Papers

Ultra-high-volume slag-cement (UHVS) blends can substantially reduce clinker ratio, but slow slag reaction limits strength development; Na2CO3 is a less caustic and lower-carbon activator for alkali-activated materials, yet its moderate alkalinity can similarly delay strength development. Here, dry-blended Na2CO3 (0-20 wt.% relative to water) was incorporated into a one-part binder with 90 wt.% ground-granulated blast-furnace slag and 10 wt.% Portland cement (PC) to determine whether this integration could mitigate slow strength development in both systems. Compressive strength testing, isothermal calorimetry, time-resolved quantitative X-ray diffraction, Fourier-transform infrared spectroscopy, aqueous solution analysis, and thermodynamic modeling were combined to determine how Na2CO3 controls phase assemblage, alkalinity, calculated porosity and strength development. At 5-10 wt.% Na2CO3, calcite-dominated carbonate reactions promoted a rapid alkalinity increase and accelerated early-age reaction and strength development; however, subsequent alkalinity decline limited later-age slag reaction and gel formation. In contrast, 20 wt.% Na2CO3 favored substantial early formation of gaylussite and carbonate-AFm phases, which moderated the initial pH rise and delayed early gel accumulation. The larger alkali inventory and evolving phase-solution partitioning helped sustain alkalinity at later ages, enabling continued slag dissolution and gel formation. This pathway produced higher reaction extent and lower calculated porosities, with compressive strength approaching that of neat PC. Screening-level cradle-to-gate life-cycle assessment indicates a 66-72% reduction in global warming potential relative to PC, depending on Na2CO3 production pathways. These results identify carbonate-mediated control of alkalinity persistence as key to sustaining slag reaction in UHVS systems.

We investigate how parameter-efficient adaptation of an atmospheric foundation model affects downstream regional precipitation in a controlled Aurora-WRF coupling experiment over the Beijing-Tianjin-Hebei region. A single-step, precipitation-weighted LoRA adaptation of AuroraPretrained is trained on May-September 2020-2021 and selected using 2022 validation data. Five inference-time adaptation strengths are coupled to an unchanged 9-km WRF configuration and compared with a GFS-driven control under common ERA5 initialization and auxiliary-field rules. Evaluation uses 17 initializations in 2023, hourly ERA5 precipitation, and conservative remapping to a fixed 356-cell, 0.25-degree verification grid. Heavy rainfall is defined exclusively as at least 50 mm in a continuous 24-hour window, advanced hourly. For window starts from 0 to 48 hours, unadapted Aurora attains the highest mean critical success index (CSI), 0.216, compared with 0.144 for the GFS control. An intermediate LoRA strength of 0.75 reduces the Aurora-driven 24-hour precipitation mean squared error by 30.7% and brings pooled frequency Bias from 1.510 to 1.024, but lowers CSI to 0.182. GFS retains the lowest whole-domain error. These results characterize a trade-off between rainfall detection, frequency calibration, and intensity error, showing the importance of evaluating adaptation strength against multiple downstream criteria within a common coupling framework.

Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.

We ask whether Kochen-Specker contextuality is Lorentz invariant. On the full Hilbert space, it is, since boosts act unitarily. Restricted to spin, it is not: momentum acts as an environment applying momentum-dependent Wigner rotations, leaving spin observables unsharp and breaking the operator identities behind state-independent contextuality. For spin $1/2$ one scalar governs the loss, the packet average $\Delta$ of $\sin^2(\theta_W/2)$ (where $\theta_W$ is the Wigner angle); for any spin, a ray degrades at a rate set by its spin variance transverse to the boost. In the spin-only account, the Free Will Theorem's SPIN axiom fails for every $\Delta>0$; the Yu-Oh set loses contextuality between $\Delta\approx0.008$ and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at $\Delta\approx0.059$ or $0.074$ by orientation; singlet CHSH loses nonlocality for $\Delta\geq0.159$; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at $\Delta\approx0.206$. A $q$-plate implements the channel exactly on photon polarisation, with a retardation in place of the rapidity, so the nonlocality, GHZ and aimed-source results are testable without motion.

