We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation procedures for this model are typically based on likelihood methods or monotone-loss robust M-estimators. They may be highly sensitive to vertical outliers, leverage points in the functional predictor, and numerical instability induced by strong spatial dependence. To address these issues, we propose a new estimation framework that first applies robust functional principal component analysis to obtain a contamination-resistant finite-dimensional representation of the functional predictor and then estimates the resulting spatial regression model through a bias-corrected system of M-estimating equations. The proposed method allows redescending loss functions, including Andrews' sine and Danish losses, and jointly estimates the regression coefficients, spatial dependence parameter, and scale parameter within a unified Fisher-consistent framework. For computation, we develop a hybrid IRLS-Newton algorithm that combines weighted least-squares updates for the regression parameters with a Newton-Raphson update for the spatial parameter. We establish Fisher consistency, consistency, asymptotic normality, and the asymptotic distribution of the reconstructed slope function. Monte Carlo experiments show that the proposed estimators remain competitive under clean data and substantially outperform classical and Huber-type robust competitors under contamination, particularly in severe outlier settings. An application to French air-quality data further demonstrates improved predictive performance and stable estimation of spatial dependence. Our method has been implemented in the fcsar R package.

Given a symmetrizable Kac-Moody algebra $\mathfrack{g}$, we study its $π$-systems, which are subsets of real roots, the pairwise differences of whose elements are not roots. Such systems arise as simple systems of regular subalgebras of $\mathfrack{g}$, and were originally studied by Dynkin, Morita and Naito. We show that the binary relation introduced by Morita defines a partial order on the set of $\mathfrack{g}$ of finite, untwisted affine or hyperbolic type. We also formulate general principles for constructing $π$-systems as well as for finding forbidden diagrams that cannot occur as Dynkin diagrams of $π$-systems of a given $\mathfrack{g}$. Among other applications, we use this to determine the set of maximal hyperbolic Dynkin diagrams in ranks $3$-$10$ relative to the Morita partial order.

While vertical GaN-on-silicon architectures promise a transformative leap in cost-effective power electronics and high-resolution micro-LEDs, their deployment remains bottlenecked by the high electrical resistance of conventional epitaxial buffer layers. Here, a universal and straightforward sputtering-based strategy is presented to realize high quality GaN epitaxial films on Si(111) substrates characterized by exceptionally low vertical resistance, ohmic behavior, and robust thermal stability. This technique centers on the in-situ formation of a sub nanometer (0.5 nm) silicide-based template via rapid thermal annealing method demonstrating unprecedented versatility across 25 different metallic species. Scanning transmission electron microscopy (STEM) reveals that a unique amorphous like interlayer (AL-IL) effectively accommodates lattice mismatch and relaxes epitaxial strain. These AL-IL templates further serve as high performance platforms for metalorganic chemical vapor deposition (MOCVD) overgrowth, successfully bridging the gap between scalable, low-cost fabrication and device-grade vertical performance.

This paper explores the dimension theory of non-Noetherian graded rings by introducing the class of Hilbert-Serre rings. We generalize Krull's dimension theorem and Smoke's dimension theorem by establishing the fundamental inequalities $\dim(R) \le \operatorname{GKdim}_k(R) \le d(R)$ for any Hilbert-Serre ring $R$, where $d(R)$ is the pole order of its Poincaré series at $t=1$. Furthermore, we apply these results to initial algebras, proving that all these dimensions, including the transcendence degree, coincide for monomial algebras. Finally, we provide explicit examples demonstrating that these inequalities can be strict in general, even for integral domains.

