Papers

Understanding a nonlinear dynamical system from time series requires not only reproducing its trajectories, but also identifying a simple representation that preserves its essential dynamical structure. Almost-linear recurrent neural networks (AL-RNNs) are piecewise-linear RNNs in which only a subset of units use ReLU nonlinearities, so that nonlinear capacity is explicitly controlled by the number of ReLU units. Their activation patterns define linear regions, represented as symbols, whose observed transitions form a symbolic transition graph. However, directly training AL-RNNs with few ReLU units to realize minimal dynamical representations can be unreliable. We ask whether an AL-RNN with more ReLU units can instead be trained first and systematically reduced to a minimal dynamical representation. We introduce a fixed-point-guided hierarchical reduction procedure that progressively linearizes selected ReLU units, merging neighboring linear regions and graph nodes while preserving distinct symbols containing fixed points (FPs). The resulting reduction tree defines a hierarchy of progressively simpler candidates. Each reduced candidate is initialized from the parent parameters and retrained under guidance from the parent dynamics. We also prove that reproducing $Q$ distinct fixed points requires at least $Q$ FP-containing symbols, providing a certificate of symbol-level minimality when this bound is attained. On the 3-scroll Chua system, direct training with the theoretical minimum of three ReLU units achieves high-fidelity minimal realizations in only 20% of seeds, whereas our learn-reduce-retrain strategy increases the seed-macro success rate to approximately 71% at the same final nonlinear capacity. These results show that redundant nonlinear capacity can serve as a scaffold for discovering and realizing minimal dynamical representations.

In this paper, a unmanned aerial vehicle (UAV) corridor-assisted network is proposed to study the joint sensing and communication (JCAS) coverage probability (CP) of a terrestrial (BS) equipped with a realistic three-dimensional (3D) 3GPP antenna pattern. By employing the 3D binomial point process (BPP) to model the spatial locations of the UAV-UEs, a fixed number of UAV-UEs are deployed in an aerial corridor modeled as a finite cylinder. The BS exploits radar sensing capabilities to track a known UAV-UE under a 3D beam misalignment error, which follows a multivariate normal distribution. Subsequently, under clutter and uplink communication interference, exact- form analytical expressions for JCAS CP are derived and used to analyze the performance at the terrestrial BS. The results highlight corridor-length saturation at high UAV heights and the beamwidth trade-off between interference suppression and misalignment sensitivity.

Safety-aligned Large Language Models remain vulnerable to fine-tuning on small sets of harmful or benign-looking samples. However, prior studies typically assume that poisoned samples directly enter downstream fine-tuning, overlooking quality-based selection in practical training pipelines. To fill this gap, we systematically evaluate both the filtering effects against poisoning and the downstream safety impact of retained data. The results reveal that selection removes many overtly harmful samples, yet some retained high-quality samples can still degrade model safety alignment possibly due to their harmful-like training-update patterns at the layer-wise gradient level. Together, these findings expose a practical vulnerability: safety-degrading influence can pass through quality-based selection via retained high-quality samples. To examine its systematic exploitability, we propose Bi-Stage Quality-Constrained Safety-Degradation Text Optimization (Bi-QSTO), which optimizes poisoned samples under an explicit quality constraint to survive selection while preserving their safety-degrading influence. Across poisoning settings, target models, and filtering rates, Bi-QSTO maintains attack effectiveness before and after selection. Even at 90% filtering, harmful-seeded samples achieve a Poisoning Retention Rate above 90% and Harmful Score of 3.30–4.01. Their attack effectiveness strongly transfers across models and their retention advantage generalizes to additional selection methods.

