Complex real-world optimization problems often involve both discrete decisions and nonlinear relationships between variables. Many such problems can be modeled as polynomial-objective integer programs, encompassing cases with quadratic and higher-degree variable interactions. Nonlinearity makes them more challenging than their linear counterparts. In this paper, we propose a hypergraph neural network (HNN) based method to solve polynomial-objective integer programming (POIP). Besides presenting a high-degree-term-aware hypergraph representation to capture both high-degree information and variable-constraint interdependencies, we also propose a hypergraph neural network, which integrates convolution between variables and high-degree terms alongside convolution between variables and constraints, to predict solution values. Finally, a search process initialized from the predicted solutions is performed to further refine the results. Comprehensive experiments across a range of benchmarks demonstrate that our method consistently outperforms both existing learning-based approaches and state-of-the-art solvers, delivering superior solution quality with favorable efficiency. Note that our experiments involve both polynomial objectives and constraints, demonstrating our HNN's versatility for general POIP problems and highlighting its advancement over the existing literature.

Legal Judgment Prediction (LJP) predicts applicable law articles, charges, and penalty terms from case facts. Beyond accuracy, LJP calls for intrinsically interpretable and legally grounded reasoning that can reconcile statutory rules with precedent-informed standards. However, existing methods often behave as static, one-shot predictors, providing limited procedural support for verifiable reasoning and little capability to adapt as jurisprudential practice evolves. We propose VERDICT, a self-refining collaborative multi-agent framework that simulates a virtual collegial panel. VERDICT assigns specialized agents to complementary roles (e.g., fact structuring, legal retrieval, opinion drafting, and supervisory verification) and coordinates them in a traceable draft--verify--revise workflow with explicit Pass/Reject feedback, producing verifiable reasoning traces and revision rationales. To capture evolving case experience, we further introduce a Hybrid Jurisprudential Memory (HJM) grounded in the Micro-Directive Paradigm, which stores precedent standards and continually distills validated multi-agent verification trajectories into updated Micro-Directives for continual learning across cases. We evaluate VERDICT on CAIL2018 and a newly constructed CJO2025 dataset with a strict future time-split for temporal generalization. VERDICT achieves state-of-the-art performance on CAIL2018 and demonstrates strong generalization on CJO2025. To facilitate reproducibility and further research, we release our code and the dataset at https://anonymous.4open.science/r/ARR-4437.

Introduction: Evaluating compliance with the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement can be time-consuming and subjective. This study compares STROBE assessments from large language models (LLMs), a human reviewer panel, and the original manuscript authors in observational rheumatology research. Methods: Guided by the GRRAS and DEAL Pathway B frameworks, 17 rheumatology articles were independently assessed. Evaluations used the 22-item STROBE checklist, completed by the authors, a five-person human panel (ranging from junior to senior professionals), and two LLMs (ChatGPT-5.2, Gemini-3Pro). Items were grouped into Methodological Rigor and Presentation and Context domains. Inter-rater reliability was calculated using Gwet's Agreement Coefficient (AC1). Results: Overall agreement across all reviewers was 85.0% (AC1=0.826). Domain stratification showed almost perfect agreement for Presentation and Context (AC1=0.841) and substantial agreement for Methodological Rigor (AC1=0.803). Although LLMs achieved complete agreement (AC1=1.000) with all human reviewers on standard formatting elements, their agreement with human reviewers and authors declined on complex items. For example, regarding the item on loss to follow-up, the agreement between Gemini 3 Pro and the senior reviewer was AC1=-0.252, while the agreement with the authors was only fair. Additionally, ChatGPT-5.2 generally demonstrated higher agreement with human reviewers than Gemini-3Pro on specific methodological items. Conclusion: While LLMs show potential for basic STROBE screening, their lower agreement with human experts on complex methodological items likely reflects a reliance on surface-level information. Currently, these models appear more reliable for standardizing straightforward checks than for replacing expert human judgment in evaluating observational research.

