Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphisms satisfying the analogous properties as the well known core-nilpotent decomposition of matrices. In this paper we present a new description of core-nilpotent endomorphisms using the $k[x]-$module structure they define in the base vector space. Moreover, our approach provides us with a ``new'' generalized inverse that restricts to the well known Drazin inverse under certain conditions. Similarly, we present a generalized core-nilpotent decomposition for endomorphisms over arbitrary vector spaces.

The memory effects in open quantum systems can induce information backflow and revive quantum correlations, thereby providing a powerful way to protect and recover useful quantum resources in realistic noisy environments. However, such dynamics remains experimentally unexplored in multipartite quantum steering. Here we observe different non-Markovian evolution of tripartite quantum steering using Greenberger-Horne-Zeilinger-type mixed states, covering both death and revival processes. In particular, we experimentally demonstrate the more intricate asymmetric steering structure of tripartite quantum steering through different bipartitions, which do not arise in bipartite systems. Our results provide foundational insights into the hierarchical and directional structures in multipartite quantum steering, and highlight its potential as a useful resource for asymmetric quantum information processing.

Zero-knowledge proofs (ZKPs) are an emerging technology that has become the solution to efficiently provide security and privacy along with the transparency requirement of blockchains. ZKPs are usually expressed by means of arithmetic circuits and, more generally, systems of polynomial equations in a large prime field (commonly ranging from 64-bit to 256-bit values). An increasing interest to apply formal verification techniques to ensure soundness and completeness properties of ZKP protocols has shown the need of developing powerful SMT solvers able to handle such constraint systems. In this paper we consider the problem of deciding the satisfiability of existentially quantified first-order formulas defined over polynomial equations on a prime field. We present a new DPLL($T$)-based approach in which the theory solver orchestrates several modules with different trade-offs between completeness and efficiency. We have implemented the proposed techniques in a prototype that already shows better results than existing state-of-the-art tools on both benchmarks from the domain of ZKP compiler correctness and new benchmarks coming from the verification of arithmetic circuits for ZKPs. \keywords{SMT \and Finite field \and Polynomials \and Zero-Knowledge Proofs.

In many analyses the object reported at the end is not fixed in advance, but is chosen after a preliminary search over variables, subgroups, transformations, models or contrasts. Classical selective-inference methods are most effective when this search can be written as an explicit selection event. This note treats the less structured case in which the selection rule is a black box and inference is required for the target indexed by the selected object. We show that, for any fixed-target confidence procedure, selected-target noncoverage is bounded by the nominal fixed-target noncoverage plus the average total variation distance between the marginal law of the inferential data and its conditional law given the selected object. A mutual-information bound follows immediately. The result recovers sample splitting as the zero-leakage case and gives explicit guarantees for noisy screening through a Gaussian information bound. Thus the inferential cost of black-box selection is quantified by the information that the selected object carries about the inferential sample.

We present a classical theory of relativistic surface plasmon (RSP) excitation at a smooth plasma-vacuum interface driven by either a ponderomotive force or an electric field of an intense laser pulse. Starting from Maxwell equations coupled to a cold-fluid plasma response, we derive a general driven wave equation for the RSP and solve it analytically. We show that an infinite planar surface enforces conservation of the in-plane wavevector. A finite longitudinal interaction length or axial modulation supplies a finite kz spectrum, while cylindrical curvature replaces one continuous transverse in-plane wavenumber by a discrete azimuthal mode index m. This partially relaxes the planar in-plane constraint, while axial phase matching remains controlled by the longitudinal spectrum of the drive. The excitation strength is controlled by the overlap between the drive and the surface eigenfield, which is determined by the surface geometry. This provides a general principle for controlling RSP excitation. We also show that relativistic effects can substantially modify the dielectric response and can be preliminarily verified by particle-in-cell simulations. Within the local relativistic dielectric model, the overlap-normalised planar source saturates at large a0, and cylindrical curvature partially alleviates this reduction before strong surface softening develops. The role of surface geometry is analysed. A cylindrical surface can sustain an on-axis accelerating field, enabling highly nonlinear wakefield generation for particle acceleration. In addition, the cylindrical geometry imposes a precise mode-selection rule that provides intrinsic control over RSP excitation. Axisymmetric ponderomotive drive selects fundamental mode m=0. A linearly polarised laser field selects a superposition of m=+1 and m=-1 modes, and a circularly polarised laser field selects a single helical mode.