We carry the deadline-resolved Information Leakage Score (ILS-dl) framework of Nechepurenko (2026a, 2026b) from a single-case proof of concept to a population-scale evaluation across 12,708 Polymarket markets, October 2020 to April 2026. We frame the paper as a scope-discovery study: scaling reveals that the framework's effective domain is materially narrower than initial framing suggested, and the principal obstacle is not score computation but resolution semantics. We report four findings. First, only 88 of 12,708 candidate markets (0.7%) yield computable ILS-dl values; only 1 of 32 markets in the ForesightFlow Insider Cases (FFIC) inventory is in scope, and 14 of 32 FFIC markets are flagged unclassifiable due to genuine resolution-criterion ambiguity. Second, only 12 of the 88 computed markets (13.6%) satisfy anchor-sensitivity, and an independent-second-pass T_event validation reaches 57.8% exact-date agreement, below the 90% ex-ante criterion. Third, raw ILS-dl medians are negative across all six (sub-bucket by period) cells, but a hazard-decay baseline correction we introduce yields a heterogeneous result: regulatory_formal post-2024 shifts to near-zero (-0.21 to -0.02), while regulatory_announcement post-2024 retains a 95% bootstrap CI entirely below zero. Fourth, the constant-hazard exponential of Nechepurenko (2026b) is rejected in favor of Weibull on the pooled post-2024 cell, but a per-subcategory check confirms the preference reflects category mixture rather than within-cell duration dependence. The implication is that detection of informed flow requires methodological refinement on the resolution-typology and score-baseline axes, not only on the score-computation axis where prior work concentrated.

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization of the Caputo memory term and the nonlocal fractional Laplacian by Monte Carlo simulation of the associated fractional dynamics. Each Picard update is approximated by stochastic label generation and realized through supervised neural-network regression, thereby avoiding residual minimization involving fractional differential operators. The fractional trajectories are generated by coupling a discretized beta-stable subordinator with a walk-on-spheres-type simulation of the rotationally symmetric alpha-stable Lévy process. Numerical experiments on two-dimensional and high-dimensional test problems ddemonstrate stable Picard convergence and accurate approximation, with tests reported up to dimension d=100.

Predictive Bayesian inference (PBI) represents a model-and prior-agnostic approach to standard Bayesian inference which allows users to quantify uncertainty for a functional of interest only by specifying a forward predictive model for future unobserved data. The flexibility and generality of this framework have led to a host of novel algorithms for implementing this approach, and many empirical applications, yet the reliability of the resulting inferences for the underlying statistical functional of interest remains unclear. Herein, we demonstrate that when using PBI for a population functional of interest, the resulting posterior concentrates onto a well-defined quantity that explicitly depends on the forward predictive model used to implement the predictive recursion underlying the method. Furthermore, the forward predictive model entirely determines the uncertainty quantification produced in PBI. Consequently, our results show that if the predictive model does not capture all relevant features of the data, and, even in very simple examples, the coverage of predictive Bayes credible sets for the population value of the functional of interest can be arbitrarily close to zero. We carefully explain why this occurs, and show that this behavior is directly tied to the inaccuracy of the forward predictive model used to produce future observations within the PBI framework. As a consequence, our results imply that in order for PBI to deliver calibrated posterior inferences, the resulting predictive engine used to generate posterior samples must contain, in a well-defined sense, the true DGP, else inferences generated under this framework will not be calibrated.

We study exclusive vector meson production in ultra-peripheral collisions (UPCs) of a wide range of nuclei, and assess the potential of measurements to constrain the small-$x$ structure of oxygen and neon nuclei. We employ an impact-parameter-dependent color glass condensate framework incorporating JIMWLK evolution, with parameters constrained by a recent global Bayesian analysis of $γ+p$ and $γ+\mathrm{Pb}$ data. We present predictions for coherent and incoherent $\mathrm{J}/ψ$ production in $\mathrm{O}+\mathrm{O}$ and $\mathrm{Ne}+\mathrm{Ne}$ UPCs at LHC energies, and quantify theoretical uncertainties using posterior samples from the calibration. We employ several nuclear structure models and find that $t$-differential observables are sensitive to the chosen model. We further study the mass-number dependence of saturation effects through nuclear suppression factors for coherent and incoherent vector meson production. Saturation-induced suppression increases systematically with both nuclear mass number and energy. Our results provide a unified framework for the systematic study of the onset of gluon saturation and nuclear structure at high energy, accessible in future UPC measurements at the LHC and at the Electron-Ion Collider.

