Ising machines are physical platforms designed to minimize the energy of classical Ising Hamiltonians, yet accessing specific excited states remains an open challenge of both fundamental and practical relevance. In this letter we show that a network of Kerr parametric oscillators (KPOs) naturally implements an Ising selector machine. By tuning the frequency detuning between the parametric pump and the oscillator resonances, the system can be steered to converge close to the ground state, the highest-energy configuration, or targeted intermediate excited states. Beyond mean field, numerical simulations based on the truncated Wigner approximation demonstrate that noise insertion preserves the energetic structure of the landscape. The targeted state emerges with an exponentially enhanced probability over the rest of the Ising spectrum. Our results establish the pump-cavity detuning as a control knob for navigating the full Ising energy landscape, opening a route to applications in Boltzmann sampling, hardness characterization, and spectral analysis of combinatorial problems.

In this work, we investigate the scattering of spin-$3/2$ fermionic particles mediated by a Yukawa-like coupling in the context of the massive Rarita-Schwinger model. The interaction is introduced by replacing $m \to m_ψ + gϕ$ in the free spin-$3/2$ Lagrangian. The analysis is performed at both zero and finite temperatures. In the latter case, thermal effects are incorporated using the Thermofield Dynamics (TFD) formalism. In both regimes, we obtain the differential and total cross sections and examine their behavior in the short-range ($m_ϕ \neq 0$) and long-range ($m_ϕ = 0$) limits, in order to analyze the influence of zero- and finite-temperature effects.

This paper presents EPAC, a RISC-V-based accelerator chip developed within the European Processor Initiative (EPI) as part of a multi-year, multi-partner effort to build a European HPC processor ecosystem. EPAC is implemented in GlobalFoundries 22FDX (GF22FDX) technology, covers an area of 27 sq mm with approximately 0.3 billion transistors, and integrates three distinct RISC-V compute tiles targeting different workload classes: VEC, a vector processing tile for double-precision HPC workloads; STX, a many-core tile optimized for stencil and machine learning computations; and VRP, a variable-precision tile for iterative numerical solvers requiring extended floating-point formats. All tiles are connected through a Coherent Hub Interface (CHI) based network-on-chip with a distributed L2 cache system and communicate with external memory via a SerDes link. The chip was taped out in GF22FDX technology and successfully brought up, with all major IP blocks validated. This paper describes the architecture of each tile and the uncore infrastructure, the integration and physical implementation process, and the board-level bring-up activities. It also reflects on the engineering and coordination lessons learned from a full chip design effort distributed across academic and industrial partners in Europe.

Within the volume-limited subsample at $z<0.06$ of the Zwicky Transient Facility (ZTF) DR2 sample, we confirm a statistically significant excess of Type Ia supernovae (SNe Ia) at $z \simeq 0.02$-$0.04$, previously reported but not explained by survey selection effects. Forward simulations assuming a uniform volumetric SN Ia rate and realistic ZTF detection efficiencies fail to reproduce the feature at the $5$-$7σ$ level. We also detect an excess in the rates compared to our survey simulations at $z \simeq 0.08$ and $0.14$, albeit at smaller significance. To investigate the origin of these inhomogeneities, we compare the observed SN distribution to constrained reconstructions of the local matter density field from the Manticore project, based on Bayesian forward modelling of the 2M++ galaxy catalogue. While SN overdensities are spatially associated with prominent nearby structures such as the Perseus, Coma, and Hercules superclusters, the amplitude of the SN excesses significantly exceeds that expected from matter overdensities alone. By reconstructing a redshift-dependent volumetric SN Ia rate, we find that local enhancements can reach factors of two to five within specific clusters, while the sample-averaged rate remains consistent with previous low-redshift measurements. These results indicate that the SN Ia rate is not a linear tracer of the underlying matter density and suggest a strong environmental dependence in dense structures. We discuss possible physical origins and highlight the implications for low-redshift SN cosmology, including correlated peculiar velocities and additional covariance beyond standard linear corrections.

