AI for Science

Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; in contrast, flexible data-driven neural methods lack physical insight. Hybrid modeling aims for the best of both worlds by combining a prescribed or symbolic, physics-based component with a flexible neural network. A critical challenge, however, is that the neural component may relearn mechanistic parts, yielding redundant and uninterpretable models, especially when the symbolic structure itself is discovered from data. Existing methods based on standard $L^2$ regularization rely on a projection argument that breaks when the symbolic component is learned through sparse discovery, allowing the neural augmentation to overlap with symbolic structure. We introduce \textbf{OrthoReg} (Orthogonal Regularization), which directly penalizes overlap between the symbolic and neural components, preventing symbolic structure from being absorbed by the neural residual. This yields a complementary decomposition: the symbolic part captures what the library can express, and the neural part captures what remains. On benchmark dynamical systems with partial library mismatch, OrthoReg improves symbolic recovery and out-of-distribution behavior.

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.

This work investigates the application of a domain-shift aware neural network for regression tasks aimed at estimating unbalance masses in rotating shafts under varying operating conditions. Experimental data were collected from a test rig in which a primary shaft, equipped with a flange carrying unbalanced masses, was driven at different rotational speeds, while a secondary shaft could be optionally activated to introduce domain discrepancy. The unbalance masses were positioned at a fixed radial distance, and the dynamic response of the system was recorded using triaxial accelerometers. The inverse problem of mass estimation is formulated within a domain adaptation framework, where the network is trained with a maximum mean discrepancy strategy to align feature representations across source and target distributions. The results demonstrate the effectiveness of explicitly addressing domain shift in improving prediction accuracy, especially when the system's physical behavior and sources of domain discrepancy are not fully known and fall outside the training conditions. These findings highlight the potential of domain-shift aware models for regression tasks in Structural Health Monitoring.

We study the propagation of coupled surface and internal equatorial internal waves. A model of two vertically stratified fluid layers with different constant densities is employed. Taking Coriolis forces into account, we derive explicit solutions to the linearized governing equations which assumes irrotational fluid motion in both layers separately, and further obtain the dispersion relation which determines the phase speeds of propagating surface and internal waves. We prove a result on solutions to the dispersion relations which greatly simplifies our subsequent analysis of the nonlinear dynamical systems which describe the motion of the fluid in the upper layer. Phase portraits for all possible streamlines in both fluid layers are presented, while furthermore a Lagrangian description of the fluid flow is obtained, and the particle trajectories of the fluid particles are determined.

In a standard two-level Ramsey interferometer, the measured phase accumulates linearly during the interrogation time. Here, we introduce three-level Ramsey interferometry that employs a noncyclic geometric phase response to enhance phase sensing, with projected internal-path interference reshaping the mapping from accumulated signal phase to readout phase. Near a geodesic-closure transition, a small accumulated signal phase produces a sharply amplified readout-phase shift. We quantify the accompanying gain--visibility tradeoff and identify a finite operating window in which the amplified response yields a net signal-to-noise-ratio gain under technical-noise-limited conditions. By tuning an initial Ramsey phase offset, this high-slope window can be positioned at a desired operating point and sampled repeatedly with shorter cycles, providing a geometric shortcut to improved projected stability. More broadly, these results establish a multilevel Ramsey route to enhanced phase sensitivity in quantum platforms, where two signal-collecting internal paths interfere to produce a noncyclic geometric response.