Integrating Spiking Neural Networks (SNNs) with Transformer architectures offers a promising pathway to balance energy efficiency and performance, particularly for edge vision applications. However, existing Spiking Transformers face two critical challenges: (i) a substantial performance gap compared to their Artificial Neural Networks (ANNs) counterparts and (ii) high memory overhead during inference. Through theoretical analysis, we attribute both limitations to the Spiking Self-Attention (SSA) mechanism: the lack of locality bias and the need to store large attention matrices. Inspired by the localized receptive fields (LRF) and membrane-potential dynamics of biological visual neurons, we propose LRF-Dyn, which uses spiking neurons with localized receptive fields to compute attention while reducing memory requirements. Specifically, we introduce a LRF method into SSA to assign higher weights to neighboring regions, strengthening local modeling and improving performance. Building on this, we approximate the resulting attention computation via charge-fire-reset dynamics, eliminating explicit attention-matrix storage and reducing inference-time memory. Extensive experiments on visual tasks confirm that our method reduces memory overhead while delivering significant performance improvements. These results establish it as a key unit for achieving energy-efficient Spiking Transformers.

Portfolio construction traditionally relies on separately estimating expected returns and covariance matrices using historical statistics, often leading to suboptimal allocation under time-varying market conditions. This paper proposes a joint return and risk modeling framework based on deep neural networks that enables end-to-end learning of dynamic expected returns and risk structures from sequential financial data. Using daily data from ten large-cap US equities spanning 2010 to 2024, the proposed model is evaluated across return prediction, risk estimation, and portfolio-level performance. Out-of-sample results during 2020 to 2024 show that the deep forecasting model achieves competitive predictive accuracy (RMSE = 0.0264) with economically meaningful directional accuracy (51.9%). More importantly, the learned representation effectively captures volatility clustering and regime shifts. When integrated into portfolio optimization, the proposed Neural Portfolio strategy achieves an annual return of 36.4% and a Sharpe ratio of 0.91, outperforming equal weight and historical mean-variance benchmarks in terms of risk-adjusted performance. These findings demonstrate that jointly modeling return and covariance dynamics can provide consistent improvements over traditional allocation approaches. The framework offers a scalable and practical alternative for data-driven portfolio construction under nonstationary market conditions.

Predicting stock prices presents challenges in financial forecasting. While traditional approaches such as ARIMA and RNNs are prevalent, recent developments in Large Language Models (LLMs) offer alternative methodologies. This paper introduces an approach that integrates LLMs with daily financial news for stock price prediction. To address the challenge of processing news data and identifying relevant content, we utilize stock name embeddings within attention mechanisms. Specifically, we encode news articles using a pre-trained LLM and implement three attention-based pooling techniques -- self-attentive, cross-attentive, and position-aware self-attentive pooling -- to filter news based on stock relevance. The filtered news embeddings, combined with historical stock prices, serve as inputs to the prediction model. Unlike prior studies that focus on individual stocks, our method trains a single generalized model applicable across multiple stocks. Experimental results demonstrate a 7.11% reduction in Mean Absolute Error (MAE) compared to the baseline, indicating the utility of stock name embeddings for news filtering and price forecasting within a generalized framework.

Timely channel information is necessary for vehicles to determine both the serving base station (BS) and the beamforming vector, but frequent estimation of fast-fading mmWave channels incurs significant overhead. To address this challenge, we propose a Beam-aware Kernelized Contextual Upper Confidence Bound (BKC-UCB) algorithm that estimates instantaneous transmission rates without additional channel measurements by exploiting historical contexts such as vehicle location and velocity, together with past observed transmission rates. Specifically, BKC-UCB leverages kernel methods to capture the nonlinear relationship between context and transmission rate by mapping contexts into a reproducing kernel Hilbert space (RKHS), where linear learning becomes feasible. Rather than treating each beam as an independent arm, the beam index is embedded into the context, enabling BKC-UCB to exploit correlations among beams to accelerate convergence. Furthermore, an event-triggered information sharing mechanism is incorporated into BKC-UCB, enabling information exchange only when significant explorations are conducted to improve learning efficiency with limited communication overhead.

With the rapid advancement of large language models (LLMs), LLM-based heuristic search methods have demonstrated strong capabilities in automated algorithm generation. However, their evolutionary processes often suffer from instability and premature convergence. Existing approaches mainly address this issue through prompt engineering or by jointly evolving thought and code, while largely overlooking the critical role of algorithmic category diversity in maintaining evolutionary stability. To this end, we propose Category Driven Automatic Algorithm Design with Large Language Models (CDEoH), which explicitly models algorithm categories and jointly balances performance and category diversity in population management, enabling parallel exploration across multiple algorithmic paradigms. Extensive experiments on representative combinatorial optimization problems across multiple scales demonstrate that CDEoH effectively mitigates convergence toward a single evolutionary direction, significantly enhancing evolutionary stability and achieving consistently superior average performance across tasks and scales.