Quantum networks composed of loop-like structures provide a rich platform for exploring electronic transport phenomena and have been widely studied in various contexts. However, their thermal response remains relatively unexplored, motivating us to investigate it in the present work. We consider a tight-binding (TB) quantum network composed of a finite number of triangular plaquettes, where neighboring plaquettes are connected through single bonds and each triangular loop is threaded by an Aharonov-Bohm (AB) flux $\phi$. The interplay of nonuniform site coordination, hopping asymmetry, and quantum interference gives rise to both dispersive and completely flat energy levels. We derive an analytical condition involving the TB parameters under which one of the energy branches becomes independent of the electronic momentum. We further show that the AB flux $\phi$ provides a direct means of tuning the position of the flat band. The characteristic features of the energy spectrum associated with this quantum geometry are reflected in the thermal response, which we investigate through the electronic specific heat (ESH). In particular, we demonstrate that the position of the flat band manifests itself as a distinct feature in the ESH, establishing a direct connection between the flat-band formation and the thermal response of the system. Thus, the ESH provides an alternative route for identifying the presence of a flat band, consistent with the analytical condition and the corresponding energy dispersion. Moreover, the AB flux allows the ESH to be selectively regulated through the tuning of the flat-band position. The proposed approach provides a simple complementary means of identifying momentum-independent energy levels and may be extended to other simple and complex quantum networks supporting flat bands.

The sample complexity of identifying an unknown pure stabilizer state has been a longstanding problem in quantum information. In this paper, we resolve the entire exact critical crossover for the uniform ensemble of pure $n$-qubit stabilizer states under arbitrary collective measurements and without side information. For $k=n+c$, with fixed integer $c$, the optimal success probability converges to an explicit positive series $P_{\infty}(c)$. In particular, $P_{\infty}(0)=0.1760837896\ldots$, while its two tails obey a quadratic-exponential law below threshold and $1-P_{\infty}(c)\sim2^{-c}$ above threshold. The pretty-good measurement is exactly optimal for every finite $n$ and $k$. The proof diagonalizes the stabilizer Gram operator through Clifford tensor-power duality and a defect filtration, including the exceptional binary sectors. The resulting integer-scale law quantifies the $n+O(1)$ copy threshold.

We associate to finite block size data \[ \bm n=(n_d)_{d\ge1},\qquad n_1>0, \] a positive definite cyclotomic form and a Householder reflection representation. Writing \[ N=\operatorname{lcm}\{d:n_d\ne0\},\qquad \wt=\sum_d d^2n_d, \] the form on the cyclic group $C_N$ is \[ B_{\bm n}(g,h)=\frac1{\wt}\sum_{(g^{-1}h)^d=1}d^2n_d. \] Its labelled Fourier spectrum reconstructs the complete multiplicity sequence by Möbius inversion. If the $n_d$ are the Wedderburn multiplicities of a split semisimple algebra $S=\prod_d M_d(k)^{n_d}$, the divisibility widths are dimensions of characteristic sums of Wedderburn blocks, and the form together with $\dim_kS$ recovers the isomorphism type of $S$. The main theorem is an arithmetic rigidity result. For $N\ge2$, the reflection group is finite if and only if it preserves a full rank lattice, equivalently \[ \supp(\bm n)=\{1,N\},\qquad n_1=N^2n_N. \] In this case $B_{\bm n}=\frac12(I+J)$ and the group is $W(A_N)\cong S_{N+1}$. In semisimple algebra terms, finiteness is equivalent to \[ S\cong k^{N^2m}\times M_N(k)^m \] for some $m\ge1$. For $N=2$, every nonfinite case is a dense copy of $D_\infty$ in the corresponding orthogonal group. For contraction algebras of threefold flops, Toda's width formulas identify the total scale and primitive Fourier mode with $\dim A_{\con}$ and $\dim A_{\con}^{\ab}$. This yields infinitude for all irreducible flops of length at least three and, in length two, \[ \Gamma_f\text{ finite}\quad\Longleftrightarrow\quad \dim A_{\con}=2\dim A_{\con}^{\ab}. \] The final part gives a complementary BPS/Riemann–Hilbert realization of the same reflection matrices.