Non-abelian infrared radiation can be seen as both a practical ingredient for QCD phenomenology and a window on the long-distance structure of gauge theories. During the last decade, a novel viewpoint was developed on infrared phenomena: soft currents are seen as arising from asymptotic symmetries realised on the celestial sphere, and soft colour correlations similarly emerge from a two-dimensional conformal field theory on the sphere. In this contribution, we briefly review the status of this approach. We begin with the standard bulk picture, presenting the infrared factorisation of massless scattering amplitudes, and then we show how universal infrared information gets mapped to marked points on the celestial sphere. In particular, soft colour-dipole singularities are reproduced to all orders by a correlator of vertex operators in a free-boson theory on the sphere. We then proceed to study soft-gluon currents, and show how bulk results constrain the structure of the celestial theory beyond the free-field limit. For single emission, we note that all logarithms in dipole-like loop contributions can be absorbed into the choice of scale for the strong coupling. For multiple emission, we show how the emerging mixed-helicity celestial operator product expansion must be weighted by energy fractions, breaking holomorphic factorisation and obstructing associativity under successive collinear limits. These results illustrate a remarkable connection between the familiar physics of infrared QCD and the dynamics of a two-dimensional theory on the celestial sphere.

Beyond adapting Large Language Models (LLMs) to specialized applications, fine-tuning has recently been shown to recover private information that is no longer accessible through direct queries. Previous fine-tuning recovery attacks, however, require genuine private supervision drawn from the same distribution, i.e., the previous training dataset. We argue that such recovery remains possible without such impractical knowledge. We show that LLM-generated candidates can provide sufficient supervision to recover previously learned private associations. Based on this, we propose ReGap, a data-free attack that recovers private associations using task structure, filters them by answer-token likelihood, and updates the target model via low-rank adaptation. Specifically, ReGap requires neither target answers nor auxiliary genuine private supervision. Across six GPT-2, OPT, and Qwen3 models, ReGap improves target-association recovery by 6-21 percentage points over the post-training target model. Recovery remains substantial even when the adaptation identities are disjoint from all memorized and evaluation identities, with no exact target answers appearing in the generated or selected supervision. Moreover, the same trained adapters increase recovery from 42% to 63% on a previously exposed checkpoint, but produce no gain on a matched checkpoint that never encountered the targets. This contrast shows that adaptation alone is insufficient to explain the observed recovery and that prior target exposure strongly affects post-adaptation recoverability. Our findings highlight that routine model customization can reawaken latent privacy risks, warranting urgent attention from the academic and industrial communities.

Factories are shifting toward smaller lot sizes with high product customization, requiring frequent re-programming of flexible and reconfigurable automation systems. LLM-based agents can be deployed in two complementary roles: Offline, they generate deterministic production sequences, reducing programming effort; online, they operate live machines and handle unforeseen runtime faults that static programs cannot anticipate. We propose a solution in which each factory module is paired with a dedicated LLM-based agent and an MCP tool server that exposes the module's skills via OPC UA method calls, with agents coordinating over MQTT and grounded by real-time updates of the factory state. We compare three agent architectures (orchestrator, peer-to-peer, and monolithic) across nine production challenges of increasing complexity in a simulation of a physical six-module hexagonal factory, including silent hardware fault detection. The monolithic and peer-to-peer architectures both achieve the highest mean solve rate (93%), while the orchestrator uniquely resolves a silent conveyor-belt fault in all ten runs by autonomously rerouting plates around the blocked segment. All architectures exhibit emergent fault-diagnosis behavior without any explicit failure-handling logic, establishing standardized MCP tooling, MQTT-based inter-agent communication, and real-time state injection as a viable and reproducible foundation for LLM-programmed smart manufacturing.

We consider polynomial processes, i.e., continuous-time Markov processes that preserve polynomials without increasing degree, and augment them with resetting. Resetting means that at the jump times of an indepen- dent renewal process, the polynomial process is instantaneously reset to a new state, which can be chosen deterministically, randomly or in state-dependent fashion. We show that under certain types of resets ('affine resetting') the moments of the resulting process remain tractable and can be calculated by matrix exponentials (for Poissonian reset times) or by a matrix renewal equa- tion (for more general reset times). Our framework encompasses many models that have been considered in the existing literature, such as growth-collapse processes with deterministic growth or with Lévy inflow, and Brownian motion with resets to the origin, to a fixed distribution or by multiplying by a fixed proportion.

