without using parameter labels during refinement. Models trained from randomly initialized CNNs using only noisy spectra and TorchSpin reconstruction loss achieved median similarities of $\geq$ 0.99. CNNs trained on TorchSpin-generated libraries also transferred without adaptation to independently generated EasySpin spectra with performance comparable to EasySpin-trained controls. Once trained, the CNN produced initial parameter estimates in approximately 1 ms per spectrum while a batch of 512 was processed in approximately 1.3 ms with GPU acceleration. TorchSpin therefore provides both a tested Python implementation of established EPR calculations and a differentiable physical layer for rapid learned inference, spectral refinement, and parameter-label-free training.

Urban venues such as restaurants, shops, bars and parks host the daily life of a city, and their collective rise and fall signals how vibrant a neighbourhood is. The usual assumption is that a venue's fortunes follow its neighbourhood's, so that how wealthy an area is and how many people live there will decide a venue's performance. Yet whether there is a common performance trajectory shared by venues over time is underexplored. In this study, we use 5.5 years of Foursquare data for about 10^4 venues in London and Barcelona. We found six distinguishable shapes recur in both cities, that are (1) Fall, (2) Rise, (3) Rise & Fall, (4) Steady, (5) Ephemeral (an early hit that loses popularity fast) and (6) Underdogs (a slow starter that gains popularity late). However, no recovery shape appears, that is neither city yields a U-shaped fall-and-rise group. Additionally, we found that deprivation and population density are not indicative which shape a venue follows. We also discovered that how early a shape can be recognized depends on when its distinctive segment occurs, not a shape's complexity. Proximity between venues, however, does predict how well-performing a venue is. We uncovered a mixing pattern where venues of the same shape tend to locate together more often than chance within roughly 200 to 600 metres. Finally, our qualitative reading of two contrasting districts, one rising in London and one falling in Barcelona, show that comparable socioeconomic conditions but divergent gentrification histories can generate vastly different popularity trajectories. All in all, our results altogether point at that urban vibrancy emerges at the block- and street- level, and social and historical contexts matter in terms of the characteristics of such patterns.

A tidal bore is a nonlinear step like surge propagating on the top of a river counter-current. The scientific literature reports that the passage of the tidal front may induce local flow reversals and, in some cases, a global reversal of the river current. Here, combining Particle Image Velocimetry (PIV) measurements and 2D numerical simulations based on a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method, we show that the flow classification of tidal bores must explicitly take into account the frame of reference. When the river flow does not reverse after the bore passing, this is a consequence of the perspective imposed by the background current (itself resulting from the previous tide and the natural river discharge toward the sea). Depending on the relative magnitudes of the river current and the velocity field induced by the bore, one may observe a global reversal, a local reversal (or both), or no reversal at all. When the tide is spatially inhomogeneous, with a tidal range that varies along the estuary rather than a simple step in water depth, transitions between bore types may occur during the bore passing.

The two 4-m class telescopes at the Devasthal site in India are complementary: the 4-m International Liquid Mirror Telescope (ILMT) is dedicated to the discovery of new transient phenomena, which can be followed up using the 3.6-m Devasthal Optical Telescope (DOT) for their optical characterisation. The ILMT continuously surveys a $22.3^\prime \times 22.3^\prime$ wide strip of the zenith sky. A dedicated transient detection and classification pipeline, PyLMT, based on optimised image subtraction and convolutional neural network (CNN) techniques, enables the discovery of numerous photometric transients with the ILMT. However, these transient discoveries still require spectroscopic confirmation to determine their types, for which spectra obtained with the DOT are essential. Here, we present a selection of photometric transients, specifically supernova candidates. We investigate their photometric and spectroscopic properties using ILMT light curves, supplemented with ZTF data and DOT spectroscopic observations.

Topological boundary states offer a platform for guided-wave propagation within bulk bandgaps. Their propagation characteristics depend not only on the spectral extent of the states but also on their dispersion within the operating bandwidth. A nearly linear dispersion provides more uniform group velocity across frequency, whereas a reduced slope enables slow-wave propagation. Despite advances in inverse design of prescribed dispersion relations and topological dispersion tuning, application-oriented characteristics of boundary-state dispersion have rarely been direct inverse-design objectives. Here, we develop a supercell-enabled, surrogate-assisted framework for the inverse design of boundary-state dispersion in a phononic crystal with pseudomagnetic fields. Area-preserving anisotropic deformation shifts the local Dirac points, and independent variation of 21 rows within the supercell provides distributed control over the boundary-state branch. A constraint-preserving surrogate reconstructs the dispersion from an initial frequency and positive frequency increments, with first- and second-difference losses introduced to capture local slope and curvature. Coupled with a genetic algorithm, the framework targets two prescribed-bandwidth design tasks: highly linear dispersion and slow-wave dispersion. For the former, finite-element verification yields relative group-velocity variations of 0.142% to 1.183% over prescribed bandwidths of 4% to 6%. For slow-wave designs, mean group velocities of 190 to 385 m/s are obtained over bandwidths of 0.2% to 0.8% while satisfying a 5% group-velocity variation limit. These results establish boundary-state dispersion as a direct inverse-design target beyond conventional bandwidth optimization, opening a flexible route to group-velocity control through application-oriented dispersion engineering over prescribed relative bandwidths.