The spectral weight with which a many-body eigenstate contributes to a given channel is not fixed by the smooth one-point ETH envelope, and its higher-order correlations—the connected cumulants of three and more channel-resolved spectral functions—have lacked a systematic organization. We construct one. In random free fermions, where every channel overlap is a squared Slater minor of a Haar-orthogonal one-body eigenvector matrix, the $r$-resolvent moment admits an exact replica-sector decomposition: a sum over the double-coset sectors of the orthogonal Weingarten algebra, in which the permutation sectors are the replica contraction classes and each sector value is determined by the overlap pattern of the channels and of the eigenstates. The sector coefficients follow from an exact occupancy-matrix assembly—a signed convolution over the slot permutations, a decomposition into connected blocks, and a finite-state chain transfer matrix whose local transition rules are independent of $r$ and $k$—so the sector theorem holds at arbitrary finite multiplicity, realized exactly at $r=3$ ($k=2,3,4$), $r=4$ and $r=5$ ($k=2$). The structure carries the physical hierarchy: the fully coincident sector is the projection that yields the Selberg moment ratios $q_r$, the levels are nested by exact marginalization, and the sectors are the multi-energy spectral cumulants behind the resolvent cumulants, with the irreducible self-energy vertices of the Feshbach ladder as the connected kernel. The multi-resolvent correlations of random free fermions are therefore organized, level by level, by one replica-sector algebra—an exact microscopic benchmark for the higher-order fluctuation sector of eigenstate thermalization, with its microscopic sector geometry made explicit.

The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, $q$-para-Racah and para-Bannai–Ito polynomials followed, obtained through singular truncations of families of the Askey scheme and used in turn to design spin chains. All are orthogonal on bi-lattices; the prefix goes back to the para-Krawtchouk case, whose spectrum is that of the parabose oscillator. The representations that these polynomials provide of the corresponding algebras — Hahn, Racah, $q$-Racah, Bannai–Ito and complementary Bannai–Ito — are shown to be reducible. Each decomposes into a direct sum of two irreducible modules of the same algebra, one attached to each of the two interlaced sub-lattices, and the parameters of the submodules are given. The para polynomials are thereby expressed in terms of the classical polynomials that the submodules carry, and the pairing $\lambda_n=\lambda_{N-n}$ of their eigenvalues is accounted for; the three features of the bi-lattice setting on which the reduction rests are identified. The properties of the para families are then presented in a unified way in the light of this decomposition, together with the constructions through which these families arise and the settings in which they have been put to use.

Exact periodic solutions of the unforced incompressible Navier-Stokes equations require the convective field to be a pure gradient, absorbed into the pressure; for the cyclic trigonometric families studied previously this occurs only at isolated phases and, over the range so far classified, only at n = 3 and 4. The forced problem, we show, admits an exact construction for every phase vector and every n >= 3. For an n-parameter family of two-term cyclic fields, solenoidal and a Laplacian eigenfunction, the transverse part U^0 of its convective field serves as the body force, giving a closed-form solution with velocity, pressure and force explicit. We prove closed forms for the pressure and for both magnitudes, in every dimension and with no upper bound on n: the forcing is never trivial, and the L^2 magnitude of U^0 stands to that of the whole convective field in the constant ratio 2*sqrt(2)/3, whatever the dimension, phase or units. The forcing does no net work, so the kinetic energy decays purely viscously at arbitrary Reynolds number, giving an exact benchmark in any dimension. A numerical study of vorticity concentration at zero applied work uses it as a reference, and shows that apparent saturation can be a resolution artefact.

Stochastic quantization formulates $d$-dimensional Euclidean QFT as the equilibrium limit of a $(d+1)$-dimensional Langevin system. Using the supersymmetric formulation of stochastic systems, we apply techniques from Morse theory to study Langevin dynamics. We interpret stochastic quantization as the absolutization of a relative QFT by a bulk cohomological topological Equilibrium TFT ("EqmTFT"), and relate its enriched Neumann boundary data to the $d$-dimensional BV/BRST complex. Analytic continuation reveals connections to the A-model and non-relativistic and Carrollian limits.

Smoothed particle hydrodynamics (SPH) is well suited to large-deformation fluid problems, and the growing use of automatic differentiation in engineering applications has motivated interest in differentiable SPH solvers. In this study, a composable differentiable SPH framework, CraftSPH, has been developed. In CraftSPH, major computational operations are implemented as independent modules that users can combine to construct solvers for different purposes. This design supports high-accuracy discretization and both explicit and implicit computation within a common framework, while allowing individual components to be maintained and extended. Selected numerical operations also support automatic differentiation (AD) for physical-parameter estimation and potential coupling with deep learning models. These capabilities were demonstrated through forward and inverse analyses. Forward analyses using an implicit SPH scheme with high-accuracy discretization showed good agreement with analytical and reference solutions for Poiseuille flow and a rising bubble, while capturing the key experimental trends in two- and three-dimensional dam-break problems. In inverse analyses, explicit and implicit SPH schemes were used to estimate kinematic viscosity in Taylor-Green vortex flow and Reynolds number in lid-driven cavity flow. The results also showed that the choice of operations included in the computational graph affects the computed gradients. Together, these findings demonstrate that CraftSPH enables users to assemble problem-specific solvers for forward and inverse analyses within a common framework.

