Papers

We perform field-level likelihood-free inference of the matter density parameter $\Omega_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $\Omega_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $\sigma_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $\Omega_m$ with mean relative errors of about $10\%$ in-distribution and $10$–$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $\Omega_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.

How cultural repertoires maintain diversity under selection is a fundamental question in cultural evolution. We address this using thirteen years of weekly popularity data for approximately 20,000 Irish traditional tunes, fitting ecological birth-process models under neutral, frequency-dependent, and per-tune selection hypotheses. We find strong evidence that tunes differ in intrinsic fitness - some are systematically more likely to be learned than others. We find that 29% of the variance in fitness can be explained by a mixture of social and melodic features. Some tunes appear to be carried along via linkage due to the tradition of playing tunes in sets, analogous to selective sweeps in genetics. By measuring changes in fitness over time and comparing this with recordings we precisely identify the mechanism by which a long-dormant tune can become fit through a popular recording. Despite the directional selection, repertoire diversity increases, driven by the continual arrival of new compositions. These results demonstrate that selection and diversity can coexist in a cultural ecosystem, and establish Irish traditional music as a quantitatively tractable system for studying the evolution of cultural variants and understanding what makes a tune stand out.

We extend the KTHNY theory of defect-mediated melting in two dimensions to the case of active solids exhibiting both non-reciprocal (odd) elasticity and Cosserat (micropolar) coupling. For perturbatively small values of non-reciprocity, melting still proceeds via defect unbinding, but the melting temperature shifts due to activity. However, at a threshold value of non-reciprocity, we discover a qualitatively distinct mechanism for 2D melting, which we call topological instability. This melting occurs through the proliferation of defect pairs at any temperature. We use a combination of field theory and simulations to characterize this zero-temperature transition in terms of the defect-pair fugacity. Surprisingly, for higher activity values, we find reentrant crystallization, where the quasi-long-range order survives even at temperatures for which the equilibrium crystal would melt. Although active solids present one realization of this topological instability, we envision core-energy-driven defect proliferation as a generic and unexplored route for two-dimensional melting.

In classical anharmonic lattices, the resonance structure driving nonlinear mode mixing is reshaped by band gaps. However, it remains unclear whether a spectral gap hinders or promotes long-time thermalization. Here we study a Fermi-Pasta-Ulam-Tsingou (FPUT) chain of equal masses joined by alternating dimensionless spring constants $1\pm\Delta\kappa$, so that the chain is dimerized with strength $\Delta\kappa$, the classical vibrational analogue of the Su-Schrieffer-Heeger (SSH) model, and quantify how the acoustic-optical gap controls relaxation under $\alpha$-type (cubic) nonlinearity. Tracking modal energies and spectral entropy via long-time symplectic simulations, we find that dimerization delays long-time relaxation. At $\Delta\kappa=1/2$, set by the onset of the first umklapp process that allows two zone-boundary acoustic phonons to fuse into a zone-center optical phonon, the three-wave acoustic-acoustic-optical channel closes. The effective acoustic-to-optical scattering rate reveals an interplay between the dynamic resonance vertex and the kinematic resonance manifold, which evolve differently with the dimerization parameter. Above the threshold $\Delta\kappa=1/2$, energy redistribution can nevertheless continue through higher-order resonances and quasiresonances. Yet specific boundary conditions and initial conditions can inhibit equipartition. These results identify the phononic gap as a tunable, momentum-selective filter for nonlinear energy transport, suggesting a general route to controlling energy transfer and equipartition in dimerized or topologically gapped nonlinear lattices and in flexible mechanical systems.

Light-driven control of material symmetry enables the engineering of phenomena forbidden in equilibrium. Although electromagnetic fields have been used to break time-reversal symmetry, its dynamic control on ultrafast timescales in nonmagnetic insulating oxides remains virtually unexplored. Here, we demonstrate simultaneous magnetic symmetry lowering and timereversal-symmetry breaking in cubic SrTiO3 driven by an off-resonant, elliptically polarized THz pulse. Second harmonic generation (SHG) polarimetry reveals emergent SHG circular dichroism inconsistent with third-order nonlinear processes under cubic m3m symmetry. The SHG polar patterns exhibit mirror-symmetry breaking, indicating a transient reduction to tetragonal 4/mm'm' magnetic symmetry. Furthermore, the SHG response scales linearly with the angular momentum of THz pulse, providing direct evidence for THz-field-induced timereversal-symmetry breaking. These results establish a direct pathway for ultrafast symmetry control in non-magnetic oxides, enabling dynamic manipulation of emergent phases on ultrafast timescales.