We study disformal transformations of $\mathcal{N}$ scalar fields coupled to a Dirac fermion. The resulting axial coupling generically introduces higher derivatives in the scalar field equations of motion; for field-dependent free functions, these are absent if and only if the disformal transformation acts along a single field-space direction. We show that these higher derivatives do not signal an Ostrogradsky ghost. After the transformation, the fermion registers the derivatives of the matter-frame tetrad only through the axial current, so that every coupling to the derivatives of the scalar fields multiplies a fermion bilinear, which is Grassmann even and nilpotent. Such terms do not contribute to the body of the constraint matrix, and at each level of the Grassmann expansion the field equations are linear, with the principal part of the theory without fermions. Through a Hamiltonian analysis, we show that the number of degrees of freedom is that of the bosonic theory plus that of the fermion, both in the Einstein frame, for free functions depending on the scalar fields and their kinetic matrix, and for minimally coupled fermions in multi-field DHOST theories. The same mechanism applies to disformal transformations with higher derivatives of a single scalar field, for which fermions impose no condition beyond those required by bosonic matter.

We give an explicit construction proving that the exact stabilizer rank of $m$ copies of the qubit face-center magic state is $O(2^{3m/8})$. Two symmetry-related fifteen-term identities combine into a twenty-four-term decomposition at twelve copies. The balanced structure of this decomposition yields a substitution that adds eight copies at a cost of eight terms per existing term. The resulting bound $\gamma_T \leq 3/8$ improves the previously published exponent $\log_2(3)/4$.

Optical lattice clocks in space could improve satellite navigation systems and enable new tests of fundamental physics, including gravitational-wave detection and tests of relativity. In microgravity, atoms can tunnel to degenerate neighboring lattice sites, broadening the clock transition and limiting coherence times. We demonstrate Aubry-André localization in a bichromatic optical lattice formed by two magic-wavelength lasers, suppressing tunneling in a horizontal lattice clock emulating free fall. We recover a Fourier-limited clock Rabi spectrum and measure Ramsey coherence times of up to 2 s in shallow lattices, with up to 100-fold improvement over the delocalized regime. These results establish Aubry-André localization as a practical route to controlling tunneling in future space-based clocks, and open a path to operating terrestrial clocks at shallower lattice depths.

A dynamic optimization workflow for linear gyrokinetic stability that couples the gyrokinetic code CGYRO with the libEnsemble framework for ensemble management has been developed. The workflow is designed to efficiently explore multi-dimensional plasma parameter spaces and to address the practical challenges of simulation-driven optimization in fusion plasma physics, including expensive objective evaluations, unavailable gradient information, non-smoothness arising from transitions between dominant instability branches, and simultaneous multi-core simulations on high-performance computing resources. Rather than optimizing the growth rate at a single wavenumber, the objective maximizes the growth rate-to-wavenumber ratio over the ion-scale spectrum. A derivative-free, model-based optimization algorithm employs manifold sampling to handle the nonsmooth composite structure of the objective function. The approach is applied to the optimization of local magnetic flux-surface shaping parameters, with an equilibrium baseline drawn from DIII-D negative triangularity experimental parameters. The workflow is general and extensible and provides a foundation for future optimization studies involving nonlinear transport objectives and higher-dimensional parameter spaces.

In this paper, we present a comprehensive theoretical study of the electronic states in gapped graphene in the presence of a charge impurity and a magnetic field. We focus on the impurity-induced modification of the Landau levels under the influence of an attractive or repulsive Coulomb potential. Since analytical solutions of the Dirac equation are not available in this case, the study is carried out using the Wentzel-Kramers-Brillouin (WKB) approach. Special attention is paid to the screening of the Coulomb potential in the presence of metallic gates situated at some distances from graphene sheet, as is commonly the case in experiments. Using both analytical and numerical methods, we determine the energy spectrum as a function of the magnetic field strength and impurity charge for screened and unscreened Coulomb potentials. Our results reveal a significant dependence of the energy levels for sample-to-gate distances of less than 50 nm.