This note revisits the Cochran-Mantel-Haenszel (CMH) test in light of the increasing use of causal inference methods in clinical trials. It shows that the CMH test statistic can be interpreted as a standardized version of the augmented inverse probability weighted (AIPW) estimate of the causal average treatment effect. Consequently, it is not restricted to an interpretation as a test of the common-odds ratio in a stratified logistic regression model. The note then discusses conditional and unconditional variances for this estimator as well as variance estimation and its implications for testing. The results clarify the relationship between the classical conditional CMH test and Wald-type AIPW tests, and show that, under equal treatment allocation, the CMH test is asymptotically conservative for the weak null hypothesis of zero average treatment effect. %This note revisits the Cochran–Mantel–Haenszel (CMH) test in light of the increasing use of causal inference methods in clinical trials. For stratified randomized trials with binary endpoints and a common treatment allocation fraction across strata, we show that the numerator of the CMH statistic is proportional to an augmented inverse probability weighted estimator of the population-average causal risk difference. This provides an interpretation of the CMH test that does not depend on the common-odds-ratio model often used to motivate it. We then compare conditional and unconditional variance concepts for this estimator and discuss their implications for testing. The results clarify the relationship between the classical conditional CMH test and Wald-type AIPW tests, and show that, under equal treatment allocation, the CMH test is asymptotically conservative for the weak null hypothesis of zero average treatment effect.

Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of different types. The goal of community detection in multilayer networks is to identify groups of nodes exhibiting similar connectivity patterns, which may vary across layers. We propose a method based on a joint nonnegative symmetric matrix trifactorization for community detection in multilayer networks, where each graph is approximated by a nonnegative symmetric matrix trifactorization. Our approach enforces constraints on the factor matrices so that communities are disjoint and shared across layers, while allowing each layer to have its own connectivity patterns and node degrees. This flexibility enables the model to capture both local and global structural variations across layers. We also develop an algorithm to efficiently solve this problem. We evaluate multilayer community detection methods using the multilayer degree-corrected stochastic block model (MDCBM), a flexible framework for generating realistic multilayer graphs with heterogeneous degrees and varying connectivity patterns. Experiments show that our method reliably detects communities across diverse regimes, whereas existing state-of-the-art approaches are often limited by restrictive structural assumptions.

I present a greatly improved version of SOLARPROP, an open source framework for building models of charge-sign dependent solar modulation of cosmic rays in the heliosphere. The transport equation of charged particles is solved by converting it to a set of stochastic differential equations (SDEs). The code now includes the full set of SDEs in two spatial dimensions, allowing for magnetic fields with latitudinal components, and it has been generalized to accommodate models in three spatial dimensions. Due to code parallelization and optimization, a speedup of up to three orders of magnitude with respect to the original version is achieved. Python bindings have been added for ease of use. The code has been validated against the results of several model calculations found in the literature. While excellent agreement is found in many cases, important differences are observed for two model implementations. Possible root causes for the differences have been investigated.

In unmanned aerial vehicle (UAVs) networks, joint communication and sensing (JCAS) is emerging as a key enabler to support extended and continuous communication and sensing capabilities for sixth-generation (6G) services among UAVs operating in swarms. Within this framework, aerial corridors provide a structured environment for supporting coordinated and reliable operations. In this paper, a comprehensive frame- work is presented to investigate the JCAS coverage probability (CP) of a UAV-base station (BS) in an aerial corridor populated by UAV-user equipments (UEs). The corridor is modeled as a finite cylinder, within which a fixed number of UAV-UEs are spatially distributed according to a three-dimensional (3D) binomial point process (BPP). The UAV-BS is assumed to be equipped with a realistic 3D third generation partnership project (3GPP) antenna pattern and exploits radar sensing capabilities to track a known UAV-UE. Subsequently, the tracked UAV-UE is assumed to perform uplink communication with the UAV-BS. Accordingly, the JCAS CP at the UAV-BS is analyzed under the presence of clutter and uplink communication interference, and exact-form analytical expressions are derived. To the best of our knowledge, this is the first work to develop a stochastic geometry framework for the rigorous analysis of JCAS performance in aerial corridors, with UAV-UE locations modeled as a 3D BPP. Among several insights, results show that increasing the directivity of the UAV-BS antenna beams leads to notable JCAS performance gains, particularly for shorter UAV corridors.