The Quantum Approximate Optimisation Algorithm is the canonical near-term heuristic, yet on real superconducting hardware its behaviour is set by device physics, not by the algorithm. Hardware demonstrations rarely prove the intended coupling is realised, that genuine entanglement is prepared, or what controls it. We report a pre-registered single-device study on the nine-qubit superconducting processor Red at the Barcelona Supercomputing Center, using its five-qubit component. Across six calibrations we certify bipartite entanglement of a corrected QAOA cost layer on the good coupler at depth one by two-qubit tomographic negativity: 0.077, BCa 95% CI [0.065, 0.091], excluding zero every day, while the coupling-off twin stays separable and the degraded coupler equals zero. We then measure the device physics directly: in a pre-registered manipulation on a fixed Bell preparation (not the QAOA layer), reducing the CZ pulse amplitude causally reduces the certified negativity along a positive, well-fit slope (R^2 = 0.83-0.96), every rung-level interval excluding zero and surviving Holm and Benjamini-Hochberg correction. This is a local linearisation of a peaked response, not a global monotone law: the negativity peaks at conditional phase |zeta| = pi, which the nominal amplitude overshoots. The J=0 twin is a separate off-state control and the fringe visibility is constant, so the effect is coherent. The average gate fidelity is non-monotone in the drive and is reported only as a diagnostic. A per-circuit statevector guardrail excludes a diagonal compilation fault we disclose and repair. A randomized-measurement witness is consistent with entanglement but underpowered. The certificate collapses by depth three, and a pre-registered sixteen-instance depth-three ensemble shows no optimisation signal (one-sided Wilcoxon p = 0.15). We claim no advantage; the instances are classically trivial.

We investigate axial gravitational perturbations and shadow formation in black-bounce geometries supported by anisotropic fluids within general relativity. Two distinct classes of solutions are analyzed: a symmetric Simpson–Visser-like black bounce and an asymmetric deformation of the Reissner–Nordström metric, which can feature either a bounded interior region or an unbounded wormhole-like extension. Our findings indicate that configurations with horizons, whether symmetric or asymmetric, exhibit single-barrier effective potentials and quasinormal frequencies nearly indistinguishable from those of standard black holes. In contrast, horizonless symmetric configurations may develop multiple potential barriers, giving rise to gravitational-wave echoes whose amplitude and separation depend sensitively on the bounce parameter $a$ and the density parameter $\rho_0$. Horizonless asymmetric solutions, on the other hand, exhibit regularized effective potentials that do not produce echoes and remain phenomenologically close to the Reissner–Nordström case. From the optical perspective, both classes of solutions with horizons exhibit a single relevant photon sphere and shadow profiles nearly indistinguishable from those of their black-hole counterparts, while horizonless symmetric configurations can sustain multiple photon rings. Horizonless asymmetric configurations may instead support either a single photon ring or none. Finally, we recover the standard eikonal correspondence between quasinormal modes and the instability of circular null geodesics for configurations with horizons. For horizonless geometries, however, the emergence of multiple potential barriers prevents a straightforward extension of this relation, although the strong similarity between the wave and optical sectors suggests that a meaningful phenomenological correspondence may still persist.

Inspired by a recent ground-breaking space-based measurement of Newton's gravitational constant, we outline a proposal for a general layout of an optimized space-based approach that combines the advantages of a largely disturbance-free environment with lock-in techniques, null coordinates and the method of covariances. The method of covariances, and cross-covariances, is used for an optimized statistical analysis of data originating from two distinct experimental channels. One of two distinct measurement channels relies on an approximately constant acceleration in the gravitational field of static sources masses, while the second channel involves a lock-in measurement based on test and source masses with oscillating coordinates. Conceivable mission parameters are analyzed in terms of the optimum scale for the source masses and launch capabilities of currently available space launch systems. A candidate location for a largely disturbance-free position in geostationary orbit is identified.