We present the first detailed optical study of the cataclysmic variable SRGA J115215.0$-$510656, based on new time-resolved photometric and spectroscopic observations complemented by long-baseline Transiting Exoplanet Survey Satellite (TESS) data. The TESS light curve reveals deep, recurring eclipses consistent with a high-inclination geometry and an orbital period of 0.43567659(9)d. The eclipse morphology during outburst is consistent with a possible 'inside-out' type outburst and supports classification of the system as a U Gem-type dwarf nova. By combining eclipse phase width and ellipsoidal modulation, we constrain the system geometry to a narrow locus in the $(q,i)$ plane, with allowed mass ratios $0.28 \lesssim q \lesssim 0.84$ and inclinations $i$ $\simeq$75$-$84$^{\circ}$. The persistence of single-peaked Balmer lines during outburst, together with strong He II emission and a flattened Balmer decrement, points towards emission arising in a disc wind or vertically extended regions above the disc. Absorption features from a late-type secondary star (approximately K3) are detected, contributing roughly 30 per cent of the red optical flux. Comparison with main-sequence expectations suggests that the donor star is moderately inflated, consistent with a mildly evolved secondary. With its long orbital period, modest outburst amplitude, and emission-line characteristics, SRGA J115215.0$-$510656 appears to be a rare and compelling example of a bright, long-period dwarf nova whose optical properties are influenced by disc-wind processes during outburst.

The exact-sequence structure behind the Arnold--Douglas--Gupta family of higher-order mixed finite elements for plane elasticity on barycentric refinements is made explicit. On each macro triangle, the symmetric stress space is obtained by enriching polynomial stresses with three locally supported functions. We derive closed-form formulas for these enrichments and identify explicit Airy potentials that generate them. This leads to a concrete Hsieh--Clough--Tocher type $C^1$ potential space whose Airy image is exactly the Arnold--Douglas--Gupta stress space. By enforcing single-valued degrees of freedom, we obtain global spaces and a fully explicit finite element elasticity complex on simply connected domains. As a consequence, we construct a new family of $C^1$ finite elements on barycentric refinements, including quadratic, cubic, quartic, and higher-order elements.

Boolean networks are powerful mathematical tools for modeling the qualitative dynamics of genetic regulation. Yet inferred models often generate spurious attractors that lack biological viability. In this paper, we propose a parsimonious computational framework to systematically refine Boolean network models by eliminating these non-biological asymptotic behaviors while strictly preserving known, biologically relevant attractors. Through an exhaustive exploration of local function substitutions, we generate a comprehensive set of candidate models. To identify the most biologically consistent networks, we implement an incremental pruning protocol that filters candidates based on structural interaction digraph similarity, attraction basin topological organization, trajectorial isomorphism, and the minimization of dynamical instability and frustration. We apply this methodology to a 9-node genetic control model of the osteogenesis regulation network. Our protocol effectively evaluates a syntactic search space of 51,138 potential networks, ultimately narrowing them down to a robust family of 6 parsimonious models that are fully compatible with current biological knowledge.

In 2014, Michal Lewicki and Andrzej Olbryś proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\qquad x\leq y, \] called non-symmetrically $t$-affine, then it is $t$-affine. That is, they concluded that $f$ must fulfill the above equality without any restriction on $x$ and $y$. In the current study, first we show that the above conditional equation implies that the function in question is locally $t$-affine. Then we derive $t$-affinity on open intervals. Finally, we formulate our main result, which generalizes the theorem of Lewicki and Olbryś for any subinterval of $\mathbb{R}$.