The International Joint Conference on Neural Networks (IJCNN) is the premier international conference in the area of neural networks theory, analysis, and applications. The 2025 edition of the conference comprised 5,526 paper submissions, 7,877 active reviewers, 426 area chairs, 2,152 accepted papers, and more than 2,300 attendees. This represents a growth of about 100% in terms of submissions, 200% in terms of reviewers, and over 50% in terms of attendees as compared to the previous edition. In this paper, we describe several key aspects of the whole review process, including a strategy for ranking the scores provided by the reviewers by evaluating a score index and a calibrated version used experimentally to remove reviewer-specific bias from reviews.

The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework provides a rigorous foundation for evidence synthesis, yet the manual processes of data extraction and literature screening remain time-consuming and restrictive. Recent advances in Generative Artificial Intelligence (GenAI), particularly large language models (LLMs), offer opportunities to automate and scale these tasks, thereby improving time and efficiency. However, reproducibility, transparency, and auditability, the core PRISMA principles, are being challenged by the inherent non-determinism of LLMs and the risks of hallucination and bias amplification. To address these limitations, this study integrates human-led synthesis with a GenAI-assisted statistical pre-screening step. Human oversight ensures scientific validity and transparency, while the deterministic nature of the statistical layer enhances reproducibility. The proposed approach systematically enhances PRISMA guidelines, providing a responsible pathway for incorporating GenAI into systematic review workflows.

This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under precedence constraints, that is, if a test (or set) $X$ is a predecessor of $Y$, then in any feasible decision tree $X$ needs to be an ancestor of $Y$ (or respectively, if $Y$ is added to set cover, then so must be $X$). For the Optimal Decision Tree we consider two optimization criteria: worst case identification time (height of the tree) or the average identification time. Similarly, for the Set Cover we study two cost measures: the size of the cover or the average cover time. Our approach is to develop a number of algorithmic reductions, where an approximation algorithm for one problem provides an approximation for another via a black-box usage of a procedure for the former. En route we introduce other optimization problems either to complete the `reduction landscape' or because they hold the essence of combinatorial structure of our problems. The latter is brought by a problem of finding a maximum density precedence closed subfamily, where the density is defined as the ratio of the number of items the family covers to its size. By doing so we provide $\mathcal{O}^*(\sqrt{m})$-approximation algorithms for all of the aforementioned problems. The picture is complemented by a number of hardness reductions that provide $o(m^{1/12-ε})$-inapproximability results for the decision tree and covering problems. Besides giving a complete set of results for general precedence constraints, we also provide polylogarithmic approximation guarantees for two most typically studied and applicable precedence types, outforests and inforests. By providing corresponding hardness results, we show these results to be tight.

Effective feature selection is essential for high-dimensional data analysis and machine learning. Unsupervised feature selection (UFS) aims to simultaneously cluster data and identify the most discriminative features. Most existing UFS methods linearly project features into a pseudo-label space for clustering, but they suffer from two critical limitations: (1) an oversimplified linear mapping that fails to capture complex feature relationships, and (2) an assumption of uniform cluster distributions, ignoring outliers prevalent in real-world data. To address these issues, we propose the Robust Autoencoder-based Unsupervised Feature Selection (RAEUFS) model, which leverages a deep autoencoder to learn nonlinear feature representations while inherently improving robustness to outliers. We further develop an efficient optimization algorithm for RAEUFS. Extensive experiments demonstrate that our method outperforms state-of-the-art UFS approaches in both clean and outlier-contaminated data settings.

Large language models (LLMs) are increasingly being used to extract structured knowledge from unstructured financial text. Although prior studies have explored various extraction methods, there is no universal benchmark or unified evaluation framework for the construction of financial knowledge graphs (KG). We introduce FinReflectKG - EvalBench, a benchmark and evaluation framework for KG extraction from SEC 10-K filings. Building on the agentic and holistic evaluation principles of FinReflectKG - a financial KG linking audited triples to source chunks from S&P 100 filings and supporting single-pass, multi-pass, and reflection-agent-based extraction modes - EvalBench implements a deterministic commit-then-justify judging protocol with explicit bias controls, mitigating position effects, leniency, verbosity and world-knowledge reliance. Each candidate triple is evaluated with binary judgments of faithfulness, precision, and relevance, while comprehensiveness is assessed on a three-level ordinal scale (good, partial, bad) at the chunk level. Our findings suggest that, when equipped with explicit bias controls, LLM-as-Judge protocols provide a reliable and cost-efficient alternative to human annotation, while also enabling structured error analysis. Reflection-based extraction emerges as the superior approach, achieving best performance in comprehensiveness, precision, and relevance, while single-pass extraction maintains the highest faithfulness. By aggregating these complementary dimensions, FinReflectKG - EvalBench enables fine-grained benchmarking and bias-aware evaluation, advancing transparency and governance in financial AI applications.