White dwarfs (WDs) provide an unparalleled opportunity for detecting and characterizing exoplanets because of the large planet-to-star size ratio. However, only one transiting WD exoplanet is confirmed to date, and occurrence rate constraints remain loose because the rapid transits and weak phase curve modulations of WD exoplanets require high-precision, high-cadence photometry. The Galactic Bulge Time Domain Survey (GBTDS) of the Nancy Grace Roman Space Telescope will provide exactly this by observing thousands of WDs at 12.1-minute cadence. The expected WD exoplanet yield of this survey is not yet quantified. Here, we predict the GBTDS WD exoplanet yield over its first three high-cadence seasons, through both transiting and non-transiting (phase curve) channels. We run Monte Carlo detection probability simulations over a grid of planet radius, orbital period, and host properties for a Besançon synthetic population of WDs. Jupiter-sized planets dominate the transit yield, with a period-averaged effective survey size of $\overline{N}_\mathrm{eff}\approx8$, requiring an underlying occurrence rate of $\overline{\eta}_1\approx12\%$ for one expected detection, followed by $\overline{N}_\mathrm{eff}\approx2.6$ ($\overline{\eta}_1\approx38\%$) for Neptune-sized and $\overline{N}_\mathrm{eff}\approx1.8$ ($\overline{\eta}_1\approx55\%$) for sub-Neptune-sized planets. Source blending is the major observational challenge in the crowded GBTDS fields, removing $\approx95\%$ of the raw predicted yield. Phase curve provides marginal detections, adding at most $\approx4\%$ to the transit yield. A null detection by GBTDS would constrain $\eta_\mathrm{WD}$ to $< 28\%$ for Jupiter-sized planets at $95\%$ confidence. GBTDS will deliver the first WD exoplanet occurrence-rate constraints beyond the solar neighborhood and identify prime targets for future characterization.

We establish an exact equivalence between the fluctuations of integrated currents and the temporal statistics of current record events in continuous-time Markov jump processes. Specifically, we show that, under minimal assumptions, the Fano factor of an integrated current coincides exactly with the squared coefficient of variation of the inter-record waiting times. This result is obtained by showing that inter-record times induce a renewal structure, since each record event resets the system to a fixed state, and that their generating function can be expressed exactly in terms of a combinatorial organization governed by Narayana numbers. The equivalence extends previous results obtained for unicyclic networks to arbitrary finite-state graphs and provides a unified representation of current fluctuations in terms of record-time observables. The results are derived within a purely probabilistic framework and clarify the structural origin of current precision in terms of first-passage-like event statistics.

We systematically investigated the phase stability and pressure dependence of the elastic properties of four GeO2 polymorphs: rutile-, CaCl2-, alpha-PbO2-, and pyrite-type phases using theoretical calculations based on density functional theory. The elastic constants were calculated at 5 GPa intervals within the respective stability ranges of the four phases, as determined from static enthalpy calculations. We further employed a classical strain-coupled Landau free-energy expansion to describe the pressure evolution of the elastic response associated with the rutile- to CaCl2-type transition and to elucidate the origin of the elastic softening near the transition. The rutile- to CaCl2-type phase transition is consistent with a Landau-type second-order transition, with a critical pressure of 14.6 GPa obtained from the strain-based analysis. As the transition pressure approaches, elastic softening develops in the rutile-type phase, resulting in anomalous pressure dependence of the bulk and shear modulus. The calculated elastic-wave anisotropy increases markedly near the transition, primarily due to the rapid reduction in shear-wave velocity, reaching a maximum of approximately 122% at 22.5 GPa. Following the transition, the anisotropy decreases sharply in the CaCl2-type phase and exhibits a discontinuity at the CaCl2-type/alpha-PbO2 -type phase boundary. The higher-pressure alpha-PbO2- and pyrite-type phases exhibit comparatively weak pressure dependence of anisotropy, with a small discontinuity at their respective phase transition boundaries. The pyrite-type phase has the lowest anisotropy, reaching only approximately 4-5% at high pressure, consistent with the high-symmetry cubic structure and nearly isotropic elastic-wave propagation.