In modern condensed matter theory, phases of electronic matter--such as metals and insulators-are fundamentally distinguished by the presence or absence of charge-carrying quasiparticles or excitations near the Fermi surface at low temperatures. Here, we show that this criterion breaks down in Berry-curvature-dominated systems, where transport is governed by interband coherence across the entire Fermi sea. We develop a microscopic theory of quantum transport in bulk topological insulators with a vanishing density of states at the Fermi energy, for which the conventional Drude contribution is absent. We demonstrate that impurity-scattering-induced coherence decay generates a distinct longitudinal transport channel even in the topologically trivial regime, with edge contributions rigorously excluded. This mechanism yields a finite longitudinal conductivity even in the absence of carriers at the Fermi level and exhibits an unconventional scaling linear in impurity density in the dilute limit, in stark contrast to Drude behaviour. Importantly, this decoherence-induced conductance is inversely proportional to temperature, reminiscent of strange-metal behaviour, most prominently observed in cuprate superconductors above their critical temperature. Our findings reveal quantum decoherence as a fundamental origin of longitudinal transport beyond the Drude paradigm, challenging the traditional distinction between metals and insulators.

This letter is presenting a simple but effective mechanism that explains why ,during tritium aging, metal tritides retain most helium-3 for years and then suddenly release massive amount. The mechanism is based on the hypothesis that dislocations blocking could explain the sudden change of behavior. The modeling of this phenomenon combine a mechanical and microstructural approach. The calculations made with this mechanism fit all the aging data acquired on aged palladium tritide

Detailed Computational Fluid Dynamics (CFD) simulations are too computationally expensive for the real-time control and design optimization of multiphase flow reactors. To address these limitations, we introduce CLARA, a software toolbox that automates the generation of Compartment Models (CM) via the unsupervised clustering of CFD data. Unlike previous studies, our toolbox enables the modelling of multiphase phenomena and interphase mass transfer within each compartment. CLARA employs unsupervised clustering algorithms, graph reassignment, and optimization routines to ensure mass conservation and spatial connectivity across all compartments. Verification studies utilizing analytical benchmarks and reactive multiphase CFD simulations demonstrate that the CMs produced by CLARA accurately reproduce reactor performance and spatial species distributions. The significantly reduced computational demand of CMs compared to full CFD models enables the optimal control of multiphase reactors and facilitates their rational design and optimization.

Be X-ray binaries (BeXRBs) are key laboratories to constrain binary interaction processes such as mass transfer, angular-momentum transport, and natal kicks. The Small Magellanic Cloud (SMC), hosting a nearly complete and well-characterized BeXRB population, offers a unique opportunity to test these physical processes at low metallicity. We aim to identify the combination of binary-evolution parameters that simultaneously reproduces the observed number and the joint distribution of orbital period and optical magnitude of SMC BeXRBs. We performed an extensive grid analysis of binary population-synthesis models exploring different mass transfer efficiencies, angular-momentum transport prescriptions and Roche-lobe overflow stability criteria. We also considered the impact of natal kicks, and that of the propeller effect of rotating magnetic fields of neutron stars. Synthetic populations obtained with the binary population synthesis code \textsc{sevn} are statistically compared to observations using likelihood-based methods applied to the orbital period and $V$-band magnitude distributions, together with requirements on the total number of systems. We find that models in which mass transfer via Roche-lobe overflow is assumed to be always stable and angular momentum is recycled back into the orbit through tides when the accretor approaches critical rotation provide the best match to observations. Our best-fitting models favor low natal kicks ($\lesssim 100\ \rm km\ s^{-1}$), a moderate mass transfer efficiency ($f_{\rm MT} \simeq 0.6$), a minimum Be threshold spin close to critical rotation, and a strong suppression of accretion onto neutron stars due to the propeller effect. Specifically, the observable population is highly sensitive to the treatment of the propeller effect, which regulates the X-ray luminosity of wide, low-accretion-rate systems.