Single-particle cryo-electron microscopy (cryo-EM) has become a widely adopted technique for biomolecular structure determination. The conventional cryo-EM computational pipeline first combines many particle images to reconstruct an electrostatic potential (ESP) map and then fits an atomic model to the recovered map. Density reconstruction has high sample complexity, requiring large numbers of particle images and making structure determination high-cost and low-throughput, particularly for heterogeneous samples. Downstream atomic model building, in turn, becomes increasingly difficult as the resolution of the reconstructed map deteriorates. Protein structure prediction models provide strong sequence-derived priors on atomic structure, and experiment-guided approaches can use these priors to recover structures consistent with experimental measurements. Yet, in cryo-EM, such priors are typically integrated only after density reconstruction during atomic model fitting. We introduce Fold'EM, an inference-time framework that combines priors from protein generative models directly with cryo-EM particle images to determine atomic models from a small number of single particle images, bypassing both intermediate density reconstruction and downstream model building against the reconstructed map. Across synthetic and experimental cryo-EM datasets, Fold'EM recovers accurate atomic structures both with known particle orientations and in an ab-initio setting where orientations are inferred jointly with structure. In heterogeneous datasets, Fold'EM further resolves distinct conformational states from mixed particle populations without separately reconstructing a density map and building an atomic model for each state. We believe these results open new avenues for structure determination in the low-sample regime and for characterizing low-population conformational states directly from cryo-EM particles.

Ultrashort light pulses can drive transient photocurrents in solids, the basis of modern terahertz (THz) emitters. Ferroelectrics have recently emerged in this context as sources that require neither the bias voltage of photoconductive antennas nor the magnetic field of spintronic emitters, yet the ultrafast photocurrent generating the emission has remained debated. Here, we resolve this question in epitaxial BiFeO$_3$ thin films with engineered ferroelectric domain configurations, from single-domain to periodic stripe patterns. The stripe-domain film emits a THz field four times stronger than the single-domain configurations, reaching about half the output of a metallic spintronic reference emitter while remaining unsaturated at our highest excitation fluences. Resolving the emitted THz field in amplitude and phase as a function of the pump light polarization and the crystal orientation, we separate the coexisting photocurrents by their symmetry. This identifies the ultrafast screening of the ferroelectric polarization by photocarriers as the dominant emission mechanism in the in-plane-polarized films, enhanced in multidomain films by the strong built-in fields at the domain walls, while an out-of-plane polarization favors the bulk photovoltaic current. Our results establish the ferroelectric domain configuration as a design parameter setting both the strength and the microscopic origin of light-driven THz emission.

Stable port-Hamiltonian neural networks certify asymptotic stability by construction. Yet, their Hamiltonian is a global Lyapunov function with a single global minimum, so they can represent only dynamic systems with one attractor. We demonstrate that this excludes even simple systems with energy landscapes forming a double well, and we overcome the restriction by parametrising the Hamiltonian as a product of Bregman divergences generated by one input-convex network. We prove that the resulting model is locally Lyapunov stable, that the coexistence of stable equilibria forces additional non-asymptotically-stable equilibria to exist, that all equilibria lie in a bounded region, and under a hyperbolicity assumption that almost-everywhere stability holds. On three systems our approach is able to recover the energy surface characteristics and improve the convergence speed by 1.8$\times$-8.5$\times$.

We introduce a new framework for one-step generative modelling on finite state spaces. To extend drifting beyond continuous domains, we use discrete Wasserstein geometry to define a target-relative KL gradient flow over the transitions of a reversible Markov kernel. We realize this probability flow at the particle level through Markov jumps and amortize the resulting transport updates into a latent-conditioned generator, so that the iterative dynamics are required only during training while inference remains one-step. In a controlled setting where the underlying distributions and transport dynamics can be computed exactly, we verify KL dissipation, consistency between the particle dynamics and the probability flow, and the predicted numerical scaling. We further show that a finite-capacity neural generator can track these exact transport targets while retaining one-step generation. These results validate the basic construction and provide a foundation for scaling Discrete Drifting to structured discrete data.