FireworksWeb is a web-based event display utilizing a C++ ROOT-Eve backend with SAPUI5 frontend for interactive 3D visualization of particle physics events directly in the browser. Building upon ROOT-Eve and RenderCore, it eliminates local software installation while maintaining professional-grade event display capabilities. FireworksWeb is currently deployed for live event monitoring in the CMS control room, demonstrating its reliability for real-time data visualization in production environments. The CMS experiment has made a large amount of collision datasets publicly available through the CERN Open Data portal, which are the valuable resources for education, outreach, and research. We have extended FireworksWeb to enable visualization of these open datasets, making particle physics data accessible to diverse audiences without requiring local software installation. Our prototype implementation includes standalone cameras, event filters, configurable collection settings, and projection controls with fish-eye distortion for cylindrical geometries. The web architecture communicating via CGI enables dataset queries and filtered event selection based on physics criteria. We demonstrate the prototype with CMS Open Data events, discuss the technical architecture, and outline applications for education, public outreach, and exploratory physics analysis.

We study a globally coupled stochastic system in which each unit carries an Ising spin and a continuous phase. The spins undergo Glauber switching with relaxation rate $\gamma$, while the phases are driven by Ornstein-Uhlenbeck noise with correlation time $\tau$. A spin-dependent phase interaction supports a composite coherent mode, $Z_m=N^{-1}\sum_j\sigma_j e^{i\theta_j}$, that can order even when the ordinary phase coherence is small. Linear response about the nonmagnetic incoherent state gives the synchronization threshold $K_{\mathrm c}=[(\mu+\beta_s\gamma)\chi_\gamma]^{-1}$, where $\chi_\gamma$ is a memory-weighted Laplace transform of the free phase correlation function. The competition between the increasing Glauber response and the decreasing memory susceptibility produces a finite switching rate at which $K_{\mathrm c}$ is minimized. We derive a general sufficient condition for such an interior optimum and show that finite-time Ornstein-Uhlenbeck correlations satisfy the required fast-switching asymptotics, whereas the white-noise limit need not. Finite-size simulations reproduce the nonmonotonic threshold, its shift toward slower switching as $\tau$ increases, antiphase composite order in a nonmagnetic state, and mode mixing on a magnetized background.

Quantum physics underpins the emerging quantum technology era, yet its counterintuitive principles remain challenging for beginners. Video games offer a promising medium to make these principles accessible through an interactive experience. Conventional gameplay, even when featuring extraordinary abilities of the protagonist, largely draws on classical intuition, shaping the player's reflexes through familiar expectations of motion, action, and consequence. Here, we propose extending these reflexes into the quantum domain by embedding superposition, unitary evolution, quantum gates, and measurement into the game. Central to this approach is a new controller action, the Gate of Fate, which allows players to engage in quantum operations through their gaming decisions. We demonstrate the concept in a Tetris-based prototype, with progressively structured levels that introduce quantum operations and their consequences. We also outline extensions to role playing games, in which the behavior and difficulty of antagonists can respond to player's developing quantum gaming reflexes. By turning abstract quantum concepts into actionable game mechanics, this approach aims to cultivate quantum intuition through play, offering opportunities for both quantum pedagogy and more sophisticated game design.

A wavefront-sensor (WFS) prediction can select the photon measurement before detection or condition its likelihood afterward. This matters for reflected-light spectra requiring hundreds of hours, because subtracting residual starlight cannot remove its photon noise. In a two-mode, low-occupation model, isotropically distributed leakage makes planet-mode projection—ideal single-mode injection matched to the planet—the optimal fixed single-photon measurement, including unequal aligned backgrounds and equal Poisson detector-event rates per output. For nonzero leakage, an attainable two-output conditioned measurement is optimal and strictly more informative before differential loss. For an isotropic background, a contrast bound holds for any distribution of recorded leakage directions: relative transmission $0.80$ and relative admitted-time duty $0.90$ limit the Fisher information per scheduled time to $0.81$ of the fixed optimum at equal predictable-leakage and planet contrasts. Haar averaging sharpens this ceiling to $0.78$. The necessary leakage-to-planet ratios for gain are approximately $2.25$ for any direction law and $3.26$ for Haar directions. A concentration-model certificate identifies directional diversity sufficient to beat recalibrated fixed measurements. Independently gated fixed-basis fallback guarantees no loss of continuum-profiled spectral information when rates and costs are known. For the Habitable Worlds Observatory, the candidate regime is predictable, directionally diverse, leakage-dominated residuals, not a general sensitivity improvement.