Differential privacy is the standard method for privacy-preserving data analysis. The importance of having strong guarantees on the reliability of implementations of differentially private algorithms is widely recognized and has sparked fruitful research on formal methods. However, the design patterns and language features used in modern DP libraries as well as the classes of guarantees that the library designers wish to establish often fall outside of the scope of previous verification approaches. We introduce a program logic suitable for verifying differentially private implementations written in complex, general-purpose programming languages. Our logic has first-class support for reasoning about privacy budgets as a separation logic resource. The expressiveness of the logic and the target language allow our approach to handle common programming patterns used in the implementation of libraries for differential privacy, such as privacy filters and caching. While previous work has focused on developing guarantees for programs written in domain-specific languages or for privacy mechanisms in isolation, our logic can reason modularly about primitives, higher-order combinators, and interactive algorithms. We demonstrate the applicability of our approach by implementing a verified library of differential privacy mechanisms, including an online version of the Sparse Vector Technique, as well as a privacy filter inspired by the popular Python library OpenDP, which crucially relies on our ability to handle the combination of randomization, local state, and higher-order functions. We demonstrate that our specifications are general and reusable by instantiating them to verify clients of our library. All of our results have been foundationally verified in the Rocq Prover.

Thin sheets can be assembled into tubular origami structures that combine deployability with pronounced anisotropic stiffness, enabling applications ranging from robotics to deployable systems. However, most existing tubular origami designs remain limited to degree-four vertex topologies and are characterized primarily in axial and radial loading modes, without a full assessment of anisotropic stiffness. Here, we present an automated design framework for tubular origami that jointly explores local vertex topology through generalized degree-$n$ vertices and global tube topology through the polygonal cross-section, for the systematic design and optimization of anisotropic stiffness. Using a calibrated bar-and-hinge model together with experimental validation, we quantify large-deformation stiffness responses in axial translation, in-plane translation, torsion about the tube axis, and rotation about in-plane axes, thereby characterizing the anisotropic stiffness of the tube across its compliant and constrained deformation modes. The resulting design-space exploration showed that the polygonal cross-sectional topology is the primary factor governing the anisotropic stiffness. We further show that increasing the local vertex degree can improve global structural performance, particularly for tubes with a small number of cross-sectional vertices, demonstrating that higher local kinematic freedom does not necessarily compromise stiffness at the structural scale. Compared with a benchmark design, the optimized architectures achieve more than 50 times higher constrained rotational stiffness. Together, these results highlight higher-degree vertices and polygonal cross-sectional topology as powerful design variables for tailoring anisotropic stiffness in tubular origami.

This paper proposes a strong second-order two-step explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for solving a two-dimensional Gray-Scott model subject to appropriate initial and boundary conditions. The constructed approach discretizes at the first stage utilizing a second-order explicit method while a second-order implicit scheme is employed at the second phase. The space derivatives are approximated with the Galerkin finite element formulation combined with a spectral orthogonal basis. With this combination, the errors increased at the first stage are balanced by the errors decreased at the second phase so that the stability is maintained. Furthermore, the use of the spectral orthogonal basis minimizes the space errors. Thus, the new computational approach calculates efficiently numerical solutions and preserves a strong stability and high-order accuracy. The theoretical studies indicate that the proposed strategy is unconditionally stable, temporal second-order accurate and spatial $qth$-order convergent using the $L^{\infty}(0,T;[L^{\infty}(Ω)]^{2})$-norm, where $q$ is an integer greater than or equal $2$. Some numerical examples are performed to confirm the theory and to demonstrate the efficiency of the developed algorithm.

A precision measurement of the $W$-boson production cross-section is performed using the $W \to μν$ decay channel, based on a sample of proton-proton collision data collected by the LHCb experiment at $\sqrt{s}$ = 13 TeV and corresponding to an integrated luminosity of 5.1 $fb^{-1}$. The cross-section is measured for muons with transverse momentum between 25 and 55 GeV and pseudorapidity between 2.0 and 4.5. The integrated production cross-sections of $W$ bosons are measured to be $$ \begin{array}{lcl} σ_{W^+ \to μ^+ν} &=& 1754.2 \pm 1.5 \pm 11.9 \pm 35.1\text{ pb} \\ σ_{W^- \to μ^-\barν} &=& 1178.1 \pm 1.3 \pm 9.7 \pm 23.6\text{ pb} \end{array} $$ where uncertainties are statistical, systematic, and due to the luminosity determination, respectively. Results are in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. This measurement is significantly more precise than previous results in this kinematic regime.