Artificial intelligence (AI) increasingly participates in communication, decision-making, and collective action, making the social organisation of human-machine interaction central to Hybrid Intelligence (HI). This chapter reviews the behavioural sociology of humans and machines through an HI lens, examining how interaction and feedback shape the combination of human and artificial capabilities. Drawing on sociology, social psychology, human-computer interaction, organisational studies, collective intelligence, and science and technology studies, it traces processes from individual social perception to cooperation in hybrid groups and organisational and institutional arrangements. Particular attention is given to how machine participation alters familiar mechanisms: social categorisation attaches expectations to designed identities, reciprocity may involve unequal social obligations, and algorithmic recommendations acquire authority through organisational practices. The chapter distinguishes observable machine behaviour from human interpretations of intention, understanding, and moral responsibility. It also considers how behavioural effects can extend beyond direct human-machine encounters, while separating established findings from proposed longer-term consequences. It argues that the benefits of HI depend on how roles, incentives, reliance, and accountability are organised, and identifies priorities for empirical research on these evolving sociotechnical arrangements.

We present the new CTEQ-JLab global QCD analysis, called CJ26, that simultaneously fits parton distribution functions of the proton and nuclear effects in deuteron targets. This work includes, for the first time in a global fit, the full set of JLab 6 GeV inclusive DIS measurements and the first published JLab 12 GeV data. The analysis focuses on the large-$x$ region, and carefully treats the interplay between higher-twist effects and off-shell corrections in low-energy proton and deuteron target data. We discuss their effect on quark and gluon distributions, and highlight the importance of quantifying the experimental correlated systematic uncertainty to achieve fits of the highest accuracy. We also outline how upcoming data may help unravel the nuclear and partonic dynamics in light nuclei. The extracted next-to-leading order parton distributions are available on the CJ web pages in LHAPDF format for general use, accompanied by leading- and higher-twist structure functions calculated with the simultaneously fitted PDFs, higher-twist corrections, and off-shell corrections. This write up clarifies several points that became clearer while finalizing the CJ26 paper and can be read as a companion to the latter.

Machine learning surrogates of partial differential equations (PDEs) are commonly trained on data generated by numerical solvers. Therefore, the training data obey not the PDE but the modified equation of the numerical scheme, and the test loss, computed on data from the same solver, cannot distinguish a model that learned the physics from one that learned the discretization error. Here, we show that the difference is nevertheless visible in the trained model. We propose a suite of structure-preserving fidelity diagnostics, simple scores that measure whether a learned model respects one known property of the physics, such as a conserved quantity, a symmetry or a Hamiltonian structure, without access to the training data or the governing equation. Over five systems, the diagnostics track the error with respect to the true dynamics with a rank correlation of up to $0.94$, while the test loss is uncorrelated or anti-correlated with it. For the Burgers, Korteweg-de Vries and Navier-Stokes equations, the diagnostics separate numerical schemes that the test loss ranks as equivalent, including schemes of the same order. order.

In this work we construct three-dimensional Chern–Simons gravity theories for the six resonant $JPZ$ algebras generated by the Lorentz generators $J_a$, translations $P_a$, and an additional Lorentz-like generator $Z_a$. The resonance condition together with the Jacobi identities leaves precisely six configurations arising from the semigroup expansions. Our main result is that three of them, $B_4$, $\widetilde C_4$, and $C_4$, are isomorphic to $iso(2,1)\oplus so(2,1)$, although they yield different gravitational realizations when we keep the original $JPZ$ field identification fixed. For each case $JPZ$, we determine the invariant tensors, gauge curvatures, Chern–Simons action, field equations, and the corresponding maximal-rank coupling sectors. The field equations can be written in the compact form $\Omega_\sigma\mathbf F=0$, which makes explicit how the additional field $h^a$ contributes to the curvature, torsion, and the remaining gauge-curvature components. We use the direct-sum isomorphisms to classify the local metric sectors and to relate them to known global and asymptotic solutions, while keeping the gravitational interpretation tied to the original $(\omega,e,h)$ fields.

Cavity optomechanical models typically treat a sensor either as a perturbative polarizable object in a pre-existing optical field, or solve the field at a fixed equilibrium and linearize in a fixed optical-mode basis. Neither self-consistently determines the spatially resolved cavity field, the optical force, the mechanical equilibrium, and the back-action when a finite-thickness dielectric plate intercepts the entire optical mode and restructures the intracavity field. In this companion paper to [1], we develop that treatment by extending the vacuum two-photon formalism to finite-thickness planar dielectrics, incorporating their Fresnel reflection, internal propagation, optical forces, and mechanical back-action directly into the field equations. We derive the carrier and sideband transfer functions needed to describe the coupled optical-mechanical system, including optomechanical cooling and the response to external perturbations. The result is a systematic starting point for calculating detector response and noise budgets for cavity experiments with intracavity dielectrics, including gravitational wave detectors deploying levitated sensors.

Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure $SU(3)$ lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model $\texttt{H2-2}$, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires $\sim 25n$ entangling gates for $n$ Trotter steps.

A Dirac mass is characterized not only by its magnitude but also by its sign, which influences the Berry curvature, Hall response, and the propagation direction of chiral boundary modes. However, local spectroscopy of magnetic topological surfaces has so far accessed only the gap magnitude $|M|$. Here we show how the topological sign of $M$ can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin–orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a $C_3$ axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.

We prove that for $k=4$ the quantum uniformity measures are norms, whereas for every $k\geq5$ the triangle inequality fails. This gives a complete answer to an open question of Bu, Gu, and Jaffe. The $k=4$ case is proved using the Cauchy–Schwarz inequality for the quantum uniformity pairing $\langle\cdot,\cdot\rangle_{Q^4}$ introduced here, together with the triangle inequality in a suitable finite-dimensional Bochner $L^8$ space. For $k\geq5$, we construct systems of linear equations over a finite field and derive a contradiction from the structure theory of norming linear systems.

Altermagnetism is a rapidly emerging paradigm in condensed matter magnetism, yet the number of experimentally confirmed altermagnetic candidates remains remarkably limited. Cr$_{1/4}$NbS$_2$ has long been theoretically proposed as a promising altermagnet, but there are no reports on experimental investigation of single crystals. Here, we report the successful growth of high-quality single crystals of Cr$_{1/4}$NbS$_2$ and present its structural, thermal, magnetic, and transport properties. Single-crystal X-ray diffraction provides detailed crystallographic information and confirms the hexagonal crystal symmetry ($P6_3/mmc$), one of the criteria for altermagnetic behavior. Resistivity and heat capacity measurements unambiguously identify an antiferromagnetic Néel temperature of $T_N \sim 141$ K. Magnetotransport measurements reveal non-trivial features in the magnetoresistance and Hall response, indicative of quantum diffusive transport phenomena. Cr$_{1/4}$NbS$_2$, synthesized here for the first time in single-crystalline form, therefore serves as an experimental platform for probing the rich spectrum of phenomena predicted for altermagnetic materials.

We present a theoretical study of distributed quantum sensing using a reconfigurable network of $N$ Mach–Zehnder interferometers to simultaneously estimate weighted linear combinations of relative phase shifts. The proposed scheme relies on injecting a Perelomov coherent state, generated from the SU(1,1) group representation, into one port of a passive quantum circuit while the remaining modes are initialized in the vacuum state, thereby establishing non-trivial quantum correlations among the sensors. Based on multi-parameter quantum estimation theory, our analysis shows that this entangled strategy outperforms the standard shot-noise limit and asymptotically achieves the Heisenberg limit. Furthermore, we highlight the crucial role of the first beam splitter's asymmetry; specifically, the optimal transmission coefficient that maximizes sensitivity corresponds to its maximum imbalance. Compared to a separable approach utilizing the same total average photon number, the entangled strategy yields a more efficient use of quantum resources, guaranteeing an accuracy gain between $1$ and $N$. This demonstrates that the entangled strategy is systematically superior to its separable counterpart. Ultimately, these results illustrate the potential of entangled distributed quantum sensor networks for high-precision measurements and provide clear guidelines for optimizing interferometric architectures in quantum metrology.

The geometrical configuration of the Einstein Telescope (ET) gravitational-wave observatory is one the most important design choices to be made for this future scientific facility. Two baseline configurations are currently being considered, a single triangle or 2 distant L-shaped detectors tilted by about $45^{\circ}$. In this document we present a study of the scientific performance of the ET baseline configurations in both stand-alone mode and in the presence of either an L-shaped Cosmic Explorer detector with 40-km long arms located in the United States or the existing LIGO-Virgo-KAGRA network. We also include in the study an alternative ET configuration, which is currently not being considered and consists of a triangle plus a distant L-shaped detector. We find that in stand-alone mode this alternative configuration performs significantly better than the other two in both the compact binary coalescence and stochastic gravitational wave background scientific cases. The differences in performance between the ET configurations are reduced in the presence of the considered, additional non-ET detectors. We also show that the impact of possible correlated noise in co-located detectors on the stochastic gravitational-wave background performance can be addressed with the addition of extra detectors. Finally, we study the impact on the ET scientific performance of the relative orientation of the future detectors in the network. We find that, while the configurations that include a triangular ET detector are basically insensitive to this orientation, a balanced compromise for the ET configuration consisting of two L-shaped detectors could be represented by a tilt angle between the two detectors of about $30^{\circ}$.