We characterize two nested Walsh parity-check filters implemented on Quandela's Belenos cloud photonic processor in a single-photon eight-mode spatial register. The modes are indexed by the vertices of the cube $Q_3$. The filters realize the classical $[8,7,2]$ single-parity-check code, the zero-sum neutral subspace $\mathcal{N}$ and the $[8,4,4]$ extended Hamming code, the parity-checked subspace $\mathcal{S}\subset\mathcal{N}$ with one DC and three face-parity syndrome channels. These are first-quantized path/mode encodings of classical codes: the experiment verifies leakage suppression and syndrome routing, not error correction or protection against photon loss, and all probabilities are conditional on postselected single-photon detections. Across more than 340,000 detections, neutral inputs show residual DC-port leakage of $0.02\%$-$1.1\%$ (mean $0.6\%$), corresponding to $\approx21\times$ suppression relative to the ideal $0.125$ DC-capture baseline and $31.6\times$ relative to the measured non-neutral control. Injected DC contamination gives a monotonic soft error signal, and the three face-parity syndrome channels route to their predicted ports with $94$-$99\%$ selectivity. A sector-preserving unitary core keeps leakage far below non-neutral controls over one to three applications, with differences dominated by calibration and compilation systematics rather than gate-cycle physics. We quantify these limits, including fixed-pattern separator bias, $\pm 0.02$ calibration offsets, and compilation scatter near the $10^{-3}$ leakage level, and report a Hong-Ou-Mandel degradation episode in which suppression vanished and recovered after recalibration.

Interference of time-bin encoded signals over free-space optical channels typically requires stringent mode filtering on receivers due to wavefront distortions from atmospheric turbulence, conventionally addressed with adaptive optics. Passive multimode receivers based on field-widened interferometers present a compelling alternative, enabling direct interference without the overhead of wavefront correction. We demonstrate a field-widened interferometer design that is implemented solely with reflective surfaces and achieves a high interference visibility (greater than 0.97) for spatially multimode beams. The interference of the multimode beams is enabled by two imaging systems that consist of a cavity configuration between a spherical concave mirror and a flat mirror. The configuration enables small form-factors, is inherently achromatic, and is based on standard spherical mirrors which reduces the complexity of the system. The interferometer is applicable for spatially multimode and turbulent optical channels, such as satellite communication, and is designed for quantum systems that use time-bin encoded qubits.

We report the design, commissioning, and operation of deuterium-deuterium (DD) and deuterium-tritium (DT) gas delivery systems developed to load a diamond anvil cell (DAC) beam target for muon-catalyzed fusion (muCF). The DAC approach enables DT fuel to be compressed to GPa pressures at more than twice the liquid density and heated from cryogenic temperatures through 500 K, opening access to a substantially expanded parameter range for muCF kinetics and yield measurements. In this approach, DT is cryo-condensed to a liquid in a minichamber and then compressed in the DAC using a helium-driven pneumatic membrane, achieving high pressures in a millimeter-scale DT sample volume. A DD gas delivery system was designed and used to validate the experimental apparatus, measure the gas quantities needed for filling, develop operational experience, and collect kinetics and yield data with DD targets. The DT gas delivery system adds tritium-specific capabilities for inventory minimization, secondary containment, and activity monitoring. The DT system integrates depleted uranium storage beds and a liquid helium cryogenic condenser used for pressure building and cryopumping. High-purity delivery is provided by a rapid-response palladium permeator. The system is housed in a helium-atmosphere glovebox held at negative pressure with continuous cleanup. We present the process and instrumentation design, a failure modes and effects analysis (FMEA), and data from the experiment's in situ Raman spectrometer, which provides direct confirmation of target loading and composition through the optically clear diamond anvils. The 2024 and 2025 DT campaigns achieved repeatable target fills and operation with no measurable tritium releases to the stack, demonstrating safe, high-purity DT loading at novel density-temperature conditions for muCF studies.