In this study, the power law form of f(Q) gravity $(f(Q)=Q+mQ^n)$ has been studied in view of statistical analysis with current observed data and irreversible thermodynamics. The best fit values of model specific parameters are found with the use of of 31point Hubble data, Patntheon type Supernva and 1721 point SH0ES data and a comparative study has been performed between $f(Q)$ and standard $\Lambda$CDM model. The thermodynamic consequence using standard Eckart theory of non-equilibrium thermodynamics has been examined independently for general form of $f(Q)$ gravity followed by power law form of $f(Q)$ where the horizon entropy is calculated using unified law of thermodynamics. Suitable range of power law model specific parameters has been explored through investigating validity of generalized second law of thermodynamics and thermodynamic equilibrium. Finally evolution nature of cosmographic parameters are studied within the specific range of $m,n$ which is compatible with the results obtained from both statistical and thermodynamical analysis.

Artificial intelligence (AI)-based weather prediction is approaching the skill of physical numerical weather prediction (NWP) systems at a fraction of the computational cost. This is particularly promising for Africa, where rainfall extremes are intensifying and many forecasting centres lack the infrastructure to run physical models at extended lead times. We present a calibrated comparison of GraphCast, GenCast and the Functional Generative Network (FGN) against the physical NWP model IFS for rainfall prediction across Africa. Deterministic and probabilistic forecasts are postprocessed using Isotonic Distributional Regression and evaluated with the Continuous Ranked Probability Score against IMERG, RFEv2 and CHIRPS across seasons, wet and dry regimes, elevation zones and lead times. All models retain skill beyond climatology across most seasons and at extended lead times. AI models generally outperform IFS in wet regions, whereas IFS performs better in dry, high-elevation areas, where its finer resolution better represents orographic controls on rainfall. Across observational datasets and seasons, AI models achieve a median improvement of approximately 5% over IFS. GraphCast achieves calibrated skill comparable to the ensemble-based FGN, although FGN provides greater significant skill at longer lead times. These results highlight the potential of calibrated AI weather prediction to provide accessible and computationally efficient rainfall forecasts across Africa, while demonstrating the continuing importance of spatial resolution, ensemble design and regional characteristics.

The cross-correlation between weak lensing (WL) and the thermal Sunyaev-Zel'dovich (tSZ) effect probes the connection between the matter distribution and the thermal state of baryons at low redshift ($z\lesssim1$). A key systematic in such measurements is contamination by extragalactic foregrounds, particularly the cosmic infrared background (CIB). Here we describe the CIB spectral energy distribution (SED) with a small number of physically motivated spectral parameters, calibrated against external measurements of the radiation field intensity in galaxies. Their uncertainty is then propagated into the recovered WL$\times$tSZ signal in component separation at the level of the multi-frequency cross-power spectra rather than the map level. Applying this method to cosmic shear from the Dark Energy Survey and frequency maps from Planck, we show that the resulting measurements of the WL$\times$tSZ power spectrum are insensitive to variations in the effective CIB spectral index, radio source contamination, and the scale and redshift dependence of the SED. The measurements are robust to realistic foreground uncertainties, supporting their use as probes of baryonic feedback and cosmology, and providing a framework for future high-precision surveys. We compare our measurements with the Flamingo suite of hydrodynamical simulations and find that they are compatible with the Flamingo predictions for a low amplitude of matter fluctuations, parametrised by $S_8$, strongly disfavouring the larger $S_8$ preferred by Planck. This result is independent of the impact of baryonic feedback as modelled in Flamingo.