The containment of malware in computing networks may be naturally formulated as a network influence minimisation problem, in which one seeks to limit the expected spread of an infection while balancing the operational cost of disabling network connections. Classical approaches often rely on Monte Carlo simulation of stochastic diffusion processes and greedy optimisation over candidate edge removals, resulting in significant computational overhead due to repeated influence evaluations. In this work, we propose a hybrid quantum approach which combines Quantum Amplitude Estimation (QAE) and Grover Minimum Finding (GMF) to provide quadratic improvements in both the estimation and optimisation components of the problem. Specifically, QAE replaces classical Monte Carlo simulation, reducing the sampling complexity of influence estimation from $O(1/\varepsilon^2)$ to $O(1/\varepsilon)$ for a target additive error $\varepsilon \ll 1$, while GMF reduces the number of candidate evaluations required to identify optimal edge removals from $O(|E_C|)$ to $O(\sqrt{|E_C|})$. We present a formal problem definition, describe the construction of the corresponding quantum oracles, and analyse the resulting complexity improvements under standard oracle assumptions. Preliminary experiments, including classical simulation of QAE and small-scale execution of Grover search on real quantum hardware, support the expected theoretical scaling. While practical implementation at scale requires fault-tolerant quantum devices, our results demonstrate that quantum algorithms offer a promising long-term direction for accelerating stochastic network optimisation problems such as malware containment.

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the classification of $\mathbb{Q}$-Gorenstein degenerations of $\mathbb{P}^3$ with canonical singularities. We prove that if a degenerating threefold has canonical singularities, then the moduli space is smooth at the corresponding pair. Consequently, we find some boundary divisors of the moduli of smooth hypersurfaces. Finally, using the double cover method, we derive some information on the moduli space of threefolds $X$ with canonical singularities with the same volume and geometric genus as a double cover of $\mathbb{P}^3$ branched over a hypersurface.

Using a fully gauge-invariant approach, we compute for the first time in the literature relativistic effects on the redshift drift up to second order in cosmological perturbation theory. This is achieved by employing a set of light-cone coordinates that simplify the description of light propagation in an inhomogeneous and anisotropic universe. We show that redshift-space distortion occurs only as a second-order effect whereas, as known, it is not present among the linear perturbations. We then derive analytical expressions of the bispectrum for the leading-order perturbative contributions on sub-Hubble scales, providing some numerical evaluations. Our finding is that, at low redshift and for large momenta, the non-linearities in the bispectrum are enhanced more than the squared power spectrum.

LTLf synthesis under partial observability requires reasoning about unobservable environment variables, which is typically handled by constructing a belief-state DFA via subset construction that universally quantifies these variables. Existing approaches perform this construction as a separate step prior to game solving, often generating belief states that are unnecessary in practice. We propose an on-the-fly approach to LTLf synthesis under partial observability based on observable progression. Our method incrementally builds the belief-state DFA by progressing the specification with respect to observable variables only, universally quantifying unobservable variables on the fly. We prove the correctness of the construction and show that it naturally enables on-the-fly game solving, leading to a fully on-the-fly synthesis framework. Our implementation leverages DFAs represented using Multi-Terminal Binary Decision Diagrams: a compact representation that has proven highly effective for LTLf synthesis under full observability. Experimental results demonstrate that our approach significantly outperforms existing methods and further highlight the practical benefits of integrating on-the-fly game solving with belief-state construction.

Training large language models requires jointly configuring two interdependent aspects of the system: the global batch size, which governs statistical efficiency, and the 3D parallelism strategy, which governs hardware throughput. Existing approaches make these decisions independently: optimization work adapts the batch size to track the evolving critical batch size while keeping parallelism fixed, and systems work selects the fastest parallelism for a given fixed batch size without anticipating that the optimal batch size could change. We show that these decisions are tightly coupled: the throughput-optimal parallelism strategy may shift as the global batch size changes, so any method that fixes one while adapting the other operates with a suboptimal configuration for part of the training run. We present COPUS, a system that adaptively tunes the global batch size, parallelism strategy, and micro-batch size as training evolves. COPUS is guided by Goodput, the product of throughput and statistical efficiency, which models both hardware and statistical effects jointly and directly measures useful convergence per unit of wall-clock time. The system combines online gradient noise scale estimation under 3D parallelism with throughput-aware evaluation of candidate configurations, and supports efficient reconfiguration of both batch size and parallelism during training. We evaluate COPUS on LLM pre-training workloads across 1-4 nodes of 8xH100 and 8xMI210 GPUs and model sizes from 3B to 32B parameters, demonstrating average time-to-convergence speedups of 3.9-8.0% over the fastest baseline across four configurations, with peak gains up to 11.1%, including system overheads.