Urban to rural migration is a less-researched phenomenon compared to its counterpart: rural to urban migration. In parts of Europe, an increasing number of people living in big urban centers within the country, or moving from other countries decide to relocate to rural areas. In this paper, we examine this phenomenon by analysing content posted on TikTok that documents this transition. We collected a corpus of 901 videos posted until late 2025, documenting urban to rural migration in Romania, under three hashtags, which have collectively been played a total of 24 million times at the time when we gathered the dataset. We analyse this corpus both quantitatively and qualitatively and discuss our findings through the lens of digital rurality - a theory based on Harvey's and Soja's spatial triad, applied to rural spaces, and based on the role of digital technologies as (re-)mediators of everyday lived experience. Specifically, we analyze the corpus as: (a) digital rural localities, (b) formal representations of the digital rural, and (c) everyday lives of the digital rural. We find that (a) Social media platforms enable new forms of paid labor that sometimes involve the commodification of the self in rural areas, although many of the creators we analyze do not explicitly acknowledge this with their audiences. (b) The digital rural gains new forms of representation, and rural areas in remote Romania are highly data-rich across TikTok. (c) The everyday lives represented through the digital rural are sometimes idealized or romanticised. However, they serve as promoters for tourism and are used as sites to document and discuss a variety of topics including giving ample health advice, typically by non-specialists and sometimes criticizing Western medicine, expressing and promoting religious and political views but also acting as forms of general self-expression.

This work establishes rigorous mathematical foundations connecting spectral graph theory, algebraic geometry, and string theory. We construct a canonical mapping whereby any finite graph \(G\) defines a compact Riemann surface \(X_{G}\) (the spectral curve) whose period matrix \(Ω_{G}\) encodes the graph's coarse-grained spectral information. We demonstrate that in the continuum limit of graph sequences converging to Riemannian manifolds, these spectral curves converge in the Deligne-Mumford compactification sense to the classical stable curves associated with the manifold. We establish connections to the topological recursion framework of Eynard-Orantin, showing that under appropriate conditions the spectral curve satisfies the loop equations of multi-cut matrix models. The spectral memory field \(Φ_{G}(u)\) is introduced and shown to provide a discrete regularization of minimal string partition functions. We construct quantum scattering operators on spectral curves and prove that their unitarity is equivalent to a positivity condition on the spectral memory field. Furthermore, we apply this framework to resolve spacelike singularities in general relativity, proving that the Belinski-Khalatnikov-Lifshitz (BKL) chaotic regime is isospectral to a critical random graph ensemble. The classical singularity is replaced by an infinite nodal chain of rational curves, and the Bekenstein-Hawking entropy emerges from the automorphism group of the spectral curve. This work provides rigorous mathematical underpinnings for discrete approaches to quantum gravity and establishes new connections between graph theory, algebraic geometry, and theoretical physics.