Accurate and rapid prediction of the aerodynamic drag coefficient ($C_D$) is essential for vehicle design, particularly during early-stage design, where many candidate geometries must be evaluated. Although computational fluid dynamics (CFD) provides reliable aerodynamic estimates, its high computational cost limits large-scale design exploration. This paper proposes the hierarchical graph-pooling Transolver (HGPTrans), which combines hierarchical graph pooling with Transolver-based attention to directly predict $C_D$ from vehicle surface meshes. Motivated by the fact that vehicle aerodynamics depends on both local geometric features and long-range interactions among spatially distant surface regions, HGPTrans integrates three complementary components. Graph isomorphism convolutions encode discriminative local geometry, Transolver-style slice attention captures global interactions with linear computational complexity, and information-redundancy-aware hierarchical pooling progressively removes redundant nodes while preserving informative geometric structures. The model is trained and evaluated on the large-scale DrivAerNet and DrivAerNet++ datasets, where it achieves the lowest mean absolute error and mean squared error among the evaluated baselines. Its generalization capability is further assessed through transfer learning on a real-vehicle dataset containing both sedans and sport utility vehicles (SUVs), achieving relative $L_1$ errors of 1.56% (sedans) and 2.12% (SUVs) with an inference time of approximately $0.293$ s per vehicle. This corresponds to an acceleration of several orders of magnitude relative to high-fidelity CFD while keeping the predicted drag coefficients within a few percent of the CFD reference. Ablation studies confirm each component's contribution and reveal the effects of depth and pooling ratio.

Accretion onto magnetically charged black holes in a perfect fluid dark matter (PFDM) background opens a new window for testing strong-field gravity. This paper investigates the radiative properties and optical appearance of a thin accretion disk surrounding a charged-PFDM black hole. We numerically compute the radiative energy flux, temperature distribution, and radiative efficiency, and employ a ray-tracing method to construct the direct images, secondary images, redshift distribution, and observed flux. By comparing with the Schwarzschild and pure PFDM cases, we find that the thin-disk efficiency of the charged-PFDM black hole lies between the two, with the magnetic charge partially counteracting the dark-matter-induced efficiency enhancement; for M87*, the efficiency is estimated to be 7%–8%. The optical appearance is predominantly governed by the PFDM parameter, while the magnetic charge plays only a marginal role. Larger inclination angles give rise to stronger Doppler asymmetry, producing the characteristic “hat-like” shape. These results provide falsifiable predictions for future high-resolution observations, such as those by ngEHT, to distinguish dark-matter environments from magnetic-charge effects.

The para-Bannai–Ito polynomials are orthogonal on a Bannai–Ito bi-lattice that is two-sided — it extends on both sides of a central value $c_0$ — and depend, besides the two grid parameters, on an isospectral deformation parameter. Their Jacobi matrix $J$ is invariant under the reversal of the sites at one value of that parameter only, the persymmetric point, and we determine its continuum limit there. Because the grid is two-sided, the natural object is the shifted operator $Q=J-c_0$, and the limit is taken about the centre of the band: $Q$ contracts to a first–order Dunkl operator, a supercharge, and $H=Q^2$ to the generalized Pöschl–Teller (Scarf I) Hamiltonian, with little $-1$ Jacobi eigenfunctions — supersymmetric quantum mechanics with reflections, the reflection entering the square root of the Hamiltonian. The second grid parameter adds a reflection term to the Hamiltonian itself, and the bi-lattice is, up to a shift, the spectrum of the limiting supercharge. The convergence of the eigenvectors is proved directly on the polynomials. On this grid the persymmetric model transfers states perfectly, under an arithmetic condition on the parameters, but never revives fractionally, revival being the work of the deformation; both properties pass to the limit. These results are for an even number of sites; for an odd number of sites the limit is instead the matrix supersymmetric pair of Pöschl–Teller Hamiltonians, with the reflection in the Hamiltonian as a Dunkl potential. The bispectral pair of the discrete model goes over to the Dunkl realization of the anticommutator algebra of the little $-1$ Jacobi polynomials.

We consider generalised Casimir operators associated with irreducible representations for finite-dimensional, semisimple, complex Lie algebras. Using Klimyk's formula and Okubo's formula, we derive a rational ordinary generating function for the Casimir operator eigenvalues for simple Lie algebras which does not rely on knowledge of the Weyl group. We also directly reproduce generating function expressions for the classical Lie algebras originally due to Perelomov and Popov.