Light curves from binary systems containing white dwarfs with neutron star or stellar-mass black hole companions (WD+NS and WD+BH) with edge-on orbital planes potentially show self-lensing/eclipsing signals. Here, we evaluate the properties and detectability of these signals in the NASA's Transiting Exoplanet Survey Satellite (TESS), and the Nancy Grace Roman Space Telescope (Roman) observations. WD+NS systems with orbital periods $T\lesssim25~$days mostly have considerable finite-source sizes with the normalized source radii $ρ_{\star}\gtrsim1$. WD+BH systems with $T\gtrsim3$ days have $ρ_{\star}\lesssim1$, and $ρ_{\star}\sim0.01$ for BHs with a few tens solar-mass. Our analytical calculations show the probabilities of occurring self-lensing signals in WD+NS and WD+BH systems are $\sim10^{-3},~10^{-2}$, and maximize for systems with low-mass WDs revolving massive NSs/BHs. We simulate their light curves and generate synthetic data for them by applying the observing protocols of these two satellites. We assume self-lensing signals are detectable if (i) $1\leq T\leq T_{\rm{obs}}$ (where $T_{\rm{obs}}=62~\rm{and}~27.4$ days are the Roman and TESS continuous observing windows), (ii) $\rm{SNR}\ge3,~6$, their signals are (iii) deeper than twice the photometric error, and (iv) covered by at least one datum. Systems with detectable self-lensing signals in the TESS and Roman observations on average have small inclination angles $i\lesssim0.2^{\circ}$, with the orbital periods $\sim6,~19~$days, and their signals last $\sim[6,~30]~\rm{minutes}$. The TESS and Roman efficiencies for detecting these signals are $\sim2-6\times10^{-4}$ and $\sim2-12\times10^{-10}$. Although detecting these self-lensing signals by Roman is impossible, the TESS telescope potentially manifests at least one self-lensing signal due to these binary systems, if $8\%,~\rm{and}~3\%$ of WDs have NS and BH companions.

Core-collapse supernovae (CCSNe) in luminous infrared galaxies (LIRGs) can have extreme line-of-sight host galaxy dust extinctions, which leads to a large fraction of the events remaining undetected by optical and infrared surveys. This population of undetected CCSNe is important to constrain in order to determine the cosmic CCSN rates. Our aim is to confirm and refine our estimates for the undetectable fraction of CCSNe in LIRGs in the local Universe. Our study is based on the near-infrared K-band multi-epoch SUNBIRD survey monitoring dataset of a sample of nine LIRGs using the Gemini-South telescope with the multi-conjugate GSAOI/GeMS laser guide star adaptive optics system. We determined the limiting magnitudes for CCSN detection for each epoch in our dataset with artificial supernova injection and image subtraction methods. Subsequently, we used a Monte Carlo method to determine the combined effects of limiting magnitudes, survey cadence, CCSN subtype distribution, and their light curve evolution diversity. The intrinsic CCSN rates of the sample galaxies were estimated based on detailed modelling of their spectral energy distribution. Finally, we combined the resulting CCSN detection probabilities with the intrinsic CCSN rates for the dataset, and compared that against the real CCSN detections over the survey period. Based on our GSAOI/GeMS dataset, assuming optical or near-infrared example surveys with capabilities to detect CCSNe in local LIRGs with host extinctions of $A_V =$ 3 or 16 mag, respectively, the resulting total undetectable fractions are $86.0^{+4.7}_{-5.9}$ % and $53.6^{+15.6}_{-19.6}$ %. When folding in the results from our previous near-infrared adaptive optics assisted LIRG monitoring dataset, the corresponding total undetectable fractions are $88.3^{+2.6}_{-3.2}$ % and $61.4^{+8.5}_{-10.6}$ %, respectively.

We construct multilevel lattice codes from multiquadratic number fields for the compound block-fading wiretap channel. More precisely, we specialize Construction $π_A$ over the ring of integers $\mathcal{O}_K$ and exploit rational primes that split completely in $K$ to obtain a Chinese Remainder Theorem (CRT) decomposition into small residue alphabets, notably binary, which enables multistage decoding. The resulting nested lattices fit into the algebraic Construction A framework and, when combined with discrete Gaussian shaping and flatness-factor bounds, provide universal reliability for the legitimate receiver and strong secrecy uniformly over the eavesdropper compound set.