Detailed-balance limits for transition-metal dichalcogenide (TMD) solar cells have been reported, but existing TMD-specific limits do not simultaneously resolve thickness-dependent optics, carrier multiplication (CM), hot-carrier (HC) extraction, and finite cooling leakage. Here, we develop a generalized detailed-balance theory that provides an upper-bound framework. The model combines energy- and thickness-dependent absorptance a(E,d), exciton-resolved monolayer absorbance, an experimentally available CM quantum-yield limit (eta_CM <= 0.97), and an endoreversible HC engine with ideal energy-selective contacts and finite heat-leak coefficient kappa. The framework shows that CM and HC draw on the same above-gap photon-energy reservoir; therefore, CM does not raise the reversible HC thermodynamic limit. Instead, CM can protect finite-kappa performance only by shifting excess-energy utilization from a cooling-sensitive voltage channel into collected current. For optically thick TMDs under AM1.5G illumination, the SQ optimum lies near E_g = 1.3 eV, whereas the CM/HC-favored envelope shifts toward E_g = 1.0 eV with reversible efficiencies above 50%. For monolayer TMDs such as WSe2 (E_g = 1.63 eV), CM is essentially inactive because only about 3.7% of above-gap AM1.5G photons satisfy E > 2E_g, giving an idealized short-circuit-current gain of only about 0.6% before device nonidealities. Bulk-like TMDs can show large HC-related gains at d = 10-50 nm, but even kappa = 0.2 W m^-2 K^-1 implies about 100 W m^-2 heat leak for Delta T = 500 K. Thus, high-E_g monolayer TMDs are not promising one-sun CM candidates, whereas narrow-E_g, bulk-like TMD absorbers remain plausible beyond-SQ candidates only if energy-selective extraction and phonon-engineered cooling suppression are realized together.

The large-scale clustering of galaxies encodes both geometric and dynamical information about the Universe. The Baryon Acoustic Oscillations (BAO) phenomenon provides a standard ruler that constrains the cosmic expansion history, while Redshift Space Distortions (RSD) probe the growth of structure through the peculiar velocity field. In this work, we present a joint analysis of BAO and growth rate parameter, $fσ_{8}$, in the Local Universe out to $z = 0.1$, using the $65,331$ galaxy distances of CosmicFlows-4++ database. A distinctive property of this catalogue is the availability of real space galaxy positions in addition to the redshift space coordinates. Fitting an empirical model to the measurements we obtain $r_{\rm{BAO}}^{\rm{real}} = 132\pm 8\,h^{-1}\,{\rm Mpc}$ in real space, and $r_{\rm{BAO}}^{z} = 139 \pm 7\,h^{-1}\,{\rm Mpc}$ in redshift space, at redshift $z = 0.07$. Modeling the enhancement of the correlation function within the Kaiser formalism, we derive a constraint on the growth rate parameter $fσ_8 = 0.344 \pm 0.105$. This analysis demonstrates how the combination of real and redshift space clustering measurements enables a simultaneous probe of important observables of the large-scale structure. Their joint detection in the same dataset, therefore, provides a self consistent view of the structure and evolution of the Local Universe. This study may be used for consistency analyses of upcoming surveys, as DESI and 4MOST, that will also provide data in both real and redshift space.

Linking issue reports to the commits that resolve them is essential for software traceability, maintenance, and evolution. Accurate issue-commit links help developers to understand system changes and the rationale behind them. While numerous automated techniques have been proposed, ranging from heuristic and feature-based approaches to modern deep learning and large language model approaches, our goal is to evaluate these techniques to determine which are most effective and efficient. In this study, we revisit several established issue-commit link recovery techniques, including BTLink, EasyLink, FRLink, RCLinker, and Hybrid-Linker, and assess their performance for reranking issue-commit links. We first evaluate different retrieval methods (BM25, BM25L, SBERT-Semantic Search, ANNOY, LSH, HNSW) for their ability to efficiently retrieve relevant commits, reducing the candidate set that must be considered by more computationally expensive models. Using the best retrieval methods, we then investigate the reranking effectiveness of different machine learning-based techniques, including traditional machine learning models, a cross-encoder, and large language models (ChatGPT, Qwen, Gemma, Llama), to refine the reranking of candidate commits and improve precision. Finally, we compare the effectiveness of these techniques. Our results show that dense retrieval methods outperform sparse retrieval approaches in identifying relevant commits and that combining dense and sparse retrieval can improve recall. Additionally, we find that traditional machine learning-based reranking techniques achieve higher performance than LLM-based approaches. Our results highlight that retrieval-based pipelines remain a practical and effective solution for large-scale issue-commit linking, and that simpler models should be carefully considered before adopting computationally expensive LLM-based approaches.