Ionization stabilization is a well-known phenomenon in strongly driven Soft-Coulomb atomic models, where the ionization probability decrease as the field amplitude increases. In this work, we investigate how this mechanism is affected by introducing a repulsive Morse barrier into the binding potential, leading to a Morse-Soft-Coulomb (MsC) model. A systematic comparison between the Soft-Coulomb and Morse-Soft-Coulomb systems is performed for different values of the softening parameter. Ionization probabilities, escape-time maps computed on the field-free energy shell and representative trajectories reveal that the stabilization window observed in the Soft-Coulomb model is strongly suppressed in the Morse-Soft-Coulomb system. To elucidate the origin of this behavior, we analyze the corresponding Kramers-Henneberger effective potentials. While the Soft-Coulomb model develops a symmetric double-well structure supporting two equivalent trapping regions, the Morse-Soft-Coulomb potential exhibits a single effective minimum as a consequence of the broken left-right symmetry introduced by the Morse branch. The combined analysis of ionization probabilities, escape dynamics, representative trajectories, and Kramers-Henneberger potentials indicates that the suppression of stabilization is closely associated with the modification of the phase-space transport structures and the reduction of the effective trapping region induced by the Morse

The weakly nonlinear response of a homogeneous magnetised plasma is usually written as a double cyclotron-harmonic expansion. This representation is explicit, but the repeated use of the Jacobi-Anger expansion produces long sums of Bessel functions and nested resonance denominators. In the linear problem we recently obtained an alternative formulation by keeping the Larmor phase unexpanded and by evaluating the characteristic integral in terms of the newly introduced incomplete-Bessel function $G_μ(z,ψ)$. In this article we apply the same idea directly to the first nonlinear Vlasov-Maxwell equation. The nonlinear source contains the linear response of an inner mode. When this linear response is written in incomplete-Bessel form, the outer characteristic integral produces a bivariate orbit-resolvent $G_{μ,ν}^{(r)}(z,ψ;w,χ)$. This function emerges therefore as the natural orbit integral generated by the first nonlinear characteristic problem. We derive the nonlinear distribution function in terms of these bivariate functions, collect the identities needed for the current projection, recover an extension of the classical double-harmonic Liu-Tripathi formula by expansion, and indicate how the nonlinear susceptibility tensor is obtained from bivariate angular contractions.

Quantum technologies are rapidly advancing across multiple research domains, with a growing impact on biomedical imaging and sensing. We examine their emerging role in ophthalmology through four complementary directions: photon-limited retinal imaging, correlation based imaging, nanoscale optical probes, and quantum-limited visual perception. Advances in optical coherence tomography and single-photon detection enable imaging under strict photon budget constraints, reducing phototoxicity while preserving image quality. Correlation-based approaches, including ghost imaging, offer alternative strategies for image formation in low-light and scattering environments, although practical implementation remains limited by detection efficiency and acquisition time. In parallel, nanoscale optical platforms such as quantum dots provide tunable and photostable probes for enhanced contrast and targeted delivery, with ongoing challenges related to biocompatibility and clinical translation. Finally, experiments at the single-photon level and with structured light fields demonstrate how the visual system itself operates near physical detection limits and can be probed using controlled optical states. While many of these approaches remain at an early stage, they collectively illustrate how quantum and quantum-inspired methods may augment current ophthalmic imaging and diagnostic technologies while providing new tools for studying visual function under well-defined physical constraints.

Optical skyrmions possess topological polarization textures that can maintain topological robustness under external perturbations, making them promising carriers for disturbance-resistant optical information transmission. However, existing optical skyrmion generation schemes mostly rely on static optical elements or fixed nanostructures, making high-speed dynamic switching of the topological state difficult. Here, we propose a high-speed switchable optical skyrmion generator based on a patterned liquid-crystal spin-orbit device. The device employs the in-plane orientation of liquid crystals to imprint a fixed Pancharatnam-Berry geometric phase, while an applied voltage rapidly tunes the liquid-crystal retardance, enabling reversible switching between skyrmion and non-skyrmion states. Experimental results show that the device exhibits millisecond electrical response, with bidirectional response times of 1.76 ms and 0.72 ms, corresponding to an ideal cycling rate of approximately 403 Hz, making it the fastest switchable optical skyrmion generator to date. Furthermore, by exploiting this rapid topological refreshing capability, we demonstrate image encoding and decoding, providing a new liquid-crystal device platform for high-speed, refreshable, and disturbance-resistant topological optical information transmission.