Control synthesis under constraints is at the forefront of research on autonomous systems, in part due to its broad application from low-level control to high-level planning, where computing control inputs is typically cast as a constrained optimization problem. Assessing feasibility of the constraints and selecting among subsets of feasible constraints is a challenging yet crucial problem. In this work, we provide a novel theoretical analysis that yields necessary and sufficient conditions for feasibility assessment of linear constraints and based on this analysis, we develop novel methods for feasible constraint selection in the context of control of autonomous systems. Through a series of simulations, we demonstrate that our algorithms achieve performance comparable to state-of-the-art methods while offering improved computational efficiency. Importantly, our analysis provides a novel theoretical framework for assessing, analyzing and handling constraint infeasibility.

Genomic language models (gLMs) have shown mostly modest success in identifying evolutionarily constrained elements in mammalian genomes. To address this issue, we introduce a novel framework for training gLMs that explicitly models nucleotide evolution on phylogenetic trees using multispecies whole-genome alignments. Our approach integrates an alignment into the loss function during training but does not require it for making predictions, thereby enhancing the model's applicability. We applied this framework to train PhyloGPN, a model that excels at predicting functionally disruptive variants from a single sequence alone and demonstrates strong transfer learning capabilities.

Stemming from physics and later applied to other fields such as ecology, the theory of critical transitions suggests that some regime shifts are preceded by statistical early warning signals. Reddit's r/place experiment, a large-scale social game, provides a unique opportunity to test these signals consistently across thousands of subsystems undergoing critical transitions. In r/place, millions of users collaboratively created ''compositions'', or pixel-art drawings, in which transitions occur when one composition rapidly replaces another. We develop a machine-learning-based early warning system that combines the predictive power of multiple system-specific time series via gradient-boosted decision trees with memory-retaining features. Our method significantly outperforms standard early warning indicators. Trained on the 2022 r/place data, our algorithm detects half of the transitions occurring within 20 min at a false positive rate of just 3.6%. Its performance remains robust when tested on the 2023 r/place event, demonstrating generalizability across different contexts. Using SHapley Additive exPlanations (SHAP) for interpreting the predictions, we investigate the underlying drivers of warnings, which could be relevant to other complex systems, especially online social systems. We reveal an interplay of patterns preceding transitions, such as critical slowing down or speeding up, a lack of innovation or coordination, turbulent histories, and a lack of image complexity. These findings show the potential of machine learning indicators in socio-ecological systems for predicting regime shifts and understanding their dynamics.

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It has been observed that the optimal parameters obtained from one instance of a COP can be transferred to another instance, resulting in generally good solutions for the latter. In this work, we propose a refinement scheme in which only a subset of QAOA layers is optimized following parameter transfer, with a focus on the Max-Cut problem. Our motivation is to reduce the complexity of the loss landscape when optimizing all the layers of high-depth QAOA circuits, as well as to reduce the optimization time. We investigate the potential hierarchical roles of different layers and analyze how the approximation ratio scales with increasing problem size. Our findings indicate that the selective layer optimization scheme offers a favorable trade-off between solution quality and computational time, and can be more beneficial than full optimization at a lower optimization time.

The popularity of large language models (LLMs) continues to grow, and LLM-based assistants have become ubiquitous. Information security awareness (ISA) is an important yet underexplored area of LLM safety. ISA encompasses LLMs' security knowledge, which has been explored in the past, as well as their attitudes and behaviors, which are crucial to LLMs' ability to understand implicit security context and reject unsafe requests that may cause an LLM to unintentionally fail the user. We introduce LISAA, a comprehensive framework to assess LLM ISA. The proposed framework applies an automated measurement method to a comprehensive set of 100 realistic scenarios covering all security topics in an ISA taxonomy. These scenarios create tension between implicit security implications and user satisfaction. Applying our LISAA framework to leading LLMs highlights a widespread vulnerability affecting current deployments: many popular models exhibit only medium to low ISA levels, exposing their users to cybersecurity threats, and models that rank highly in cybersecurity knowledge benchmarks sometimes achieve relatively low ISA ranking. In addition, we found that smaller variants of the same model family are significantly riskier. Furthermore, while newer model versions demonstrated notable improvements, meaningful gaps in their ISA persist, suggesting that there is room for improvement. We release an online tool that implements our framework and enables the evaluation of new models.