Determining the highest amount of noise that quantum circuits can handle is an interesting and crucial task in the development of fault-tolerant quantum computation. Previous work has constrained this upper limit for local depolarizing noise to $\approx 45~\%$ for circuits constructed using the universal Clifford with T gate set by finding the noise threshold where the gate set loses universality. In this work, we use a similar method with the matchgate with non-Gaussian resource universal gate set to find a limit of $p=(8 - 2 \sqrt{6})/5$ or $\approx 62~\%$ for fermionic quantum computing that is independent of circuit depth. To do this, we use Uhlmann-Wootters concurrences for a 4-mode fermionic Choi state representing a resourceful gate combined with local depolarizing noise to determine when the combined channel is convex Gaussian. These bounds are not directly comparable due to differences in noise model making the bound of $\approx 62~\%$ the best known for fermions.

Prethermal states–long-lived quasi-equilibrium configurations–occur in a wide range of physical systems that exhibit fast dephasing or reconfiguration followed by slow relaxation towards thermal equilibrium. We experimentally studied the 1D interface between immiscible 2D Bose-Einstein condensates (BECs); following a quench, the interfacial capillary waves (ripplons) quickly relaxed into a long-lived prethermal state characterized by a persistent non-equipartition of energy, evoking the classic Fermi-Pasta-Ulam-Tsingou problem. We directly measured the interface's height profile as it evolved in time, identified the contribution of individual ripplon modes, and find that, though their individual amplitudes are thermally distributed, they are not in thermal equilibrium–high-momentum modes rapidly equilibrated with the bulk phonon modes of the 2D BEC, while lower momentum modes remained at elevated temperatures, forming a long-lived prethermal configuration for the whole system. We attribute this to kinematic isolation: the absence of energy- and momentum-conserving relaxation processes in our system at ultracold temperature.

Ultracold atomic quantum systems offer an unprecedentedly powerful platform for exploring interacting symmetry-protected topological phases. Here, we show that their characteristic control over temperature provides a resource for engineering effective topological regimes with no zero-temperature counterpart. Employing finite-temperature matrix-product-state calculations, we investigate experimentally accessible Hamiltonians - the interacting bosonic Su-Schrieffer-Heeger and spin-1 XXZ chains - that host a topological phase at zero temperature, as well as a fermionic dipolar ladder model whose ground state exhibits no topological order. By tracking complementary topological markers, we identify an intriguing mechanism rooted in the structure of the zero-temperature phase diagrams: in finite-size systems, excitation gaps with different magnitudes define an intermediate-temperature window where the correlations associated with the lower gap are suppressed, while those protected by the larger gap persist. This enables the emergence of effective finite-temperature regimes exhibiting topological features that are either absent or qualitatively different from those at zero temperature. Our results establish a novel route toward exploring effective topological phases in ultracold atomic quantum systems.

Palomar Observatory Sky Survey-I (POSS-I) images obtained before the launch of Sputnik contain star-like point sources consistent with sub-second flashes that are absent from all subsequent observations. The nature and origin of these transients remain poorly understood. Based on models suggesting they are in geosynchronous orbit, we estimated the latitude/longitude over which POSS-I transients appeared. From a dataset of 107,875 POSS-I transients, we selected a subset with high probability of representing real objects based on a machine learning model. Two independent approaches were used to test whether transients non-randomly grouped over specific locations (hotspots). Based on comparing transient numbers in discrete 5{\deg} x 5{\deg} Earth-projected regions to numbers randomly expected in these same regions, 16 statistically-significant hotspots were identified. Separately, two-step cluster analysis identified 6 highly-distinct hotspots (silhouette value = 0.70). The two methods identified several similar hotspots not attributable to POSS-I survey biases: 1) Pacific ocean west of southern Mexico/Central America, 2) southern Gulf of Mexico, 3) southwestern US (Sedona, AZ, White Sands, NM regions). Transients accounting for reported transient-nuclear testing associations displayed location specificity, with exclusively Pacific transient locations during Pacific nuclear testing and primarily southwestern US locations during Nevada testing. Findings hint at intriguing POSS-I transient characteristics.