Controlling magnetic phases in two-dimensional systems, where charge transport is highly sensitive to real-space spin inhomogeneities, is central to understanding emergent magnetic states in reduced dimensions. In this context, thickness-dependent magnetotransport provides access to irreversible magnetic processes that are not captured by reversible transport or bulk magnetization alone. Here we report an extensive study of hysteretic magnetoresistance in single-crystalline nanoscale thin flakes of the layered antiferromagnet MnBi2Te4. The multi-step hysteresis exhibits a pronounced non-monotonic dependence on thickness and displays nontrivial angular anisotropy. The transport signatures rule out surface-dominated magnetism and simple bulk metamagnetic transitions as the primary origin. We argue that the magnetic irreversibility is possibly governed by domain wall pinning and de-pinning processes within a spatially non-uniform magnetic landscape. These results suggest that reduced dimensionality is a key driver of magnetic irreversibility in MnBi2Te4.

We propose a mechanism of supercurrent-induced phonon angular momentum in mixed parity superconductors and s-wave superconductors with spin orbit coupling. We derive analytical expressions of phonon angular momentum induced by the supercurrent by perturbative calculation. The physical interpretation of this effect is also discussed.

Transferable excited-state dynamics offer a route to efficient screening of photophysical behavior across molecular systems, but conventional nonadiabatic simulations remain prohibitively expensive. Here we introduce X-MACE, a transferable machine-learning potential for excited-state dynamics that predicts multiple potential energy surfaces, forces and oscillator strengths, and combine it with curvature-driven surface hopping to enable data-efficient screening of photochemical pathways. We apply this framework to fluorescent chromophores as an example application, using green fluorescent protein chromophore variants to demonstrate how subtle structural modifications reshape excited-state relaxation, lifetimes and photoisomerization yields. Fine-tuning a single pretrained model with fewer than 100 reference geometries per derivative yields accurate dynamics across a chemically diverse set of analogues. The screening reveals two governing design principles: steric crowding on the phenolate ring lowers the torsional barrier and accelerates access to twisted conical intersections, whereas conjugation extension stabilizes planar excited-state configurations, suppresses non-radiative decay and prolongs fluorescence. More broadly, this workflow provides a general framework for scalable excited-state screening and interpretable design of photophysical properties.

In our paper [Tak6], we constructed eight families of quasi-smooth prime $\mathbb{Q}$-Fano threefolds, anticanonically embedded in codimension four, using weighted projectivizations of the $14$-dimensional affine variety $Π_{\mathbb{A}}^{14}$or its cone. Let $\widehat{f}\colon\widehat{X}\to X$ be the unique divisorial extraction at one specified singularity of maximal index. In this paper, we explicitly construct the Sarkisov link starting from $\widehat{f}$ for $X$ belonging to seven of these families. This is achieved by using the Sarkisov link associated with the weighted projectivization of $Π_{\mathbb{A}}^{14}$ or its cone corresponding to $X$. As a consequence, we show that the Sarkisov link ends with either a fibration whose general fiber is a del Pezzo surface of degree one or a divisorial contraction of type $(2,1)$ to weighted complete intersections of codimension at most two. We also provide more detailed descriptions of these Sarkisov links.

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can change via character insertions and deletions. A dynamic parallel constant-time algorithm is presented that can maintain LCE queries on a common CRCW PRAM with $\mathcal{O}(n^ε)$ work, for any $ε> 0$. The algorithm maintains a string synchronizing sets hierarchy, which it uses to answer substring equality queries, which it in turn uses to answer LCE queries. To achieve constant runtime, the algorithm allows parts of its information to become outdated by up to $\log n \log^* n$ updates. It answers queries by combining this slightly outdated information with a list of the recent changes. Two applications of this dynamic LCE algorithm are shown. Firstly, a dynamic parallel constant-time algorithm can maintain membership in a Dyck language $D_k, k > 0$ with $\mathcal{O}(n^ε)$ work for any $ε> 0$. Secondly, a dynamic parallel constant-time algorithm can maintain squares with $\mathcal{O}(n^ε)$ work for any $ε> 0$.