High-refractive-index materials underpin a wide range of optical technologies, including communications, imaging, lasers, and integrated photonic systems. Here, we demonstrate a self-assembled metamaterial platform based on gold nanoparticle aggregates with nanometer-scale gaps exhibit remarkably high effective refractive indices exceeding 15 in the mid-infrared regime, while simultaneously producing gap-field enhancements of at least two-orders of magnitude. This combination of high refractive index and extreme field enhancement enables exceptionally strong light-matter interactions. We demonstrate this by designing a compact high-index metamaterial device supporting an anapole, which further enhances the nanogap field. By placing quantum emitters with terahertz transitions inside the plasmonic gaps, we show a stimulated-emission response enhanced by at least three orders of magnitude, highlighting applications in non-linear optics, frequency up-conversion and vibrational strong coupling.

We consider stratified steady water waves in a two dimensional channel. Our subject is branches of Stokes waves, bifurcating from laminar flows. We assume that the mass flux and the Bernoulli constant are fixed and consider the period of the wave as a parameter, which can change its value along the branch. A new class of density and Bernoulli functions is presented, for which laminar flows generate global bifurcation branches. The laminar flows are not necessary unidirectional and we show that the bifurcation branch can bifurcate from the laminar flow with arbitrary large period.

Intermittency is one of the central features of turbulent transfer: the multi-scale energy cascade is mediated by rare and intense fluctuations. We investigate this phenomenon in a multi-branch shell model, which combines quasi-local triadic nonlinear interactions with a branching structure that mimics the growth of degrees of freedom toward small scales. Comparison with the standard Sabra model shows that branching enhances intermittency, as measured by anomalous scaling exponents of energy-flux structure functions. We further use multiplier statistics and large deviation estimates to characterize the multiplicative nature of the cascade. Our results suggest that reduced descriptions of turbulent intermittency should retain both nonlinear dynamics and geometrical organization. Implications on Navier-Stokes turbulence are discussed.

This paper explores the effectiveness of various novel deterministic and traditional stochastic data assimilation (DA) and parameter recovery (PR) algorithms given noisy data from chaotic systems. We use semi-analytic methods to numerically construct synthetic data from the Lorenz '63 and multiscale Lorenz '96 chaotic dynamical systems, adding white noise. Our findings show that, for different noise levels, deterministic PR algorithms paired with deterministic DA algorithms are shown computationally to be overall more accurate and stable than stochastic PR algorithms. Additionally, deterministic PR methods have demonstrated greater speed and efficiency, requiring less computational power than stochastic PR methods. This suggests that future work should consider exploring the full potential of deterministic PR algorithms in the presence of noise.

We study the reflection of a weak planar shock from a rigid wall in the joint limit of weak shock strength and nearly glancing incidence. In the distinguished scaling (M=1+λα^2), where (M) is the incident-shock Mach number and (α) is the glancing angle, the inner reflection region is governed by the unsteady transonic small-disturbance (UTSD) equation. The corresponding canonical shock-reflection problem is controlled by the single parameter[a=\fracα{\sqrt{2(M^2-1)}}=\frac{1}{2\sqrtλ}+O(α^2),]so the limiting inner parameter (a_0=1/(2\sqrtλ)) is independent of (γ). Consequently, the detachment value (a_d=\sqrt2) maps to the physical scaling threshold (λ_d=1/8), with Guderley--Mach reflection for (λ>1/8). The physical trajectory angle is obtained from the canonical UTSD trajectory function (g(a)) by the Mach-number strength scale[χ_{\rm phys}\sqrt{2(M^2-1)},g(a)+O(M^2-1) 2\sqrtλ,α,g(a_0)+O(α^3).]We derive the self-similar UTSD reduction, the sonic parabola, the UTSD shock polar and its regular-reflection cubic, recovering (a_d=\sqrt2) directly. We also give the local linearisation and formal adjoint solvability condition defining the first correction (H(a;γ)), without claiming a computed correction curve. Finally, a time-marching solver for the full leading-order canonical UTSD system is benchmarked against the Hunter--Tesdall (a_0=0.5) triple point: once transverse compression (u>1) behind the Mach stem is retained, the computed (u=0.5) contour passes through ((ξ,η)=(1.007,0.514)), compared with the published ((1.008,0.514)).