We study abeloid varieties over the adic space $\operatorname{Spa}(K, K^+)$, where $K$ is a complete non-Archimedean field and $K^+$ is a valuation ring of arbitrary rank. We extend the well-known Raynaud uniformization to this setting. We also show the existence of suitable Néron models in algebraic and formal situations over higher rank valuation rings: We prove the existence of algebraic (lft-)Néron models for semi-abelian varieties over valuation rings with algebraically closed fraction fields, as well as, up to finite separable base change, over complete rank one valuation rings with algebraically closed residue field. Building on this result, we show the existence of formal marked Néron models for abeloid varieties over $\operatorname{Spa}(K, K^+)$ after finite separable base change. We also investigate the connection between the higher rank Raynaud extension and the formal Néron model.

Large language models are moving from helping write up research to helping do it, which makes it important to know how the scientific text they produce differs from human writing. Work on this question has stayed mostly at the surface, using lexical and stylistic cues that light paraphrasing erases. We look instead at rhetorical structure, the sequence of argumentative moves through which a text makes its case. We study research-article introductions under Swales' CARS model, and compare original introductions from published linguistics articles with generated counterparts of the same papers. We find that human-written introductions are more flexible in which moves they use and in what order, while the generated ones are more uniform. Giving the models the CARS definitions makes them more rigid.

Open multimodal reasoning models have benefited from large-scale reasoning supervision, yet reliable post-training remains challenging due to uneven data quality, inefficient supervision construction, imbalanced difficulty, and cross-domain interference. We introduce MMVistaReason (MVR), an open-data post-training recipe with three components: (1) broader capability coverage across complementary Analytical and Real-World reasoning groups, emphasizing structured reasoning versus visual perception and spatial grounding; (2) efficient SFT and RL data construction, standardizing heterogeneous open data through staged cleaning and annotation, combining difficulty-aware cascaded teacher distillation with answer-likelihood-based trajectory selection to construct MVR-SFT-528K, and applying scale-specific frontier filtering for MVR-RL-63K; and (3) specialize-then-integrate training, which trains complementary RL experts and consolidates their capabilities through multi-teacher on-policy distillation (MOPD). Our analyses reveal a capacity-dependent interaction between supervision difficulty, trajectory quality, and model capacity: smaller students benefit more from selected supervision, while larger students are robust to trajectory variation and mixed-domain interference. Mixed-domain RL introduces benchmark-level negative transfer, whereas MOPD provides consistent capability integration, with the preferred KL direction varying across model scales. Across 15 multimodal benchmarks, MVR-4B achieves an average score of 72.8, outperforming Qwen3.5-9B (Instruct) and MMFineReason-8B while using about 70% fewer samples than MMFineReason. Scaling to 9B improves the average to 74.4, surpassing Qwen3.5-35B-A3B (Instruct). Overall, MMVistaReason demonstrates that systematic open-data construction and capacity-aware post-training provide a practical and scalable path toward reliable multimodal reasoning.

Vision-Language-Action (VLA) models have achieved high task success rates on robot manipulation task benchmarks. More recently, there has been an emphasis on evaluating the robustness of VLA models to perturbations. However, this robustness is still predominantly measured through Task Success Rate (TSR). In this work, we propose a benchmark-agnostic evaluation framework to measure the behavioural robustness of models by characterising how successful trajectories are executed under perturbation. We implement this methodology by extending the widely-used LIBERO and LIBERO-Plus benchmarks. Across three state-of-the-art VLA models, four LIBERO task suites and seven perturbation conditions, we evaluate changes in both typical successful behaviour and its variability, including metrics of motion smoothness, efficiency and gripper behaviour. We find that perturbations can alter the behaviour of successful trajectories, a phenomenon which cannot necessarily be inferred from TSR alone. Across LIBERO suites, we identify cases where state-of-the-art VLA models achieve comparable TSR under the same perturbation condition, yet behaviour on successful trajectories diverges substantially. Therefore, to have a more robust assessment of task performance, we argue that suitable measures of robustness should capture not only whether a task is completed, but also how the robot behaves while completing it. When evaluating the robustness of VLA models, TSR may be complemented by behavioural evaluation metrics that characterise the nature and variability of successful task execution by robots.