The rapid evolution of software services poses substantial challenges to the design and implementation of effective recommendation systems. Traditional service recommendation approaches often rely on static representations and historical usage data, which are insufficient for adapting to the dynamic and evolving nature of service ecosystems. Recently, large language models (LLMs) have shown strong potential to overcome these limitations by leveraging rich contextual understanding. However, their practical use faces two major challenges: outdated service facts and invalid or redundant services. To address these issues, we propose EVOREC, an evolution-aware framework for service recommendation that leverages model editing in a locate-then-edit paradigm to incorporate updated service facts without costly retraining efficiently. This allows the model to remain aligned with evolving service ecosystems. To address invalid service issues, we introduce a Finite Automata (FA)-based constrained decoding mechanism with deduplication, which enforces structural and semantic validity while eliminating repeated services. Experiments on real-world service datasets demonstrate that our framework consistently outperforms existing baselines, e.g., achieving an average relative improvement of 25.9% in Recall@5. Moreover, under evolving service scenarios, our approach outperforms model fine-tuning approaches by 22.3%, demonstrating strong adaptability to service evolution and providing a practical solution for service recommendation in dynamic ecosystems

Surface confined electronic states provide a fertile ground for discovering emergent phenomena that have no counterpart in the bulk, offering new routes to manipulate correlations, symmetry breaking, and dimensionality at the atomic scale. Here, we show that charge density wave (CDW) symmetry breaking can yield a surface states in 1T-TiSe2. Micro angle resolved photoemission spectroscopy resolves a sharp, two dimensional surface resonant state (SRS) that emerges within the CDW reconstructed low energy spectrum. The SRS exhibits notable temperature dependence and its spectral weight collapses around 160 K, while CDW transition temperature TCDW is commonly reported as 202 K. Slab DFT+U calculations reproduce a surface localized resonance when CDW folding brings valence and conduction states into near degeneracy, suggesting a correlation tuned, surface selective origin. These results point to a form of correlation-tuned surface resonance in a layered CDW compound and suggest a framework for engineering low dimensional quantum states in van der Waals materials via symmetry breaking and electronic structure tuning.

The Euclid Wide Survey (EWS) will cover the majority of the extragalactic sky with a resolution similar to the Hubble Space Telescope. This unprecedented data set will introduce a new era of precision cosmology. However, systematic effects need to be controlled better than ever. One of the sources of systematic uncertainties in weak gravitational lensing are biases introduced during the shear measurement. Determining these biases precisely allows the calibration of cosmological measurements to within Euclid's required accuracy. The simulations that are used to determine such biases, need to resemble the real observations. In this work, we aim to learn distributions of galaxy shape parameters from real Euclid data and use the new information to augment the morphological information in the Flagship galaxy mock catalogue. The morphology is extracted using single and double-Sérsic model fits to the real data, for which we use SourceXtractor++. We train our pipeline on deep Euclid observations of a field with rich auxiliary data and then use it to simulate EWS-like data. In these simulations we compare the multiplicative bias between the morphology from the Flagship catalogue, the trained single-Sérsic morphology, and the trained double-Sérsic morphology. We find that the image simulations with the updated morphology result in a percent-level change in the multiplicative shear bias compared to the original morphology from Flagship. This bias exceeds Euclid's tight error budget by a factor of five and underlines the need for this work. Furthermore, we study the sensitivity of the multiplicative bias to key morphological parameters and show that our approach satisfies the requirements for the cosmology analysis with the first data release of Euclid.

With the rapid spread of generative AI services, the token has gained value not only as a technical unit of language processing but also as an economic currency for accessing AI services. Major AI model providers have adopted token-based billing as their default service model, requiring users to purchase platform-bound, fixed token usage rights. However, the fixedness of these usage rights is grounded in the billing-policy decisions of service providers rather than in any technical necessity. This study defines the Transferability of token usage rights as a design property that allows users to flexibly reallocate purchased data resources free from the constraints of time, account, and service. Drawing on the Design Space Analysis framework of MacLean et al. (1991), we identify five design axes (Target, Direction, Unit, Control, Reversibility) and five concrete Transferability types (carry-over, co-management, transfer, conversion, and trade) by analyzing the billing policies and terms of service of four major LLM services (ChatGPT, Claude, Gemini, Grok). Our analysis reframes the token from a purely economic-technical primitive into a core element of user-centered system design that expands user choice and autonomy.