We propose a new $q$-derivative operator built directly from Jackson's $q$-number formulation, designed to preserve the structural properties of standard differential calculus while incorporating deformation effects. By analyzing $q$-deformed Heisenberg algebras, we demonstrate that this formulation maintains the consistency of thermodynamic quantities-such as internal energy, particle number, and specific heat-in dilute gas limits without requiring ad-hoc chain-rule modifications. Furthermore, we explore the physical implications of algebraic deformation using the Biedenharn-Macfarlane realization, showing how $q$-deformation induces intrinsic anharmonicity in quantum oscillator spectra and affects multi-level quantum systems ($d \ge 3$). Applying this algebraic scheme to superconducting transmon qubits, we derive analytical pulse-shaping corrections that generalize the Derivative Removal by Adiabatic Gate (DRAG) technique, offering a robust method to suppress computational leakage in ultra-fast quantum logic operations.

The para-Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter, define through their recurrence relation a mirror-symmetric tridiagonal Hamiltonian $J$. Its spectrum is a quadratic bi-lattice, the union of the squares $(s+a)^2$ and $(s+c)^2$ of two interlaced arithmetic progressions of unit step, and it exhibits fractional revival when the grid parameters $a$ and $c$ satisfy a Diophantine condition. As the number of sites grows, $J$ contracts to the trigonometric Pöschl–Teller Hamiltonian on a finite interval. We establish this twice, on the recurrence relation and on the polynomials themselves. Both grid parameters survive in the limit, the difference $c-a$ as a scalar centrifugal term at the interior point fixed by the mirror, and $a+c-1$ as the strength of two confining singular walls at the ends. These walls turn the spectrum into the quadratic pair $(s+a)^2$, $(s+c)^2$, with Jacobi eigenfunctions $P_s^{(a+c-1,\,\mp(c-a))}$, and the two sublattices converge to two families that differ only by the sign of the second Jacobi parameter. The mirror symmetry of $J$ becomes the reflection about the midpoint, which grades the two families and carries the fractional revival to the limit. Algebraically, the bispectral pair of the discrete model, which generates the Racah algebra, becomes a pair of generators of the Jacobi algebra, one rung down the Askey–Wilson hierarchy, which is the dynamical algebra of the Pöschl–Teller Hamiltonian.

Foundation machine learning interatomic potentials (MLIPs) promise near-density functional theory (DFT) accuracy across broad areas of chemistry and materials science. However, their performance in describing systems and processes relevant to heterogeneous catalysis remains underexplored. Here, we introduce HetCat26, a collection of benchmark tests designed to assess pre-trained MLIPs across key aspects of catalytic modeling, including surface energetics, metal-metal oxide interactions, adsorption, and catalytic reaction networks. Evaluating fifteen foundation models, we find that performance on existing general materials benchmarks is only weakly predictive of performance on HetCat26; transferability to heterogeneous catalysis cannot be inferred from these general benchmarks. Across the benchmark tests, current models describe surface energetics and, perhaps surprisingly, reaction barriers well, whereas larger errors are observed for adsorption, and DFT site preferences are often not reproduced. Two models, eSEN-30M-OAM and MACE-MH-1-OMAT, nevertheless achieve high accuracy across the properties evaluated. Beyond model benchmarking, HetCat26 highlights the importance of training data consistency: PBE and PBE+U calculations should not be mixed within a training set. Overall, we identify challenges limiting the transferability of current foundation MLIPs to heterogeneous catalysis and, more broadly, to chemical reactions at interfaces, providing guidance for the development of the next generation of foundation models.

The para-Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that exhibits fractional revival. We determine the continuum limit of this Hamiltonian, both from its recurrence relation and directly on the polynomials. The limit is the singular (isotonic) oscillator $-\partial_\eta^2+\eta^2+\tfrac{\gamma^2-1}{4\eta^2}$. The deformation parameter $\gamma$ survives as a central impurity of the couplings, which decays as the inverse square of the distance. This is the marginal rate, which the continuum scaling turns into a finite $\sfrac{1}{\eta^2}$ term. Using the decomposition of the para-Krawtchouk polynomials into two Hahn families, we prove the confluence, for every degree, of the eigenvectors on the two sub-lattices to generalized Hermite functions. The bispectral pair of the discrete model, which generates the Hahn algebra, becomes in the limit a pair of generators of $\su$, the dynamical algebra of the singular oscillator.