We give an $\infty$-categorical enhancement of Neisendorfer's equivalences between the homotopy categories of rational simplicial sets, commutative dg algebras (cdgas), cocommutative dg coalgebras (cdgcs) and dg Lie algebras (dgls), where these objects have respective hypotheses of connectedness, nilpotency and finite type. We do so by proving that linear duality is a partial Quillen equivalence between weak finite type connected cdgcs and cdgas, and that Quillen's Chevalley–Eilenberg adjunction is a partial crossed derivable equivalence between cdgcs and dgls, a concept we introduce in this paper to axiomatize precisely the behavior of this adjunction.

Tool-using large language model (LLM) agents turn generated text into real side effects, so poisoned tool metadata, retrieved pages, memory, and reusable skills can steer the next call. Vetting an artifact before admission does not settle this. A safe variant and a leaking variant can produce the same admission evidence, and a sound gate then cannot relax that site for either. We make that condition precise, which leaves the last boundary a deployment can still act on. We present Provenance-Aware Capability Enforcement (PACE), which mediates every tool call immediately before it executes. Path confinement proposes an executable cut of represented influence paths, while capability and effect verification checks schema-defined effects against authority compiled from the authenticated request. We distinguish the certified execution contract from the evaluated configuration, which can restore an authorized call after a proposed block or apply a declared repair. Confinement requires the final action to preserve the certified cut. On eight executable agent-security benchmarks with three target-model families, the evaluated configuration gives strictly lowest attack success in 62 of 79 eligible attack columns and ties in 14; full-benchmark native utility loses at most three points relative to the undefended agent. A complete ablation over 1167 paired cases attributes most security gains to effect verification and refusal control to boundary adaptation. A reduced-scale adaptive search succeeds on 0/30 out-of-authority targets against the defense.

When developers change one component of an agent, such as its controller, a learned model or its verifier, they usually judge the change by an aggregate task score. That score cannot tell whether improvement was attainable, which component lost value, or what the agent's own checks certify. We introduce a claim-specific verification audit for modular agents that plan, act, check and refine. Instead of scoring the agent, the audit scores the evidence: each conclusion is recorded with the evidence behind it, one of four verdicts (supported, unsupported, unresolved or not evaluated) and the boundary within which it holds. Three tools supply that evidence. Oracle policies measure attainable improvement under an explicitly stated action set, so that a low value can be traced to the evaluation rather than to the environment. Replacing one component at a time with a perfect counterpart locates lost value, with null results read as unresolved whenever a downstream component could mask them. A separate test asks whether the verifier's score identifies the quantity it is read as bounding. Applied to a constrained portfolio-allocation agent in a synthetic market with known hidden regimes, the audit shows that the value of perfect regime information depends on the action set used to measure it, that the scenario generator discards most of the regime signal while better local fidelity does not improve decisions, and that the runtime verifier can be bypassed with no visible change in outcomes. The contribution is the protocol and the evidential distinctions it enforces; the empirical findings are specific to the agent and environment studied.

We study the impact of higher-order QCD corrections on Higgs production via weak-boson fusion with subsequent decays of the Higgs boson to bottom-quark pairs. We consider realistic fiducial cuts and observe large corrections in a fixed-order calculation. They arise from the interplay of the particular fiducial cuts considered and the radiative corrections to the Higgs decay subprocess. Switching to a parton-shower-matched description of the decay captures a significant portion of the corrections already at the lowest order and improves the perturbative convergence of the calculation.