The present study develops a detailed theoretical and mathematical formulation to analyze the time and frequency domain propagation characteristics of Love waves in a stratified fractured poroviscoelastic continuum.The top stratum is modeled as a fractured poroviscoelastic material,whereas the lower semi infinite region exhibits heterogeneity and a gradual transition from viscoelastic behavior near the interface to purely elastic response at greater depths.Fractional order constitutive relations are incorporated to capture the memory-dependent mechanical behavior of the medium using Riemann Liouville fractional derivatives. Three distributed source models, namely Gaussian, Ricker and double-couple sources, are considered. To the best of our knowledge, the mathematical formulation of these distributed sources within the present framework has not been established in earlier studies, where the excitation is typically modeled using an idealized point source. By applying Fourier transform techniques in conjunction with Greens function methodology, the complex dispersion relation is obtained. Since the resulting dispersion equation yields complex roots, a hybrid Newton Raphson iterative algorithm is employedto compute these roots efficiently. Synthetic seismograms are generated to verify that the obtained solutions remain physically consistent and meaningful. Numerical simulations are then performed to investigate the effects of heterogeneity, fractional viscoelasticity and porosity on wave propagation characteristics, thereby identifying the parameters that exert the most significant influence on the system response. Furthermore, to examine the structural implications of the propagated waves, a single degree of freedom SDOF oscillator model is employed to evaluate the surface response corresponding to different types of seismic sources.

We establish a rigorous non-perturbative closure framework for the three-dimensional (3D) $ϕ^4$ scalar field theory near criticality, bypassing the long-standing limitations of perturbative Feynman diagrammatic expansions. By slicing the 3D Euclidean space along a spatial axis, the exact dressed theory is mapped onto a matrix operator evolution governed by the infinite-dimensional symplectic Lie algebra $\mathfrak{sp}(\infty)$. We generalize the classical Stroh formalism and Barnett-Lothe integral invariants from anisotropic elasticity to the quantum field Hilbert space. Crucially, we prove that the dressed operator-valued Barnett-Lothe tensors satisfy the algebraic identity $\hat{\mathbf{S}}^2 + \hat{\mathbf{H}}\hat{\mathbf{L}} = -\hat{\mathbf{I}}$ exactly and non-perturbatively, regardless of the coupling strength. By coupling this symplectic invariance with the Källén-Lehmann spectral representation and the Schwinger-Dyson equations, a novel "Symplectic Bootstrap" master spectral integral equation is formulated. The framework exhibits exact dimensional reduction, naturally degenerating to the Onsager exact solution ($η= 1/4$) in 2D and the Gaussian triviality limit ($η= 0$) in 4D. Solving the transcendental bootstrap equation under the strong-coupling conformal fixed point yields the non-perturbative anomalous dimension $η\approx 0.0363$, matching the state-of-the-art conformal bootstrap numerical limits. Finally, a profound holographic duality between the statistical state equations and the post-buckling bifurcation of fluctuating soft matters is discussed.

We construct exact, positive-energy, normalizable wave-packet solutions of the Dirac equation in the axisymmetric potential $V=-\,v_0/ρ$ -- to our knowledge, the first such solutions in any external potential. Remarkably, one family comprises only elementary functions whose longitudinal profiles reproduce the free-Schrödinger Hermite--Gauss wave packets in the nonrelativistic limit. All packets share two striking features: (i) a probability density that is pointwise decoupled from spin orientation -- despite the inherent spin-orbit coupling of the Dirac equation -- and (ii) a complete freezing of their time evolution at the critical coupling $v_0\to\hbar c/2$. We also present a simple scheme that maps solutions of the 2D Helmholtz equation to further exact Dirac wave packets.