Galaxies exhibit a broad range of star formation activity, from actively star-forming to quiescent systems. Yet, the mechanisms responsible for the rapid shutdown and continued suppression of star formation remain poorly understood, particularly for the quiescent galaxies recently uncovered by JWST at $z>3$. Neutral gas outflows provide a direct tracer of gas removal and regulation in quiescent galaxies. We therefore present a NaID $\lambda\lambda5891,5897$ absorption–line stacking analysis of 274 galaxies at $z=2$–5 drawn from the DAWN JWST Archive (DJA) and the EMBER JWST program, using JWST/NIRSpec medium-resolution grating spectroscopy and NIRCam photometry. NaID absorption is detected in all quiescent galaxy stacks spanning $z=2$–5, providing the first statistical evidence that neutral gas outflows are a ubiquitous feature of quiescent galaxies in the early Universe. Compared to the non-quiescent galaxy stacks, the quiescent stacks show mass loading factors higher by 2–4 dex, with mass outflow rates $\dot{M}_{\rm out} \sim 9$–$30\,M_\odot\,{\rm yr}^{-1}$ elevated by $\sim0.5$–$1$ dex and outflow velocities $v_{\rm out} \sim 310$–$570\,{\rm km\,s}^{-1}$ higher by a factor of $\sim2$. The extreme mass loading factor values and declining star formation histories strongly indicate that these outflows cannot be driven by current star formation alone. In the statistically reliable quiescent redshift bins at $2 \leq z < 3$ and $3 \leq z < 4$, the elevated $[\mathrm{N\,II}]/\mathrm{H}\alpha$ and $[\mathrm{O\,III}]/\mathrm{H}\beta$ ratios are consistent with a possible AGN contribution, suggesting that non-stellar feedback may play a role in sustaining quiescence in galaxies at these epochs.

Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods.

Purpose: To develop and optimize a 5DCT (3D + cardiac phase + respiratory phase) imaging simulation and reconstruction pipeline, and to compare two sinogram-space interpolation methods for reconstructing images at arbitrary combinations of cardiac and respiratory phase. Methods: Helical CT projections were simulated from the 4D XCAT phantom across a range of cardiac and respiratory motion states, with Poisson and electronic noise added. Ground-truth-matched volumes were generated at 5 cardiac phases and 10 respiratory amplitudes (50 total phase combinations). Because acquired projections are sparsely and unevenly distributed across this joint phase space, each target slice was reconstructed by interpolating rebinned sinogram rows to the target cardiac phase and respiratory amplitude, using either 2D scattered barycentric interpolation or 2D scattered local linear interpolation with a circular kernel for cardiac phase. Reconstructed volumes were compared to phantom ground truth using mean absolute error (MAE), and to conventional respiratory-gated 4DCT (r4DCT) reconstructed from the same simulated data. Results: Both interpolation methods eliminated the severe axial misalignment artifacts present when helical projections were reconstructed without phase-space interpolation. Local linear interpolation achieved lower MAE than barycentric interpolation across most tested conditions, with the largest improvement at low pitch. The 5DCT pipeline also produced respiratory-only volumes with fewer residual cardiac-motion artifacts than conventional r4DCT reconstructed from the same projection data, including at standard clinical pitch (0.1). Conclusions: 5DCT reconstruction using sinogram-space interpolation is feasible and can jointly resolve cardiac and respiratory motion with better accuracy than conventional 4DCT reconstruction.

Bars are among the most prominent dynamical structures in disc galaxies, yet their long-term evolution and the orbital families that sustain them remain only partially understood. In this work, we introduce a new methodology based on frozen potentials combined with Fourier analysis of particle trajectories to identify regular and sticky orbits in self-consistent $N$-body simulations. This approach allows us to isolate particles belonging to the $x_1$ family, directly associated with the bar, and the $x_2$ family, linked to a secondary perpendicular structure. Tracking these orbits across multiple snapshots enables us to quantify the time evolution of key bar properties, including its mass fraction, semi-axes, and density profile. Compared with established used diagnostics, our method provides the closest match to the temporal behaviour of the Fourier bar-strength parameter $A_2$, while offering a direct dynamical interpretation and full three-dimensional characterization that Fourier-based approaches cannot provide. Our analysis further reveals that the indices $n_x$, $n_y$, and $n_z$ describing the bar density distribution are anisotropic and rarely equal to the canonical $n=2$ assumed in Ferrers profiles, highlighting the limitations of standard analytical approximations. We also find strong correlations between bar growth, orbital chaoticity, and angular momentum redistribution, with the bar acting both as a sink and as a driver of angular momentum transfer. A comparison between the two models analysed shows that rapidly forming bars are weaker and less stable than those that grow more gradually. Altogether, our methodology provides a robust framework for linking orbital structure to the dynamical evolution of barred galaxies.