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any dependence with enough samples, standard tests may require an exorbitant amount of samples for detecting subtle dependencies between high-dimensional random variables with complex distributions. In this work, we study two related ways to learn powerful independence tests. First, we show how to construct powerful statistical tests with finite-sample validity by using variational estimators of mutual information, such as the InfoNCE or NWJ estimators. Second, we establish a close connection between these variational mutual information-based tests and tests based on the Hilbert-Schmidt Independence Criterion (HSIC); in particular, learning a variational bound (typically parameterized by a deep network) for mutual information is closely related to learning a kernel for HSIC. Finally, we show how to, rather than selecting a representation to maximize the statistic itself, select a representation which can maximize the power of a test, in either setting; we term the former case a Neural Dependency Statistic (NDS). While HSIC power optimization has been recently considered in the literature, we correct some important misconceptions and expand to considering deep kernels. In our experiments, while all approaches can yield powerful tests with exact level control, optimized HSIC tests generally outperform the other approaches on difficult problems of detecting structured dependence.

There are many networks in real life which exist as form of Scale-free networks such as World Wide Web, protein-protein interaction network, semantic networks, airline networks, interbank payment networks, etc. If we want to analyze these networks, it is really necessary to understand the properties of scale-free networks. By using the properties of scale free networks, we can identify any type of anomalies in those networks. In this research, we proposed a methodology in a form of an algorithm to predict hidden links and missing nodes in scale-free networks where we combined a generator of random networks as a source of train data, on one hand, with artificial neural networks for supervised classification, on the other, we aimed at training the neural networks to discriminate between different subtypes of scale-free networks and predicted the missing nodes and hidden links among (present and missing) nodes in a given scale-free network. We chose Bela Bollobas's directed scale-free random graph generation algorithm as a generator of random networks to generate a large set of scale-free network's data.

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather simple algebraic proof being made straightforward, above all, by the introduction of two novel algebraic tools. Indeed, on the one hand, we introduce the notion of delta-distribution which merely stands for the difference of two arbitrary probability distributions, and which mainly serves to alleviate the sign constraint inherent to a traditional probability distribution. On the other hand, we develop an approximation framework of general discrete functions by means of an orthogonal projection expressing in terms of linear combinations of function margins with respect to a given collection of point subsets, though, we rather exploit the latter approach for the purpose of modeling locally consistent sets of discrete functions from a global perspective. After that, as a first step, we develop from scratch the expectation optimization framework which is nothing else than a reformulation, on stochastic grounds, of the convex-hull approach, as a second step, we develop the traditional LP relaxation of such an expectation optimization approach, and we show that it enables to solve the MAP inference problem in graphical models under rather general assumptions. Last but not least, we describe an algorithm which allows to compute an exact MAP solution from a perhaps fractional optimal (probability) solution of the proposed LP relaxation.

The scale-dependent bias in halo and galaxy power spectra is a key signature of local primordial non-Gaussianity (local PNG), with PNG sensitivity scaling as $b_ϕ/b_1$ -- the ratio of their responses to long-wavelength primordial potential $b_ϕ$ and late-time density fluctuations $b_1$. For number density fluctuations, these responses are closely tied by the universality relation, limiting the achievable ratio. We show that size density fluctuations strongly violate this relation, thus evading the limit. For galaxy-mass halos, sizes have a vanishingly small density response but a sizable, negative local PNG response, implying an effective $b_ϕ/b_1$ that is large in magnitude and opposite in sign to that of number counts. This makes galaxy sizes complementary probes of local PNG from the same galaxy sample, without any sample split. For a DESI-like survey, a multi-tracer analysis combining galaxy numbers and sizes improves the local-PNG detection significance by a factor of $\sim\!3.6$. Due to the sign flip, the number-size cross power spectrum further provides a handle on systematics in the event of a detection.