This paper presents a model-free, data-driven control synthesis method called dynamic mode adaptive control (DMAC) for systems whose mathematical models are unavailable or unsuitable for classical control design. The proposed approach combines data-driven dynamics approximation with adaptive control synthesis to enable online controller design using measured system data. DMAC comprises two main components: a dynamics-approximation module and a controller-synthesis module. The dynamics approximation module estimates a local linear representation of the system dynamics directly from measurements using a matrix recursive least-squares algorithm with a forgetting factor. The estimated dynamics are then used to compute an online stabilizing controller with full-state feedback and integral action. Theoretical analysis establishes convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. The performance of the proposed method is demonstrated through numerical examples involving representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies further demonstrate the robustness of DMAC with respect to both algorithm hyperparameters and variations in system parameters.

Magnetic skyrmions are topologically protected spin textures that can act as reconfigurable nanoscale information carriers. In synthetic antiferromagnets (SAFs), interlayer exchange coupling offers an additional control parameter beyond the interfacial Dzyaloshinskii-Moriya interaction (DMI) and magnetic anisotropy. Here, we engineer a SAF composed of two chemically distinct ferromagnets (CoB and CoFeB), in which the external magnetic field and interlayer exchange act asymmetrically on the sublattices. The competition of these effects, acting as a resultant effective-field, gives rise to two distinct skyrmion families in different field regimes. In large fields, conventional-polarity skyrmions nucleate, with core antiparallel to the external field, whereas in smaller fields an inverse-polarity skyrmion state emerges as the effective-field reverses sign and almost saturates the CoFeB layers. Return-point memory measurements confirm independent nucleation pathways for the two families. Using element-resolved x-ray magnetometry, correlative magnetic force and Lorentz transmission electron microscopies, and parameter-matched micromagnetic modelling, we show that all textures reside only in the CoFeB layers, which experience a Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange field originating from the CoB layers. This effective-field method provides a robust route to programmable three-dimensional spin textures with controlled polarity in selected layers of a multilayer with potential for applications in skyrmion-based computing and spin-logic architectures.

LLM-as-a-judge approaches have emerged as a scalable solution for evaluating model behaviors, yet they rely on evaluation criteria often created by a single individual, embedding that person's assumptions, priorities, and interpretive lens. In practice, defining such criteria is a collaborative and contested process involving multiple stakeholders with different values, interpretations, and priorities; an aspect largely unsupported by existing tools. To examine this problem in depth, we present a formative study examining how stakeholders collaboratively create, negotiate, and refine evaluation criteria for LLM-as-a-judge systems. Our findings reveal challenges in human oversight, including difficulties in establishing shared understanding, aligning values across stakeholders with different expertise and priorities, and translating nuanced human judgments into criteria that are interpretable and actionable for LLM judges. Based on these insights, we developed MultEval, a system that supports collaborative criteria by enabling multiple evaluators to surface and diagnose disagreements using consensus-building theory, iteratively revise criteria with attached examples and proposal history, and maintain transparency over how judgments are encoded into an automated evaluator. We further report a case study in which a team of domain experts used MultEval to collaboratively author criteria, illustrating how coordination and collaborative consensus-making shape criteria evolution.

We consider a two-dimensional wave system containing a subwavelength hole, such as an aperture in an interface supporting surface electromagnetic or acoustic waves, or an island in a fluid surface sustaining gravity-capillary waves. Recent studies have revealed the emergence of pronounced wave vortices around such structures, termed type-II vortices, in contrast to conventional (type-I) vortices associated with phase singularities and intensity nulls. A striking natural manifestation of type-II vortices occurs in ocean tides around islands such as New Zealand, Madagascar, and Iceland, where the tidal phase increases by $\pm 2π$ around the island. Although this phenomenon is usually associated with the Coriolis effect from the rotation of the Earth, here we demonstrate the controlled generation of type-II vortices using a minimal and tunable setup: a dipole-oscillating subwavelength hole and a single incident plane wave. Using laboratory gravity-capillary waves and an oscillating subwavelength `island', we directly measure the resulting phase structure, topological charge, and wave angular momentum. We show that the emergence and handedness of the vortices can be precisely controlled via the relative phase between the dipolar source and the incident wave. Our results offer a simple and versatile mechanism for engineering subwavelength wave vortices, with potential applications in a variety of two-dimensional wave systems.