We consider main-sequence stars orbiting close to a supermassive black hole (SMBH), which are potential gravitational wave (GW) sources for LISA if their orbital periods are of the order of an hour. At such a short orbital period, mass transfer from the star to the SMBH occurs. The evolution of the semi-major axis and GW frequency depends on the evolution of the stellar mass and radius. We use MESA to study stars that transfer mass to SMBHs similar to Sagittarius A* starting on the zero-age main sequence (MS). We identify 4 evolutionary phases. (I) Stars initially with mass $>2 M_\odot$ remain on the MS as their mass and radius decrease. (II) Below $2 M_\odot$, the separation is sufficiently small so that the GW timescale is too short for the stars to maintain thermal equilibrium. They evolve adiabatically off the MS and shrink rapidly as they lose their high-entropy envelope. (III) Below $0.5-1 M_\odot$, depending on the initial mass, the uniform low-entropy core is exposed and stars expand adiabatically. (IV) Below $0.15-0.4 M_\odot$, the thermal and GW timescales become comparable, and stars cool and shrink while maintaining this balance. Overall, mass transfer causes the orbit to expand, slowing down the orbital evolution and leading to GW emission at lower frequencies making the GW signal harder to detect. If located around Sagittarius A*, mass transferring stars spend most of the time relatively close to the LISA sensitivity curve, with maximal SNR reaching around 600 during the transition between stages II and III.

Lutetium hydrides (LuH$_x$, $1.75 \leq x \leq 3$) form a diverse series of phases, several of which superconduct under pressure. Characterizing their electronic properties has remained challenging owing to a high propensity for hydrogen defect formation, and recent angle-resolved photoemission (ARPES) measurements reveal puzzling flat-band regions that position these materials as candidates where superconductivity and flat-band physics may intersect. Here, by combining density functional theory, dynamical mean-field theory, and the constrained random-phase approximation, we uncover the microscopic origin and correlation nature of these flat bands. Across all compositions, the screened on-site Coulomb interaction is larger for H-s states than for Lu-$d$ states due to compact hydrogen orbitals. Nevertheless, these systems remain weakly correlated metals: the nearly filled H-$s$ shell admits little charge fluctuation, so its large interaction acts as a static level shift rather than a source of correlation. Although hydrogen primarily occupies tetrahedral sites at $x=2$, we discover that anti-site defects–where hydrogens occupy slightly unfavorable octahedral sites–generate both the ARPES flat-band features and the low-energy optical absorption peak, attesting to the usual defective nature of such materials in experimental samples. We further find that correlation strength is governed primarily by hydrogen orbital filling at these sites rather than the interaction magnitude itself. Consequently, we identify hydrogen orbital filling as the fundamental organizing principle dictating correlation and low-energy flat-band physics in lutetium hydrides.

We investigate the UV viability of strongly first-order electroweak phase transitions (SFOEWPTs) in the Type-I two-Higgs-doublet model (2HDM), considering both the Normal and Inverted Scenarios (NS and IS). For each scenario, we scan $5\times10^6$ physical parameter points and determine the cutoff scale $\Lambda_{\rm c}$ through a two-loop renormalization-group analysis, where $\Lambda_{\rm c}$ is set by the first violation of perturbativity, tree-level unitarity, or vacuum stability. For one-step transitions, the SFOEWPT strength and high-scale UV validity exhibit a pronounced tension: the maximal transition strength $\xi_p$ decreases with increasing $\Lambda_{\rm c}$. Requiring $\Lambda_{\rm c}>10~\text{TeV}$ limits the transition strength to $\xi_p\lesssim2.7$ in the NS and $\xi_p\lesssim1.8$ in the IS, while requiring $\xi_p>1$ restricts the cutoff scale to $\Lambda_{\rm c}\lesssim O(10^6)~\text{GeV}$ in both scenarios. Multistep transitions exhibit qualitatively different behavior. Two-step SFOEWPTs, found in appreciable numbers only in the IS, can remain theoretically consistent up to $\Lambda_{\rm c}\sim O(10^{15})~\text{GeV}$ while reaching $\xi_p\simeq7$, without exhibiting the pronounced $\xi_p$-$\Lambda_{\rm c}$ anticorrelation characteristic of one-step transitions. Imposing UV validity also sharpens the phenomenologically viable parameter space. In particular, increasing the minimum allowed cutoff scale for two-step SFOEWPTs in the IS favors a light scalar spectrum and moderate $\tan\beta$, providing a promising target for current and future collider searches.