Following Miyamoto, we consider Q-charts, a class of subductions $\phi\colon X\to Y$ of diffeological spaces along which Blohmann's elasticity descends. We show that the Riemannian apparatus of elastic diffeology—vertical, horizontal and full connections, Riemannian metrics, Levi-Civita connections and geodesics—also descends along Q-charts. More precisely, structures on $Y$ correspond bijectively to structures on $X$ that are invariant under the pseudogroup $\Psi(\phi)$ of fibre-preserving transitions, and torsion-freeness, effectivity, flatness, fullness, the Levi-Civita property and the geodesic equation are preserved in both directions. The key input is that the iterated tangent bundles $T^nX$ and their fibre products $T_kX$ are the pullbacks along $\phi$ of the corresponding bundles over $Y$. For quotients by principal actions of diffeologically discrete groups, we lift geodesics globally, prove that the class of elastic spaces on which $\R$ is a curve object is closed under such quotients, and show that complete geodesic flows descend. As an application, we determine the Riemannian geometry of the irrational tori $\Tor_\alpha=\R/(\Z+\alpha\Z)$ completely. Let $\vartheta$ be the one-form on $\Tor_\alpha$ induced by $dt$ on $\R$. Every Riemannian metric is a positive constant multiple of $\vartheta^2$, and the vertical connections form a one-parameter family of flat effective connections, a single member of which is the unique Levi-Civita connection of every metric. This connection has a complete geodesic flow, yet the induced pseudo-distance vanishes identically.

Regulatory compliance checking - deciding whether a target document satisfies the obligations of a regulation - requires interpreting dense legal text, identifying which provisions apply, and grounding each decision in explicit evidence. We present ARCCS, an end-to-end, automated, agentic, and regulation-agnostic Legal NLP system for compliance checking. ARCCS decomposes raw regulatory text into atomic, traceable requirements and evaluates a target document against them using retrieved evidence, confidence scores, and human-interpretable justifications. This design decouples compliance assessment from any fixed regulatory template or predefined rule set, enabling the pipeline to operate over regulations of varying size and structure. We evaluate ARCCS in two complementary settings. First, in a GDPR policy-document evaluation, LLM-based judges find its decisions and justifications legally and evidentially consistent in up to 96.67% of the assessed cases. Second, on an EU public-procurement benchmark comprising more than 1,200 individual rule checks, the system attains 98.8% accuracy in violation detection. ARCCS is, to our knowledge, the first fully open-source system for end-to-end regulatory compliance checking and auditable report generation.

Reinforcement learning offers the prospect of a reusable sequential decision-making mechanism for spacecraft trajectory design, motivating policy interfaces that connect learned decisions to the underlying maneuver geometry. This paper develops Reachability Analysis-Informed Reinforcement Learning (RARL) for deterministic multi-impulse interplanetary transfers, placing intermediate waypoint selection at the center of the learned decision process. Local first-order reachability maps bounded velocity perturbations into an ellipsoidal set of next-node positions, within which the policy selects its waypoint. Lambert reconstruction then determines the corresponding maneuver to reach this selected waypoint along a dynamically consistent ballistic arc, coupling learned transfer-geometry selection with classical astrodynamics. A terminal two-impulse reconstruction completes the rendezvous, supported by a linear maneuver-demand assessment used for reward shaping. Numerical studies characterize this interface on a two-body Earth-Mars benchmark. Across three independent training runs, RARL achieves a mean maneuver cost of 10.23 km/s, 1.72% above a validated local sequential convex programming reference. Training over dispersed initial states extends policy reuse across a departure family with fixed target state and transfer duration. Each of the three independently trained multi-state policies completes all 10,000 held-out Monte Carlo departures without impulse-cap violations, compared with a mean feasibility rate of 6.49% for single-state policies. This broader sampled feasibility is accompanied by a 0.61% increase in mean nominal maneuver cost, without further training across departures. These results demonstrate that a reachability-informed decision interface supports benchmark-quality trajectory construction and policy reuse across dispersed departure conditions.