A new measurement of the Hubble constant $H_0$ is presented using the statistical dark siren method applied to a sample of seven well-localized gravitational-wave (GW) events from the fourth LIGO-Virgo-KAGRA (LVK) observing run and ten additional events from the first three runs. Galaxy catalogs from the DESI Legacy Imaging Survey (LS) are combined with a deep learning model to compute photometric redshift probability density functions. We extend our previous analysis by including the events GW230731_215307 and GW230927_153832, using sky maps from the fourth Gravitational-Wave Transient Catalog (GWTC-4), and introducing key methodological improvements: $r$-band luminosity weighting of host galaxies; an extended GW likelihood that incorporates information from the binary black hole component masses; and a consistent treatment of selection effects that accounts for the incompleteness of the magnitude-limited LS galaxy catalog. Using a total of 17 well-localized dark sirens (seven from the first part of the fourth observing run, O4a), we obtain $H_0 = 78.8^{+14.6}_{-12.2}$ km/s/Mpc without luminosity weighting and $H_0 = 78.2^{+12.0}_{-11.0}$ km/s/Mpc when applying $r$-band luminosity weighting. Finally, we combine the luminosity-weighted dark siren sample with the bright siren GW170817, including constraints on the jet viewing angle and corrections for the host galaxy peculiar velocity, to obtain a final constraint of $H_0 = 69.9^{+4.1}_{-4.0}$ km/s/Mpc, representing an improvement of approximately 11% in the uncertainty relative to the GW170817-only result.

Machine learning interatomic potentials (MLIPs) trained on large, chemically diverse datasets are revolutionizing computational chemistry, enabling molecular dynamics simulations of battery electrolytes with near-DFT accuracy over 10,000 times faster than DFT. While previous MLIP training datasets with suitable elemental coverage for electrolytes have been based on inorganic materials, the Open Molecules 2025 (OMol25) dataset provides large-scale molecular DFT MLIP training data with broad elemental coverage and specifically samples tens of millions of electrolyte configurations. Here, we integrate computational modeling with experimental validation to systematically assess the ability of large-scale MLIPs pre-trained on materials data or on OMol25 to accurately resolve nanoscale structural organization and ion-solvation characteristics in Na-ion battery electrolytes across diverse physicochemical conditions and compositional regimes. We find that the OMol25-trained Universal Model of Atoms (UMA-OMol) predicts experimentally measured densities and X-ray structure factors in substantially better agreement compared to state-of-the-art models trained only on inorganic materials data. Using UMA-OMol, we further analyze systematic trends in solvation structure as a function of cation identity, anion chemistry, salt concentration, and solvent topology. We observe that increasing system temperature amplifies the heterogeneity within the solvation environment, perturbing cation-solvent interactions and promoting the formation of contact ion pairs (CIPs). Moreover, subtle variations in the solvent topology of glyme-based electrolytes cause pronounced changes in ion-correlations and solvation structure. The experimental agreement and microscopic insights shown here position OMol25-trained MLIPs as a practical route to predictive, high-throughput electrolyte simulations.

Construction of creation operators which can properly sample the underlying energy eigenstates remains a fundamental first step in lattice QCD spectroscopy calculations, particularly when the spectrum includes states with different composition such as mesons, glueballs, multi-particle states, etc. We tackle this issue in the study of the scalar glueball and charmonium mixing, where we use improved operators for both types of states to resolve the low-lying spectrum and identify the dominant composition of each state in a mass regime where the glueball is stable. We include derivative-based meson operators combined with distillation profiles, as well as glueball operators built from the chromo-magnetic field and its derivatives which retain angular momentum information from their continuum counterparts. We comment on the advantages of these operators, particularly on the construction and implementation of the glueball ones, thanks to which we identify the lightest iso-scalar state as glueball-dominated $0^{++}$.

We show that for every complete metric space $M$ there exists another complete metric space $N$ of the same density character such that the curve-flat quotient of $N$ is isometric to $M$. Moreover, we show that if $M$ is compact and $α$ is any countable ordinal, there exists a compact $N$ such that its curve-flat quotient of order $α$ is bi-Lipschitz equivalent to $M$, with arbitrarily small distortion. Our constructions rely on a new method for constructing (compact) metric spaces, which consists in attaching iteratively compact spaces at countably many pairs of points to a snowflake-like distortion of a given (compact) metric space. We apply our results on high-order curve-flat quotients to obtain a new result concerning universality of Lipschitz quotients. Specifically, we show that there cannot exist a compact metric space $K$ such that every compact metric space is a Lipschitz quotient of $K$. This result stands in contrast to a theorem of Johnson, Lindenstrauss, Preiss and Schechtman, who showed that any separable Banach space containing $\ell_1$ has every separable geodesic complete metric space as a Lipschitz quotient.