We prove a `nonlinear graviton theorem' for higher-spin self-dual gravity. We consider small deformations of the complex structure of the non-projective twistor space that are bounded in a specified region near the origin and investigate the space $M_{HS}$ of holomorphically embedded complex planes $\mathbb{C}^2$ that intersect the origin. We show that this space is an infinite dimensional complex manifold with a canonical projection onto a four-dimensional holomorphic self-dual spacetime $\mathcal{M}$, and discuss the geometry induced on this new higher-spin space. Solutions of higher-spin self-dual gravity are then obtained by choosing an embedding of spacetime $\mathcal{M}$ into higher-spin space $M_{HS}$, with higher-spin symmetries arising from the different choices of embedding. Integrability of the theory is manifested in the form of a Lax pair for the system that we present. We conjecture that chiral higher-spin gravity can similarly be realized by considering deformations that are unconstrained at the origin.

By incorporating leading $c\,$-dependent corrections to the Carroll transformations, we introduce the ``post-Carroll transformations''. We demonstrate that these transformations are consistent with post-Carrollian mechanics \cite{Najafizadeh:2025ksm}; furthermore, they give rise to the so-called ``post-Carroll algebra''. We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the ``Carroll-Bargmann algebra''. To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariant under this symmetry. We then construct the conformal extension of the Carroll-Bargmann algebra, referred to as the ``Carroll-Schrödinger algebra'', and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll-Schrödinger theory \cite{Najafizadeh:2024imn}. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in $1+1$ dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.

We study the semiclassical limit of SL_2-opers on the four-punctured sphere in Nekrasov-Rosly-Shatashvili Darboux coordinates. Using exact Wentzel-Kramers-Brillouin (WKB) connection formulae, we express the trace coordinates of the corresponding SL_2(C) character variety as finite Laurent sums of Voros exponentials. Tropicalizing these formulae and the NRS relations gives a chamberwise integer affine linear system for the leading logarithms of the NRS coordinates. In chambers where this system is unimodular and the selected cycles form a primitive symplectic pair, the leading asymptotics agree, up to flavor-period shifts, with Seiberg-Witten periods of the N=2 SU(2) theory with N_f=4 fundamental hypermultiplets. We verify this mechanism in a sample chamber and in the weak-coupling degeneration. No global coordinate-independent recovery theorem is claimed; non-unimodular or degenerate chambers are treated as limitations of the chosen NRS chart. In the weak-coupling degeneration, we show that the NRS chart can be chosen compatibly with the plumbing limit so that the resulting chamber is unimodular and non-degenerate away from tropical walls.

A long-standing conjecture claims that Virasoro conformal blocks exponentiate in the semiclassical limit $c \to \infty$ with $h/c$ finite. However, this has been proven only for four-point blocks on the sphere and one-point blocks on the torus. Here we extend the proof to general conformal blocks for higher-point functions and higher-genus backgrounds in arbitrary channels. The statement is to be understood at the level of a formal power series. Our proof builds upon a novel extension of the oscillator method for the computation of conformal blocks to cases where three internal lines meet at a vertex. This extension also gives a new constructive method to compute global conformal blocks in 2d CFTs at general genus.

We establish a new connection between supersymmetric theories and scattering amplitudes. We show that the Coon amplitude coincides with the 3d $\mathcal{N}=2$ half-index of the XYZ model with nontrivial boundary conditions. Our 3d theory, intrinsically defined in the UV, flows to a sigma model in the IR whose partition function is the Veneziano amplitude. Crossing symmetry is realized as a consequence of 3d $\mathcal{N}=2$ mirror symmetry between XYZ and SQED. We use this correspondence to construct a meromorphic modification of the Coon amplitude by promoting the long-standing dressing factor $\mathfrak{q}^{ST}$ responsible for a branch cut to an elliptic completion thereof. This illustrates that one does not have to give up single-valuedness to achieve positivity at the physical poles.