We theoretically investigate charge transport in a junction between a conventional superconductor and a V$_2$O-based altermagnet exhibiting distinctive spin-split quasi-one-dimensional Fermi surfaces. The altermagnet is described by a microscopically motivated six-orbital model that incorporates sublattice degrees of freedom associated with both V and O sites. Based on calculations performed under various boundary conditions, we demonstrate the robust emergence of specular Andreev reflection with a distinctive spin polarization. Furthermore, we propose an efficient multiterminal setup to detect this specular Andreev reflection through nonlocal conductance measurements. Our results establish V$_2$O-based altermagnets as a promising platform for realizing spin-resolved Cooper pair splitting, which is essential for generating energy-entangled electron pairs.

We study the Banach-Mazur distance between random normed spaces generated by centrally symmetric random polytopes associated with isotropic log-concave measures in $\mathbb{R}^n$. We show that, in a wide range of parameters, if $x_1,\dots,x_m$ and $y_1,\dots,y_m$ are independent samples from an isotropic log-concave probability measure on $\mathbb{R}^n$, then the corresponding normed spaces $X_{B_m}$ and $Y_{A_m}$ generated by their absolute convex hulls satisfy, with high probability, $$d_{\rm BM}(X_{B_m},Y_{A_m}) \geqslant \frac{cn}{\ln(1+m/n)},$$ which is sharp in both $n$ and $m$ and recovers the extremal order $n$ when $m \approx n$. Our results extend Gluskin's theorem from the Gaussian setting to general isotropic log-concave measures, providing evidence for a universality phenomenon in the extremal geometry of the Banach-Mazur compactum. In addition, we investigate operator-theoretic properties of the associated random spaces and, as consequences, we derive sharp estimates for their basis constant and show that these random spaces are far from the class of spaces with a $1$-unconditional basis. The proofs combine probabilistic and geometric methods with recent advances related to Bourgain's slicing problem.

Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schrödinger Hamiltonians on metric graphs, with a focus on results related to quantum chaos, periodic orbit theory and spectral theory. We summarise related seminal results, and give an overview over a few more recent developments.

We present an approach for synthesising observational data with elastodynamic finite element models by extending the statistical finite element method (statFEM) framework. The proposed formulation adopts a Bayesian filtering approach to account for uncertainties in the data, the finite element model, and the discrepancies between the model and the physical system. Observational data are assimilated while the state of the spatially discretised finite element problem is advanced in time using the stochastic variant of the explicit Newmark scheme. The prior probability density of the state is obtained by solving an incremental probabilistic forward problem, and the corresponding posterior density is obtained by conditioning on the data available at each time step. In the probabilistic forward problem, spatio-temporal Gaussian random fields representing the forcing, model misspecification, and material parameters are specified via their stochastic PDE formulation. The resulting non-Gaussian prior probability density is approximated using a perturbation approach, yielding a Gaussian posterior with closed-form mean and covariance. The hyperparameters of the random field representing model misspecification are calibrated by maximising the marginal likelihood of the data. The proposed approach is illustrated on one- and two-dimensional elastodynamic examples with synthetic data.

This paper investigates DeGroot-Friedkin (DF) dynamics over signed influence networks with interdependent topics. We propose a multi-topic signed framework that combines repelling interpersonal interactions with cross-issue self-appraisal, examining how antagonism and topic interdependence shape the evolution of agent-level social power. When the logic matrices (for topic interdependence) of all agents share a common dominant left eigenvector, we identify structural conditions under which the original dynamics admit an exact reduction to an explicit scalar DF map. This yields a complete classification of limiting social power configurations into pluralistic, mixed, and vertex-dominant types. In all three cases, the dynamics are globally convergent, and in the first two the ordering induced by the interaction centrality is preserved. We further show local robustness under small heterogeneous perturbations of the logic matrices. We also clarify what changes when this common-eigenvector structure is lost. These results extend signed social power dynamics beyond the standard nonnegative scalar setting and shed light on the robustness and scope of centrality-based social power formation in multi-topic signed influence systems.

Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework for stabilizer codes that relaxes these constraints while preserving the symplectic commutation structure on the binary symplectic space $\mathbb{F}_{2}^{2}$. The approach permits controlled overlap between X- and Z-check supports, leading to quasi-orthogonal Pauli operators and a generalized notion of effective distance defined via induced anti-commutation with logical operators. This relaxation expands the stabilizer design space, enabling codes that approach the Gilbert-Varshamov regime with improved logical rates at moderate distances. Finite-length constructions, including quasi-orthogonal variants of the $[[8,3,\approx 3]]$, $[[10,4,\approx 3]]$, $[[13,1,5]]$, and $[[29,1,11]]$ codes, demonstrate consistent improvements over strictly orthogonal counterparts. Under depolarizing noise with error rates up to $p=0.30$, logical error rates, fidelities, and trace distances improve by up to two orders of magnitude. These improvements reflect the increased connectivity of the underlying stabilizer geometry while remaining compatible with standard decoding schemes. The proposed framework offers a principled extension of stabilizer code design through quasi-orthogonal geometric structures.

Observing the structure of quantized vortices can provide evidence for the pairing nature of a superfluid or superconductor and pinpoint its order parameter. Spin-triplet superfluid $^3$He supports a variety of vortices, calculated and identified so far in bulk fluid. We show numerically that the vortex core in $^3$He is strongly altered near a surface, resulting in a structure inhomogeneous along the vortex line. The effect is asymmetric with respect to the relative orientation of the core order parameter anisotropy axis and the surface normal. In a wide range of external conditions, the vortex structure at the surface is found to be completely different from that in bulk. The effect originates from the combination of spin-orbit interaction in triplet pairing with the symmetry breaking by the surface. As an implication, surface-limited vortex core observations in a triplet-candidate system may not reflect the bulk structure. We propose an experimental verification of the effect by measuring a transition in the vortex structure in thin slabs of superfluid $^3$He-B.

We present a quantitative framework for on-axis optical transduction of vertical InP nanowire resonators, correlating laser position to signal amplitude, calibration, and frequency stability. Photothermal resonance detuning is used to reconstruct the local beam intensity profile and to calibrate the photodetector signal using the thermomechanical noise. A noise model incorporating shot noise and spatial variation in substrate reflectance predicts the position-dependent Allan deviation. We find that the optimal detection position lies near the steepest intensity gradient, and that increasing laser power does not significantly improve frequency stability, because the accompanying temperature rise enhances thermomechanical noise and offsets the signal gain. These results establish design guidelines for optimizing nanowire-based sensors in on-axis optical detection schemes.

We revisit the Kahn-Priddy theorem from the perspective of modern equivariant homotopy theory. This allows for a short proof that may be applied in other settings with sufficiently robust analogues of multiplicative norms and the Adams isomorphism. We illustrate this by establishing new Kahn-Priddy theorems in $L_n$ and $L_n^f$-local homotopy theory, motivic homotopy theory, and synthetic homotopy theory.

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the Galerkin-projected ODE system as a statistical inverse problem, in which the coefficients are inferred through Bayesian inference. By accounting for model uncertainty arising from POD mode truncation and data uncertainty introduced by data noise and numerical postprocessing, the framework systematically updates the ODE system coefficients using an analytical, sampling-free solution based on Gaussian likelihood and inverse-Gamma priors. The approach is first validated using a self-sustained oscillating flow over a dimpled surface at a moderate Reynolds number (Re=3000), demonstrating stable and accurate reproduction of the temporal dynamics and phase trajectories of coherent structures when compared with direct numerical simulation (DNS). It is then applied to a centrifugal compressor featuring strong tip-leakage vortex breakdown and impeller-diffuser interactions at Re=100000, where the model successfully captures dominant unsteady structures and frequency characteristics despite limited mode retention. Overall, the results show that Bayesian inference substantially enhances the robustness, stability, and predictive fidelity of Galerkin-POD models for compressible flow systems. The proposed methodology combines the physical interpretability of Galerkin projection with the statistical rigour of Bayesian inference, offering a general, computationally efficient, and uncertainty-aware reduced-order modelling framework for complex fluid dynamic applications.