Quantum-memory models often reduce complex level structures to an idealized $Λ$ system, potentially missing nearby levels and unwanted couplings that can qualitatively alter the predicted performance. Here, we study an extension of a cavity-based $Λ$-type ensemble memory, a four-level model with unwanted couplings from both the control field and signal, using a fully quantum treatment. We derive explicit expressions for the single-photon storage efficiency, retrieval efficiency, and fidelity, and on this basis identify three distinct dynamical regimes: stable, threshold, and unstable. Within the stable regime, we additionally discriminate between two qualitatively different sub-regimes. Applying the theory to warm-vapor-inspired parameters, we determine the conditions under which the system can still operate as a high-quality quantum memory. More generally, our results provide a practical framework for distinguishing genuine memory operation from amplification and for optimizing realistic quantum memories beyond idealized models.

In this work, we construct a novel two-dimensional discrete neuron map by incorporating a cosine-based memristor into the reduced Chialvo neuron map to examine the dynamical analysis of electromagnetic modulation. The nonlinear current-voltage characteristics of the memristor enrich the neuron map's behavior, leading to diverse firing regimes, stability behaviors, and chaotic attractors. This study begins to establish the equilibrium points using both analytical and numerical methods. Additionally, we determine the conditions on parameters under which the proposed map exhibits a Neimark-Sacker bifurcation. Further, the numerical study reveals the antimonotonicity structure through the forward and backward bifurcation diagrams. The model exhibits a wide range of codimension-one and codimension-two bifurcation patterns, including Neimark-Sacker, period-doubling, saddle-node, generalized period-doubling, cusp-point, fold-flip, and various resonance structures (1:1, 1:2, 1:3, and 1:4). We also observe that the coexistence of multistable attractors including a stable limit cycle, a period-five attractor, and a chaotic attractor, along with their respective basins of attraction. Furthermore, we extend this analysis to the network of neurons under the ring-star configuration and discuss several spatiotemporal patterns. This network investigation reveals complex collective patterns, including imperfect synchronization, clustered patterns, and multi-chimera state phenomena, which have not been previously observed in existing Chialvo-based studies. These results highlight the potential of the discrete memristor-based neuron map for advancing theoretical neurodynamics and offer a robust framework for investigating low-dimensional yet dynamically rich neuron systems.

We develop a thermodynamic description of accumulation-layer heterostructures in which the induced sheet density is partitioned between the near-interface accumulation-layer charge and a complementary screening charge in the surrounding structure. Treating this partition as the central state variable yields a complete Helmholtz free energy, a corrected locked-branch chemical potential, and a shifted release potential that separates energetic path selection from geometric capacitance. The physical path is selected spectrally: compressible segments remain fully screened, whereas incompressible segments evolve along a locked branch until release is triggered by the relevant gap. Differential capacitance, tunnel current and plateau width then emerge as different projections of the same coupled thermodynamic structure. A canonical two-stage self-consistent Poisson--Schrödinger reduction supplies universal master functions for the isolated accumulation layer and master surfaces for its finite-buffer extension, making the theory calculable across density and geometry. Comparison with magnetocapacitance and magnetotunneling data supports a picture in which nearby extended charge refills the accumulation layer and the effective screening depth grows with magnetic field.