We prove $L^p$ estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain $r$-variation estimates for bilinear ergodic averages in the sharp range $r > 2$, a sharp bilinear Hörmander multiplier theorem, and a $\log$-Dini theorem for bilinear singular integrals.

Satellite galaxies in the Local Group tend to be distributed in thin, planar configurations, with many sharing coherent orbital motion. Galaxy formation simulations in $Λ$CDM have historically struggled to produce similar structures, leading to the so-called "planes of satellites problem". In this work, we investigate whether the emergence of such structures is connected to the mass of a major merger at $z\sim2$, analogous to the Gaia-Sausage-Enceladus (GSE) event in the Milky Way. We use the VINTERGATAN-GM suite of high-resolution zoom-in simulations, comprising five realizations of the same Milky Way-mass halo generated through targeted genetic modifications of a GSE progenitor. The GSE-like merger mass ratio is systematically varied from 1:10 to 1:2.1, while keeping the final dynamical mass and large-scale environment fixed. We find a clear and consistent trend: more massive GSE-like mergers lead to satellite populations that are both more planar and more kinematically coherent. In particular, simulations with merger mass ratios larger than 1:6 develop Kinematic Persistent Planes (KPPs), in which at least 40% of satellites co-orbit around a common axis over extended periods, comparable to those observed in the Milky Way. These structures arise when sufficiently massive mergers, accreted along the direction of maximum compression of the Lagrangian volume, produce flattened host halos with anisotropic velocity dispersions aligned with the merger direction. The merger aligns the host halo's minor axis with the direction of flattening of the surrounding cosmic web, and planes of satellites then emerge through two complementary processes: (i) satellites preferentially infall along the host's equatorial plane, and (ii) anisotropic dynamical friction in the non-spherical halo gradually reshapes their orbits toward this plane, generating coherent and long-lived planar configurations.

High-dimensional Schrödinger systems arising from tensor-product discretizations suffer from exponential state growth, making direct controller synthesis and real-time closed-loop simulation computationally challenging. Hierarchical Tucker (HT) tensor representations offer scalable low-rank surrogates, but the impact of fixed-rank truncation on closed-loop stability is not well understood. This paper develops a local robustness framework for sampled-data feedback control implemented with fixed-rank HT projections. By viewing each truncation as a bounded, rank-dependent perturbation of the nominal closed loop, and assuming a local phase-invariant contraction certificate together with trajectory-level hierarchical spectral decay, we show that the HT-projected dynamics are practically exponentially stable: trajectories converge to a dimension-independent tube whose radius decreases with the prescribed rank. We further obtain an explicit logarithmic rank-accuracy relation and establish conditions under which controllers designed on the HT-truncated surrogate model retain practical exponential tracking guarantees when deployed on the full system, together with an explicit bound quantifying the resulting surrogate-to-plant mismatch. A compact lattice example demonstrates the applicability of the framework.

Quantum extreme learning machines (QELMs) are unconventional computing architectures that bear remarkable promise in both classical and quantum machine-learning tasks, such as the estimate of quantum state properties. However, the probabilistic nature of quantum measurements demands extensive repetitions for training to precisely estimate expectation values, imposing stringent trade-offs among experimental resources, acquisition time, and signal-to-noise ratio, particularly for large datasets. Here we introduce a paradigm shift by harnessing the correspondence between stimulated and spontaneous emission. The QELM is trained exclusively with intense classical fields, yet it performs inference directly on previously unseen quantum input states to predict their quantum properties. This strategy dramatically reduces acquisition times while substantially enhancing the signal-to-noise ratio. Using frequency-bin-encoded biphoton states, implemented here for the first time in a quantum machine-learning architecture, we demonstrate entanglement witnessing of two-qubit states with (93 +- 4)% accuracy, multi-dimensional entanglement detection, and learning of the Hamiltonian governing photon-pair generation with a fidelity of (96 +- 4)%. By establishing classical training as a scalable route to quantum feature extraction, our results bridge macroscopic observables and nonclassical correlations, opening a new pathway toward faster and more robust quantum neural networks