We study sample covariance matrices $K = \frac{1}{N} \sum_{i=1}^N \mathbf{x}_i \mathbf{x}_i^* \in \mathbb{R}^{n \times n}$ in the proportional regime $n \asymp N$. The columns $ \mathbf{x}_1, \ldots, \mathbf{x}_N \in \mathbb{R}^n$ are independent and centered, with common covariance $\mathbb{E} \mathbf{x}_i \mathbf{x}_i^* = \Sigma$, but may otherwise have strongly and nonlinearly dependent coordinates. Assuming only that quadratic forms of the columns concentrate uniformly at the optimal rate $| \mathbf{x}_i^* A \mathbf{x}_i - \mathrm{Tr} \Sigma A | \prec \| A \|_F$, together with polynomial norm moments and a standard nondegeneracy condition on $\Sigma$, we prove the optimal anisotropic local law: on regular spectral domains, uniformly down to spectral scales $\eta:= \mathrm{Im}\, z \geq N^{-1 + \tau}$, \[ \big| \langle \mathbf{u} , \big( (K-z)^{-1} - (-zI_n-z\widetilde m_0(z)\Sigma \big)^{-1} \big) \mathbf{v} \> \big| \prec \sqrt{\frac{\mathrm{Im}\, \widetilde m_0 (z)}{N\eta}} + \frac{1}{N\eta} \] for all deterministic unit vectors $ \mathbf{u}, \mathbf{v} \in \mathbb{C}^n$, where $\widetilde m_0(z)$ is the Stieltjes transform of the deformed Marchenko-Pastur law. This removes the higher-cumulant tensor assumption of Fan, Ma, Paquette, and Wang (2026), thereby answering the question raised in their work. The result applies, among other examples, to every centered log-concave column distribution with bounded, nondegenerate covariance, nonlinear tilts of Gaussian vectors, deep random features, and a high-temperature spherical 4-spin model for which the cumulant assumption is known to fail.

Critical systems sit near boundaries between qualitatively distinct behaviors. When inferring models of neural activity, this proximity to criticality is thought to require the precise tuning of parameters. Here, we show that as the number of neurons increases, criticality can emerge naturally without fine-tuning. When computing observable statistics from parameters (the forward problem), some small regions in parameter space map to large regions in statistics space. These special parameters are precisely those near criticality. Thus, when inferring parameters from experimental measurements (the inverse problem), models concentrate near critical points, and this concentration becomes stronger as the system grows. We illustrate this flow toward criticality across many large-scale recordings in the mouse brain. In the Curie-Weiss model of Ising spins, we find that all of the recordings collapse to a first-order phase transition, despite substantial differences in the underlying systems. Together, these results suggest a resolution to the tension between criticality and fine-tuning in models of neural activity.

Starting from the known differential expansions, we express the HOMFLY-PT polynomials of twist and antiparallel double-braid knots in rectangular representations \([r^s]\) as determinants of \(r\times r\) and \(s\times s\) matrices. We first give an elementary derivation for the figure-eight knot and then re-sum the KNTZ formulas for twist and double-braid evolution. The resulting matrices are constructed from single-hook evolution coefficients and explicit representation-dependent weights. These formulas provide a starting point for investigating possible extensions of knot polynomials to KP/Toda \(\tau\)-functions. Extensions to non-rectangular representations and to more general knot families remain open problems.

Powerful nonstationary processes such as flares and coronal mass ejections are detected mainly near the solar cycle maxima. However, the analysis of the great flares since 1975, when the GOES monitoring started, leads us to more precise conclusions. We have traced the latitudinal distribution of X-class flares and their dependence on the phase of the cycle throughout four cycles. Besides, we compared directly their positions with the magnetic field structure. It was found that the relatively weak X4–7 flares occur at relatively high latitudes (15 – 20 degrees), where two waves of activity converge, one moving toward the equator and the other, the wave of the following cycle, directed poleward. Such events are observed almost constantly 1 – 2 years before the cycle maximum. At the same time, the number of the powerful X-ray flares increases sharply during the maximum phase, but the greatest X10 flares are observed at the beginning of the decline phase, where wave interactions still persist, and throughout the decline phase. Note that they are virtually absent during the cycle growth phase. Thus, we conclude that the greatest X-ray flares begin to appear 1 – 2 years before the maximum number of sunspots in the overlapping phase, when different kinds of activity waves coexist on the Sun at relatively high latitudes, and, then, continue to appear at the boundary, which separates the wave of local fields and the poleward wave of the following cycle.