Development of nondestructive ultrasound molecular imaging (UMI) is essential for early cancer detection through real-time screening using clinical ultrasound systems. Current techniques face challenges in accurately detecting targeted microbubbles (MBs) bound to specific biomarkers, primarily due to false-positive detections of unbound free-floating MBs. We propose a transformer model for time-series video processing to improve the differentiation of bound MBs. We propose a hierarchical transformer, termed MBFormer (microbubble transformer), featuring a positional-embedding-free encoder and a lightweight decoder. Leveraging attention within 3D spatio-temporal data to effectively capture stationary signals from bound MBs while suppressing nonstationary signals from unbound MBs. Since MBs appears as relatively small textures compared with conventional segmentation targets in medical imaging, such as organs and tumors, we optimized the model with two hierarchical layers, each with an attention block, to process ultrasound video data. The network outputs the molecular signal amplitude to visualize fine MB textures. Performance was evaluated using an in vivo breast cancer model, compared against a prior CNN-based UMI method and SegFormer3D baseline, a representative 3D transformer. MBFormer (AUC = 0.943) outperformed both CNN (AUC = 0.897) and SegFormer3D (AUC = 0.766) in detecting bound MBs. The CNN showed residual molecular signal from free MBs in the cardiac chambers, whereas SegFormer3D failed to detect fine MB textures. Overall, MBFormer demonstrated enhanced detection of bound MBs while suppressing free MBs and achieved a frame rate of 16.7 to 18.1 FPS, demonstrating its potential for real-time application. We anticipate that this transformer-based UMI model can facilitate real-time, free-hand nondestructive UMI in clinical systems.

We characterize the source environments of a sample of fast radio bursts (FRBs) detected with the Deep Synoptic Array (DSA-110). We present new analyses of a sample of 24 FRBs which have been localized to host galaxies with spectroscopic redshifts. Four of these bursts have been confidently associated with galaxies near or beyond redshift 1, and several are published here for the first time. Combining these new bursts with previously analyzed DSA-110 sources, we use a sample of 43 DSA-110 FRBs with known redshifts to measure host-galaxy contributions to dispersion measure (DM) and Faraday rotation measure (RM). We find characteristically large and significantly correlated host-galaxy contributions to DM and RM, suggesting that most FRBs reside in overdense, magnetized regions within their host ISM. Additionally, we identify a subset of FRBs with detectable scattering, and show that their scattering timescales and inferred host DM values are broadly consistent with an empirical relation established for Galactic pulsars. Combined with two-screen modeling of some bursts, our results indicate that density fluctuations within the host-galaxy ISM are the dominant source of extragalactic scattering. Comparisons of FRB host-galaxy properties with pulsars and simulations of young and old progenitor populations support a scenario in which FRBs preferentially form and remain associated with HII regions throughout their emission lifetime, favoring magnetars formed in core-collapse supernovae as the sources of FRBs.

In the hierarchical model of galaxy formation, the Milky Way's stellar halo assembles through the successive accretion of dwarf galaxies. While many resulting substructures have been identified, the origin of the recently discovered Typhon stellar stream remains ambiguous, as dynamical data alone are insufficient to distinguish between a globular cluster and a dwarf galaxy progenitor. To resolve this, we combine astrometry from Gaia with spectroscopic data from available surveys to comprehensively analyze the stream's chemical and dynamical properties. We identify 107 candidate members, significantly expanding the known sample. Three of these candidates lie beyond $55\,\mathrm{kpc}$, with the farthest at $67\,\mathrm{kpc}$, lending further support to Typhon's inferred large apocentric distance. Our analysis yields a mean metallicity of $\rm[Fe/H]=-1.42\pm0.07$ and a metallicity dispersion of $\sigma_{\text{[Fe/H]}} = 0.26^{+0.06}_{-0.05}$ dex. This metallicity dispersion supports a dwarf-galaxy origin for the Typhon stream. Typhon's high orbital energy is consistent with a relatively recent accretion of a fully disrupted dwarf galaxy with a stellar mass in the range of $10^6 M_{\odot} < M_\star \lesssim 10^7 M_{\odot}$. Furthermore, Typhon is the only major dwarf-galaxy stellar stream in the Milky Way's halo to exhibit such an extreme orbital eccentricity of $e \gtrsim 0.85$. We conjecture that dwarf-galaxy streams from high-eccentricity mergers are fully dissolved much more rapidly than those on circular orbits, in line with Typhon's proposed recent accretion. Additional dwarf-galaxy stellar streams on high-eccentricity orbits should be discoverable with next-generation photometric surveys as well as future releases from the Gaia space mission.