We investigate constraints on the high-density equation of state (EOS) of neutron star matter by analyzing the probability distributions of the endpoints of mass-radius M(R) sequences within a Bayesian weighting framework. Starting from two representative hadronic baseline EOSs, SFHo and DD2, matched at higher densities to an extended linear sigma model description and constrained to approach perturbative QCD (pQCD) results, we construct families of causal hybrid EOSs spanning a broad range of stiffness at supranuclear densities. Observational constraints from the binary neutron-star merger GW170817, mass-radius measurements from the Neutron Star Interior Composition Explorer (NICER), and candidate low-mass and mass-gap compact objects are incorporated through Bayesian likelihood weighting. This approach allows us to determine probability distributions for the maximum neutron-star mass M$_{\rm TOV}$ and the corresponding radius R$_{\rm TOV}$, i.e., the endpoints of the M(R) sequences. We find that the maximum-mass distributions are largely determined by observational constraints and show only weak sensitivity to the choice of baseline EOS, favoring values around 2.2-2.3 M$_\odot$ when the most robust constraints are applied. In contrast, the corresponding radius distributions exhibit a stronger dependence on the underlying hadronic EOS, with typical preferred values near $12\pm 1$ km. Additional tidal-deformability constraints further restrict the allowed parameter space and disfavor very stiff EOS realizations when interpreted together with the possible mass-gap neutron-star candidate. Our results demonstrate that endpoint distributions of M(R) sequences provide a sensitive and complementary diagnostic for constraining the high-density behavior of the neutron-star EOS within a multimessenger Bayesian framework.

In a spin-1 hadron, tensor-polarized parton distribution functions (PDFs) exist. The twist-2 function is $f_{1LL}$ and a twist-3 one is $f_{LT}$. Because an experiment is under preparation at the Thomas Jefferson National Accelerator Facility (JLab) to measure the cross section of electron-deuteron deep inelastic scattering with the tensor-polarized deuteron target, these PDFs need to be understood theoretically. Especially, measurements will be done in a relatively low-$Q^2$ region at JLab, so that twist-3 contributions could become sizable in the cross section. In a previous work, a twist-2 relation was derived for $f_{LT}$ in terms of $f_{1LL}$ by using a nonlocal operator, and it corresponds to the Wandzura-Wilczek (WW) relation between $g_1$ and $g_2$. In addition, another relation similar to the Burkhardt-Cottingham (BC) sum rule was obtained. It is known that a formal way to derive the WW relation and the BC sum rule is to use the operator product expansion (OPE) with local operators. In this work, the WW-like relation and the BC-like sum rule for $f_{LT}$ are derived by using the local OPE method as a reliable independent way to establish these relations.

Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs. Its iterative Voronoi sweep for interference detection leads to redundant predicate evaluations and scales poorly on rotationally symmetric structures (e.g., spheres, cones or cylinders), where candidate counts grow quadratically. We propose P2M++ to address these limitations through three key contributions. First, we adaptively augment the set of mesh vertices with auxiliary sites in regions of high Voronoi vertex density to localize complex interference within minimal spatial regions. Second, we reformulate interference detection as a series of sphere-triangle collision tests centered at Voronoi cell corners, which are efficiently resolved using the base mesh's BVH. Finally, we enhance runtime performance by replacing the standard kd-tree search with a faster recursive dynamic programming implementation. Experimental results demonstrate that P2M++ is 3x-10x faster than the original P2M during preprocessing and 1.5x faster in queries, with even more pronounced gains on rotationally symmetric geometries.

Strong experimental papers in electrical and computer engineering and computer science (ECE/CS), especially in systems, networking, and applied machine learning, rest on more than a single impressive number. They rest on a chain of design, measurement, analysis, and validation choices that, taken together, make a result believable. This tutorial is a compact, example-driven guide to that chain for beginning researchers. We organize it as an evaluation workflow: claim, hypothesis, unit of analysis, baseline, regime sweep, uncertainty estimate, validation check, and reporting. Within that workflow we cover the classical statistical foundations (descriptive statistics, the central limit theorem, normal- and $t$-based confidence intervals, Student's $t$-test, ANOVA, chi-squared and Pearson correlation, linear regression) alongside the modern, distribution-free techniques (the bootstrap, Wilcoxon and Mann--Whitney tests, Cliff's delta) that are usually preferred for ECE/CS data. We also discuss factorial design, randomization and blocking, multiple-comparison correction, latency-specific pitfalls, simulation verification and validation, equivalence-style claims, and reproducibility. A running example, a comparison of two job-scheduling algorithms on simulated workloads with truncated heavy-tailed job sizes, threads through the tutorial, with Python snippets the reader can paste and adapt. The paper closes with a pre-submission checklist; companion student-facing material (project-type translation tables, an evaluation-plan worksheet, exercises, and a worked ``bad evaluation autopsy'') is collected in a separate workbook released alongside this paper.