For every right half we determine the unique left half whose Rule 30 central trace is constant: an alternating tail selected by the leading one of the right half when the initial center is 0, and a single universal checkerboard when it is 1. Every nonzero member of either fiber carries infinitely many ones, so the zero row is the only finite configuration with a constant trace. For support radius w the sharp maximum constant-prefix length is 2*ceil(w/2)+1 when the initial center is 0 and 2*floor(w/2)+2 when it is 1, so the maximum over both is w+2, attained by exactly 2^w configurations for even w and 2^w - 1 for odd w. Hence no column of a nonzero finite Rule 30 orbit is eventually constant.

Estimating the preconsolidation pressure ($\sigma'_p$) from one-dimensional consolidation (oedometer) tests is critical in geotechnical engineering for settlement analysis. Traditional graphical methods, such as the Casagrande procedure, may introduce uncertainties, particularly when interpreting rounded $e$-log($P$) curves typical of disturbed specimens of soft clays and silt deposits. This paper introduces PyelogP, an open-source Python library designed to calculate $\sigma'_p$ using the strain-energy method proposed by Becker et al. (1987) as an automated and reproducible alternative. The algorithm combines natural cubic spline interpolation, knee-point detection via the Kneedle algorithm, and split-point linear regression within the work-pressure space. Physically informed thresholds, including overconsolidation ratio limits and second-derivative maxima (${d^2 e}/{d(\log \sigma')^2}$), are incorporated to establish pre-yield and post-yield fitting boundaries. The performance of PyelogP is evaluated against a suite of 22 experimental consolidation datasets covering various clay deposits, including Saint-Alban clay and San Francisco Old Bay Clay. The results demonstrate strong agreement with the published values ($R^2$ = 0.912, RMSE = 0.374, MBE = -0.080), while the $O(N^2)$ algorithm requires only a few milliseconds per curve for typical oedometer datasets and less than 150 milliseconds for the largest datasets.

The Josephson energy $E_J$ is a key parameter governing the properties of transmon superconducting qubits. In Al/AlO$_x$/Al junctions, $E_J$ is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute $E_J$ by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al$_2$O$_3$ barrier against ten junctions with melt–quenched amorphous Al$_2$O$_3$ barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar–Baratoff relation, we obtain a mean $E_J/h$ of $2.78$ GHz for the amorphous ensemble, with a standard deviation of $4.67$ GHz, compared with $0.73$ GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic $200\times200$ nm$^2$ junction self-averages over more than $2\times10^4$ such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale $E_J$.

Fractional quantum anomalous Hall effect (FQAHE) has been discovered in twisted MoTe$_2$ and rhombohedral graphene/hBN moiré superlattices. Such van der Waals heterostructures feature a tuning knob of gate displacement field $D$, which is absent from the conventional fractional quantum Hall systems in two-dimensional electron gases. $D$ plays a critical role in engineering FQAHE and other emergent quantum states and provides an exciting new opportunity to explore their quantum phase transitions. However, the microscopic details of such transitions and temperature-dependent transport have remained mostly elusive. Here we report systematic resistance measurements in rhombohedral pentalayer graphene/hBN moiré superlattices. We found that the displacement field-driven phase transitions between Composite Fermi liquid, Fermi liquid, Fractional Chern insulators, and insulating states are described by semi-circle relations of the longitudinal and transverse resistivities (or conductivities), largely unexplored in the fractional quantum Hall systems. This agrees with a spatially separated two-phase picture for the phase transitions and further indicates a new insulator phase–fractional quantized anomalous Hall insulator. By comparing the temperature-dependence of longitudinal resistance with the thermal activation model, we estimated the transport gap sizes in three fractional Chern insulator states. Our work shed light on the quantum and temperature evolutions of fractional Chern insulator states–providing necessary background for anyon-braiding and gate-defined junctions in rhombohedral graphene.