The Ashtekar-Lewandowski (AL) volume operator of loop quantum gravity is central to the Hamiltonian constraint, but its vertex action is usually obtained from dense spectral decompositions of finite recoupling matrices, obstructing numerical analysis on large kinematical Hilbert spaces or high-valence vertices. We formulate a matrix free action of the $SU(2)$ AL vertex volume operator in standard recoupling basis, making use of the Brunnemann-Thiemann expression for the oriented AL volume density $Q_{v}$ whose matrix elements can be generated locally from recoupling theory without forming the full matrix. Based on the Balakrishnan-Stieltjes representation of $(Q_{v}^{2})^{1/4}$ we approximate the volume by shifted-resolvent quadrature (SRQ). The resulting action uses only repeated applications of $Q_{v}$ and shifted positive linear solves, making it compatible with multi-shift Krylov methods. We prove exact preservation of the volume kernel, provide operator-norm and residual error estimates, discuss sector-wise scaling bounds, and validate the method on an embedded $K_{5}$ graph at small spin cutoffs against exact dense local-block operators. Numerical simulations show rapid convergence of vertex expectation values, controlled dependence on bound parameters, and exact preservation of zero-volume modes. We further demonstrate matrix free Monte Carlo estimates at doubled-spin cutoff $2j=250000$ beyond dense materialisation, and show that SRQ can be combined with stochastic Lanczos quadrature to estimate fixed-sector volume spectral measures without dense volume matrices.

Superconducting qubits are artificial atoms whose spectra and interactions can be engineered through appropriate circuit design, a versatility that can be exploited for quantum simulation. We theoretically investigate a linear array of capacitively coupled transmons, effectively described by a Bose-Hubbard Hamiltonian with attractive interaction. We revisit the discrete-soliton nature of the lowest-energy band of the spectrum, and identify spatially localized quantum solitons. The solitonic character of these states is revealed through their time evolution, which displays a quantum interference pattern, or quantum walk, highlighting their composite nature. We discuss protocols for preparing spatially localized quantum solitons that are compatible with current state-of-the-art tunable-transmon circuits. Our results demonstrate that superconducting circuits provide a promising and experimentally accessible platform for the investigation of quantum soliton physics.

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Sparse matrix kernels form the computational backbone of scientific computing, traditionally relying on C/C++ and Fortran implementations that prioritize performance over memory safety. This work evaluates Rust as a systems-level alternative for sparse linear algebra by implementing and benchmarking three core workloads: sparse matrix-vector multiplication (SpMV), Lanczos-based Krylov methods, and matrix-exponential evaluation. We compare native Rust code against established baselines (Intel oneMKL, Eigen, PETSc, and PSBLAS) across a suite of representative matrices. Our results show that Rust's sparse kernels achieve performance comparable to Eigen and PSBLAS, tracking the state-of-the-art for CSC formats, while trailing PETSc's advanced blocked CSR optimizations. By analyzing compile-time monomorphization, SIMD vectorization, and FFI boundaries, we assess the practical impact of Rust's safety model and ecosystem readiness. The study provides concrete, evidence-based guidance for modernizing high-performance numerical software stacks.

We study the $I^G(J^{PC})=0^+(1^{++})$ $K\bar Kπ$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $πa_0$-$K\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_Sπ^0$ invariant-mass distribution in the $J/ψ\toγ(K^0_SK^0_Sπ^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \begin{align} \sqrt{s_{f_1(1285)}}&= \left(1277\pm2\pm1\right) -i\left(12\pm1\pm0\right)\text{MeV}\,,\notag\\ \sqrt{s_{f_1(1420)}}&= \left(1435\pm2\pm7\right) -i\left(40\pm2\pm1\right)\text{MeV}\,.\notag \end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $πa_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.