We study the classical single-machine scheduling problem of minimizing the sum of completion times of jobs in a non-clairvoyant setting, where the processing time of each job remains unknown until its completion. This is a hard problem for which no constant competitive algorithm is possible. Inspired by robust optimization and learning-augmented algorithms, we introduce a novel robustness framework that leverages structural information provided by a classification model to overcome this limitation. Specifically, we assume that jobs are partitioned into classes and we have access to the confusion matrix of the classifier, whose entry $(k,\ell)$ indicates the number of jobs predicted to belong to class~$k$ but that actually belong to class~$\ell$. In this manner, we are able to characterize uncertainty as a set of permutations within each predicted class, rather than as a collection of discrete numerical scenarios, avoiding the computational difficulty of classical robust metrics, such as Min-Max and Min-Max Regret. In addition to these worst-case metrics, we also consider the expected objective over all scenarios. We first propose an optimal non-adaptive strategy that is oblivious with respect to all three robust criteria. We then investigate adaptive and randomized algorithms, showing that they can outperform the optimal non-adaptive strategy when the matrix exhibits particular structural properties.

The error of regression using noisy function values naturally decomposes into an approximation error from the choice of model space and stochastic error from the noise on the observations. Statistical theory is mostly concerned with the stochastic error while approximation theory focuses on the approximation error, often subject to the assumption of noiseless observations. We combine the tools from approximation theory and statistics into a framework for bounding both errors in generalized least squares regression. The results cover weighted sup-norms and $L^2(\mu)$-norms, real- and complex-valued functions, and correlated noise under a range of tail and moment assumptions. Weighted Lebesgue functions and constants control the amplification of the best approximation error, while concentration inequalities provide bounds on the stochastic error. We organize these results into reusable bounds with explicit constants and establish sharpness where possible. For the common strategy of randomized regression we prove concentration of the Lebesgue function and constant around those of the corresponding $L^2(\mu)$-projection. For Fourier and Chebyshev regression on standard sampling grids, we obtain explicit, asymptotically tight $\mathcal O(\log m)$ bounds on the Lebesgue constants where $m$ is the model dimension. This improves upon the previous $\mathcal O(\sqrt{m})$ bound obtained for the regression setting and matches the bounds known for interpolation. A catalogue of approximation bounds and worked examples illustrates how to turn these results into explicit regression guarantees.

Studying brain lateralization and the resulting hemispheric asymmetry has been a topic of interest for many researchers. Very few studies have focused on differences in brain lateralization and hemispheric asymmetry associated with neurodegeneration. Additionally, Quantitative Susceptibility Mapping (QSM) has not been extensively used to investigate these differences. This article aims to study differences in hemispheric asymmetry between healthy and Alzheimer's disease (AD)-affected brains by calculating the Myelin Hemispheric Ratio (MHR) and Oxygen Extraction Fraction Hemispheric Ratio (OEFHR) between the two hemispheres using QSM as an intermediate marker of neurodegeneration. The estimations and corresponding results show marginal yet promising differences between healthy subjects and AD patients. These encouraging initial results emphasize the need to further investigate structural brain asymmetry and its alteration as a potential marker of AD-related neurodegeneration.

The distance between two points is provided by the length of their test connecting path. However, there is no unique way to attain this path in the space $R^2$, which is split by a straight line $L$ into two regions, $\Omega_p$ and $\Omega_q$, with $\ell_{p}$- and $\ell_q$-norms, respectively, where $1<p\leq q $ and $L\subset\Omega_q$. In this paper, given a point $P\in \Omega_p$, the locus of points $Q\in\Omega_p$, called $p$-curve, is found, such that there are two ways to attain the distance between $P$ and $Q$. For each $P\in \Omega_p$, there are two $p$-curves which are two branches of two different $p$-parabola. These two branches split $\Omega_p$ into three subregions using a three-link shortest path in two of these regions. The implicit equation of each $p$-parabola is given. Furthermore, by using the $p$-curve, an improved algorithm, called P-MFP, based on the MFP algorithm, is developed in order to solve the single-facility location problem in two regions with $\ell_{p}$ and $\ell_{q}$-norms. The results obtained with the new algorithm are better than those obtained with the MFP algorithm.ike subheadings, citations, or equations are permitted.