Understanding HPC facilities users' behaviors and how computational resources are requested and utilized is not only crucial for the cluster productivity but also essential for designing and constructing future exascale HPC systems. This paper tackles Challenge 4, 'Analyzing Resource Utilization and User Behavior on Titan Supercomputer', of the 2021 Smoky Mountains Conference Data Challenge. Specifically, we dig deeper inside the records of Titan to discover patterns and extract relationships. This paper explores the workload distribution and usage patterns from resource manager system logs, GPU traces, and scientific areas information collected from the Titan supercomputer. Furthermore, we want to know how resource utilization and user behaviors change over time. Using data science methods, such as correlations, clustering, or neural networks, our findings allow us to investigate how projects, jobs, nodes, GPUs and memory are related. We provide insights about seasonality usage of resources and a predictive model for forecasting utilization of Titan Supercomputer. In addition, the described methodology can be easily adopted in other HPC clusters.

For each $i \geq 0$, we study the trace ideal of the $i$-th exterior power of the module of differentials. We show that these ideals characterize the polynomial rank of graded rings and the formal power series rank of complete local rings, namely the maximal number of variables for a polynomial or formal power series extension over a subring. For the top exterior power, we introduce the top differential trace and prove that it precisely defines the singular locus of reduced equidimensional local or graded rings. Motivated by this, we introduce and investigate nearly regular rings, which are Noetherian rings whose top differential trace contains the maximal ideal.

The paper analyzes and characterizes the algebraic and logical structure of the multiset semantics for SPARQL patterns involving AND, UNION, FILTER, EXCEPT, and SELECT. To do this, we align SPARQL with two well-established query languages: Datalog and Relational Algebra. Specifically, we study (i) a version of non-recursive Datalog with safe negation extended to support multisets, and (ii) a multiset relational algebra comprising projection, selection, natural join, arithmetic union, and except. We prove that these three formalisms are expressively equivalent under multiset semantics.

The anomalous behavior of liquid water is widely associated with a liquid-liquid phase transition between high- and low-density states in the supercooled regime. At the microscopic level, tetrahedral hydrogen-bond networks govern these properties, motivating structural descriptors that characterize local molecular environments. These structural descriptors quantify features such as tetrahedral order, local density, and the separation between the first and second coordination shells; however, they have largely been proposed independently, with limited systematic comparison. Here we evaluate 16 previously proposed descriptors using a neural-network-based temperature classification framework, enabling an objective assessment of their ability to distinguish temperature-dependent structural changes in supercooled water. We further apply an explainable artificial intelligence method that identifies the structural features responsible for the model predictions. This approach reveals how different descriptors encode local structural information and establishes a data-driven framework for benchmarking structural descriptors in liquid water.

Ensuring the reliability of the Rust compiler is of paramount importance, given increasing adoption of Rust for critical systems development, due to its emphasis on memory and thread safety. However, generating valid test programs for the Rust compiler poses significant challenges, given Rust's complex syntax and strict requirements. With the growing popularity of large language models (LLMs), much research in software testing has explored using LLMs to generate test cases. Still, directly using LLMs to generate Rust programs often results in a large number of invalid test cases. Existing studies have indicated that test cases triggering historical compiler bugs can assist in software testing. Our investigation into Rust compiler bug issues supports this observation. Inspired by existing work and our empirical research, we introduce a bracket-based masking and filling strategy called clozeMask. The clozeMask strategy involves extracting test code from historical issue reports, identifying and masking code snippets with specific structures, and using an LLM to fill in the masked portions for synthesizing new test programs. This approach harnesses the generative capabilities of LLMs while retaining the ability to trigger Rust compiler bugs. It enables comprehensive testing of the compiler's behavior, particularly exploring edge cases. We implemented our approach as a prototype CLOZEMASTER. CLOZEMASTER has identified 27 confirmed bugs for rustc and mrustc, of which 10 have been fixed by developers. Furthermore, our experimental results indicate that CLOZEMASTER outperforms existing fuzzers in terms of code coverage and effectiveness.