The interplay between real-space topology such as magnetic skyrmions and momentum-space topology characterized by topological surface states (TSSs) is predicted to realize novel phenomena and functionalities, yet materials hosting both topologies are scarce. Skyrmion-hosting helimagnet family EuGa$_2$Al$_2$ and EuAl$_4$ has been a prime candidate for such a dual-topology system, but conclusive evidence for its momentum-space topology has remained elusive. We provide this evidence by directly observing TSSs that stem from bulk Dirac nodal lines using high-resolution angle-resolved photoemission spectroscopy. These TSSs are exceptionally robust against various perturbations such as a 2$\times$1 surface reconstruction, a chemical change in the termination of the crystal surface, and the onset of helical antiferromagnetic order. Crucially, below the Neel temperature, we observe replica bands driven by the magnetic ordering. Moreover, we demonstrate clear surface-termination dependence of this magneto-topological coupling. Our findings establish Eu(Ga$_{1-x}$Al$_x$)$_4$ as a dual-topology material and offer a rare platform to explore and control the interaction between the two fundamental topological realms.

We consider the category $\mathbf{AOVS}$ of Archimedean ordered vector spaces with linear maps which preserve all existing suprema, and its full subcategories $\mathbf{DAOVS}$, $\mathbf{DVL}$ and $\mathbf{UVL}$, consisting of directed spaces, Dedekind complete vector lattices and universally complete vector lattices, respectively. We deduce from some results in the literature that $\mathbf{DVL}$ and $\mathbf{UVL}$ are reflective subcategories of $\mathbf{DAOVS}$, with the usual Dedekind completion being the reflector in $\mathbf{DVL}$. In contrast to these facts, we show that a non-directed Archimedean ordered vector space of dimension greater than $1$ has no reflector in either $\mathbf{DVL}$ or $\mathbf{UVL}$. In particular, there are no free Dedekind complete vector lattices over a set with more than one element. We also use the occasion to show that a free vector lattice with $α$ generators embeds into a free vector lattice with $β$ generators if and only if $α\leβ$, and explore the concept of the free completion of an Archimedean vector lattice with a strong unit.

The Dzyaloshinskii-Moriya (DM) interaction has been considered essential for skyrmion formation, however, the discovery of skyrmion lattices (SkLs) in nominally centrosymmetric materials where the DM interaction is forbidden, such as Eu(Ga$_{1-x}$Al$_x$)$_4$, has challenged this established view. Recent structural investigations of Eu(Ga$_{1-x}$Al$_x$)$_4$ have further complicated this issue by revealing that the charge-density wave breaks local symmetry, theoretically allowing DM interaction. This raises a fundamental question: are the complex magnetic phases driven by the DM interaction or by alternative mechanisms? Here, using soft-x-ray angle-resolved photoemission spectroscopy, we determine the three-dimensional bulk electronic structure of Eu(Ga$_{1-x}$Al$_x$)$_4$, and elucidate the electronic origins of its rich magnetic orders. We directly observe an x-dependent Lifshitz transition leading to the emergence of a Fermi-surface pocket. Importantly, multiple nesting vectors derived from this pocket match the symmetries and periodicities of the multiple SkLs. Moreover, these nesting vectors can also account for other magnetic orders, such as the zero-field helical magnetism, suggesting a common electronic origin of the complex magnetic phases. These findings suggest that competing nesting-induced Ruderman-Kittel-Kasuya-Yosida interactions and their engineering can generate and control various SkLs and related topological spin textures.

Large enterprises often operate extensive Continuous Integration (CI) pipelines on large, heterogeneous compute clusters, where conservative, statically defined resource requirements are used to ensure build reliability. This practice leads to substantial system memory over-allocation, reduced cluster utilization, and increased operational costs. In this paper, we motivate the need for intelligent resource prediction by analyzing over 300,000 historical build executions from a production CI environment with more than one thousand compute nodes. Our analysis shows that, on average, more than 60% of allocated system memory remains unused. We then compare multiple machine learning approaches for predicting build task memory usage, including classification-based methods and regression-based quantile prediction. Our final solution employs a LightGBM-XGBoost quantile regression ensemble optimized to minimize under-allocation while reducing over-provisioning. We integrate this solution into the production CI pipeline via a microservice-based orchestration layer, achieving average memory savings of approximately 36GB per build and reducing under-allocation rates to below 0.3% without negatively impacting build execution times.