In the research of automated program repair (APR), benchmark datasets consisting of known defects in combination with test suites that indicate the defects are of high importance. They allow for an evidence-based comparison of different APR approaches. In our own work on APR we found significant challenges when working with widely used defect datasets, which go beyond mere repeatability of defects via test cases. We summarize these identified challenges and related lessons learned to bring them to the attention of the APR community and quantify the potential impact of them. In particular, we investigate the widely used benchmark Defects4J, which has according to Google Scholar over 1,800 citations. It consists of 835 defects from 17 open-source Java projects; a hand-curated collection of defects, test suites that clearly indicate the defect, and human patches where any unrelated changes are removed. We find that, when executing the test suites with strict requirements for reproducibility in APR settings (beyond merely reproducing the defect via test cases), 180 (21.6 %) of the defects are not suitable for evaluation experiments. Further, we find that an additional 59 (7.1 %) defects have test suites that are obviously under-specified, as deleting a single statement from the code base makes all test cases pass, although the human-written patch does not only delete code. Our contributions are: a systematic collection of requirements for defect datasets for APR beyond traditional reproducibility of defects, a description of practical experiences and quantitative analysis of problems with the Defects4J dataset, as well as an implementation of an evaluation framework for APR tools for Java programs. This evaluation framework does stricter checking for indications of inadequate test suites, to avoid otherwise unnoticed problems in the test suite, such as flaky tests.

Understanding how software defects manifest and evolve in production environments is critical for improving reliability. While previous research has largely focused on pre-release defects, the nature of residual faults, i.e., those escaping testing and surfacing post-release, remains poorly understood. This paper presents a large-scale characterization of pre- and post-release defects across C/C++ and Java systems, encompassing over 14k defects mined from open-source projects. We employ a broad suite of software metrics to capture diverse code attributes such as complexity, size, structure, and development history. Results show that post-release defects are concentrated in older, frequently modified, and high-churn components, typically requiring longer and more complex fixes than pre-release ones. These findings highlight that residual defects arise more from evolutionary and process dynamics than code structure alone, suggesting that reliability engineering should prioritize targeted testing in mature and complex code regions.

Microservice root cause localization is fundamentally challenged by the inherent heterogeneity of cloud-native systems, which encompasses diverse observability data and multiple system entities. Existing approaches typically focus on only one aspect of heterogeneity and thus fail to capture its full diagnostic value. In this work, we systematically examine the multifaceted role of heterogeneity within both microservice systems and the RCL process. This analysis motivates a deeper investigation into how entity-level distinctions and their asymmetric dependencies influence fault behavior. Our empirical analysis of two microservice benchmarks reveals that entity-level heterogeneity naturally gives rise to heterogeneous fault propagation, which is highly asymmetric and dominated by cross-layer interactions between services and hosts. In light of this, we propose NexusRCL, a semi-supervised framework that internalizes these propagation patterns by formalizing services and hosts as distinct node types within a heterogeneous graph. This design, coupled with an event-based abstraction mechanism, allows NexusRCL to effectively capture both data level and entity-level heterogeneity while minimizing labeling costs through active learning. Comprehensive evaluations on two industrial benchmark datasets demonstrate NexusRCL's superior performance, achieving improvements of up to 49.85\% in Top-1 accuracy (A@1) and 32.70\% in Average Top-5 accuracy (A@5) compared to state-of-the-art methods.

Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems involve nonlinear relationships among variables. In this paper, we address probabilistic forecast reconciliation with nonlinear constraints for the first time. We extend both reconciliation via projection and conditioning to the case of nonlinear constraints. The projection approach reconciles forecast samples by mapping them onto the nonlinear coherent manifold. The conditioning approach adopts a sampling algorithm inspired to the Unscented Kalman Filter (UKF). We evaluate both methods on synthetic and real datasets. Empirically, both reconciliation approaches generally improve forecast accuracy. The UKF-based approach achieves the best overall performance while being substantially faster than the projection one.