Budget-feasible procurement auctions play a pivotal role in various AI-driven marketplaces, such as data acquisition and crowdsourcing, where a buyer with a limited budget seeks to procure services from strategic sellers with private costs. While numerous budget-feasible mechanisms have been proposed for the classic objective of maximizing the buyer's valuation, the more challenging and economically significant objective of social welfare maximization has only recently been studied, and existing approaches still sacrifice budget feasibility, thereby limiting their practical applicability. In this paper, we bridge this gap by proposing BFM-SWM, the first budget-feasible mechanism with provable approximation guarantees for submodular welfare maximization in procurement auctions. Our mechanism satisfies standard economic properties, including truthfulness, individual rationality, and non-negative auctioneer surplus. As a by-product, we develop BFM-VM, a variant tailored for valuation maximization, which achieves a deterministic approximation ratio of $1/(12+4\sqrt{3})$ for general submodular functions, substantially improving upon the best-known deterministic ratio of $1/64$ established by [Balkanski et al., SODA 2022], while reducing the running time from $\mathcal{O}(n^2\log n)$ to $\mathcal{O}(n\log n)$. Extensive experiments demonstrate the efficiency and effectiveness of our mechanisms.

We propose a numerical procedure to solve an inverse problem that estimates the state of a magma reservoir from observed surface displacement of a volcano. Our variational approach aims to find the minimizer of a cost function consisting of a norm concerning both data and derivative, which evaluates the misfit between the estimated and observed displacement. The extremal of the cost function leads to a linear system, to find the stress distribution on the reservoir surface, has very high condition number, but it is feasible to get appropriate solution by using high precision arithmetic.

We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and square-integrable, and which, in finite time, transition to $C^{1-μ}$ regularity for $μ\in [1/2,1)$ near the boundary, leading to the gradient blowup at the boundary. It is based on stability analysis of self-similar waiting time solutions \cite{JLN2025} recently constructed by the authors.

Selection artefacts are common in science. A method of selecting samples from a larger population may produce bias, in either direction. It may induce correlations between variables independent in the full population, or mask correlations between variables dependent in the full population. Here we propose a surprising application of these familiar ideas. We argue that they are relevant to puzzling correlations uncovered in quantum theory by John Stewart Bell (Bell 1964). In the light of Bell's work and subsequent experiments it is widely believed that the quantum world is 'nonlocal', in apparent tension with relativity. Many hold that the only alternative is to abandon 'realism', the view that there is an objective world independent of measurement. We propose instead that Bell correlations are selection artefacts, in tension neither with relativity nor realism.

Recent advances in precise phasor measurement units are enabling new approaches to estimate distribution and transmission grid parameters in real-time. In this paper, we investigate voltage and current phasor measurement requirements to estimate the electric grid topology and admittance parameters. We show necessary and sufficient conditions for the number of independent operating points (measurements) required to determine the topology and admittance of a completely unknown electric grid. With prior topology information, we also show that there is a minimum number of measurements required to uniquely determine the admittance matrix and corresponding grid topology. In the presence of noisy phasor measurements, we show that the admittance matrix can be estimated using a structured total least squares approach. By means of numerical simulations on the IEEE 13-node distribution feeder, the IEEE 14-node transmission network, and the IEEE 123-node distribution feeder, we demonstrate our approach is suitable for applications in radial and mesh grid topologies in the presence of measurement noise.